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                    |   HOST: An Electronic Bulletin   |
                    |  for the History and Philosophy  |
                    |    of Science and Technology     |
                    |        Volume 1, Number 2        |
                    |          Spring/Summer           |
                    |           June, 1993.            |
                    |        ISSN # 1192-084 X.        |

       |  Institute for the History  | Produced  by  IHPST through |
       |  and Philosophy of Science  | the HOST BBS on EPAS and    |
       |  and Technology, Room 316,  | E-Mail, through INTERNET at |
       |  73 Queen's Park Crescent,  | JSMITH@EPAS.UTORONTO.CA     |
       |  Toronto, Ontario, Canada.  |  IHPST@EPAS.UTORONTO.CA     |
       |  M5S1K7           [IHPST].  |-----------------------------|
       |  Phone:   (416)  978-5047.  | Editors: Julian A. Smith    |
       |  Fax:     (416)  978-3003.  |          Gordon H. Baker    |


                              |  Contents  |

Subscriber's Information

About our Contributors

Articles/Works in Progress

(1) Peter J. Burkholder:
    Alciun of York's _Propositiones ad Acuendos Juvenes_; ("Propositions
    for Sharpening Youths"); Introduction and Commentary.

(2) Peter J. Burkholder:
    _Propositiones Alcuini Doctoris Caroli Magni Imperatoris ad Acuendes
    Juvenes_; _Propositions of Alciun, A Teacher of Emperor Charlemagne,
    for Sharpening Youths_; Translation.

(3) Sharon Low:
    Richard Goldschmidt and William Bateson: Opposition to the Classical
    Conception of the Gene; Obstructionists or Visionaries?

Electronic Resources

(1) Julian A. Smith:
    LISTSERVER Mailing Lists/Discussion  Groups  on BITNET/INTERNET for
    the Historian and Philosopher of Science and Technology.

(2) Julian A. Smith:
    Using "Newsgroups" through BITNET/INTERNET.

Book Reviews

(1) _Storms of Controversy: The Secret Avro Arrow Files Revealed_, by
    Palmiro Campagna.
(2) _The People's Railway: A History of Canadian National_, by Donald
(3) _The American Way of Birth_, by Jessica Mitford
(4) _Loss of Eden: A Biography of Charles and Anne Morrow Lindbergh_,
    by Joyce Milton.
(5) _The Art of Medieval Technology_, by Richard W. Ungur.
(6) _Hidden Attraction:  The  Mystery and History of  Magnetism_,  by
    Gerrit L. Verschuur.
(7) _Gates:  How Microsoft's Mogul Reinvented an Industry -- And Made
    Himself the Richest Man in America_,  by  Stephen Manes  and Paul
(8) _The  Hacker  Crackdown:   Law  and  Disorder  on  the Electronic
     Frontier_, by Bruce Sterling.

Information for Authors


                       | Subscriber's Information |

   HOST:   An Electronic Bulletin for the History and Philosophy of Science
and Technology,is  produced by the Institute for the History and Philosophy
of Science  and Technology  (or IHPST)  at Victoria  College, Room  316, 73
Queen's Park Crescent, University of Toronto, Toronto, Ontario, Canada, M5S
1K7.   HOST appears  2 times  a year,  Spring/Summer and  Fall/Winter,  and
contains articles,  works in  progress,   research  notes,  communications,
book  reviews,   electronic  resources,    and  news  of  interest  to  the
   The HOST  Bulletin is distributed in several formats.  Copies through E-
available   free.   Printed copies  ($8) or  disk copies  ($5) may  also be
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or fax  at 416-978-3003.   Inquiries, subscription orders, submissions, and
review copies of books should be sent to IHPST,  addressed
to the HOST Bulletin editors.


                        | About our Contributors |

Gordon H.  Baker is  a B.A.  candidate at  IHPST, and an editor of the HOST
Bulletin. Mr. Baker's research interests include 19th century medicine, and
the history of science in Canada.

Julian A.  Smith is  a Ph.D.  candidate at  IHPST, and a History of Science
Instructor at Ryerson Polytechnical University, Toronto.  He is also one of
the editors  of the  HOST Bulletin.  Mr. Smith's research interests include
medieval physics,   19th  century medicine,  astronomy and  cartography  in
Canada, and the history of mathematics.

Sharon  Low   has  recently  completed  her  undergraduate  degree  at  the
University of Toronto's Trinity College.  She specializes in zoology, has a
psychology major  and is  interested in  Biological Rhythms (the subject of
her thesis).   She  is now taking graduate level studies in neuroscience in
the United States.  Her paper on Goldschmidt and Bateson  (in this journal)
was the winner of the 1992 IHPST Undergraduate Essay Competition.

Peter Burkholder  was recently  a graduate  student (MA)  at IHPST, but has
recently transferred his Doctoral studies to the University of Minnesota in
Minneapolis.   His interests  are in  medieval studies  and the  history of

Steven Walton  is  a  graduate student  (MA) at IHPST.  He has completed an
M.A. in Engineering  at Cornell University.   His interests are in medieval
studies and the history of technology.


                     | Articles/Works in Progress |


            Alciun of York's _Propositiones ad Acuendos Juvenes_
                  ("Propositions for Sharpening Youths")
                        Introduction and Commentary
                          By Peter J. Burkholder
                            Received May, 1992
                           Revised  March, 1993


   In the  year 782,  Alcuin of York (735-804) was summoned to the court of
Charlemagne in  Frankia.  By this point, the Frankish king's domain covered
much of  modern France;  Lombardy had  been subjected;  authority had  been
established on the Spanish March; and Bavaria was soon to be Christianized.
With his  sphere of  influence thus  extended, Charlemagne was able to turn
his interests to the revitalization of education among his peoples.  It was
for this reason that Alcuin's presence was requested on the Continent.
   Alcuin, also known by his Latin name of Albinus, was born in Northumbria
in the  year of  the Venerable  Bede's death.[1]  He spent time studying in
Italy and  taught at the cathedral school of York before assuming his place
at the  court of Charlemagne in 782.  Alcuin played an integral part in the
so-called "Carolingian  Renaissance," founding the palace school at Aix-la-
Chapelle where  the  seven  liberal  arts  were  taught  according  to  the
educational system  of Cassiodorus  (ca.  490-580).    His  most  important
writings were  his revisions  of the Vulgate and his voluminous letters,[2]
the latter  being collated  in the  ninth  century  as  a  model  of  Latin
composition.   Alcuin eventually assumed the position of abbot at the abbey
of St-Martin of Tours where he founded an important library and school, and
where he remained until his death on May 19, 804.
  During the course of his tenure, Alcuin is credited with having written a
set of  mathematical exercises entitled "Propositiones ad acuendos juvenes"
or  "Propositions  for  Sharpening  Youths."    These  problems  and  their
solutions, 53  in number,  serve as  valuable  evidence  of  the  state  of
mathematical education  under the  Carolingian kings.   To  the best  of my
knowledge, a  complete translation  of, and commentary on, the Propositions
has never  been undertaken,  while scholarly  treatment of  them  has  been
cursory at  best.  It is hoped that such an endeavor will shed new light on
our knowledge  of medieval  mathematics and mathematical education.  Before
delving into  the  Propositions  themselves,  however,  discussion  of  the
problem of authorship is offered.

The Problem of Authorship

  The composition of the Propositions can only be tentatively attributed to
Alcuin.   The most  compelling reason  to ascribe them as such is the title
given  at   the  head  of  the  manuscript  used  for  the  Migne  edition:
"Propositiones  Alcuini  doctoris  Caroli  Magni  imperatoris  ad  acuendos
juvenes."[3]   This particular  manuscript is  a codex  from the  monastery
Augia Dives,  known today  as Richenau  near Constance,  Switzerland.   The
monastery was  secularized in  1803, with  the manuscripts  being dispersed
between Karlsruhe, London, Stuttgart, St. Paul in Carinthia, and Zurich.[4]
The manuscript  is described by the editor as being "very old," but this is
by no means conclusive evidence of its origin.[5]
   J.A.  Giles,  who  edited  Bede's  works  in  which  a  version  of  the
Propositions  appears,[6]   judges  that   the  style  of  the  queries  is
sufficiently like  that of  Alcuin to imply that he was indeed the original
author.[7]   Conversely, the  literary manner in which the Propositions are
stated is  very unlike  anything produced  by  Bede,  and  thus  cannot  be
considered his.   Corroborating  evidence that  Alcuin may  have  been  the
author of the Propositions comes from a letter sent to Charlemagne in which
Alcuin states,  "I have  sent to your Excellency...some simple arithmetical
problems for  reason of  pleasure."[8]    Such  testimony  is,  of  course,
tenuous, for  Alcuin's authorship  of the Propositions is in no way assured
simply because he sent a copy of them to his king.
  There  is  other evidence,  though inconclusive, which indicates that the
Propositions  may   have  been   penned  by  Alcuin.    In  an  interesting
mathematical correspondence  which took  place around  1025, two  monks  of
Cologne and Liege make reference to a work entitled _Albinus_ the Latinized
form of  Alcuin's name.[9]   The  context in  which the  work is  used is a
debate over  the relation of a square's side to its diagonal.  Although the
Propositions specifically  treat no  such problems,  there are instances of
geometrical  methods   employed  for  questions  of  land  measurement  and
circumference.   Thus, we  have an instance where Alcuin's Propositions may
have  been  widely   utilized  in  the early eleventh century, and commonly
known as his work.
  As stated,  there is  evidence  suggesting that the Propositions may have
been the  work of the  Venerable Bede  (672-735).   An almost word-for-word
version of  this  treatise  appears  under  the  heading  "Incipiunt  aliae
propositiones ad  acuendos juvenes"  in Bede's  works.[10]   If  this  were
indeed the  case, Alcuin obviously could not have been the original author.
However, it  is worth  noting that  Bede never  makes any  mention  of  the
Propositions, even  in his own listing of his works.  Moreover, Giles cites
a  number   of  scientific  writings  attributed  to  Bede,  including  the
Propositions, which must be considered unauthentic.[11]  For these reasons,
Bede's version  of the  Propositions appears  in Migne  under  the  heading
"Dubious and Spurious Works."
   Based on  a manuscript  at Leyden,[12]  Smith argues  that the  probable
compiler of  the Propositions  was a  monk named  Ademar or  Aymar  of  the
ancient house  of Chabanais,  who lived  from 988  to 1030.   The  problems
contained therein  seem to  be based  on Aesop's  Fables,  begun  by  Aesop
himself in  Samos during  the seventh century B.C., and modified by Babrius
around the  third century.   What  the connection  is between  Aesop's  and
Alcuin's works is not readily apparent, and Smith fails to elaborate on his
point.   However, based  in part  on the  method  of  presentation,  Thiele
believes that Ademar did indeed author the Propositions.[13]
   Except for  Giles, scholars  are reluctant  to give  Alcuin  credit  for
production of  the Propositions,  mainly on the grounds that he contributed
little or nothing of originality to learning, and because the vast majority
of his  writings were  works on theology.  Thus, Alcuin assumes the typical
medieval scholastic  role as  transmitter of knowledge, not producer of new
material.   A comprehensive study of the various manuscripts would no doubt
help determine the actual author of the Propositions.

The Problems Themselves

   The fifty-three  problems which  make up the Propositions follow a basic
general pattern:   a  brief heading,  a statement of the problem, a request
for an  answer to  the problem,  and a solution.  There can be little doubt
that the  problems were  read aloud,[14] possibly with the students copying
them down  on papyrus,  tree bark  or parchment.[15]  A call for a response
was then  elicited of  the form,  "Let him say, he who is able..."  Some of
the problems  such as  those pertaining  to logic exercises could have been
deciphered  with  no  recourse  to  writing;  others  involving  drawn  out
arithmetic computations  could have  taken quite  some effort  to  compute,
particularly when working with clumsy Roman numerals.
   There is  no strict  categorical framework  for the  problems,  although
clusters of  certain types  appear intermittently.   Only two problems (1 &
26) pertain to rates and distances, the first being a very odd hypothetical
situation involving a snail's arduous and drawn out trek to a luncheon; the
second and  more advanced  problem involves  a dog's pursuit of a hare,[16]
and actually  involves two  rates over  differing  distances.    It  is  as

   There is  a field  which is  150 feet  long.  At one end stood a dog, at
the other,  a hare.  The dog advanced behind the hare, namely, to chase the
hare.   But whereas the dog went nine feet per stride, the hare went [only]
seven.   Let him  say, he  who wishes, How many feet and how many leaps did
the dog take in pursuing the fleeing hare until it was caught?

   Alcuin's solution  is ingenious, though cryptic.  Whereas we might solve
such a  problem by  two equations  and two  unknowns, Alcuin notes that the
differing rates of the animals is the key to the entire problem:

   The length of the field was 150 feet.  Taking half of 150 makes 75.  The
dog was  covering nine  feet per  stride, and nine times 75 makes 675.  The
dog thus  ran this  many feet  in chasing  the rabbit  until it  caught the
rabbit with its tenacious teeth.  And indeed, because the rabbit went seven
feet per  stride, take  75 seven  times.  This is how many feet the fleeing
rabbit travelled before being caught.

   The reason  for dividing  the field  in half may not be so clear, but it
simply corresponds  to partitioning  the field  by the  difference  of  the
animals' feet  per stride,  in this  case, two.    Alcuin  then  takes  the
measurement obtained  by thus  dividing and multiplies it by the respective
rates of dog and hare to arrive at the correct answer.
  This method can be generalized as follows.  The dog must always cover the
space between  it and the hare (d1) plus the additional distance covered by
the hare  (d2).   If the dog's rate is r1, then the equation describing the
distance traversed  by the  dog is  given by  d1+d2=r1t. (1)   In a similar
fashion, the  hare's flight  is denoted  by d2=r2t.  (2)   Substituting the
value of d2 in (2) into (1) yields d1+r2t=r1t.  Thus d1=t(r1-r2). (3)  From
(1), we  know that  t=(d1+d2)/r1, and  putting this  value of  t  into  (3)
results  in   d1=(d1+d2)(r1-r2)/r1.    Rearranging  this  equations  yields
d1+d2=r1d1/(r1-r2).   This is  exactly what  Alcuin's method does.  It says
that the  total distance  covered by,  for instance,  the dog is simply the
intervening expanse  divided by  the difference  of the two animals' rates,
times the  dog's rate.  It is easy to see the advantages that such a method
offers in an oral instruction setting.
   A much  larger corpus of problems (e.g. 2, 3, 4) might best be described
as those of an unknown quantity.  In each exercise, the reader is told that
a certain  quantity of  people, animals or objects, if doubled, tripled, or
in some  other way  arithmetically manipulated,  adds up to 100.  A typical
example is problem 36:

   A certain old man greeted a boy, saying to him:  "May you live, boy, may
you live  for as  long as  you have [already] lived, and then another equal
amount of time, and then three times as much.  And may God grant you one of
my years,  and you  shall live  to be 100."  Let him solve, he who can, How
many years old was the boy at that time?

  The answer is a bit trickier than it might appear at first glance, for it
must  be remembered  that  it  is  difficult  to  use base-10 arithmetic in
solving a problem dealing with a 12-month year:

   When [the  old man]  said "may  you live for as long as you have lived,"
[the boy]  had [already]  lived eight  years, three  months.  Another equal
number of  years would  make 16 years, six months, while another equal span
makes 33  years.  Three times this makes 99 years, which with one more year
added makes 100.

   It would  have been  a rather  simple affair for Alcuin to have invented
such an  exercise by  starting with  100 and  working backwards,  and  then
extrapolating the  procedure to  other problems  of  the  same  genre.    A
slightly more  complicated query  of this  type can be found in problem 40,
where portions  of the  original quantity  are doubled,  halved,  and  then

   A certain man saw from a mountain some sheep grazing and said, "O that I
could have  so many,  and then  just as many more, and then half of half of
this [added],  and then  another half  of this  half.  Then I, as the 100th
[member], might head back to my home together."  Let him solve, he who can,
How many sheep did the man see grazing?

   Again, such  a scenario could have easily been derived by beginning with
100, and  then arithmetically manipulating it until the desired problem was
in order:

  36 sheep were first seen by the man when he said, "O that I could have so
many."   Adding an  equal number makes 72, and a half of half of this, that
is, of  36, makes  18.   And again,  a half  of this, that is, of 18, makes
nine.  Therefore add 36 and 36, making 72.  Add to this 18, which makes 90.
Then add nine to 90, making 99.  The man himself added to these will be the
100th one.

   The only  precaution which would be necessary would be to make sure that
fractions do not occur, and this could be easily checked.
   A third  type of problem which Alcuin presents to the student is that of
dividing quantities  amongst various  parties.  This sometimes involves the
division of an inheritance between sons, as in problem 12:

   A certain  father died  and left  as an inheritance to his three sons 30
glass flasks,  of which  10 were  full of  oil; another  10 were half full,
while another  10 were  empty.   Divide, he  who can, the oil and flasks so
that an  equal share  of the  commoditites should  equally come down to the
three sons, both of oil and glass.

  There is little doubt that anyone, whether trained in mathematics or not,
could solve  such a  problem.   One need  only pour  all of  the oil into a
central vat  and divide  the liquid and glass equally from there.  However,
as  an   exercise,  Alcuin  demonstrates  how  such  a  division  might  be
accomplished without recourse to such crude means:

  There are three sons and 30 glass flasks.  However, of the flasks, 10 are
full [of  oil], 10  half full,  and 10  empty.   Take three times 10, which
makes 30,  so each  son shall  receive 10 flasks as his portion.  Divide up
the three portions, that is, give to the first son 10 half [filled] flasks,
to the  second son  five full and five empty [flasks].  Do the same for the
third son, and the brothers' portions of glass and oil shall be the same.

  Questions pertaining to division of an estate are traceable back to Roman
law and  what is  known as  the Testament Problem.[17]  Roman precepts made
definite provisions for the division of property upon a father's death, and
thus we  find problems  like number  35.   Here, a  father leaves  behind a
pregnant wife,  with instructions  for division  of his  inheritance in the
case of  either a  boy or girl being born.  To complicate matters, opposite
sex twins  are produced.   A  long-winded  solution  of  how  the  father's
possessions are to be divided follows.
  These types of problems seem to stress logic more than arithmetic skills.
The exercises  involving distribution  of  corn  by  a  head  of  household
(paterfamilias) to his servants are slightly more complicated, as differing
amounts of corn are allowed for men, women and children:

   A certain  head of household had 30 servants whom he ordered to be given
30 modia  of corn  as follows:   The  men should  receive three  modia; the
women, two;  and the children, a half [modium].  Let him solve, he who can,
How many men, women and children were there?

   As in  the problems  dealing with  an unknown quantity, Alcuin had to be
sure that  his numbers  worked out  evenly in  the end.  Note, too, that he
treats fractional  measurements here,  as each child receives half a modium
of corn:

   If you  take thrice three, you get nine; if you take two five times, you
get 10;  and if  you take half of 22, you get 11.  Thus, three men received
nine modia;  five women  received 10;  and 22  children received  11 modia.
Adding three  and five and 22 makes 30 servants.  Likewise, nine and 11 and
10 makes 30 modia.  Hence there are 30 servants, and 30 modia [of corn].

   Problems of  exactly the same type, but with varying numbers of servants
and corn,  can be  found in exercises 32 and 34, indicating that it was the
procedure which Alcuin wished his pupils to understand.
  Alcuin's logic problems, or slight variations of them, can still be found
today in  textbooks and  on examinations.   The most famous no doubt is the
conundrum of the man, she-goat, wolf and cabbage which needed to be ferried
across a  river. (Problem  18)   As only  two passengers fit in the boat at
once, and  since certain  combinations of  animals and  vegetable cannot be
left alone,  the reader  is left  to solve how a successful transport might
take place.   Alcuin  assumes the role of ferryman and leads us through the
problem step by step:

   ...I would  first take  the she-goat  and leave  behind the wolf and the
cabbage.   When I had returned, I would ferry over the wolf.  With the wolf
unloaded, I  would retrieve  the she-goat and take it back across.  Then, I
would unload  the she-goat and take the cabbage to the other side.  I would
next row back and take the she-goat across.  The crossing should go well by
doing thus, and absent from threat of slaughter.

   Problems of exactly this type appear in exercises 17, 19 and 20 as well.
In each  case, a long explanation of how a successful transnavigation might
be performed is offered.
   Other logic  problems are  more straightforward  and exhibit  a  certain
amount of  humor.  The answer to Alcuin's problem of how many footprints an
ox makes  in the  last furrow  is, of course, none, "because the ox goes in
front of the plow and the plow follows it.  For however many footprints the
ox makes on the ploughed earth by going first, so many the plough following
behind destroys  by ploughing." (Problem 14)  Another question of this type
entails a  man who  wishes to  slaughter 300 pigs in three days, but with a
odd number  being butchered  per day  -- a  problem which Alcuin states "is
indissoluble and composed for rebuking." (Problem 43)
   Alcuin's problems  pertaining to  area are of particular interest.  They
consist of queries as to how many measurements or objects can fit inside of
a larger  confine.   Certain exercises  we might  define  as  dealing  with
acreage, although  such a term is not entirely accurate for measurements of
aripenna, the  standard land  quantity.[18]    Other  problems  are  of  no
immediate practical  value whatsoever, and are thus clearly meant as purely
mathematical exercises.    Take  for  example  the  question  of  how  many
rectangular houses can fit within a circular city (problem 29):

  There is a city which is 8000 feet in circumference.  Let him say, he who
is able, How many houses should the city contain, such that each [house] is
30 feet long, and 20 feet wide?


   The city measures 8000 feet around, which is divided into proportions of
one-and-a-half to  one, i.e.  4800 and  3200.   The length and width of the
houses are  [also] of  these [dimensions].   Thus, take half of each of the
above [measurements],  and from  the larger number there shall remain 2400,
while from  the smaller,  1600.   Then, divide 1600 into twenty [parts] and
you will  obtain 80  times 20.   In  a similar fashion, [divide] the larger
number, i.e. 2400, into 30 pieces, deriving 80 times 30.  Take 80 times 80,
making 6400.   This  many houses  can be  built in  the city, following the
above-written proposal.

   Essentially, what  Alcuin does  is to  force the  ratio of the length to
width of each house onto the city.  Thus, as each house measures 30x20, the
ratio of length to width is 3:2.  Alcuin breaks up the circumference of the
town into  two pieces  such that  their ratio  is 3:2 as well.  Having done
this, he  simply straightens  out the pieces and sets them perpendicular to
one another.   This,  however, yields  an unclosed figure.  He thus divides
each side  in two  and rearranges  the four sides in order to make a closed
structure.   The ratio  of 3:2 is preserved since 4800/2:3200/2 equals 3:2.
Now Alcuin  has a  rectangular town  with a circumference of 8000 feet, and
whose dimensions  are proportional  to the  dimensions of the houses.  From
there, the  problem of  the number  of houses  which can fit in the town is
  The most obvious shortcoming of Alcuin's method is that the area enclosed
by different  curves of equal length is not the same.  The area of a circle
is given  by pi-r-squared,  whereas the  area for a rectangle is denoted by
length  times  width.    Thus,  the  area  enclosed  by  a  circle  with  a
circumference of  8000 feet  is roughly  5,092,958 square  feet, whereas  a
rectangle measuring  1600 by  2400 encloses only 3,840,000 square feet -- a
difference of  over 1.2 million square feet.  The only conclusion which can
be drawn is that Alcuin was unaware of the consequences of modifying shape,
as he  employs the same methodology in problems 27 and 28.  In addition, we
need only  note the  absence of allowance for streets to realize the purely
hypothetical nature of such a problem.
   There is  further evidence  that Alcuin's  Propositions sought merely to
stir the  minds of  their readers  as opposed  to serving as a handbook for
quotidian problems.  Glaring examples of this are exercises 13 and 41, both
of which  teach the  lesson of  geometric growth.[19]   In  the  former,  a
servant is  ordered by  his king  to assemble  an army  from 30 villages as

  He should bring back as many men [from each successive village] as he had
taken there.   Thus, [the servant] came to the first village alone; he came
with one other person to the next; three people came to the third, etc...

   Such a gathering can be mathematically modelled by the relation N=2^(v),
where v is each successive village and N is the number of people assembled.
Hence, the total number of villagers conscripted would be given as S 2^(v),
with the  summation beginning  at v=0  and continuing  to v=30  -- a figure
representing an  army which  was far  beyond the  capabilities of  even the
richest or  most ambitious  of kings  to field.   Alcuin's  solution  gives
figures up  to v=15,  while the  edition ascribed to Bede continues all the
way to  v=30, although  with errors beginning at v=22.  Neither attempts to
sum the  figures, nor  is it  expected that a student would be expected to;
rather, it  was the  process which  undoubtedly lay  at the  heart  of  the
   A similar  hypothetical problem  demonstrates  the  idea  of  arithmetic
progression.   It has  been related that when Gauss (1777-1855) was a young
student, his  mathematics teacher  one day  instructed the class to add the
numbers one through 100.  No sooner had the assignment been made than Gauss
somehow magically produced the correct figure of 5050.  How had he done it?
  The key to the problem is to realize that by adding corresponding low and
high figures,  a simple  multiplication problem  unfolds.  Thus, 1+100=101;
2+99=101; 3+98=101;...;49+52=101; 50+51=101.  It is manifest from this that
one need  only multiply  the constant  sum, 101, by 50, the number of sums.
In this way, the correct response of 5050 is obtained.
  Alcuin's  ladder problem  (42)  shows that this concept was already known
by the ninth century:

   There is  a ladder which has 100 steps.  One dove sat on the first step,
two doves  on the  second, three  on the third, four on the fourth, five on
the fifth,  and so  on up  to the hundredth step.  Let him say, he who can,
How many doves were there in all?


   There will  be as  many as  follows:  Take the dove sitting on the first
step and add it to the 99 doves sitting on the 99th step, thus getting 100.
Do the  same with the second and 98th steps and you shall likewise get 100.
By combining  all the steps in this order, that is, one of the higher steps
with one  of the  lower, you shall always get 100.  The 50th step, however,
is alone and without a match; likewise, the 100th stair is alone.  Add them
all and you will have 5050 doves.

   We can  see that  with only  slight  modification,  the  above-described
concept was  in place  almost a  thousand years  before Gauss  dazzled  his
schoolteacher.  Perhaps the young Gauss wasn't so clever after all!

Conclusion and Topics for Further Study

   Whether or  not Alcuin  himself authored  the Propositions  may never be
known, but  this is  not  of  great  consequence.    The  Propositions  are
interesting problems  in their  own right  and reveal the general state and
method of  mathematical instruction  around the  time of  Charlemagne.    A
thread of  continuity with  classical education  can be  discerned in these
puzzles as  well as  the influence of Barbarian values of practical methods
for everyday problems.  However, it must be concluded that the Propositions
sought only  to instill  various simple  methods in  its users,  this being
accomplished by repeated problems of the same genre.
   It should  not be  concluded that the Propositions are indicative of the
general state of mathematics during the eighth or ninth centuries.  We have
prima facie  evidence[20] that  these problems  were utilized primarily for
didactic purposes;  thus, to  argue that the Propositions are an example of
the poor state of mathematics is erroneous.  While such a conclusion may be
justified, it  by no  means is  a necessary  deduction from the evidence at
   The Propositions  are also  potentially valuable  for the  economic  and
social insight  they offer,  and  a  spreadsheet  of  various  weights  and
measures which  appear throughout  the problems is included as an appendix.
Whether or  not these  values are  consistent with  contemporary conditions
awaits another study.

An Introduction to the Translations

   In translating  the 53  problems and answers of the Propositions, I have
utilized the  Migne edition  of Alcuin's works.  I have annotated this text
and supplied alternate or additional versions of problems as they appear in
Bede's supposed  previous work.   Where  differences occur,  a footnote  is
provided beginning  with "Bede,"  hence  referring  the  reader  to  Bede's
edition.   A further comparison with Heruagius's edition of Bede's writings
revealed only  trivial discrepancies, and thus alternate readings from this
work have been omitted.
   A quality translation must be true both to the original language and the
language into  which the  material is converted.  With this is mind, I have
tried to  keep verb  tenses consistent  according to  English usage despite
Alcuin's variations  within a given problem.  English words which have been
read into  the Latin  are contained  within square  brackets [   ]  and are
either interpretive  or corroborated  by Bede's  edition.    Certain  words
referring to  weights and measures (e.g. aripennum, denarius, solidus) have
been left in the original.  Though aripennum might be rendered "arpent" and
solidus a  "sous," such  translations either  do little in helping us grasp
what is involved in the usage, or are modernly deceitful.


[1] Since  the Propositions  to be  discussed cannot  be ascribed to Alcuin
with certainty,  I will offer only a very brief biographical account of the
man.  Secondary literature on Alcuin is plentiful.  See for example Stephen
Allott,  _Alcuin   of  York_,   (York,  1974);   L.  Wallach,  _Alcuin  and
Charlemagne_, (New  York, 1959);  Eleanor Duckett,  _Alcuin,  A  Friend  of
Charlemagne_, (New  York, 1951);  C.J.B. Gaskoin,  _Alcuin:   His Life  and
Works_, (Cambridge,  1904); Andrew  West,  _Alcuin  and  the  Rise  of  the
Christian Schools_,  (London, 1893);  and Frederick  Lorenz, _The  Life  of
Alcuin_, Jane  Slee, trans.,  (London, 1837).   For  a listing  of Alcuin's
texts and  translations, see George Sarton, _Introduction to the History of
Science_, 3 vols., (Baltimore, 1927), vol. 1, part 1, pp. 528-529.

[2] See Rolph Page, _The Letters of Alcuin_, (New York, 1909).

[3] _Alcuini  opera omnia_,  J.P. Migne, ed., vol. 2, found in _Patrologiae
latinae cursus completus..._, vol. 101, (Paris, 1863).

[4] Frederick  Hall, _A  Companion to Classical Texts_, (Oxford, 1913), pp.
294 & 342.

[5] D.E.  Smith tells  us that  the oldest manuscript of the problems dates
from the  eleventh century.   _History of Mathematics_, 2 vols., (New York,
1923; reprint, 1951), vol. 1, p. 186.

[6] One  such manuscript  ascribing the  Propositions  to  Bede  is  _Codex
Latinus Monacensis_,  no. 14272.   Its  origin is  either tenth or eleventh
century.  See _Catalogus codicum Latinorum bibliothecae regiae monacensis_,
(Hildesheim, 1975), vol. 2,2, pp. 152-153.  (This is the only ascription to
Bede noted by Lynn Thorndike, _A Catalog of Incipits of Medieval Scientific
Writings_, (Cambridge, MA, 1963).)

[7] Giles, ed., _The Miscellaneous Works of Venerable Bede, in the Original
Latin_, 6 vols., (London, 1843), vol. 6, p. xiv.

[8] "Misi excellentiae vestrae...aliquas figuras arithmeticae subtilitatis,
laetitiae causa."   Migne,  op. cit., vol. 100, letter 101, col. 314, dated
anno 800.

[9] An  edition of the correspondence, along with scholarly commentary, can
be found  in Paul  Tannery's _Memoires  scientifiques_, vol. 5 of _Sciences
exactes au  moyen-age-, (Paris,  1922), pp.  264-288.   An earlier  partial
edition is  contained in  Jules Clerval's _Les Ecoles de Chartres au moyen-
age, du  ve au xvie siecle_, (Paris, 1895; reprint, Geneva, 1977), pp. 459-
464.   I have  studied these  letters anew  and hope  to make  my  findings
available in  the near  future in  a paper  entitled "Speculum  geometricae
undecimo saeculo:   The Mathematical Correspondence of Ragimbold of Cologne
and Radulf of Liege, ca. 1025."

[10] Migne,  op. cit., vol. 90, cols. 667-676.  These also appear in volume
one of  Joannes Hervagius's edition of Bede's _Opera Bedae Venerabilis..._,
8 vols. bound in 4, (Basil, 1563), but are not included in Giles's edition.
The most  notable difference  between Bede's  version and that of Alcuin is
the lack of solutions for problems 36-53 in the former.

[11] Giles, op. cit., vol. 6, pp. ix-xv.

[12]  Georg  Thiele,  ed.,  _Der  Illustrierte  lateinische  Aesop  in  der
Handschrift des  Ademar_, Codex  Vossianus  Lat.  Oct.  15,  Fol.  195-205,
(Leiden, 1905).

[13] Ibid., pp. 23-25.

[14] Vera  Sanford specifically  places  Alcuin's  Propositions  under  the
rubric "Verbal  Problems."   _A Short  History  of  Mathematics_,  (Boston,
1930), pp. 212-213.

[15] For  the materials  available to  schoolchildren,  see  Pierre  Riche,
_Education  and  Culture  in  the  Barbarian  West,  Sixth  through  Eighth
Centuries_, trans.  from the third edition by John Contreni, (Columbia, SC,
1976), pp. 458-462.

[16] Smith  describes this  problem as  being "already ancient" by Alcuin's
time, but  fails to  cite any  precedents.   Op. cit.,  187.  Sanford dates
pursuit problems  to Roman  legionaries, whose  stride was  so uniform that
time schedules  could be  worked out for marching from place to place.  Op.
cit., pp. 217-218.

[17] See Sanford, op. cit., pp. 218-219.

[18] The  use of aripenna and the smaller perticae, of course, implies that
such measurements were standard and well-known to all.  From problem 25, we
can deduce that one aripennum equals 184.53 perticae.

[19] Sanford  regards problems  of geometric  progression as  some  of  the
oldest types of mathematical endeavors, and cites extant Babylonian tablets
from ca. 2000 b.c. to this effect.  Op. cit., pp. 174-176.

[20] See problem 43.


               _Propositiones Alcuini Doctoris Caroli Magni
                   Imperatoris ad Acuendes Juvenes_ [1]
              _Propositions of Alciun,  A Teacher of Emperor
                   Charlemagne, for Sharpening Youths_
                          By Peter J. Burkholder
                            Received May, 1992
                           Revised March, 1993.

I.  propositio de limace.
Limax fuit  ab hierundine  invitatus ad prandium infra leucam unam.  In die
autem non  potuit plus  quam unam unciam pedis ambulare.  Dicat, qui velit,
in quot diebus [2] ad idem prandium ipse limax perambulabat?
1.  proposition concerning the snail.
A snail was invited by a swallow to lunch a league away.  However, it could
not walk  further than  one inch  per day.  Let him say, he who wishes, How
many [years and] days did it take for the snail to walk to that lunch?

Sequitur solutio de limace.
In leuca  una sunt  mille quingenti  passus; vii  d pedes  xc unciae.  Quot
unciae, tot dies fuerunt, qui faciunt annos ccxlvi, et dies ccx.
Here follows the solution of the snail.
In one  league, there  are 1500  passus [3].   7500  feet  [equals]  90,000
inches. There are as many days as there are inches, that is, 246 years, 210

II.  propositio de viro ambulante in via. [4]
Quidam vir  ambulans per  viam vidit sibi alios homines obviantes, et dixit
eis:   Volebam [5],  ut fuissetis  alii tantum,  quanti estis;  et medietas
medietatis; et  hujus numeri  medietas [et  rursum de  medietate medietas];
tunc una mecum c fuissetis.  Dicat, qui velit, quanti fuerunt, qui in prima
ab illo visi sunt?
2.  proposition of the man walking in the street.
A certain  man walking  in the street saw other men coming towards him, and
he said  to them:   "O  that there  were so  many [more]  of you as you are
[now]; and  then half  of half  of this [were added]; and then half of this
number [were  added], and  again, a  half of [this] half.  Then, along with
me, you  would number 100 [men]."  Let him say, he who wishes, How many men
were first seen by the man?

Solutio de eadem propositione.
Qui imprimis ab illo visi sunt, fuerunt xxxvi.  Alii tantum lxxii. Medietas
medietatis xviii.   Et  hujus numeri  medietas sunt  viiii.   Dic ergo sic:
lxxii et  xviii fiunt  xc.   Adde viiii, fiunt xcviiii.  Adde loquentem, et
habebis c.[6]
Solution of the same proposition.
Those who  were first  seen by the man were 36 in number; double this would
be 72.   A  half of  half of this is 18, and a half of this number makes 9.
Therefore, say  this:   72 and  18 makes  90.   Adding 9  to this makes 99.
Include the speaker and you shall have 100.

III.  propositio de duobus proficiscentibus.[7]
Duo homines  ambulantes per  viam, videntesque ciconias, dixerunt inter se:
Quot sunt?   Qui  conferentes numerum dixerunt:  Si essent aliae tantae; et
ter tantae,  et medietas  tertii, adjectis  duobus, c  essent.   Dicat, qui
potest, quantae fuerunt, quae imprimis ab illis visae sunt?
3.  proposition concerning the two travellers.
Two men  were walking  in the  street when  they noticed some storks.  They
asked each  other, "How many are there?"  Discussing the matter, they said:
"If [the storks] were doubled, then taken three times, and then half of the
third [were  taken] and  with two more added, there would be 100."  Let him
say, he who is able, How many [storks] were first seen by the men?

Solutio de ciconiis.
xxviii et  xviii,[8] et  tertio sic:   fiunt  lxxxiiii.  Et medietas tertii
fiunt xiiii.  Sunt in totum xcviii.  Adjectis duobus, c apparent.

Solution concerning the storks.
28 taken  three times  makes 84.  Half of a third makes 14.  Thus, in total
there are 98.  By adding two, there are 100.

IV.  propositio de homine et equis.[9]
Quidam homo vidit equos pascentes in campo, optavit dicens:  Utinam essetis
mei, et  essetis alii tantum, et medietas medietatis; certe gloriarer super
equos c.   Discernat,  qui  vult,  quot  equos  imprimis  vidit  ille  homo
4.  proposition concerning the man and the horses.
A certain  man saw  some horses  grazing in a field and said longingly:  "O
that you  were mine, and that you were double in number, and then a half of
half of this [were added].  Surely, I might boast about 100 horses."    Let
him discern,  he who  wishes, How  many horses  did the  man originally see

Solutio de equis.
xl equi erant, qui pascebant.  Alii tantum fiunt lxxx.  Medietas medietatis
hujus, id est, xx, si addatur, fiunt c.
Solution concerning the horses.
There were  40 horses  grazing; double  this makes  80.   A half of half of
this, i.e. 20, if added, makes 100.

V.  propositio de emptore denariorum.[10]
Dixit quidam  emptor:[11]   Volo de  centum denariis  c porcos  emere;  sic
tamen, ut  verres x  denariis ematur;  scrofa autem  v denariis;  duo  vero
porcelli denario  uno.   Dicat, qui  intelligit, quot verres, quot scrofae,
quotve porcelli  esse debeant,  ut in neutris numerus nec superabundet, nec
5.  proposition concerning the buyer and his denarii.
A certain  buyer said:   "I want to buy 100 pigs with 100 denarii in such a
way that  a mature  boar is  bought for 10 denarii; a sow for five denarii;
and two  small female  pigs for  one denarius."  Let him say, he who knows,
How many  boars, sows,  and small female pigs should there be so that there
are neither too many nor too few of either [pigs or denarii]?

Solutio de emptore.
Fac viiii  scrofas et unum verrem in quinquaginta quinque denariis; et lxxx
porcellos in  xl.  Ecce porci xc.  In residuis v denariis, fac porcellos x,
et habebis centenarium numerum in utrisque.
Solution concerning the buyer.
Buy nine  sows and  one boar with 55 denarii, and 80 small female pigs with
40; behold, 90 pigs.  With the remaining five denarii, buy ten small female
pigs, and you shall have 100 pigs for 100 denarii.

VI.  propositio de duobus negotiatoribus c solidos habentis.
Fuerunt duo  negotiatores, habentes  c  solidos  communes,  quibus  emerent
porcos.   Emerunt autem  in solidis duobus porcos v, volentes eos saginare,
atque iterum  venundare, et  in solidis  lucrum facere.   Cumque  vidissent
tempus non  esse ad  saginandos porcos,  et ipsi eos non valuissent tempore
hiemali pascere,  tentavere venundando,  si potuissent,  lucrum facere, sed
non potuerunt;  quia non  valebant eos  amplius venundare,  nisi  ut  empti
fuerant, id  est, ut  de  v  porcis  duos  solidos  acciperent.    Cum  hoc
conspexissent, dixerunt  ad invicem:   Dividamus  eos.  Dividentes autem et
vendentes, sicut emerant, fecerunt lucrum.  Dicat, qui valet, imprimis quot
porci fuerunt;  et dividat ac vendat et lucrum faciat, quod facere de simul
venditis non valuit.
6.  proposition of the two businessmen who had 100 solidi.
There were two businessmen who had 100 solidi between them, with which they
bought some pigs.  For two solidi, they bought five pigs, wishing to fatten
them and  to sell  them again at a profit.  But when they saw that the time
was not right to fatten the pigs, and being unable to pasture them over the
winter, they  tried to  make a  profit by selling them.  However, they were
unsuccessful because  they could  only sell the pigs for what they had paid
(i.e., five  pigs for  two solidi).   When they realized this, they said to
each other,   "We  shall divide the pigs."  But by dividing and selling the
pigs for as much as they had paid, they made a profit.  Let him say, he who
can, How many pigs were there at first, and how did the men divide and sell
for a profit that which they could not do together?

Solutio de porcis.
Imprimis ccl  porci erant, qui c solidis sunt comparati, sicut supra dictum
est, in  duobus solidis  v porcos:   quia  sive  quinquagies  quinos,  sive
quinquies l  dixeris, ccl numerabis.  Quibus divisis unus tulit cxxv, alter
similiter.   Unus vendidit deteriores tres semper in solido; alter meliores
duos in  solido.   Sic evenit, ut is qui deteriores vendidit, de cxx porcis
xl  solidos  est  consecutus.[12]    Qui  vero  meliores,  lx  solidos  est
consecutus; quia  de inferioribus  xxx semper  in x  solidis; de melioribus
viginti autem  in x  solidis sunt  venundati:   et remanserunt  utrisque  v
porci, ex quibus ad lucrum iiii solidos et duos denarios facere potuerunt.

Solution concerning the pigs.
There were  250 pigs  to begin  with.  These were bought for 100 solidi, as
stated above,  at the  price of  two solidi per five pigs.  Because whether
you say  "50 times  five" or  "five times  50," you arrive at 250.  One man
sold three  inferior pigs  at a  price of one solidi; the other, two better
pigs per  solidi.   Thus it  happened that  he who  sold the  inferior pigs
obtained 40  solidi for  120 pigs,  whereas the  better pigs  brought in 60
solidi. This  is because it was always 30 inferior pigs for ten solidi, and
20 better  pigs for  ten solidi.   For  each man, there remained five pigs,
from which they could make four solidi and two denarii in profit.

VII.  propositio de disco pensante libras xxx.
Est discus  qui pensat  libras xxx  sive solidos  dc, habens  in se  aurum,
argentum, aurichalcum,  et stannum.   Quantum  habet auri, ter tantum habet
argenti.   Quantum argenti, ter tantum aurichalci.  Quantum aurichalci, ter
tantum stanni.  Dicat, qui potest, quantum in unaquaque specie pensat?
7.  proposition concerning the plate weighing 30 pounds.
There is  a plate  weighing 30 pounds or 600 solidi.  In it, there is gold,
silver, brass  and tin.   It has three times are much silver as gold, three
times as  much brass  as silver, and three times as much tin as brass.  Let
him say, he who can, How much does each type of metal weigh?

Aurum pensat  uncias novem:  argentum ter incias viiii, id est, libras duas
et tres uncias.  Aurichalcum pensat ter libras duas et [ter] iii uncias, id
est, libras  vi et  viiii uncias.   Stannum  pensat ter  libras vi,  et ter
uncias viiii,  hoc est,  libras xx,  et iii  uncias.   viiii unciae,  et ii
librae cum  iii unciis:   et  vi librae cum viiii unciis:  et xx librae cum
iii unciis adunatae, xxx libras efficiunt.
The gold  weighs nine ounces.  The silver weighs three times this, i.e. two
pounds, three  ounces.   The brass  weighs three  times two  pounds,  three
ounces, i.e.  six pounds,  nine ounces.   The  tin weighs  three times  six
pounds, nine  ounces, i.e.  20 pounds,  three ounces.  Nine ounces, and two
pounds, three  ounces, and  six pounds,  nine ounces,  and 20 pounds, three
ounces, taken together, make 30 pounds.

Item aliter  ad solidum.   Aurum pensat solidos argenteos xv.  Argentum ter
xv, id  est, xlv.   Aurichalcum  ter xlv, id est, cxxv.  Stannum ter cxxxv,
hoc est,  ccccv.   Junge ccccv,  et cxxxv:  et xlv:  et xv; et invenies dc,
qui sunt librae xxx.
Another method.     The gold  weighs 15 silver solidi.  The silver is three
times the gold, i.e. 45.  The brass is three times 45, i.e. 125 [sic].  The
tin is  three times  135, i.e. 405.  Add 405 and 135 and 45 and 15, and you
will get 600 [solidi], which equals 30 pounds.

VIII.  propositio de cupa.
Est cupa  una, quae  c metretis  impletur capientibus  singulis modia tria;
habens fistulas  iii.   Ex numero  modiorum tertia  pars  et  vi  per  unam
fistulam currit:   per alteram tertia pars sola:  per tertiam sexta tantum.
Dicat nunc, qui vult, quot sextarii per unamquamque fistulam cucurrissent.
8.  proposition concerning the cask.
There is  a cask  which has  three cracks  in it.   It  is filled  with 100
metretae, each  holding three  modia.  Of the modia, a third and sixth part
run out through one crack.  Through another [crack], only a third part runs
out.   Only a  sixth part runs out of the third crack.  Let him say now, he
who wishes, how many sextarii ran out through each crack.

Per primam fistulam iii dc sextarii cucurrerunt.  Per secundum ii cccc.[13]
Per tertiam i cc.
3600 sextarii  run through  the first  crack; 2400  through the second; and
1200 through the third.

IX.  propositio de sago.
Habeo sagum habentem in longitudine cubitos c, et in latitudine lxxx.  Volo
exinde per  portiones sagulos  facere, ita  ut unaquaeque  portio habeat in
longitudine cubitos  v, et in latitudine cubitos iiii.  Dic, rogo, sapiens,
quot saguli exinde fieri possint?
9.  proposition concerning the cloak material.
I have  a material  for cloaks  which is  100 cubits  long, 80 cubits wide.
From it,  I wish  to make  smaller cloaks  from portions in such a way that
each portion  is five  cubits in length and four cubits wide.  I ask you to
tell me, wise one, How many smaller cloaks can be made from [the material]?

De quadrigentis  octogesima pars  v sunt;  et centesima  iiii.   Sive  ergo
octuagies v,  sive centies  iiii duxeris,  semper cccc  invenies.  Tot sagi
An eightieth  part of  400 is five, and a hundredth part, four.  Therefore,
whether you  measure off 80 [lengths] of five [cubits], or 100 of four, you
shall always arrive at 400.  There shall be this many cloaks.

X.  propositio de linteo.[15]
Habeo linteamen  unum longum  cubitorum lx, latum cubitorum xl.  Volo ex eo
portiones facere,  ita ut  unaquaeque portio  habeat in longitudine cubitos
senos, et  in latitudine  quaternos, ut  sufficiat ad  tunicam  consuendam.
Dicat, qui vult, quot tunicae exinde fieri possint?
10.  proposition concerning the linen cloth.
I have  a single  linen cloth  which is  60 cubits long, 40 cubits wide.  I
wish to  make it  into smaller  portions, each  being six cubits in length,
four cubits  in width, so that each piece is ample for making a tunic.  Let
him say,  he who  wishes, How  many tunics  can be  made [from  the  larger

Solutio. [16]
Decima pars sexagenarii vi sunt.  Decima vero quadragenarii iiii sunt. Sive
ergo decimam sexagenarii, sive decimam quadragenarii decies miseris, centum
portiones vi cubitorum longas; et iiii cubitorum latas invenies.
One tenth  of 60 is six, and a tenth of 40 is four.  Therefore, whether you
shall have  taken ten  times a tenth of 60 [cubits] or ten times a tenth of
40, you  will arrive  at 100  portions of  six cubits  in length,  and four
cubits wide.

XI.  propositio de duobus hominibus sorores accipientibus.
Si duo  homines ad  invicem, alter alterius sororem in conjugium sumpserit;
dic, rogo, qua propinquitate filii eorum sibi pertineant?
11.  proposition concerning the two men marrying [one another's] sister.
If two  men should marry one another's sister, tell me, I ask, What will be
the sons' relations to each other?

Solutio ejusdem. [17]
Verbi gratia:  si ego accipiam sororem socii mei, et ille meam, et ex nobis
procreentur filii;  ego denique  sum patruus  filii sororis  meae; et  illa
amita filii mei.  Et ea propinquitate sibi invicem pertinent.
Solution of the same [proposition].
As stated,  if I should marry my friend's sister, and he should marry mine,
sons would  be produced  by us.   Thus, I shall be the paternal uncle of my
sister's son, and she shall be my son's maternal aunt.  The relation of the
two men [to the sons] shall be the same.

XII.  propositio de quodam patrefamilias et tribus filiis ejus.
Quidam paterfamilias  moriens dimisit [18] haereditatem tribus filiis suis,
xxx ampullas  vitreas, quarum  decem fuerunt  plenae  oleo.    Aliae  decem
dimidiae.   Tertiae decem  vacuae.  Dividat, qui potest, oleum et ampullas,
ut unicuique  eorum de tribus filiis aequaliter obveniat tam de vitro, quam
de oleo.
12.  proposition concerning a certain father and his three sons.
A certain father died and left as an inheritance to his three sons 30 glass
flasks, of  which 10  were full  of oil;  another 10  were half full, while
another 10  were empty.   Let him divide, he who can, the oil and flasks so
that an  equal share  of the  commodities should  equally come  down to the
three sons, both of oil and glass.

Tres igitur  sunt filii,  et xxx ampullae.  Ampullarum autem quaedam x sunt
plenae, et  x mediae,  et x  vacuae.  Duc ter decies; fiunt xxx.  Unicuique
filio veniunt  x ampullae  in portionem.   Divide autem per tertiam partem,
hoc est,  da primo filio x semis ampullas, ac deinde da secundo v plenas et
v vacuas.   Similiter  dabis tertio, et erit trium aequa germanorum divisio
tam in oleo, quam in vitro.
There are  three sons  and 30 glass flasks.  However, of the flasks, 10 are
full [of  oil], 10  half full,  and 10  empty.   Take three times 10, which
makes 30,  so each  son shall  receive 10 flasks as his portion.  Divide up
the three portions, that is, give to the first son 10 half [filled] flasks,
to the  second son  five full and five empty [flasks].  Do the same for the
third son, and the brothers' portions of glass and oil shall be the same.

XIII.  propositio de rege.
Quidam rex  jussit famulo suo colligere de xxx villis exercitum, eo modo ut
ex unaquaque  villa tot  homines sumeret  quotquot illuc  adduxisset.  Ipse
tamen ad  villam primam solus venit; ad secundam cum altero; jam ad tertiam
tres venerunt.   Dicat,  qui potest,  quot homines fuissent collecti de xxx
13.  proposition concerning the king.
A certain  king ordered  his servant  to gather an army from 30 villages as
follows:   He should  bring back as many men [from each successive village]
as he  had taken  there.   Thus, [the  servant] came  to the  first village
alone; he  came with one other person to the next; three people came to the
third.   Let him  say, he who is able, how many men were collected from the
30 villages.

Solutio. [19]
In prima igitur mansione duo fuerunt; [20] in secunda iiii, in tertia viii,
in quarta  xvi, in  quinta xxxii,  in sexta  lxiiii, in septima cxxviii, in
octava cclvi,  in nona  dxii, in decima i xxiiii, in undecima ii xlviii, in
duodecima iiii  xcvi, in  quarta decima  xvi ccclxxxiiii.  In quinta decima
xxxii dcclxviii, etc.

In the  first village, there were two [people]; in the second, four; in the
third, eight; in the fourth, 16; in the fifth, 32; in the sixth, 64; in the
seventh, 128;  in the eighth, 256; in the ninth, 512; in the 10th, 1024; in
the 11th,  2048; in  the 12th, 4096; in the 14th, 16, 384; in the 15th, 32,
768; etc.

XIV.  propositio de bove.
Bos qui tota die arat, quot vestigia faciat in ultima riga?
14.  proposition concerning the ox.
How many  footprints in  the last  furrow does  an ox  make which  has been
plowing all day?

Nullum omnino  vestigium facit  bos in  ultima riga, eo quod ipse praecedit
aratrum, et  hunc aratrum  sequitur.   Quotquot  enim  hic  praecedendo  in
exculta terra  vestigia figit,[21]  tot ille subsequens excolendo resolvit.
Propterea illius nullum reperitur vestigium in ultima riga.
An ox  makes no  footprints whatsoever in the last furrow.  This is because
the ox  goes in  front of  the plow,  and the plow follows it.  For however
many footprints  the ox makes on the ploughed earth by going first, so many
the plough  following behind destroys by ploughing.  On account of this, no
footprints appear in the last furrow.

XV.  propositio de homine.
Quaero a te ut dicas mihi quot rigas factas habeat homo in agro suo, quando
de utroque capite campi tres versuras factas habuerit?
15.  proposition concerning the man.
I ask  you in  order that  you might  tell me, How many furrows might a man
have in  his field  if he  shall have  made three turns at each head of the

Ex uno capite campi iii.  Ex altero iii, quae faciunt rigas versuras vi.
Three [furrows]  from one  head of  the field,  and three  from the  other,
making six plowed furrows.[22]

XVI.  propositio de duobus hominibus boves ducentibus.
Duo homines  ducebant boves  per viam, e quibus unus alteri dixit:  Da mihi
boves duos;  et habeo tot boves quot et tu habes.  At ille ait:  Da mihi et
tu duos  boves, et habeo duplum quam tu habes.  Dicat, qui vult, quot boves
fuerunt, quot unusquisque habuit.
16.  proposition concerning the two men leading oxen.
Two men  were leading oxen along the road when one said to the other, "Give
me two  oxen, and  I shall have as many oxen as you."  Then the other said,
"You give  me two  oxen, and  I shall  have twice as many as you."  Let him
say, he who wishes, how many oxen there were, and how many each man had.

Prior, qui  dari sibi  duos rogavit,  boves habebat  iiii.   At  vero,  qui
rogabatur,  habebat  viii.    Dedit  quippe  rogatus  postulanti  duos,  et
habuerunt uterque  sex.   Qui enim  prius acceperat,  reddidit  duos  danti
priori, qui  habebat sex, et habuit viii, quod est duplum a quator, et illi
remanserunt iiii, quod est simplum ab viii.
At first,  the man who asked for two to be given to him had four oxen.  But
indeed, the  man who was asked had eight.  Of course, having been asked, he
gave two  to the  one asking, and each of the two had six.  For the man who
first asked  returned two to the one first giving (who now had six), and he
had eight,  which is  double four,  and four remained to that one, which is
half of eight.

XVII.  propositio de tribus fratribus singulas habentibus sorores.
Tres fratres  erant qui  singulas sorores  habebant,  et  fluvium  transire
debebant (erat  enim unicuique  illorum concupiscentia  in  sorore  proximi
sui), qui venientes ad fluvium non invenerunt nisi parvam naviculam, in qua
non potuerunt  amplius nisi  duo ex  illis transire.   Dicat,  qui  potest,
qualiter fluvium transierunt, ne una quidem earum ex ipsis maculata sit?
17.  proposition concerning the men [23] who had unmarried  sisters.
There were  three men, each having an unmarried sister, who needed to cross
a river.   Each  man was  desirous of  his friend's  sister.  Coming to the
river, they  found only  a small boat in which only two persons could cross
at a  time.   Let him say, he who is able, How did they cross the river, so
that none of the sisters were defiled by the men?

Primo omnino  ego et  soror mea  introissemus in  navem et transfretassemus
ultra;  transfretatoque   fluvio  dimisissem   sororem  meam  de  nave,  et
reduxissem navem  ad ripam.   Tunc vero introissent sorores duorum virorum,
illorum videlicet,  qui ad  littus remanserant.   Illis igitur feminis navi
egressis, soror  mea [quae  prima transierat], intraret, navemque reduceret
ad nos.   Illa  egrediente foras, duo in navem fratres intrassent, ultraque
venissent.   Tunc unus  ex illis  una cum  sorore sua navem ingressi ad nos
transfretassent.   Ego autem et ille, qui navigaverat, sorore mea remanente
foras, ultra  venissemus.   Nosque ad  littora vectos,  una ex illis duabus
quaelibet mulieribus,  ultra navem  reduceret, sororeque  mea secum recepta
pariter ad  nos ultra  venissent.   Et ille,  cujus soror ultra remanserat,
navem ingressus  eam secum  reduceret.  Et fieret expleta transvectio nullo
maculante contagio. [24]

First of  all, my  sister and  I got  into the  boat and  crossed.   Having
crossed the  river, I  let my sister out and recrossed the river.  Then the
sisters of  the two  men who remained on the bank got in.  When these women
had gotten  out of the boat, my sister, who had already gone across, got in
and brought  the boat  back to  us.  She then got out, and the two brothers
crossed in the boat.  Then, one of the brothers and his sister crossed over
to us.   However,  I and the brother who piloted the boat went across while
my sister remained behind.  When we had been taken to the [other] side, one
of the  other women took the boat back across, and my sister came across to
us with  her at  the same  time.  Then the man whose sister had remained on
the other  side got in the boat and and brought it back with her.  Thus the
crossing was accomplished, with no one being defiled.

XVIII.  propositio de homine et capra et lupo.
Homo quidam  debebat  ultra  fluvium  transferre  [25]  lupum,  capram,  et
fasciculum cauli.   Et  non potuit  aliam navem  invenire, nisi  quae  duos
tantum ex  ipsis ferre  valebat.  Praeceptum itaque ei fuerat ut omnia haec
ultra illaesa transire potuit? [26]
18.  proposition concerning the man, the she-goat, and the wolf.
A certain  man needed  to take  a wolf,  a she-goat  and a  load of cabbage
across a  river.   However, he could only find a boat which would carry two
of these  [at a  time].   Thus, what rule did he employ so as to get all of
them across unharmed?

Simili namque  tenore ducerem  prius capram  et dimitterem  foris lupum  et
caulum.  Tum deinde venirem, lupumque transferrem: [27] lupoque foris misso
capram  navi  receptam  ultra  reducerem;  capramque  foris  missam  caulum
transveherem ultra;  atque iterum  remigassem,  capramque  assumptam  ultra
duxissem.   Sicque faciendo  facta erit remigatio salubris, absque voragine
In a  similar manner,  I would first take the she-goat and leave behind the
wolf and  the cabbage.   When  I had returned, I would ferry over the wolf.
With the  wolf unloaded,  I would  retrieve the  she-goat and  take it back
across.   Then, I  would unload  the she-goat  and take  the cabbage to the
other side.   I  would next  row back,  and take  the she-goat across.  The
crossing should  go well  by doing  thus, and  absent from  the  threat  of

XIX.  propositio de viro et muliere ponderantibus [plaustri pondus onusti].
De viro  et muliere,  quorum uterque  pondus habebat  plaustri onusti, duos
habentes infantes  inter  utrosque  plaustrali  pondere  pensantes  fluvium
transire debuerunt.  Navem invenerunt quae non poterat ferre plus nisi unum
pondus plaustri.   Transfretari  faciat,  qui  se  putat  posse,  ne  navis
19.   proposition concerning  the man and his wife, [each] weighing as much
as a loaded cart.
A man  and his wife, each the weight of a loaded cart, who had two children
each the  weight of  a small  cart, needed  to cross a river.  However, the
boat they  came across  could only  carry the  weight of one cart.  Let him
devise [a way] of crossing in order that the boat should not sink.

Eodem quoque  ordine, ut  superius.    Prius  intrassent  duo  infantes  et
transissent unusque  ex illis  reduceret navem.   Tunc mater navem ingressa
transisset.   Deinde filius  ejus reduceret  navem.   Qua transvecta frater
illius navim  ingressus ambo  ultra transissent, rursusque unus ex illis ad
patrem reduceret  navem.  Qua reducta, filio foris stante, pater transiret:
rursusque filius,  qui ante  transierat, ingressus  navim eamque ad fratrem
reduceret:     jamque  reductam  ingrediantur  ambo  et  transeant.    Tali
subremigante ingenio erit expleta navigatio forsitan sine naufragio.
Also in  the same  manner, first,  the two  children get  in [the boat] and
cross; one  of them then brings the boat back.  Then the mother gets in the
boat and  crosses; her  son brings  the boat back.  With the boat back, the
brother of  this one  gets in  the boat  and both  cross; one  of them then
brings the  boat back  to the  father.  When the boat has returned and with
the son  on the  bank, the father may cross.  Then the brother who had gone
across before  get in the boat and brings it back to his brother.  Now with
the boat  returned, both  brothers get in and cross.  By such a clever plan
of crossing,  the navigation  can  perhaps  take  place  without  the  boat

XX.  propositio de hirtitiis.[28]
De hirtitiis  masculo et femina habentibus duos natos libram ponderantibus,
flumen transire volentibus.
20.  proposition concerning the hirtitii.
A masculine  and feminine [....] who had two children weighing [29] a pound
wished to cross a river.

Similiter, ut  superius, transissent  prius duo  infantes, et unus ex illis
navem reduceret;  in quam pater ingressus ultra transisset; et ille infans,
qui prius  cum fratre  transierat, navim ad ripam reduceret, in quam frater
illius rursus  ingressus ambo  ultra venissent;  unusque propterea ex illis
foras egressus; et alter ad matrem reduceret navim:  in quam mater ingressa
ultra venisset:   qua  egrediente foras,  filius ejus,  qui ante  cum patre
transierat, navim  rursus ingressus eam ad fratrem ultra reduceret; in quam
ambo  ingressi   ultra  venissent,  et  fieret  expleta  transvectio  nullo
formidante naufragio.
Again, as above, first the two children go across.  One of them brings back
the boat,  in which the father crosses.  Then, the child who had first gone
across with  his brother  brings the boat back to the river, and he and his
brother both  go across.  One of them gets out on the [opposite] shore; the
other takes  the boat  back to the mother.  The mother gets in and crosses.
When she  has unloaded at the [opposite] shore, her son, who had previously
crossed with  his father,  gets in  the boat again and takes it over to his
brother.   Both brothers  get in  and cross.  A crossing can be carried out
thusly, free from dread of accident.

XXI.  propositio de campo et ovibus in eo locandis.
Est campus  qui habet  in longitudine  pedes cc,  et in latitudine pedes c.
Volo ibidem  mittere oves;  sic tamen  ut unaquaeque  ovis habeat  in longo
pedes v,  et in  lato pedes  iv.   Dicat, rogo,  qui valet,  quot oves [30]
ibidem locari possint?
21.  proposition concerning the field and the sheep to be placed in it.
There is  a field  which is  200 feet  long, 100  feet wide.  I want to put
sheep in  it as  follows:   Each sheep should have [an area] five feet long
and four  feet wide.  Let him say, I ask he who is able, How many sheep can
be put in such a place?

Ipse campus  habet in longitudine pedes cc.  Et in latitudine pedes c.  Duc
bis [31]  quinquenos de cc, fiunt xl.  At deinde c divide per iiii.  Quarta
pars centenarii  xxv.   Sive ergo  xl vicies quinquies; sive xxv quadragies
ducti, [32]  millenarium implent  numerum.   Tot ergo ibidem oves colfocari
[33] possunt.

The field  is 200  feet long and 100 feet wide.  Divide 200 by five, making
40.   Then, divide  100 by  four, a  fourth part  of which  is 25.   Hence,
whether 40  times 25,  or 25  times 40,  the number 1000 is obtained.  This
many sheep can inhabit such a place.

XXII.  propositio de campo fastigioso.
Est campus  fastigiosus, qui  habet in  uno latere perticas c, et in altero
latere perticas  c, et in fronte perticas l, et in medio perticas lx, et in
altera fronte  perticas l.  Dicat, qui potest, quot aripennas [34] claudere
22.  proposition concerning the slanting field.
There is  a slanting  field which is 100 perticae on each side, 50 perticae
on one  front, 60  perticae in  the middle,  and 50  perticae on  the other
front.   Let him  say, he who is able, How many aripennae does [this field]

Longitudo hujus campi c perticis, et utriusque frontis latitudo l, medietas
vero lx  includitur.   Junge utriusque  frontis numerum  cum medietate,  et
fiunt clx.   Ex  ipsis assume  tertiam partem,  id est, liii, et multiplica
centies, fiunt  v ccc.   Divide  [35] in  xii aequas partes, et inveniuntur
ccccxli. [36]   Item  eosdem divide  in xii  partes, et reperiuntur xxxvii.
Tot sunt in hoc campo aripenni. [37]

The field  is 100  perticae in  length, 50  perticae on  each front, and 60
perticae in  the middle.   Add  the length  of each  front with the middle,
making 160.   Take  one third of this, that is, 53, and multiply it by 100,
making 5300.   Divide  this into  12 equal  parts, and  you arrive  at 441.
Likewise, divide  this into 12 equal parts, and you get 37.  There are this
many aripenni in the field.

XXIII.  propositio de campo quadrangulo.
Est campus  quadrangulus qui  habet in  uno latere perticas xxx, et in alio
perticas xxxii, et in fronte perticas xxxiiii, et in altera perticas xxxii.
Dicat, qui potest, quot aripenni in eo concludi debent?
23.  proposition concerning the quadrangular field.
There is  a field which is 30 perticae on one side, 32 perticae on another,
34 perticae  in the  front, and 32 perticae on the remaining side.  Let him
say, he who can, How many aripenni are contained in such a field?

Duae ejusdem  campi longitudines  faciunt lxii.   Duc  dimidiam lxii, fiunt
xxxi.   Ac duae  ejusdem campi  latitudines junctae  fiunt lxvi.   Duc vero
mediam de  lxvi, fiunt  xxxiii.   Duc vero  [38] terties semel, fiunt i xx.
Divide per duodecimam partem bis sicut superius, hoc est, de mille viginti,
duc per  xii, fiunt lxxxv, rursusque lxxxv divide per xii, fiunt vii.  Sunt
ergo in hoc aripenni numero septem.

Two lengths  of this  field make  62 [perticae].  Half of 62 makes 31.  But
[the other]  two sides  of the  field added  together make  66.  Half of 66
makes 33.   Take  [33] 31 times, making 1020.  Divide [1020] twice by 12 as
above, first  getting 85,  then 85  by 12,  making 7.  Thus there are seven
aripenni in this field.

XXIV.  propositio de campo triangulo.
Est campus  triangulus qui  habet in  uno latere  perticas xxx,  et in alio
perticas xxx,  et in  fronte perticas  xviii. [39]  Dicat, qui potest, quot
aripennos concludere debet?
24.  proposition concerning the triangular field.
There is  a field which is 30 perticae on one side, 30 perticae on another,
and 18  perticae in  the front.  Let him say, he who can, How many aripenni
must be contained [in such a field]?

Junge duas longitudines istius campi, et fiunt lx.  Duc mediam de lx, fiunt
xxx, et  quia in  fronte perticas  xviii habet,  duc mediam de xviii, fiunt
viiii.  Duc vero novies triginta, fiunt cclxx.  Fac exinde bis xii, id est,
divide cclxx,  per duodecimam,  fiunt xxii  et semis;  atque iterum xxii et
semis per  duodecimam divide partem....[40]  fit aripennis unus et perticae
x, et dimidia.
Adding two  lengths of  the field  makes 60.  Removing half of 60 makes 30.
Because there  are 18  perticae in  front, take  half of  this away, making
nine.   Taking nine  times 30  makes 270.   Then,  divide [270]  by twelve,
making 22-and-a-half.   Again, divide 22-and-a-half by twelve, [making two,
[41] with  four left  over, which  is a  third of  12.   Thus there are two
aripenna in  this amount and three parts of a third aripennum.]  This makes
one aripennum, and 10-and-a-half perticae.

XXV.  propositio de campo rotundo.
Est campus  rotundus, qui  habet in gyro perticas cccc.  Dic quot aripennos
capere debet?
25.  proposition concerning the round field.
There is a round field which contains 400 perticae in its circle.  Tell me,
How many aripenni ought it to hold?

Quarta quidem  pars hujus campi, qui cccc includitur perticis est c, hos si
per semetipsos  [42] multiplicaveris,  id est, si centies duxeris, x millia
fiunt, hos in xii partes dividere debes; etenim de x millibus duodecima est
dcccxxxiii, quam  cum item  in xii  partitus fueris, invenies lxviiii.  Tot
enim aripennis hujusmodi campus includitur. [43]

A quarter  of this  field, which  contains 400  perticae, is  100.   If you
multiply [100] by 100, you get 10,000, which you must divide into 12 parts.
For indeed,  a twelfth  of 10,000 is 833, which when again partitioned into
twelfths gives 69. [44]  This many aripenni are included in the field.

XXVI.  propositio de cursu cbnks. bc. fvgb. lfp:rks. [45]
Est campus  qui habet in longitudine pedes cl.  In uno capite stabat canis,
et in  alio stabat  lepus.   Promovit namque  canis ille  post illum,  [46]
scilicet leporem  currere.   Ast ubi ille canis faciebat in uno saltu pedes
viiii, lepus  transmittebat vii.   Dicat,  qui velit,  quot  pedes  quotque
saltus canis  persequendo, et  lepus fugiendo, quoadusque comprehensus est,
fecerunt? [47]
26.   proposition concerning  the chase  of the  dog and  the flight of the
There is  a field  which is  150 feet long.  At one end stood a dog, at the
other, a  hare.   The dog  advanced behind [the hare], namely, to chase the
hare.   But whereas the dog went nine feet per stride, the hare went [only]
seven.   Let him  say, he  who wishes, How many feet and how many leaps did
the dog take in pursuing the fleeing hare until it was caught?

Longitudo hujus  videlicet campi  habet pedes  cl.  Duc mediam de cl, fiunt
lxxv.   Canis vero  faciebat in  uno saltu  pedes viiii, quippe lxxv novies
ducti fiunt  dclxxv, tot  pedes leporem  consequendo [48]  canis  cucurrit,
quoadusque eum  comprehendit dente  tenaci.   At vero  quia lepus  faciebat
pedes vii, in uno saltu, duc ipsos lxxv septies. [49]  Tot vero pedes lepus
fugiendo peregit, donec consecutus est.

The length  of this  field was 150 feet.  Taking half of 150 makes 75.  The
dog was  covering nine  feet per  stride, and nine times 75 makes 675.  The
dog thus  ran this  many feet  in chasing  the rabbit  until it  caught the
rabbit with its tenacious teeth.  And indeed, because the rabbit went seven
feet per  stride, take  75 seven  times.  This is how many feet the fleeing
rabbit travelled before being caught.

XXVII.  propositio de civitate quadrangula.
Est civitas  quadrangula quae habet in uno latere pedes mille centum; et in
alio latere pedes mille; et in fronte pedes dc, et in altera pedes dc. Volo
ibidem tecta  domorum ponere, sic, ut habeat unaquaeque casa in longitudine
pedes xl,  et in latitudine pedes xxx.  Dicat, qui velit, quot casas capere
27.  proposition concerning the quadrangular city.
There is  a quadrangular city which has one side of 1100 feet, another side
of 1000 feet, a front of 600 feet, and a final side of 600 feet.  I want to
put some  houses there so that each house is 40 feet long and 30 feet wide.
Let him say, he who wishes, How many houses ought the city to contain?

Si fuerunt  duae  hujus  civitatis  longitudines  junctae,  facient  ii  c.
Similiter duae,  si fuerunt  latitudines junctae,  faciunt i  cc.  Ergo duc
mediam de  i cc,  faciunt [50] dc, rursusque duc mediam de ii c, fiunt i l.
Et quia  unaquaeque domus  habet in  longitudine [51]  pedes xl, et in lato
xxx: deduc  [52] quadragesimam partem de mille l, fiunt xxvi.  Atque iterum
assume tricesimam de dc, fiunt xx.  Vicies ergo xxvi ducti, fiunt dxx.  Tot
domus capiendae sunt.

If the  two lengths  of this  city were joined together, they would measure
2100 [feet].   Likewise,  if the  two sides were joined, they would measure
1200.  Therefore, take half of 1200, i.e. 600, and half of 2100, i.e. 1050.
Because each  house is 40 feet long and 30 feet wide, take a fourtieth part
of 1050,  making 26.  Then, take a thirtieth of 600, which is 20.  20 times
26 is 520, which is the number of houses to be contained in the city.

XXVIII.  propositio de civitate triangula.
Est civitas  triangula quae  in uno habet latere pedes c, et in alio latere
pedes c,  et in  fronte  pedes  xc,  volo  enim  ibidem  aedificia  domorum
construere, [53] sic tamen, ut unaquaeque domus habeat in longitudine pedes
xx, et  in latitudine  pedes x.  Dicat, qui potest, quot domus capi debent?
28.  proposition concerning the triangular city.
There is  a triangular city which has one side of 100 feet, another side of
100 feet,  and a  third of  90 feet.   Inside  of this,  I want  to build a
structure of  houses, however,  in such a way that each house is 20 feet in
length, 10  feet in width.  Let him say, he who can, How many houses should
be contained [within this structure]?

Duo igitur  hujus civitatis latera juncta fiunt cc, atque duc mediam de cc,
fiunt c.   Sed  quia in fronte habet pedes xc, duc mediam de xc, fiunt xlv.
Et quia  longitudo uniuscujusque  domus habet pedes xx, et latitudo ipsarum
pedes x, duc xx partem in [54] c, fiunt v.  Et pars decima quadragenarii iv
sunt.   Duc itaque  quinquies iiii,  fiunt xx.  Tot domos hujusmodi captura
[55] est civitas.

Two sides  of the  city joined  together make 200; taking half of 200 makes
100.   But because  the front  is 90 feet, take half of 90, making 45.  And
since the  length of  each house  is 20 feet while the width is 10, take 20
into 100,  making five.   A  tenth part of 40 is four; thus, take four five
times, making 20.  The city is to contain this many houses in this way.

XXVIIII.  propositio de civitate rotunda.
Est civitas  rotunda quae  habet in circuitu pedum viii millia.  Dicat, qui
potest, quot  domos capere  debet, ita  ut unaquaeque habeat in longitudine
pedes xxx, et in latitudine pedes xx?
29.  proposition concerning the round city.
There is  a city  which is 8000 feet in circumference.  Let him say, he who
is able, How many houses should the city contain, such that each [house] is
30 feet long, and 20 feet wide?

In hujus  civitatis ambitu  viii millia  pedum numerantur, qui sesquialtera
proportione dividuntur  in xxxx  dccc, et  in  iii  cc.    In  illis  autem
longitudo domorum;  in istis latitudo versatur.  Subtrahe itaque de utraque
summa medietatem, et remanent de majori ii cccc:  de minore vero i dc.  Hos
igitur i  dc divide  in vicenos  et invenies  octoagies viginti,  rursumque
major  summa,   id  est   ii  cccc,  in  xxx  partiti,  octoagies  triginta
dinumerantur.   Duc octoagies  lxxx, et  fiunt vi  millia  cccc.    Tot  in
hujusmodi civitate  domus, secundum  propositionem supra scriptam, construi
[56] possunt.

This city  measures 8000  feet around, which is divided into proportions of
one-and-a-half to  one, i.e.  4800 and  3200.   The length and width of the
houses are  to be  of these  [dimensions].   Thus, take half of each of the
above [measurements],  and from  the larger number there shall remain 2400,
while from  the the  smaller, 1600.   Then, divide 1600 into twenty [parts]
and you will obtain 80 times 20.  In a similar fashion, [divide] the larger
number, i.e. 2400, into 30 pieces, deriving 80 times 30.  Take 80 times 80,
making 6400.   This  many houses  can be  built in  the city, following the
above-written proposal.

XXX.  propositio de basilica.
Est basilica  quae habet  in longitudine  pedes ccxl, et in lato pedes cxx.
Laterculi vero  stratae ejusdem unus laterculus habet in longitudine uncias
xxiii, hoc  est, pedem unum et xi uncias.  Et in latitudine uncias xii, hoc
est, pedem i.  Dicat, qui velit, quot laterculi eamdem debent implere?
30.  proposition concerning the basilica.
There is a basilica which is 240 feet long, 120 feet wide.  One tile of the
tiled basilica is 23 inches long, that is, one foot, 11 inches, while being
12 inches  wide, i.e. one foot.  Let him say, he who wishes, How many tiles
are needed to cover the basilica?

cxl pedes  longitudinis implent  cxxvi laterculi;  et cxx pedes latitudinis
cxx laterculi;  quia unusquisque  laterculus in  latitudine pedis  mensuram
habet.   Multiplica itaque  centum vicies  cxxvi,  in  xv  cxx  [57]  summa
concrescit.     Tot  igitur  in  hujusmodi  basilica  laterculi  pavimentum
contegere possunt.

126 tiles  build 140  [sic] feet of length, [58] and 120 tiles, 120 feet of
width, because  each brick measures one foot in length.  Thus, multiply 120
by 126,  obtaining 15,120.  Therefore in this way so many tiles are able to
cover the ground of the basilica.

XXXI.  propositio de canava. [59]
Est canava  quae habet  in longitudine pedes c, et latitudine pedes lxiiii.
Dicat, qui  potest, quot cupas capere debet?  ita tamen, ut unaquaeque cupa
habeat in  longitudine pedes  vii, et in lato, hoc est in medio pedes iiii,
et pervius unus habeat pedes iiii. [60]
31.  proposition concerning the wine cellar.
There is  a wine  cellar which  is 100 feet long and 64 feet wide.  Let him
say, he  who can, How many casks can it hold, given that each cask is seven
feet long  and four  feet wide,  and given that there is an aisle four feet
wide in the middle [of the cellar]?

In centum  autem quaterdecies  vii  numerantur,  in  lxiiii  vero  sedecies
quaterni continentur,  ex quibus  iiii ad  pervium reputantur, [61] quod in
longitudinem ipsius  canavae ducitur.  [62]   Quia ergo  in  lx  quindecies
quaterni sunt;  et in  centum quaterdecies  septeni; duc  quindecies xiiii,
[63] fiunt  ccx.   Tot cupae  juxta suprascriptam magnitudinem in hujusmodi
canava [64] contineri possunt.

There are  fourteen sevens  in 100,  and sixteen fours in 64, of which four
are needed  for the  aisle which runs the length of this cellar.  And since
there are  fifteen fours in 60, and since there are fourteen sevens in 100,
take 15 times 14, making 210.  This many casks can be stored in the type of
wine cellar described above. [65]

XXXII.  propositio de quodam patrefamilias.
Quidam paterfamilias habuit familias xx.  Et jussit eis dare [66] de annona
modios xx.   Sic jussit, ut viri acciperent [67] modios ternos, et mulieres
binos, et infantes singula semodia.  Dicat, qui potest, quot viri, aut quot
mulieres, vel quot infantes esse debent? [68]
32.  proposition concerning a certain head of household.
A certain head of household had 20 servants. He ordered them to be given 20
modia  of  corn  as follows: The men should receive three modia; the women,
two; and  the children,  half a  modium.  Let him say, he who can, How many
men, women and children must there have been?

Duc semel  ternos,  fiunt  iii,  hoc  est,  unus  vir  ut  modios  accepit.
Similiter et  quinquies bini, fiunt x, hoc est, quinque mulieres acceperunt
modia [69]  x.  Duc vero septies binos, fiunt xiiii, hoc est xiiii infantes
acceperunt modios  vii.   Junge ergo  i et  v et xiiii, fiunt xx.  Hae sunt
familiae xx.   Ac  deinde junge  iii et vii et x, fiunt xx, haec sunt modia
xx.  Sunt ergo simul familiae xx, et modia [70] xx.
Take one  three times  which makes  three; that  is, each man received this
many modia.   Likewise, take five twice, making 10; in this way, five women
received 10  modia.   Then, take  two seven  times,  making  14;  thus,  14
children received seven modia.  Add one and five and 14, making 20; this is
the number  of servants.   Then, add three and seven and 10, this being the
number of modia.  Thus there are 20 servants and 20 modia [of corn].

XXXIII.   propositio de  alio patrefamilias erogante suae familiae annonam.
Quidam paterfamilias  habuit familias  xxx, quibus  jussit dari  de  annona
modios xxx.  Sic vero jussit, ut viri acciperent modios ternos, et mulieres
binos, et infantes singula semodia.  Sovat, qui potest, quot viri, aut quot
mulieres, quotve infantes fuerunt?
33.   proposition concerning another head of household distributing corn to
his servants.
A certain  head of household had 30 servants whom he ordered to be given 30
modia of  corn as  follows:  The men should receive three modia; the women,
two; and  the children, a half modium.  Let him solve, he who can, How many
men, women and children were there?

Si duxeris  ternos ter,  fiunt viiii.  Et si duxeris quinquies binos, fiunt
x, ac  deinde duc  vicies bis semis, fiunt xi, hoc est, viri iii acceperunt
modia viiii,  et quinque mulieres acceperunt x, et xxii infantes acceperunt
xi modia.   Simul juncti iii et v, et xxii faciunt familias xxx.  Rursusque
viiii et  xi, et  x, simul  juncti faciunt  modia xxx.    Quod  sunt  simul
familiae xxx, et modii xxx. [71]

If you take thrice three, you get nine; if you take two five times, you get
10; and  if you take half of 22, you get 11.  Thus, three men received nine
modia; five  women received  10; and 22 children received 11 modia.  Adding
three and  five and  22 makes  30 servants.   Likewise,  nine and 11 and 10
makes 30 modia.  Hence there are 30 servants, and 30 modia [of corn].

XXXIV.  propositio altera de patrefamilias partiente familiae suae annonam.
Quidam paterfamilias  habuit familias  c, quibus  praecepit dare  de annona
modios c, eo vero tenore, ut viri acciperent modios ternos, mulieres binos,
et infantes  singula semodia.   Dicat  ergo, qui  valet,  quot  viri,  quot
mulieres, aut quot infantes fuerunt?
34.   another proposition  concerning a head of household distributing corn
to his servants.
A certain  head of  household had  100 servants.   He  ordered that they be
given 100  modia of  corn as  follows:  The men should receive three modia;
the women,  two; and the children, half a modium.  Thus let him say, he who
can, How many men, women, and children were there?

Undecim terni  fiunt xxxiii.   Et  xv bis  ducti fiunt xxx, [72] id est, xi
viri acceperunt  xxxiii modios;  et xv  mulieres acceperunt  xxx et lxxiiii
infantes acceperunt  xxxvii, qui simul juncti, id est, xi et xv, et lxxiiii
fiunt c,  quae sunt  familiae c.   Similiter junge xxxiii, et xxx et xxxvii
faciunt [73]  c, qui sunt modii c.  His ergo simul junctis habes familias c
et modios c.
11 times three makes 33, and twice 15 makes 30; that is, 11 men received 33
modia [of  corn].   15 women  received 30 [modia], and 74 children received
37.   Adding these together, that is, 11 and 15 and 74, makes 100, which is
the number of servants.  Likewise, adding 33 and 30 and 37 makes 100, which
is the  number of  modia.  Thus with these sums, you have 100 servants, and
100 modia [of corn].

XXXV.  propositio de obitu cujusdam patrisfamilias.
Quidam paterfamilias  moriens  reliquit  infantes,  et  in  facultate  sua,
solidorum dcccclx,  [74] et  uxorem praegnantem.    Qui  jussit  ut  si  ei
masculus nasceretur,  acciperet de  omni massa  dodrans,  hoc  est,  uncias
viiii.   Et mater ipsius acciperet quadrans, hoc est, uncias iii.  Si autem
filia nata esset, [75] acciperet septunx, hoc est vii [76] uncias, et mater
ipsius acciperet  quincunx, hoc  est, v  uncias.  Contigit autem ut geminos
parturiret, id est, puerum et puellam.  Solvat, qui potest, quantum accepit
mater, et quantum filius, quantumve filia?
35.  proposition concerning the death of a certain father.
A certain  father died  and left  behind children, a pregnant wife, and 960
solidi from  his estate.  [However, on his deathbed], he stipulated that if
a son  should be  born to her, then the son should receive three fourths of
the inheritance -- that is, nine twelfths.  The mother should get a quarter
[of the  estate], that  is, three  twelfths.   However, if  a daughter were
born, she should receive seven twelfths, and the mother, five twelfths. But
as it  happened, she gave birth to twins -- both a boy and a girl.  Let him
solve, he who can, How much did the mother, son and daughter each receive?

Solutio. [77]
Junge ergo  viiii et  iii, fiunt  xii, xii  namque unciae  libram  faciunt.
Rursusque junge  similiter vii  et v,  fiunt iterum  xii.   Ideoque bis xii
faciunt xxiiii,  xxiiii autem  faciunt duas  libras, id  est,  solidos  xl.
Deinde ergo [duc] per vicesimam quartam partem dcccclx solidos, et vicesima
quarta pars  eorum fiunt  xl.   Deinde duc,  quia facit  [78] dodrans  sive
dodrans, xl  in nonam partem, ideo novies xl accepit filius, hoc est, xviii
libras, quae  faciunt solidos  ccclx.   Et quia mater tertiam partem contra
filium accepit,  et quintam  contra filiam,  iii et  v, fiunt viii.  Itaque
duc, quia  legitur, quod  faciat bis  seu bisse  xl in parte octava; octies
ergo xl  accepit mater,  hoc est,  libras xvi,  quae faciunt solidos cccxx.
Deinde duc,  quia legitur, quod faciat septunx, xl in vii partibus:  postea
duc septies  xl, fiunt xiiii librae, quae faciunt solidos cclxxx, hoc filia
accepit.   Junge ergo  ccclx et  cccxx et  cclxxx, fiunt  dcccclx solidi et
xlviii librae.
Add nine and three, making 12.  12 ounces make a pound.  Then add seven and
five which make another 12.  12 taken twice makes 24 [ounces], equaling two
pounds, itself  equal to  40 solidi.  Then take a twenty-fourth part of the
960 solidi  which is  40.   Then, because the son received three fourths or
nine twelfths  [of the  inheritance], take a ninth of 40.  The son received
nine times  40 [ounces],  that is, 18 pounds, which equals 360 solidi.  And
since the  mother received  a third as much as the son received and a fifth
as much  as the  daughter, [she  got] three  and five  which  makes  eight.
Therefore, as  prescribed, take  twice 40  and divide  it into eight parts.
Thus the mother received eight times 40 [ounces], that is, 16 pounds, which
is 320  solidi.   Then, as  stipulated, divide 40 into seven parts so as to
get seven  twelfths.   After this, take seven times 40, that is, 14 pounds,
which equals  280 solidi.  This is what the daughter received.  Add 360 and
320 and 280, making 960 solidi, 48 pounds.

XXXVI.  propositio de salutatione cujusdam senis ad puerum.
Quidam senior salutavit puerum, cui et dixit:  Vivas, filii, vivas, inquit,
quantum vixisti,  et aliud  tantum, et ter tantum.  Addatque tibi Deus unum
de annis  meis, et  impleas annos centum.  Solvat, qui potest, quot annorum
tunc tempore puer erat?
36.  proposition concerning a certain old man's greeting to a boy.
A certain  old man  greeted a  boy, saying to him:  "May you live, boy, may
you live  for as  long as  you have [already] lived, and then another equal
amount of time, and then three times as much.  And may God grant you one of
my years,  and you  shall live  to be 100."  Let him solve, he who can, How
many years old was the boy at that time?

In eo  vero, quod dixit, vivas, quantum vixisti, vixerat ante annos viii et
menses tres:   et  aliud tantum  fiunt anni  xvi et  menses vi,  et alterum
tantum fiunt  anni xxxiii,  qui ter  multiplicati fiunt  anni xcviiii, unum
ipsis additum fiunt c.
When [the  old man] said "may you live for as long as you have lived," [the
boy] had  [already] lived  eight years, three months.  Another equal number
of years  make 16  years, six  months, while  another equal  span makes  33
years.   Three times  this makes  99 years,  which with one more year added
makes 100.

XXXVII.  propositio de quodam homine volente aedificare domum.
Homo quidam,  volens aedificare  domum, locavit  artifices vi,  ex quibus v
magistri et  unus discipulus  erat, et  convenit inter  eum, qui aedificare
volebat; et  artificies, ut  per singulos  dies xxv  denarii eis in mercede
darentur, sic tamen, ut discipulus medietatem de eo, quod unus ex magistris
accipiebat, acciperet.  Dicat, qui potest, quantum unusquisque de illis per
unamquamque diem accepit?
37.  proposition concerning a certain man wishing to build a house.
A certain  man, wanting  to build  a house, found six workmen, of whom five
were masters  and one  an apprentice.   It  was agreed  between the man who
wanted to build and the workmen that 25 denarii should be given to them per
day as  pay, and  that the  apprentice should receive half what the masters
receive.   Let him  say, he  who can, How much did each of them receive per

Tolle primum  xxii denarios  et divide  eos in vi partes.  Sic unicuique de
magistris, qui  quinque sunt, iiii denarios; nam quinquies quatuor xx sunt.
Duos, qui  remanserunt, quae est medietas de uno, tolle et da discipulo; et
sunt adhuc  iii denarii  desidui; quos  sic distribues.   Fac  de unoquoque
denario partes  xi, ter  undecim fiunt xxxiii, tolle illas triginta partes,
divide eas  inter magistros  v.   Quinquies seni  fiunt xxx.  Accidunt ergo
unicuique  magistro   partes  vi.    Tolle  tres  partes,  quae  super  xxx
remanserunt, quod est medietas senarii, et da discipulo.
First, take  22 denarii  and divide them into six parts.  Give four denarii
to each  of the  five masters,  since five  times four  is 20.    Take  the
remaining two  denarii, which  is half  of [a  share], and give them to the
apprentice.   There are  still three denarii remaining which you distribute
thusly:   Divide each  denarius into  11 parts, making 33.  Take 30 of them
and divide  them amongst  the five  masters, as  five times  six makes  30.
Hence, six parts go to each master.  Take the remaing three parts, that is,
half of  the six  [which the  masters  received],  and  give  them  to  the

XXXVIII.  propositio de quodam emptore in animalibus centum. [79]
Voluit quidam  homo emere  animalia promiscua  c de solidis c, ita ut equus
tribus solidis  emeretur; bos vero in solido i, et xxiiii [80] oves in sol.
i. Dicat, qui valet, quot caballi, vel quot boves, quotve fuerunt oves?
38.  proposition concerning a certain purchaser and [his] 100 animals.
A certain  man wanted to buy 100 various animals for 100 solidi.  He wished
to pay  three solidi per horse, one solidus per cow, and one solidus per 24
sheep.   Let him  say, he  who can,  How many  horses, cows  and sheep were

Duc ter  vicies tria  i, fiunt  lxviiii.   Et duc bis vicies quatuor, fiunt
xlviii.   Sunt ergo  caballi xxiii,  et solidi lxviiii.  Et oves xlviii, et
solidi ii.   Et  boves xxviiii,  in solidis  xxviiii.   Junge ergo xxiii et
xlviii et  xxviiii, fiunt  animalia c.   Ac  deinde junge  lxviiii et ii et
xxviiii, fiunt solidi c.  Sunt ergo simul juncta animalia c, et solidi c.

Take three times 23, making 69.  Then, take two times 24, making 48.  There
are thus  23 horses  [which cost] 69 solidi, 48 sheep [costing] two solidi,
and 29  cows [which  cost] 29  solidi.   Therefore, add  23 and  48 and 29,
making 100  animals.  Then, add 69 and two and 29, making 100 solidi.  Thus
there are 100 animals and just as many solidi.

XXXVIIII.  propositio de quodam emptore in oriente.
Quidam homo  voluit de c solidis animalia promiscua emere c in oriente; qui
jussit famulo  suo, ut  camelum v  solidis acciperet;  asinum solido i.  xx
oves in  solido compararet.   Dicat, qui vult, quot cameli, vel asini, sive
oves in negotio c solidorum fuerunt?
39.  proposition concerning a certain purchaser in the east.
A certain  man wished  to buy  100 assorted  animals for  100 solidi in the
East.  He ordered his servant to pay five solidi per camel, one solidus per
ass, and  one solidus  per 20  sheep.  Let him say, he who wishes, How many
camels, asses and sheep were obtained for 100 solidi?

Si duxeris x novies, [et] v fiunt xcv, hoc est, cameli xviiii sunt empti in
solidis xcv.   Adde  cum ipsis  unum, hoc  est, in solido i asinum i, fiunt
xcvi.  Ac deinde duc vicies quater, fiunt lxxx, hoc est, in quatuor solidis
oves lxxx.   Junge  ergo xviiii et i et lxxx, fiunt c.  Haec sunt animalia.
Ac deinde  junge xcv,  et i  et iiii,  fiunt solid.  c.   Simul ergo juncti
faciunt pecora c, et solidos c.

If you  take 10 nine times and add five, you get 95; that is, 19 camels are
bought for 95 solidi.  Add to this one solidus for an ass, making 96. Then,
take 20 times four, making 80 -- that is, 20 sheep for four solidi.  Add 19
and one  and 80,  making 100 -- this is the number of animals.  Then add 95
and one  and four,  making 100  solidi.  Hence there are 100 beasts and 100

XL.  propositio de homine et ovibus in monte pascentibus.
Quidam homo vidit de monte oves pascentes, et dixit, utinam haberem tantum,
et aliud  tantum et  medietatem de  medietate, et  de hac  medietate  aliam
medietatem, [81]  atque ego centesimus una cum ipsis ingrederer meam domum.
Solvat, qui potest, quot oves vidit ibidem pascentes?
40.  proposition concerning a man and [some] sheep grazing on a mountain.
A certain  man saw  from a  mountain some sheep grazing and said, "O that I
could have  so many,  and then  just as many more, and then half of half of
this [added],  and then  another half  of this  half.  Then I, as the 100th
[member], might  head back  to my home together with them."  Let him solve,
he who can, How many sheep did the man see grazing?

In hoc  ergo, quod  dixit; haberem  tantum; xxxvi oves primum ab illo visae
sunt.   Et aliud  tantum fiunt  lxxii,  atque  medietas  de  hac  videlicet
medietate, hoc  est, de  xxxvi, fiunt  x et viii.  Rursusque de hac secunda
scilicet medietate  assumpta medietas, id est, de xviii fiunt viiii.  Junge
ergo xxxvi  et xxxvi,  fiunt lxxii.   Adde cum ipsis xviii, fiunt xc.  Adde
vero viiii  cum xc,  fiunt xcviiii.   Ipse vero homo cum ipsis additus erit

36 sheep  were first  seen by the man when he said, "O that I could have so
many."   Adding an  equal number makes 72, and a half of half of this, that
is, of  36, makes  18.   And again,  a half  of this, that is, of 18, makes
nine.  Therefore add 36 and 36, making 72.  Add to this 18, which makes 90.
Then add nine to 90, making 99.  The man himself added to these will be the
100th one.

XLI.  propositio de sode et scrofa.
Quidam paterfamilias  stabilivit curtem  novam, [82] in qua posuit scrofam,
quae peperit  porcellos vii in media sode, qui83 una cum matre, quae octava
est, pepererunt  igitur unusquisque  in omni angulo vii.  Et ipsa iterum in
media sode  cum omnibus  generatis peperit  vii.   Dicat, qui vult, una cum
matribus quot porci fuerunt?
41.  proposition concerning the pigsty and the sow.
A certain  head of household set up a new [quadrangular] enclosure in which
he placed  a sow.  The sow gave birth to seven piglets in the middle of the
sty.  The offspring, along with the mother, the eighth pig, each gave birth
to another  seven piglets in each corner [of the sty].  Then, in the middle
of the  sty, the  mother and  all her  offspring [each] gave birth to seven
more.   Let him  say, he who wishes, How many pigs were there [in the end],
including the mother?

In prima  igitur parturitione,  quae fuit  facta  in  media  sode,  fuerunt
porcelli vii,  et mater  eorum octava.   Octies  igitur  octo  ducti  fiunt
lxiiii.   Tot porcelli  una cum  matribus fuerunt  in i  angulo.  Ac deinde
sexagies quater  octo ducti  fiunt dxii.  Tot cum matribus suis porcelli in
angulo ii.   Rursusque  dxii octies  ducti fiunt  i.ii xcvi.  Tot in tertio
angulo cum  matribus suis  fuerunt.   Qui si  octies multiplicentur,  fiunt
xxxii dcclxxxviii,  tot cum  matribus in quarto fuerunt angulo.  Multiplica
quoque octies  xxxii dcclxxxviii,  fiunt cc  lxii et  ccciiii.    Tot  enim
creverunt, cum in media sode novissime partum fecerunt.
In the  first birth,  which took place in the middle of the sty, there were
seven piglets,  with the  mother being  the eighth  [member].   Eight taken
eight times  is 64 -- this many piglets, along with the mother, were in the
first corner.   Then,  64 taken eight times makes 512 -- this many piglets,
including their  mothers, were in the second corner.  512 taken eight times
yields 4096  -- this  many piglets,  along with  their mother,  were in the
third corner.   If  [4096] is multiplied eight times, one gets 32,788 [sic]
[84] -- this many piglets, including the mother, were in the fourth corner.
Taking eight times 32,788 [sic] makes 262,304 [sic]. [85]  There grew to be
this many [pigs] in the last stage in the middle of the sty.

XLII.  propositio de scala habente gradus centum.
Est scala  una habens  gradus c.   In  primo gradu  sedebat columba una; in
secundo duae;  in tertio  tres; in  quarto iiii;  in quinto v.  Sic in omni
gradu usque  ad centesimum.   Dicat,  qui potest,  quot columbae  in  totum
42.  proposition concerning the ladder having 100 steps.
There is a ladder which has 100 steps.  One dove sat on the first step, two
doves on  the second,  three on  the third, four on the fourth, five on the
fifth, and  so on  up to  the hundredth step.  Let him say, he who can, How
many doves were there in all?

Numerabitur autem  sic:   a primo  gradu in  quo una sedet, tolle illam, et
junge ad  illas xcviiii,  quae nonagesimo [nono] gradu consistunt, et erunt
c.   Sic secundum  ad nonagesimum octavum et invenies similiter c.  Sic per
singulos gradus,  unum de  superioribus gradibus, et alium de inferioribus,
hoc ordine conjunge, et reperies semper in binis gradibus c. Quinquagesimus
autem gradus  solus et  absolutus  est,  non  habens  parem;  similiter  et
centesimus solus remanebit.  Junge ergo omnes et invenies columbas vl.

There will  be as many as follows:  Take the dove sitting on the first step
and add  to it the 99 doves sitting on the 99th step, thus getting 100.  Do
the same with the second and 98th steps and you shall likewise get 100.  By
combining all  the steps  in this  order, that  is, one of the higher steps
with one  of the  lower, you shall always get 100.  The 50th step, however,
is alone and without a match; likewise, the 100th stair is alone.  Add them
all and you will find 5050 doves.

XLIII.  propositio de porcis.
Homo quidam habuit ccc porcos, et jussit, ut tot porci numero impari in iii
dies occidi  deberent. [86]   Similis  est et de xxx sententia.  Dicat, qui
potest, quot  porci impares  sive de  ccc sive  de  xxx,  inter  tres  dies
occidendi sunt?  Haec ratio indissolubilis ad increpandum composita est.
43.  proposition concerning the pigs.
A certain  man had  300 pigs.   He ordered all of them slaughtered in three
days, but  with an uneven number being killed each day.  He wished the same
thing to be done with 30 pigs.  Let him say, he who can, What odd number of
pigs out  of 300  or 30  were to  be killed  in three days?  (This ratio is
indissoluble and was composed for rebuking.)

Ecce fabula!  quae a  nemine solvi  potest, ut  ccc porci, sive triginta in
tribus diebus  impari numero  occidantur.  Haec fabula est tantum ad pueros

Behold an  impossibility which  is able  to be solved by nobody!, in such a
way that  30 [pigs]  be killed  in three  days by  an odd  number.  Such an
implausible story is only for teasing young boys.

XLIIII.  propositio de salutatione pueri ad patrem.
Quidam puer  salutavit patrem;  Ave, inquit,  pater!   Cui pater:   Valeas,
fili! vivas,  quantum vixisti,  quos annos  geminatos triplicatos;  [87] et
sume unum  de annis  meis; et  habebis annos  c.   Dicat, qui  potest, quot
annorum tunc tempore puer erat?
44.  proposition concerning the boy's greeting to his father.
A certain  boy addressed  his father,  saying, "Greetings,  father!"    The
father responded,  "May you fare well, my son, and may you live three times
twice your  years.   Then, adding  one of my own years, you will live to be
100."  Let him say, he who can, How many years was the boy at the time?

Erat enim  puer annorum xvi, et mensium vi, qui geminati cum mensibus fiunt
anni xxxiii,  qui triplicati  fiunt xcviiii.   Addito  uno  patris  anno  c
They boy  was 16  years, six  months.   Double this  makes 33  years, which
tripled is 99.  Having added one year of the father, there are 100.

XLV.  propositio.
Columba sedens in arbore vidit alias volantes; dixit eis:  Utinam fuissetis
aliae tantum et ternae tantum, [88] tunc una mecum fuissetis c.  Dicat, qui
potest, quot columbae erant in primis volantes?
45.  proposition.
A dove  sitting in  a tree saw some other doves flying and said to them, "O
that you  were doubled,  and then  tripled.  Then, along with me, you would
number 100."   Let  him say,  he who  can, How  many doves  were  initially

Triginta iii  erant columbae,  quas prius  conspexit volantes.   Item aliae
tantae fiunt  lxvi.   Et tertiae tantum, fiunt xcviiii.  Adde sedenteni, et
erunt c.
There were  33 doves  flying at  first.   Double this makes 66, while three
times [33] makes 99.  Adding in the sitting dove makes 100.

XLVI.  propositio de sacculo ab homine invento.
Quidam homo  ambulans per  viam invenit  sacculum cum talentis duobus.  Hoc
quoque alii  videntes dixerunt  ei:  Frater, da nobis portionem inventionis
tantum. [89]  Qui renuens noluit eis dare.  Ipsi vero irruentes diripuerunt
sacculum, et  tulit sibi  quisque solidos  quinquaginta.   Et ipse postquam
vidit se  resistere non  posse, misit manum et rapuit solidos quinquaginta.
Dicat, qui vult, quot homines fuerunt?
46.  proposition concerning the small bag found by the man.
A certain  man walking  in the  street found  a small  bag  containing  two
talents.   Some other people saw this and said to him:  "Brother, give us a
portion of your discovery."  But the man shook his head and did not want to
give them any.  The others then rushed at him and tore apart the sack, each
obtaining for  himself 50  solidi.   And when  the man saw that he could no
longer resist  [their attack],  he grabbed  50 solidi for himself.  Let him
say, he who wishes, How many men were there?

Apud quosdam  talentum lxxii  vel pondo vel habet libras.  Libra vero habet
solidos aureos  lxxii.   Sexagies quinquies  lxxii ducti  fiunt v cccc, qui
numerus duplicatus  fiunt decies  dccc.   In x millibus et octingentis sunt
quinquagenarii ccxvi.  Tot homines idcirco fuerunt.

Each talent  has 72  pounds in  it by  weight, and  a pound  equals 72 gold
solidi.   65 times 72 equals 5400 [sic], [90] twice which makes 10,800.  50
goes into  10,800 216  times, which  is the number of men [in the problem].

XLVII.  propositio de episcopo qui jussit xii panes dividi.
Quidam episcopus  jussit xii  panes dividi in clero.  Praecepit enim sic ut
singuli  presbyteri  binos  acciperent  panes;  diaconus  dimidium,  lector
quartam partem:   ita  tamen fiat, ut clericorum et panum unus sit numerus.
Dicat, qui vult, quot presbyteri, vel quot diacones, aut quot lectores esse
47.  proposition concerning the bishop who ordered 12 loaves of bread to be
A certain bishop ordered 12 loaves of bread divided amongst the clergy.  He
stipulated that  each priest  should receive  two loaves;  a deacon, half a
loaf; and  a lector,  a quarter  part.   Hence, it should turn out that the
number of  clerics and  loaves is  the same.   Let him say, he who can, How
many priests, deacons and lectors must there have been?

Quinquies bini  fiunt x,  id est,  v presbyteri decem panes receperunt:  et
diaconus unus  dimidium panem:   et  inter lectores  vi habuerunt  panem et
dimidium.  Junge v et i et vi in simul, et fiunt xii.  Rursusque junge x et
semis et  unum et  semis, fiunt  xii.   Et illi  sunt xii  panes; qui simul
juncti faciunt  homines xii et panes xii.  Unus est ergo numerus clericorum
et panum.
Twice five is 10; that is, five priests received 10 loaves.  The deacon got
half a loaf, and there was a loaf and a half for the six lectors.  Add five
and one  and six,  making 12.   Then  add 10-and-a-half and one-and-a-half,
making 12,  this being  the number  of loaves.   Hence,  there are  12  men
altogether and  12 loaves.   Therefore, the number of clerics and loaves is
the same.

XLVIII.  propositio de homine qui obviavit scholaribus.
Quidam homo  obviavit scholaribus,  [92] et  dixit eis:   Quanti  estis  in
schola? Unus  ex eis respondit dicens:  Nolo hoc tibi dicere, tu numera nos
bis, multiplica  ter; tunc  divide in  quatuor partes.  Quarta pars numeri,
[93] si  me addis cum ipsis, centenarium explet numerum.  Dicat qui potest,
quanti fuerunt, qui pridem obviaverunt ambulanti per viam?
48.  proposition concerning the man who met [some] students.
A certain  man met some students and asked them, "How many of you are there
in school?"   One  of [the  students] responded  to him:  "I do not want to
tell you  [except as  follows]:   double the number of us, then triple that
number; then,  divide that number into four parts.  If you add me to one of
the fourths,  there will  be 100."   Let  him say,  he who  can,  How  many
[students] first met the man?

Terties ter  bini [id est, bis xxxiii] fiunt lxvi:  tanti erant, qui pridem
obviaverunt  ambulanti;   qui  numerus  bis  ductus  cxxxii  reddit.    Hos
multiplica ter, fiunt cccxcvi, horum quarta pars xcviiii sunt.  Adde puerum
respondentem et reperies c.

Twice 33  makes 66; this is the number [of students] who first met the man.
Twice this  number yields  132, and  three times  this number  gives 396, a
quarter part  of which  is 99.   Add in the responding boy and you will get

XLVIIII.  propositio de carpentariis.
Septem carpentarii septenas rotas fecerunt.  Dicat, qui potest, quot carrae
rexerunt? [94]
49.  proposition concerning the carpenters.
Seven carpenters  [each] made  seven wheels.   Let him say, he who can, How
many carts did they build?

Duc septies  vii fiunt  xlviiii, tot rotas fecerunt.  xii vero quater ducti
xlviii reddunt.   Super  xl et  viiii rotas  xii carra  sunt erecta, et una
superfuit rota.
Take seven  times seven,  making 49,  this being  the number of wheels.  12
taken four  times yields  48.   12 carts were assembled from the 49 wheels,
with one wheel left over.

L.  propositio de vino in vasculis.
Centum metra  vini, rogo,  ut dicat,  qui vult, quot sextarios capiunt? vel
ipsa etiam centum metra quot meros habent?
50.  proposition concerning the wine in small vessels.
I ask so that one who wishes might respond:  How many sextarii do 100 metra
of wine contain, and how many meri do 100 metra have?

Unum metrum  capit sectarios xl et viii.  Duc centies xlviii, fiunt quatuor
millia dccc.   Tot  sextarii sunt.   Similiter  et unum  metrum habet meros
cclxxxviiii, duc centies cclxxxviiii fiunt xxviii dcccc.  Tot sunt meri.

One metrum  containes 48 sextarii.  Take 48 a hundred times, making 4800 --
this is  the number  of sextarii  [in 100  metra].   Likewise,  one  metrum
contains 289  meri.   100 times 289 is 28,900 -- this is the number of meri
[in 100 metra].

LI.  propositio de vini in vasculis a quodam patre divisione. [95]
Quidam paterfamilias  moriens dimisit  [96] iiii filiis, iiii vascula vini:
in primo vase erant modia xl, in secundo xxx, in tertio xx, et in quarto x;
qui vocans  dispensatorem domus  suae ait:   Haec  quatuor vascula cum vino
intrinsecus manente  divide  inter  quatuor  filios  meos;  sic  tamen,  ut
unicuique eorum una [97] sit portio tam in vino, quam in vasis.  Dicat, qui
intelligit, quomodo  dividendum est,  ut omnes  aequaliter ex  hoc accipere
51.   proposition concerning the wine in small vessels divided by a certain
A certain dying father left four small vessels of wine to his four sons. In
the first  vessel, there were 40 modia [of wine]; in the second, 30; in the
third, 20;  and in  the fourth,  10.  Calling his house treasurer, he said:
"Divide these  four vessels  containing wine amongst my four sons in such a
way that  each son  receives an equal portion of wine and vessels." Let him
say, he  who can,  How must  the vessels have been divided so that all [the
sons] received an equal amount from this?

In primo  siquidem vasculo  fuerunt modia xl, in secundo xxx, in tertio xx,
in quarto  x.   Junge igitur  xl et  xxx et  xx et x, fiunt c.  Tunc deinde
centenarium idcirco  numerum per quartam divide partem.  Quarta namque pars
centenarii xxv  reperitur, qui  numerus bis  ductus quinquagenarium  de  se
reddit numerum.   Eveniunt  ergo unicuique filio in portione sua xxv modia;
et inter duos l.  In primo xl, et in quarto sunt modii x, hi juncti faciunt
l, hoc  dabis inter duos.  Similiter junge xxx et xx modia, quae fuerunt in
secundo et tertio vascula, et fiunt l et hoc quoque, similiter ut superius,
dabis inter  duos, et  habebunt singuli  xxv  modia;  eritque  id  faciendo
singulorum aequa filiorum divisio, tam in vino, quam et in vasis.
In the  first vessel,  there were 40 modia [of wine]; in the second, 30; in
the third,  20; and  in the  fourth, 10.  Thus add 40 and 30 and 20 and 10,
making 100.   Then, divide 100 into four parts, by which 25 is ascertained.
This number,  taken twice,  makes 50.   Thus  25 modia  go to each son as a
portion, and  between two [sons], 50 [modia].  In the first [vessel], there
are 40  [modia], and  in the  fourth, 10.  Together, these make 50 [modia],
which you should divide among two [of the sons].  In a similar fashion, add
the 30  and 20  modia which  are in the second and third vessels, making 50
[modia].   As above, divide this among the two [other] sons, they will each
have portions of 25 modia.  By doing this, there shall be an equal division
of wine and vessels between the sons.

LII.  propositio de homine patrefamilias.
Quidam pater  familias jussit  xc modia frumenti de una domo sua ad alteram
deportari; quae  distabat leucas  xxx:  et vero ratione ut uno camelo totum
illud frumentum deportaretur in tribus subvectionibus, [98] et in unaquaque
leuca comedat  [99] modium  unum.   Dicat, qui  velit, quot  modii  residui
fuissent? [100]
52.  proposition concerning the head of household.
A certain  head of  household ordered  that 90 modia of grain be taken from
one of  his houses  to another  30 leagues  away.   Given that this load of
grain can  be carried  by a camel in three trips, and that [the camel] eats
one modium per league, Let him say, he who wishes, How many modia were left
over [at the end of the transport]?

In prima subvectione portavit camelus modios xxx super leucas x, et comedit
in unaquaque leuca modium unum, id est, modios xx comedit et remanserunt x.
In secunda  subvectione similiter  deportavit modios xxx, et ex his comedit
xx,  et   remanserunt  x,  in  tertia  vero  subvectione  fecit  similiter;
deportavit medios  xxx, et  ex his  comedit xx, et remanserunt decem.  Sunt
vero de his, qui remanserunt, modia xxx, et de itinere leucae x.  Quos xxx,
in quarta  subvectione domum  detulit, et  ex his  x in itinere comedit, et
remanserunt de tota illa summa modia tantum xx.

On the  first trip,  the camel  carried 30  modia for  10 leagues, eating a
modium [of grain] per league; that is, it ate 20 modia, leaving 10.  On the
second trip  it also  carried 30  modia, eating 20, and leaving 10.  On the
third trip  it did  the same, carrying 30 modia, eating 20, and leaving 10.
Thus there  were 30  modia [of  grain] remaining  and  10  leagues  of  the
journey.   [The camel]  carried these  30 [modia] in a fourth trip [101] to
the house, of which it ate 10 [sic] on the way, leaving only 20 [sic] modia
outof the original amount. [102]

LIII.  propositio de homine patrefamilias monasterii xii monachorum.
Quidam Pater monasterii habuit xii monachos, qui vocans [103] dispensatorem
domus suae dedit illis ova cciiii, jussitque, ut singulis aequalem daret ex
eis portionem.   Sic  tamen jussit, ut inter v presbyteros daret ova lxxxv.
[104]   Dicat, rogo,  qui valet,  quot ova  unicuique ipsorum  in portionem
venerunt, [105] ita ut in nullo nec superabundet numerus, nec minuatur; sed
omnis, ut supra diximus, aequalem in omni accipiat portionem? [106]
53.  proposition concerning the head of a monastery with 12 monks.
A certain Father of a monastery had 12 monks.  Calling the treasurer of his
chapter, he  gave them  [the priests]  204 eggs,  and he  ordered that [the
treasurer] should  give an  equal portion  to each  individual.  He further
stipulated that [the treasurer] give 85 eggs to the five priests,[68 to the
four deacons,  and 51  to the  three lectors].   Let  him say, I ask he who
can, How  many eggs  did each [monk] receive as his portion, so that no one
received too  many, nor  too little,  but so  that as  we stated  above, he
willtake an equal portion to all?

Ducentos igitur  quatuor per  xii partem  divide.  Horum quippe pars xii in
septima decima  resolvitur parte;  quia sive  duodecies xvii,  sive  decies
septies xii  miseris, cciiii  reperies.   Sicut enim  octogenarius  quintus
numerus  septimum   decimum  quinarium   reddit  numerum   de  se,  ita  et
sexagenarius octavus quadrifarie, et quinquagesimus primus trifarie.  Junge
v et iiii et iii, fiunt xii.  Isti sunt homines xii.  Rursusque junge lxxxv
et lxviii  et li,  fiunt cciiii.   Haec  sunt ova  cciiii.    Veniunt  ergo
singulorum ex  his in  partes ova  xvii per  duodecimam partem.    Septimum
decimum aequa lance dividi fiunt....
Divide 204 into 12 parts.  12 parts of this leaves 17 in each part, because
whether you  take 12 times 17, or 17 times 12, you will arrive at 204.  For
just as  the number  85 contains  17 parts  of  five  within  it,  thus  68
[contains 17  parts] of  four, and 51 [contains 17 parts] of three.  Adding
five and  four and  three makes 12 -- this is the number of men.  Then, add
85 and 68 and 51, making 204 -- this is the number of eggs.  Therefore, the
eggs will  be divided  into 17  parts of  12 each.  The 17 [parts] are then
divided equally....


[1] As  given in cod. ms. _Augiae Divitis_.  Bede's title reads: "Incipiunt
aliae propositiones ad acuendos juvenes."

[2] Bede:  " quot annis vel diebus..."

[3] One passus equals five feet.

[4] Bede:  "De homine et aliis hominibus in via sibi obviantibus."

[5] Bede:  "Utinam."

[6] Bede  gives the  following alternate  solution:   "Alia, 28  et 28,  et
tertio sic,  fiunt 84,  et medietas  tertiae fiunt  14; sunt  in totum  98:
adjectis duabus, 100 apparent."

[7] Bede:  "De duobus profiscientibus visis ciconiis."

[8] Bede  gives this  number as  28.   Alcuin's  solution  is  only  Bede's
alternative.   Bede's first  solution is  as follows:   "Qui primis ab illo
visi sunt fuerunt 36, et hujus medietas medietatis sunt 18, et hujus numeri
medietas sunt  9.   Dic ergo sic, 72 et 18 fiunt 90; adde 9, fiunt 99; adde
loquentem, et habebis 100."

[9] Bede adds "in campo pascentibus."

[10] Bede:  "De emptore in denariis centum."

[11] Bede:  "mercator."

[12] Bede:  "...est adeptus."

[13] Bede: "...1400."

[14] Bede  continues:   "Decima  pars  sexagenarii,  6  sunt;  decima  vero
quadragenarii, 4  sunt.    Sive  ergo  decimam  sexagenarii,  sive  decimam
qua[d]ragenarii decies  miseris, 100  portiones 6  cubitorum longas,  et  4
cubitorum latas invenies."

[15] Bede:  "De linteamine."

[16] Bede fails to give a solution for this problem.

[17] Bede provides no answer for this problem.

[18] Bede:  "divisit."

[19] Bede's solution is in columnar form with the number of villages in one
column, the  number of  people in  the other.   He  gives values for all 30
villages.  However, his answers are incorrect starting at v = 22, where the
number 4,194,214 appears instead of the correct 4,194, 304.

[20] Bede:  "In villa 1 fuerunt collecti milites 2."

[21] Bede:  "facit."

[22] The  correct answer  should be  seven.  Bede answers properly, but his
explanation is unsupported.

[23] I  have translated "fratres" as men instead of brothers, since the men
are only brothers relative to their respective sisters, not each other.  If
the men were indeed brothers, it would mean that they desired an incestuous
relation with their own sisters-a situation I highly doubt Alcuin intended.

[24] Bede:   "Tali  igitur sicque  sollicitante studio facta est navigatio,
nullo fufcante inquinationis contagio."

[25] Bede:  "transire."

[26] Bede  continues:    "Dicat  qui  potest  quomodo  eos  illaesos  ultra

[27] Bede:  "ultra transirem."

[28] Bede:   "hiriciis."   I  have been  utterly unable  to find any likely
translation for this word.

[29] Grammatically,  the present active participle "ponderantibus" modifies
the man  and woman.   It  does not  seem likely,  however, that the man and
woman would  weigh only a pound each.  The topic of weight does not come up
in the solution; thus, it is impossible to know the reasoning behind giving
the weights of the subjects.

[30] Bede:  "quod omnes."

[31] The meaning of "bis" here is not understood.

[32] Bede:  "duxeris."

[33] Bede:  "collocari."

[34] Bede:  "aripennos."

[35] Bede:  "deinde."

[36] Bede:  "351."

[37] Bede:  "Tot sunt in hujus aripenni numero."

[38] Bede:  "namque."

[39] Bede:  "novemdecem."

[40] Bede  continues:   " fiunt  2, et remanent 4, quae est 3 pars 12.
Sunt ergo aripenni in hoc numero 2 et 3 pars de aripenno 3."

[41] 22.5 divided by 12 is 1.875.

[42] This should probably be "semel ipsos."

[43] Bede:  "includit."

[44] Such a scenario implies that one aripennum equals 184.53 perticae.

[45] An  anagram which substitutes vowels with following consonants.  Thus,
the heading  should read  "Propositio de  cursu  canis  ac  fuga  leporis."
Bede's heading is "De campo et cane ac fuga leporis."

[46] Bede:  "post leporem currere."

[47] Bede:  "confecerint."

[48] Bede:  "persequendo."

[49] Bede continues:  "...fiunt 526."

[50] Bede:  "fiunt."

[51] Bede:  " longo."

[52] Bede:  "duc."

[53] Bede:  "Volo ut fiat ibi domorum constuctio..."

[54] Bede:  "de."

[55] Bede:  "capienda."

[56] Bede:  "constitui."

[57] Bede:  "1512."

[58] The correct answer should be 241.5 feet.  Notice, too, that the length
of the basilica has changed from 240 feet to 140 feet.  Since Alcuin's (and
Bede's) figures  are inconsistent,  his final answer will be wrong as well.
The final  number of tiles needed, assuming a length of 240 feet, should be
1253; assuming a length of 140 feet, 731.

[59] Bede:  "cavana."

[60] Bede:  "...ut unaquaeque cupa habeat in longitudine pedes 7 et in lato
pedes 4,  et pervius  unus habeat  pedes 4, et unaquaeque cupa habeat pedes

[61] Bede:  "deputantur."

[62] Bede:  "cavanae."

[63] Bede:  "10."

[64] Bede:  "cavana."

[65] If the aisle runs down the middle of the cellar, only 196 casks can be

[66] This  should no  doubt be  the passive infinitive "dari."  See problem

[67] Bede:  "accipiant."

[68] Bede:  "...quotve infantes fuerunt."

[69] Bede:  "modios."

[70] Bede:  "modii."

[71] Bede continues "...tantum 36."

[72] Bede continues as follows:  "...duc vero octogies quatuor semis, fiunt
37, id est 11 acceperunt 17, quod simul..."

[73] Bede:  "fiunt."

[74] Bede:  "860."

[75] Bede:  "nasceretur."

[76] Bede:  "quinque."

[77]  Bede's  heading  reads  "De  animalibus  emptis,"  which  is  clearly
incorrect. Such  a heading  would seem  to be appropriate for problem 38 or

[78] At  this point in Bede's text, the scribe apparently no longer saw any
reason for  providing answers,  saying:  "Reliquae solutiones desiderantur:
potest autem  quisque ratione  arithmetica propositiones illas solvere; ita
ad exercendum ingenium omissa valebant."

[79] Bede:  "De animalibus emptis."

[80] Bede:  "35."

[81] Bede:  " de hac medietate aliam idcirco medietatem..."

[82] Bede:  "...curtem novam quadrangulam..."

[83] Bede:  "quia."

[84] 8 x 4096 = 32,768.

[85] 32,768 x 8 = 262,144.

[86] Bede:  "occiderentur."

[87] Bede:  "triplicabis."

[88] Bede:  "...aliae tantae et adhuc tantae."

[89] Bede:  "...inventionis tuae."

[90] 65 x 72 = 4680.

[91] There  are two  possible  alternate  interpretations  here.    Working
backwards:  10,800/2 = 5400; 5400/72 = 75, while 5400/65 = 83.076923. Since
Alcuin probably  intended only to deal with whole numbers, it is reasonable
to assume that 65 is a mistake for the correct figure of 75. However, is 75
the number of pounds in a talent, or the number of gold solidi in a pound?

[92] Bede:  "scholariis."

[93] Bede:  "nostrum."

[94] Bede:  "carra fecerunt."

[95] Bede:  "De patre familias distribuente."

[96] Bede:  "divisit."

[97] Bede:  "aequalis."

[98] Bede's  presentation is  slightly different:    "Quidam  paterfamilias
habebat de  una domo  sua ad alteram domum leucas 30, et habens camelum qui
debebat in  tribus subjectionibus ex una domo sua ad alteram de annona fere
modia 90..."

[99] Bede:  "comedebat."

[100] Bede:  "...modia residua fuerint."

[101] A  fourth trip  contradicts the  earlier statement  that  the  entire
transport can be completed in only three trips.

[102] The camel carried the remaining 30 modia for 20 leagues.  At the rate
of  one  modium  per  league,  only  10  modia  would  reach  the  intended

[103] Bede:  "convocans."

[104] Bede continues:  " inter 4 diaconos 68, et inter tres [lectores]

[105] Bede:  "evenerunt."

[106] Bede:  "...sed omnes, ut supra diximus, aequalem in omnibus accipiant


                  Richard Goldschmidt and William Bateson:
            Opposition to the Classical Conception of the Gene;
                      Obstructionists or Visionaries?

                              By Sharon Low
                                HPS 200Y
                           Received January, 1993.
                            Revised April, 1993.

  When the laurels are awarded in science, past and present, the recipients
are invariably  those who  have directly contributed to our current, mighty
body  of   scientific  "truth".    Regarding  the  scientists  whose  ideas
conflicted with  those now considered "right", we are inclined to shake our
heads and  persuade  ourselves  that  they  simply  lacked  the  perception
required  to   grasp  a  certain  reality  that,  elusive  though  it  was,
nevertheless lay  before them.   The  weakness of this type of meritocracy,
however, is  that among  those denied  entry into  our history  books are a
handful of truly great thinkers, some of the most respected of their times.
Tremendous  intellectual   courage,  sharpness   of  mind   and  unwavering
conviction are the rare characteristics that drive an  effective opposition
to predominant  belief.  This is not to glorify blatant obstructionism; the
practitioners of  willful hindrance  of another's work for its own sake are
not those  to whom  we refer.   Rather one should seek to acknowledge those
conscientious scientists who decide against the path of least resistance --
to "buy  into" a burgeoning, apparently successful science -- because to do
so would violate their own sensibilities.  Excellence in scientific thought
ought not  to be  confined to  a parochial  criterion of  "rightness",  but
gauged by  the import  of the  questions asked.   In  this is the essential
spirit of  science.  It is a creative process rather than a race to an end,
because no end ultimately exists, and proximate goals are always changing.
    Having  said  this,  let  us  consider  and  compare  two  accomplished
geneticists of  this  century,  William  Bateson  and  Richard  Goldschmidt
(although the  term "geneticist"  as  it  is  currently  understood  is  an
appellation either  may be  loathe to  adopt).  Both of these investigators
were opposed to the reductionistic, atomistic, materialistic concept of the
chromosonal gene as it was proposed by Thomas Hunt Morgan and his classical
school of  genetics, in  the early  decades of  the field.   The scientific
establishment has,  of course,  since evaluated  Morgan's rendition  of the
gene as being, in essence, right.  To the historiographer of science, these
two figures  are interesting  for they  and their  kind, in  a sense,  best
exemplify the  ability of  personal and  cultural influences,  in the  most
reputable of  scientists, to  triumph over  what might  otherwise stand  as
naked fact.   One  is compelled  to ask,  then, why Bateson and Goldschmidt
rejected  the   evidence  that   was  presented.     Were   they  in   fact
obstructionists, and as such has the respect accorded them been undeserved?
Could their inability to conform be attributed to personal biases or to the
philosophical climate  of their time?  Perhaps the blame may be cast on the
inadequacy of  the theory  itself, nevertheless cast as so flawlessly lucid
in history-book  style hindsight.   In considering the contribution of each
to  the  field  of  genetics,  his  background,  his  world  view  and  the
alternative notions  of the  gene proposed,  it  is  hoped  that  we  might
comprehend the  reason and  the feeling  behind their  discontent, and  the
value of the remarkably similar concerns that they separately raised.
  The son of the master of St. John's college at Cambridge, William Bateson
(1861-1926)  distinguished  himself  as  a  college  student.    Awarded  a
fellowship to  study the  evolutionary morphology of a marine invertebrate,
Balanoglossus, at  the Chesapeake Bay Zoology Station in the United States,
he was  influenced by  the eminent embryologist, W.K. Brooks.  Bateson came
to believe  that  minor  fluctuating  variations,  posited  by  Darwin  and
accepted  by  most  biologists,  might  not  be  the  exclusive  source  of
evolution.   After a decade of amassing numerous examples of "discontinuous
variations, he  published his  _Materials for  the Study  of Variation_  in
1894, promoting  the idea  of "sports"  of nature,  to the  dismay  of  the
Darwinist biometrical  school [1].  Bateson subsequently began to hybridize
related varieties  of organisms  in  the  hope  of  understanding  how  the
characters distinguishing  them would  be inherited.   The framework of his
thought in  this endeavour  would prove  remarkably akin  to  that  of  his
predecessor, Mendel.   Indeed  in 1900, encountering an account of Mendel's
laws, Bateson  immediately recognized  in  them  a  mechanism  which  might
support his idea of saltatory variation [2].
   In 1902,  Bateson's work, _A Defence of Mendel's Principles of Heredity_
-- the  first textbook  in elementary  genetics, was  published.    Busying
himself with  the establishment  of a new science, some of his most lasting
contributions to  the field  of genetics soon followed.  These included the
terms that  he established  for some  of  Mendel's  concepts,  among  them:
heterozygote, homozygote,  allelomorph and unit character.  In addition, he
created a  scheme for the notation of breeding crosses.  His continued work
as an experimental breeder repeatedly confirmed Mendel's results as well as
their general  applicability using  a number  of different plant and animal
species.   Within a  short time,  he had presented preliminary ideas on the
inheritance of  lethal factors  and the occasional appearance of homozygous
recessive forms  in cross  breeds.   He was  also the first to describe the
effect of  multiple genes  on a  single trait  as well as epistatic effects
between genes  [3].   Bateson's vigorous  champion of  Mendel's  principles
contributed much  to the  rapid spread  of the new science.  W.E. Castle, a
pioneer in  genetics in  the U.S.  later said  of Bateson: "he was the real
founder of  the science  of genetics  as well  as the  one who gave it that
name." [4]   The  latter auspicious  event occurred  in 1906  when  Bateson
addressed a  conference suggesting, "for the consideration of this congress
the term  Genetics, which  sufficiently  indicates  that  our  labours  are
devoted to the elucidation of the phenomena of heredity and variation." [5]
It is  clear that  Bateson was  instrumental in  setting the  precedents to
achieve this goal.
   Bateson's own discoveries in genetics were a result of breeding analyses
of apparent  exceptions to  Mendel's rules  and careful  observation.   The
value he  placed on  exceptional occurrences  would later  factor into  his
objections to  the classical  gene theory.  "Treasure your exceptions!", he
urged, "keep  them always  uncovered and in sight.  Exceptions are like the
rough brickwork  of a  growing building  which tells  that there is more to
come and shows where the next construction is to be." [6]  Comfortable only
with breeding  analysis,  however,  he  would  later  remain  skeptical  of
conclusions drawn  from most  other methods  of genetic study, particularly
technical cytology of which he confessed to be, "one who had never seen the
marvels of  cytology, save  as through  a glass darkly" [7], and histology:
"...I mean no disrespect to that study of the physiology of reproduction by
histological means  (but) order  to  pursue  directly  the  course  of
Heredity and  Variation, it  is evident  that we  must fall  back on  those
tangible manifestations  which are  to be studied only by field observation
and experimental breeding." [8]
   Unsurprisingly, doubt  was cast  upon the  earliest implication  of  the
chromosones in  heredity by  Sutton and Boveri.  He wrote:  "I cannot avoid
attaching importance  to  this  want  of  connection  between  the  nuclear
phenomena and  the features  of  bodily  organisation.    All  attempts  to
investigate Heredity  by cytological  means lie under the disadvantage that
it is  the  nuclear  changes  which  can  alone  be  effectively  observed.
Important as they must surely be, I have never been persuaded that the rest
of the  cell counts  for nothing.   What  we  know  of  the  behaviour  and
variability of  the chromosomes seems in my opinion quite incompatible with
the belief  that they  alone are  the sole agents responsible in heredity."
   Bateson's preferences  clearly hearkened back to those characteristic of
the nineteenth  century.  The value of the cell as the main functional unit
was not  easily relinquished,  as were not, it turns out, most of the other
notions that  were the  legacy of  his morphological  background.  The fact
that the  form of  the chromosomes  -- their behaviour and variation -- did
not correlate  with the  form of  the developing  organism,  in  his  view,
disqualified them  as hereditary  determinants.   As  early  as  1904,  his
nostalgia was  evident:  "This state of things in a progressive science has
arisen, as  I think,  from a loss of touch with a main line of
spite of  that perfecting  of the instruments of research characteristic of
our time, and an extension of the area of scrutiny, the last generation was
nearer the  main quest.   No  one can  study the history of biology without
perceiving that in some essential respects the spirit of the naturalists of
fifty years ago was truer in aim..." [10].
   Originally intended  as a means to study evolutionary processes, Bateson
evidently had  not forseen  the immense implications that genetics held for
heredity.   Needless to say, his aversion to technological advances did not
bode well for a friendly reception of the events that were to soon follow.
   The first  success of  the Morgan  school around  1910 marked a definite
beginning to  Bateson's fall  back from  the forefront of genetic research.
Morgan and  his colleagues  held that units called "genes" were to be found
linearly arranged  on the  chromosomes in  the nucleus  of the  cell.  Even
after the  publication of the group's _The Mechanism of Mendelian Heredity_
in 1915,  which converted  most biologists  to the  doctrine of  the  gene,
Bateson remained  unmoved.    "Many  competent  biologists  have  satisfied
themselves that  these powers are conferred alone by the nuclei of the germ
cells.   Others still  going further  declare that  each  property  of  the
organism is  determined by  a specific  particle of  nuclear material,  and
believe that  as the result of certain very remarkable experiments they are
even able  to decide  the order  in which  these particles  are grouped.  I
mention this  interesting line of inquiry to illustrate the scope of modern
genetic analysis,  though I  am unconvinced of the cogency of the arguments
employed." [11]
   A critical  observation that  Morgan used to support his theory, linkage
phenomena, had  been previously attributed by Bateson and his colleague, R.
C. Punnett,  to their  own idea  of reduplication. [12]  They proposed that
characters that  tended to  stay together  in inheritance  did  so  because
gametes containing  them underwent  additional post-meiotic  divisions, and
were thus  particularly well-represented  among the  offspring.   This  was
found not to be the case.
     For  years,  Bateson  continued  to  formulate  counter-proposals  and
contradictions to  the steady  stream of  small victories  that flowed from
Morgan's lab  [13].   Another of  his beliefs,  the  presence  and  absence
hypothesis concerning  dominance and  recessiveness, also failed to survive
the  early  years  of  genetics  [14].    His  contentions,  however,  were
conspicuously lacking  in experimental  support, indulging  in  theoretical
speculation and commentary on the findings of others.
   Behind his defensiveness lay the belief that a common solution could and
would be found for the phenomena of heredity and development, which he held
as inseparable.   By  this criterion,  the  still  admittedly  inconclusive
evidence for  the gentic  role of  the chromosome,  and the  reality of the
gene, fell  short.   He was  waiting for  the time,  "when  it  (would  be)
possible to  trace in  the maturing  germ an  indication of  some character
afterwards recognizable  in the  resulting organism." [15]  Furthermore, he
required that  the form  and complexity  of the germinal material correlate
with ontogenetic features of various species.  Clearly they did not -- "The
chromosomes of  nearly related  creatures may  be utterly different both in
number, size and form". [16]
  Bateson preferred to believe that the phenomena of heredity and variation
were due  to  cell  division,  the  chromosomes  being  a  conspicuous  but
secondary manifestation.  [17]    It  is  telling  that  his  _Problems  of
Genetics_  (1913)   consisted  mostly  of  embryological  and  evolutionary
questions,  scarcely   mentioning  the   classical  geneticists   or   even
cytological observations.   Asked  to review  the Drysophila  group's first
book, his comments were keenly critical [18].  Firstly, the connection made
between crossing-over  and chiasmata  seemed not  to apply  to the  male Y-
chromosome despite  its being  paired; yet,  originally though unpaired, it
was used  to demonstrate that unpaired (i.e. without chiasmata) chromosomes
do not cross-over.  How then, Bateson asked, could this conclusion still be
held as  valid?  Furthermore, Sturtevant's mapping techniques did not prove
conclusively that  the putative  genes were  linearly arranged.    However,
despite these  denials, Bridges'  discovery of  non-disjunction provided an
irrefutable association  of the  sex-linked factors,  at  least,  with  the
chromosomes.   Still, this  did not necessitate any causal relation between
the two.   Nor  did it  oblige Bateson  to concede  to the verity of either
linkage or  crossing-over.   By 1921,  having been convinced by Bridges, in
person, that  abnormals are  aberrant in  both genotype and phenotype [19],
Bateson could not but grudgingly approve of parts of the chromosome theory.
Still, he  could not  accept the  generalization that chromosomes determine
all heredity.   His  doubts never  really left  him.    In  any  case,  his
endorsement no  longer mattered  much since  by this time his protests were
largely ignored by the genetics community [20].
   All things  considered, one  suspects that  the main  contention held by
Bateson against the classical geneticists was their neglect of development.
If "the  geneticist" was to be "the successor of the morphologist" [21], it
was his  responsibility  to  explain  the  forms  of  organisms  and  their
development,  rather   than  engaging  solely  in  intangible  mathematical
treatment of  the germinal  components.   Bateson's evolutionary  interests
predisposed him  to a  primary concern with form, since it is the substrate
for selection.   Furthermore,  if changed  greatly,  it  was  the  mark  of
speciation.   It is  understandable, though  not commendable, why he should
have  been   so  unforgiving  towards  Morgan's  group  and  the  proposals
altogether -- they had distorted his agenda for genetics in the future.
   William Coleman,  in his  essay, "Bateson  and chromosomes: conservative
thought in  science", suggests  that  Bateson  was  affected  by  J.  Clerk
Maxwell's replacement of the indivisible-atom theory by the "vortex atom" -
- a  hypothetical dynamic  node in  the ether  [22].  As a model, it was an
attractive theory  to non-materialists,  and was  convincingly supported by
spectral analyses indicating a basical vibrational component of all that is
considered to  be matter.   The  only true  matter, in this scheme, was the
ether.   Bateson's training  at Cambridge  around the  turn of  the century
placed him  at the  sight of  the development  of Maxwell's  school, at the
prime of its effect on attitudes and methodologies of all areas of science.
Models were  Maxwell's chosen mode of science and Bateson, correspondingly,
proposed quite  an array  of his  own [23].   Possessing only a rudimentary
knowledge of  physics, nevertheless his suggestions for models of heredity,
bear close  parallels to  physical science:   "...[cells]  must be  able to
divide, and  to segment  as a  vibrating plate or rod does, or as an icicle
can do as it becomes ribbed in a continuous stream of water." [24]
   An absorption  of Maxwell's  idea is  obvious in  his description  of "a
living creature"  as "a  vortex of  chemical and molecular
through which  matter is  continually passing". [25]  An anti-materialistic
perspective led  him to  "incline to the expectation that the heterogeneity
of the  determining elements as factors lies rather in forces, of which the
cell materials are the vehicle, than in the nature of the material itself."
Cell division  was the  process by  which "numbers of characters, or rather
the elements  upon which  they depend,  are sorted  out among the resulting
germ cells  in orderly  fashion" and  being non-material,  it was suspected
"that the  properties depend  on some  phenomenon of arrangement." [25]  In
addition, "The  geometrical symmetry  of living  things is  the  key  to  a
knowledge of  their regularity,  and the  forces which  cause it.   In  the
symmetry of  the dividing  cell, the  basis of  that  resemblance  we  call
Heredity  is   contained."  [27]    These  aspects  of  his  theories  were
essentially held throughout.  Otherwise, the vague and non-committal nature
of his  arguments presented  here reflects a similar general evasiveness in
his own  writing.   Yet, with  all of his complicated postulations, Bateson
was  engaging  in  a  pseudo-physics  of  sorts,  using  terms  laden  with
implications related to kinetics, but in an altogether nonspecific way.
   The abandoning  of experimentation and the concerted attempts to explain
causal elements  of inheritance  by alternative  theories --  what do these
facts reveal  about Bateson  as a  scientist?   Coleman has written that in
turning from  the early years of hybridization studies to explaining causal
elements of  inheritance, Bateson  chose a  new tactic of "employing in the
most immediate  manner conceivable  what he took to be the first principles
of  physical   science."  [28]    I  would  like  to  suggest  a  different
interpretation.   It is  conceivable that Bateson felt rather disillusioned
by the  monopoly gained  by the  monopoly gained  by the cytologists over a
field that  once followed closely behind him, a science that he had groomed
as a  tool for  evolutionary studies.   Alienated by his unfamiliarity with
the new  techniques, which  he had deeply distrusted, he could not help but
react negatively  to the  usurpers of  his authority,  and the  ideas  they
proposed.     This  was   not  difficult   since  Bateson  already  held  a
fundamentally different  philosophy.   Furthermore, he found himself forced
to defend  his own original notions of heritary phenomena against a growing
body of contradictory evidence.  A response was called for.  The only level
at which  he was  on equal  footing with  the classical  geneticists was in
theoretical model-building  so this became his necessary recourse, short of
retreat.   Enlisting the  language and  notions of physics and chemistry to
lend weight  to his  theories, Bateson  was able  to suspend  his belief in
chromosonal heredity  for longer  than most.   This  was his  defence.   An
antagonistic reception to all of the ideas of the competition served as his
attack.   His priorities  in these later years lay not in converting anyone
to his own theories -- they were formulated to convey general ideas, not to
furnish rigorous  explanations; his interest, rather, was in contradiction.
It must  be pointed  out that  this scenario  could have  occurred  without
Bateson's conscious  intent.   The effect  of his  negativity,  regardless,
remains a dark shadow over his formidable repute.
   Richard Goldschmidt  (1878-1958), a contemporary of William Bateson, was
born into  a prosperous  German  family  in  Frankfurt-am-Main.    Entering
Heidelberg University  as a  medical student,  he found  himself under  the
tutelage of  illustrious zoologist  Butschli,  Gegenbauer  the  comparative
anatomist, and  Kossel the biochemist.  Leaving medicine after two years of
study with  Richard Hertwig,  he later  returned to Butschli's lab where he
obtained his  Ph.D. in  maturation fertilization  and early  development of
Polystomum, a trematode.  While his primary work was a typically nineteenth
century brand  of morphology,  a further  area of  interest  belonged  more
directly to  his time  period.   Great late  nineteenth century discoveries
concerning chromosomes,  mitosis, maturation  and fertilization had brought
many pressing  and fundamental  questions.  [29]    In  the  early  1900's,
Goldschmidt was  attracted to  cytology by  meosis and  the observation  of
chromatic material  in the  cytoplasm.   By 1910,  he was  a prominent  and
influential scholar,  having  founded  a  cytological  journal,  written  a
genetics textbook  and become  a respected  professor.   In 1909,  however,
unsatisfied with  purely descriptive  work, Goldschmidt turned to genetics.
Though unrecognized  at the  time, his  first  accomplishment  was  in  the
description of the increase in melanism among nun-moths (Lymantria Monacha)
using  the  Hardy-Wineberg  mathematical  law,  as  yet  unnamed,  and  its
importance unacknowledged.   In this work, Goldschmidt's agility of mind is
demonstrated --  a pioneer in population genetics, he used a method foreign
not only  to his  way of  thinking, but  novel to  the field.  This quality
would be  evident throughout his career.  A second question that he pursued
concerned what  he termed  "sex intergrades"  [30] resulting from interbred
strains among  gypsy moths (Lymantria Dispar).  From this he formulated his
Balance Theory of sex determination.  In his work he achieved what had been
his underlying  goal to combine Mendelism with developmental physiology.  A
further observation  that hybrid  Lymantria caterpillars  seemed to express
different colour phenotypes at various times during development, led to the
Time Law  theory of  intersexuality.   Combining  Mendelian  genetics  with
physiology and  biochemistry, the  theory described a changing influence of
relevant factors for colour over the course of development [31].
   Arriving in  the United  States  in  1914  as  a  refugee  of  the  war,
Goldschmidt's  colleagues'   esteem  was  not  well-won  by  his  immediate
proclamation in  the homeland  of the  Drysophila group that the "Theory of
the gene  is dead."  [32]   Golschmidt had  begun to  propound his  general
theory of genic determination of development, based on an interpretation of
the action  of the  Lymantria sex factors:  "the genes must be things which
produce their typical effects by catalyzing chains of reaction, their speed
of which,  and given  the specific substance of each gene and the plasmatic
substratum, is proportional to the quantity of the gene and therefore fixed
within the entire system of simultaneous coordinated reactions of different
speed." [33].
   This conception  of genetics  as enzymes  reflected a  holistic  outlook
towards the  totality of  the genic  effect.  Goldschmidt recognized that a
quantitative shift  in one  gene would  necessitate corresponding shifts in
the  others,   and  their   dependent  reactions,  thus  producing  a  new,
physiological balance.
   Meanwhile, his  work began  to be  punctuated by  harsh attacks  on  the
Drosophila  genticists.    While  according  them  high  praise  for  their
discoveries, Goldschmidt  nevertheless faulted  their refusal  to accept  a
quantitative theory  of allelism  and mutation.   His  publication in 1937,
_Physiological  Genetics_,  comprehensively  and  critically  reviewed  and
analyzed all  of the  important facts  known by that time, of genic action.
In it,  he revealed  an alteration  to his own concept of the gene:  "
genes are  existing but only points, loci, in a chromosome which have to be
arranged in  a proper  order or pattern to control normal development.  Any
change in  this order  may change  some detail  of development...The  whole
chromosome is the unit controlling normal development." [34]
   Now denying  that genes  were  discrete  hereditary  units,  Goldschmidt
contended "that  gene mutation  and position  effects are  one and the same
thing." [35]   Muller  had  earlier  assumed  that  point  mutations  arose
linearly with  x-ray dosage whereas chromosomal rearrangements were thought
to arise  exponentially, differentiating  the two.   Later, however, it was
found  that   small  rearrangements   also  arose  linearly,  allowing  for
Goldschmidt's conclusion.   Furthermore, "the gene as a unit is, of course,
a concept  derived from  the existence  of a  thing called the mutant gene.
But this inference is not necessarily valid.  There is a possibility that a
condition exists  at a definite locus...that we call a mutant gene but that
no corresponding plus condition exists as a separate unit." [36]
   Thus, the phenomenon of position effect in which the effect of a gene is
influenced by  its chromosomal  neighbours had  disposed Goldschmidt to the
revision of  the notion  of materially  and physiologically  separate genic
elements.   By discarding  the  idea  of  individualy  separate  genes,  he
simultaneously abandoned  his  own  idea  of  genes  as  separate  enzymes.
Mutations simply changed the total chemical reactivity of the chromosome by
upsetting the  balance of  chemical reactions  that catalyzed.  A wild type
state was then a certain normal arrangement for the chromosome.
   The new theory was partly a result of Goldschmidt's original interest in
geographic variation as it related to genetics and physiology, and his hope
to enlighten  the understanding  of speciation  [37].   The new  chromosome
concept allowed  him to  conclude, as Bateson had, that the small mutations
promoted by  the Neo-Darwinists  were explanation  only  for  intraspecific
diversity.   Macromutations of  "hopeful  monsters"  were  invoked  as  the
mechanism of  speciation in  that "the developmental system of a species is
capable of  being changed  suddenly so  that a  new type may emerge without
slow accumulation  of new  steps." [38]  Experimental work on Drosophila to
test these  ideas occupied  the latter  part of his career.  The result was
his discovery  of phenocopies,  which were induced mimics of the postulated
naturally occurring  macromutants.   Goldschmidt's book _The Material Basis
of Evolution_  (1940) has been recently lauded as "a book...clearly too far
ahead of its time...finally coming into its own." [39]
  Goldschmidt has described the reception to his general theory as, "called
by some  critics the  beginning of  a new  era in  genetics and  by  others
bunkum, neither  sound genetics  nor sound physiology; a reception which in
view of historical parallels seems rather encouraging..." [40]  Indeed, the
genetics community  gradually came  to appreciate  the concept  as  it  was
later,  in   its  physiological   emphasis,  echoed  upon  the  arrival  of
microbiology.  Despite the validity of many of his criticisms, however, his
rejection of the unitary gene was in error.
   It is clear that Goldschmidt, like Bateson, trained in the old school of
morphology, retained a sensitivity to the problem of how hereditary factors
translate into adult traits.  To Goldschmidt, only an integrated structural
and functional  approach would  yield the  correct picture of the nature of
the gene.   In  this, he  was  profoundly  at  odds  with  the  mechanistic
philosophy which guided the work of most of the classical geneticists.
   Garland Allen has traced Goldschmidt's philosophy to that of the Machian
school of  physics which,  around the  turn of  the century,  rejected  the
mechanistic materialism  which prevailed  among the  sciences [41].    Mach
claimed that  science should  assume nothing  of the  ultimate or proximate
nature of  matter.   In this anti-materialistic attribution, Goldschmidt is
cast in  an interesting  parallel with  Bateson --  the former  of a German
flavour, the  latter, British.   Yet  perhaps the  confidence is not overly
striking, considering  that the  decades from 1895-1915 were witness to the
development of quantum theory, Bohr's revision of atomic structure, growing
debate on  the physical  reality of atoms and their relation to energy, and
the promulgation of Einstein's general and specific theories of relativity.
A resultant  trend towards idealism had begun in the philosophy of physics,
led largely  by Alfred  North Whitehead,  a close  friend of  Bateson [42].
This movement  similarly questioned the validity of seeking explanations in
terms of  real, material  and ultimate  particles of matter, now that atoms
had revealed  an even  smaller structural  level.   Unlike Bateson's strict
antimaterialism, Goldschmidt  manifested the  influence of physics as anti-
atomism [43].   He,  like Mach, was disinclined to advocate explanations of
complex processes  in terms  of ultimate  units.   Heredity, in  his  view,
should be  explicable without  having to  postulate units  such  as  genes,
although he  never denied  its material  basis.   Instead, he  rejected the
"atomism" that  was being  applied to  the problem,  in  the  form  of  the
corpuscular gene.
   In a  revealing paper  entitled "Different  Philosophies  of  Genetics",
Goldschmidt's aversion  to atomism as well as his functional, physiological
approach are  clearly articulated.   Bateson  would surely  have  approved:
"Now to  the two  philosophies of  genetics to  be contrasted...statistical
thinking tries  to explain  all basic  features  of  genetic  phenomena  by
introducing more  genes in the form of modifier systems...which I must call
hyperatomism.  In my personal opinion it will lead in the end to impossible
consequences.   The physiological,  or dynamic  approach...tries  first  to
understand general  phenomena in  terms of  genic action  and developmental
systems with  all their  consequences of  interaction, embryonic regulation
and  prefers to  find out  how far explanations based upon
the dynamics  of the  organism and its development under genic control will
go." [44]
     More  than  simply  a  philosophical  reaction  to  atomism,  however,
Goldschmidt's objections  also belied  a deeply  rooted  holistic  outlook.
Compared with Bateson's dogged holism regarding the cell, insisting "always
to  unify,   never  to  distinguish"  [45],  Goldschmidt  conveyed  a  more
insightful intent.  The tendency of the mechanistic philosophy to see parts
rather than  wholes obscured what Goldschmidt considered the most important
questions that  biologists  should  be  asking.    They  assumed  that  the
knowledge of  the parts would combine additively to an understanding of the
whole; but,  "it is  not the  sum but  the  orderly  relationships  of  the
components that  are responsible for the actions at the different levels of
the hierarchy"  [46], wrote  Goldschmidt --  and for good reason.  His work
had demonstrated  the multiplicity  of  interactions  between  the  systems
underlying heredity,  development and evolution.  He discerned that how one
viewed the  structure of the gene was how one approached its function [47].
Indeed, as feared, the field of genetics did come to regard heredity as the
study of what genes do -- as if in a sense genes act independently of their
environments and  each other.   Even  today, the field has not been able to
fully  extricate   itself   from   the   consequences   of   this   blatant
   The early  twentieth century  was a  fine time  to be  a scientist.  The
revolutionary  era,   however,  also   brought  widespread   confusion  and
uncertainty.   While, doubtless  it  was  difficult  for  the  majority  of
biologists to  abandon their previous beliefs and adopt unfamiliar notions,
it was  arguably more  difficult for  scientists such  as  Goldschmidt  and
Bateson  to   retain  their   strength  of  conviction.    Goldschmidt,  in
particular, admirably  demonstrated that  it was  possible to contribute to
the new movement, while opposed to the prevailing paradigm.  His scientific
style was  exemplary, illustrating  the rare breed of scientist to whom was
originally referred.  Bateson, while a proficient observer, lacked the more
profound level  of  perceptiveness  to  be  found  in  Goldschmidt's  work.
Although at  a superficial  level,  it  may  seem  that  Goldschmidt  would
advocate a  return to  the  nineteenth  century  merging  of  heredity  and
development, closer  scrutiny reveals  that he  genuinely  appreciated  the
advances wrought  by the  modern methods.   In  this respect,  he stands in
contrast to Bateson, whose backward glances betrayed a reluctance to face a
progressive future for the science that he helped to launch.  It is telling
that biographical  literature invariably  describes Goldschmidt's  work  as
"modern" and  applicable to  the future,  while Bateson is characterized as
tenaciously "clinging"  to his  earliest beliefs.   To the end of his life,
Goldschmidt was  an active  part  of  the  genetics  community,  rising  to
prominence in  his adopted homeland, honorary speaker at countless genetics
congresses and  symposiums, and author of a 563 page _Theoretical Genetics_
at age  76 which  was written  during his recuperation from a heart attack;
Bateson, on  the other  hand, was  gradually displaced from his position of
glory, and faded from view.
   Furthermore, in  their problem-solving  strategies -- the common problem
being the  theoretical relationship  of development  to the gene concept --
Goldschmidt actively  sought experimental  evidence for his ever-developing
theories, despite  the methodological  limitations that  are the inevitable
burden of  developmental biology.  He fearlessly and offensively challenged
the Mendelian  geneticists' dazzling  statistics with  detailed biochemical
analyses of  his own.   Bateson,  despite attempting  some  rough  physical
models, regressed  into a  defensive, mostly passive stance with respect to
his committment to developmental issues.  In their intellectual flexibility
and willingness  to learn  -- Goldschmidt  consistently  entertained  novel
ideas, even  if not  adopting them  as his  own, while  Bateson refused  to
consider the  validity of even basic technology, understand its workings or
acknowledge the conclusions it yielded.
   It would  be presumptuous and misleading to claim that these elements of
the two  subjects' careers  are the only ones relevant to the determination
of their  ultimate success.   Indeed,  those mentioned are only the factors
related to  the classical  gene concept  and how it fit into their thought.
Still, in  considering these,  how can  it be  that the  ideas of  two such
exceptional, discerning,  proficient  scientists  with  strikingly  similar
world views  can  have  arrived  at  such  divergent  fates?    All  things
considered, it  seems that  Bateson's obstructionist  tone in responding to
the Morgan  school and  modern cytological research doomed his own ideas to
ineffectiveness  in   the  face  of  compelling,  competing  evidence.    A
revolutionary thinker  is not made by ignoring existing beliefs, but rather
by recognizing where their weaknesses might be replaced by strengths.  Such
was the  method of  Goldschmidt who,  though mistaken  in the  details, was
constructive in  the spirit  of  his  theories.    As  an  iconoclast,  his
important questions,  well-placed suggestions and profound insight into the
broad  scope   of  genetics   continue  to   inspire  and  instruct  modern
geneticists.   Rather than  impede the forward progress or detract from the
remarkable advances  achieved by  the  classical  geneticists,  Goldschmidt
encouraged lateral  growth  in  hopes  of  achieving  his  vision  for  the
integration of  transmission genetics  into  the  continuum  of  scientific
endeavour.   Allen has  remarked that,  "Our understanding of, and approach
to, genetic  processes today bears the mark of the kinds of questions which
Goldschmidt persisted  in asking, often irreverently, throughout his entire
career." [48]
     Curt  Stern   echoes  the   praise  in  describing  Goldschmidt  as  a
"...contributor of  permanent parts,  some very large; perceptor and critic
of his era; [and a] designer of frameworks for the future." [49]


[1] W. Coleman, "Bateson and chromosomes: conservative thought in science",
_Centaurus_, 15: 228-314, p. 249.

[2] L.C. Dunn, _A Short History of Genetics_ (New York: 1965), 63.

[3] Coleman, "Bateson and Chromosomes", 252.

[4] Dunn, _A Short History of Genetics_, 65.

[5] Ibid., 68.

[6] W.  Bateson, "The  Methods and  Scope of  Genetics",  _William  Bateson
F.R.S. Naturalist.  His Essays and Addresses_ [hereafter cited as WBN], ed.
B. Bateson (Cambridge: 1928), 234.

[7] W. Bateson, "Evolutionary Faith and Modern Doubts" (1922), WBN, 392.

[8] W.  Bateson, "Presidential  Address to  the Zoological Section, British
Association: Cambridge Meeting, 1904", WBN, 242.

[9] W. Bateson, "Heredity and Variation in Modern Lights" (1909), WBN, 222.

[10] W. Bateson, "Presidential Address" (1904), WBN, 234.

[11] W. Bateson, "Gamete and Zygote.  A Lay Discourse" (1917), WBN, 202.

[12]  W.   Bateson  and   R.C.  Punnett,   "On  gametic   series  involving
reduplication of certain terms", _Journal of Genetics_, 1: 239-302.

[13] Dunn, 71.

[14] Ibid., 71.

[15] Bateson, "Presidential Address", (1904), WBN, 243.

[16] W.  Bateson, "Presidential  Address to  the  Agricultural  Subsection,
British Association" (1911), WBN, 278.

[17] W. Bateson, _A Defence of Mendel's Principles of Heredity_ (Cambridge:
1902), 271.

[18] W.  Bateson, "The Mechanism of Mendelian Heredity" (1916), _Scientific
Papers of William Bateson_, _1-2_, ed. R.C. Punnett (Cambridge: 1928).

[19] Coleman, 260.

[20] Ibid., 252.

[21] Bateson, "Evolutionary Faith and Modern Doubts" (1922), WBN, 390.

[22] Coleman, 264.

[23] Ibid., 265.

[24] Bateson, "Heredity and Variation in Modern Lights" (1909), WBN, 228.

[25] Bateson, "Gamete and Zygote" (1917), WBN, 209.

[26] Bateson, "Presidential Address" (1911), WBN, 280.

[27] Bateson, "Heredity and Variation in Modern Lights" (1909), WBN, 228.

[28] Coleman, 292.

[29] C.  Stern, "Richard  Benedict Goldschmidt  (1878-1958): a Biographical
Memoir" (1967),  [hereafter cited  as "Goldschmidt"], _Richard Goldschmidt.
Controversial Geneticist  and Creative  Biologist_ (Basel: 1980) [hereafter
cited as RG], 71.

[30] R. Goldschmidt, "The determination of sex", _Nature_, 107: 780-784.

[31] R. Goldschmidt, _Physiological Genetics_ (New York: 1938), 309.

[32] Quoted by Stern, "Goldschmidt", RG, 83.

[33] R.  Goldschmidt, "Genetics  and Development"  (1932), _The  Biological
Bulletin_, 63: 337-56.

[34] R.  Goldschmidt, "The  theory of  the gene" (1938), _Science Monthly_,
46: 268-73.

[35] Ibid., 268.

[36] Goldschmidt, _Physiological Genetics_, 310.

[37] Stern, "Goldschmidt", RG, 82.

[38] R. Goldschmidt, _The Material Basis of Evolution_ (New Haven: 1940).

[39] V.  Sarich, "A  Macromolecular perspective  on _The  Material Basis of
Evolution_", RG, 31.

[40] R.  Goldschmidt, "The Gene" (1928), _The Quarterly Review of Biology_,
3: 307-323.

[41] G.  Allen, "The Historical Development of 'Time Law of Intersexuality'
and its  Philosophical Implications"  [hereafter cited  as "Time Law"], RG,

[42] G.  Allen, "The  Physiological and  Developmental Genetics  of Richard
Goldschmidt" (1974), _Journal of the History of Biology_, 7: 49-92, p. 82.

[43] Allen, "Time Law", RC, 46.

[44]  R.   Goldschmidt,  "Different   Philosophies  of   Genetics"  (1954),
_Science_, 119: 703-710, p. 705.

[45] W. Bateson, "Progress in Biology" (1924), WBN, 408.

[46] Goldschmidt, "Different Philosophies of Genetics", 709.

[47] Allen, "Time Law", RG, 47.

[48] Ibid., 41.

[49] Stern, Goldschmidt, RG, 88.


Allen, Garland  E., (1974), "Opposition to the Mendelian-Chromosome Theory:
the Physiological  and  Developmental  Genetics  of  Richard  Goldschmidt",
_Journal of the History of Biology_, 7: 49-92.

Bateson, B. (ed.), (1928), _William Bateson, F.R.S. Naturalist.  His Essays
and Addresses_.  Cambridge University Press.

Bateson, W.,  (1902), _A  Defence  of  Mendel's  Principles  of  Heredity_.
Cambridge University Press.

Carlson, E.A.,  (1966), _The  Gene: a  Critical  History_.    Philadelphia:

Coleman, W.,  (1965), "Bateson  and Chromosomes:  Conservative  Thought  in
Science", _Centaurus_, 15: 228-315.

Dunn, L.C., (1965), _A Short History of Genetics_.  New York: McGraw-Hill.

Goldschmidt, R., (1938), _Physiological Genetics_.  London: McGraw-Hill.

Goldschmidt, R.,  (1940), _The  Material  Basis  of  Evolution_.    Reprint
(1982), introd. S.J. Gould.  New Haven: Yale University Press.

Goldschmidt, R.,  (1954), "Different  Philosophies of Genetics", _Science_,
110: 703-710.

Piternick,  L.K.   (ed.),  (1980),  _Richard  Goldschmidt.    Controversial
Geneticist  and   Creative  Biologist.     A   Critical   review   of   His
Contributions_.  Introd. K. von Frisch.  Basel: Birkhauser Verlag.

Punnett, R.C. (ed.), (1928), _Scientific Papers of William Bateson_, _1-2_,
Cambridge University Press.


                     |    Electronic Resources    |


      LISTSERVER Mailing Lists/Discussion Groups  on BITNET/INTERNET
       for the Historian and Philosopher of Science and Technology:
                            By Julian A. Smith
                          Received May 10,  1993
                           Revised June 1, 1993

   One of  the fastest  ways of  disseminating recent scholarly information
through the  computer involves  the INTERNET/BITNET discussion groups known
as  LISTSERVERS  or  Electronic  mailing  lists.    These  are  essentially
electronic "gatherings"  which share  letters, questions, book reviews, job
postings, conference and symposia announcements, calls for papers, research
findings, and  other news  and information  of interest  to  the  scholarly
community.   There are  several  thousand  electronic  conferences  on  the
INTERNET, covering  virtually  all  areas  of  scholarship,  including  the
history and philosophy of science and technology.
   Because the  history of  science is  an interdisciplinary  field, recent
research findings  and scholarly  news is often spread over a host of areas
in the  sciences and  humanities, making  it very  difficult for  the time-
pressed scholar  to keep  "up to date".  Few historians of science have the
time or  money to  subscribe to  both the  historical  and  the  scientific
journals and  periodicals of interest to them!  Moreover, lists of computer
journals and discussion groups are often compiled with either the scientist
or the historian in mind; rarely are both combined into an organized whole.
This list  has been assembled from various INTERNET/BITNET mailing list and
discussion group bibliographies, and is intended to provide a comprehensive
guide to  the LISTSERVER groups of interest to historians of science.  Many
of the  groups here  are designed  for the  scientific community,  and  are
interested  in  history  only  as  a  secondary  concern;  but  others  are
specifically formed  with the historian in mind.  Technology, of course, is
a broad  topic spanning  almost everything;  but I  have tried to provide a
guide to  those discussion  groups that  cover the history of technology as
well, even  if it  is only  something so restricted as the History of Scuba
Diving or the History of Aviation.
  Rules vary a great deal within each mailing list.  Some mailing lists are
"moderated" or  "peered"; that is, letters sent to them are cleared through
a peer review group or moderator (typically the list owner) before they are
distributed to  the rest  of the  conference.  This effectively screens out
irrelevant or  unnecessary mail, and drastically cuts down on the number of
letters you  will receive.   Other  mailing  lists  are  open;  anyone  may
contribute a letter to them, but you will have to accept the fact that many
of these  messages may  be of little interest to you!  One should take care
in subscribing to unmoderated mailing lists; traffic varies enormously, but
some of the "public" LISTSERVER groups I sampled sent me around 50 messages
a day!   Even  if you  decide against  reading them all, just deleting them
from your  mailbox can  get quite  time-consuming.   If you  are like  most
people, you  may subscribe to a large number of discussion groups at first,
and then  "weed out"  those who  consistently  return  mail  of  peripheral
interest to you.
   To subscribe to any of the LISTSERVER groups in our bibliography, simply
send an  e-mail letter  to the address listed below (usually, LISTSERV@ the
address below).  It  should not  contain any  subject heading.   The letter
should contain  only the  following information:  SUB or SUBSCRIBE   .  So, for example, let's suppose I
wanted  to  subscribe  to  a LISTSERVER  group  covering  medieval history.
Scrolling through our directory, we find the following entry:

MEDIEV-L         MEDIEV-L@UKANVM            Medieval History (283-1500 AD).

  This tells  us there is in fact  a  discussion group for medieval history
named (appropriately) MEDIEV-L. It is distributed through the LISTSERVER at
UKANVM; so to subscribe,I need to send an electronic letter requesting this
discussion group  from LISTSERV@UKANVM.  So, on BITNET, after entering  my
electronic mail program,I would mail a letter to LISTSERV@UKANVM containing
no subject heading,and only the following text: "SUB HTECH-L JULIAN SMITH".
Once the LISTSERVER receives my letter,I am automatically added to the mail
list for MEDIEV-L. On the INTERNET, I would follow a similar procedure, but
instead of emailing my letter to LISTSERV@UKANVM, I would send it to a more
detailed email  address:  LISTSERV@UKANVM.CC.UKANS.EDU  (for a full list of
these more detailed  email  addresses, see the "list of lists" from the ftp
site below).  It's as simple as that!
  Once you have subscribed to a discussion group, you should make sure that
you save the first pieces of correspondence you receive; usually, they will
tell you  what the  group's rules,  protocols and  functions are.  Not only
that, they will often include instructions on how to send mail to the list,
and how  to end  your subscription  to it  (or "Unsubscribe").   This is of
vital importance when you are on vacation or away from your e-mail account;
one of  my colleagues  who neglected  to do  this found  over  500  letters
waiting for  her after  her week-long  holiday!  Some e-mail systems gave a
NOMAIL function,  but for  those that  do not,  you will  have to  send  an
"UNSUBSCRIBE" or  "UNSUB" command  to the  discussion groups  you no longer
wish to  participate in.   In  our example  (HTECH at SIVM) , I would again
send an  electronic letter to LISTSERV@SIVM with no subject; but this time,
the body of my letter would say "UNSUB HTECH-L JULIAN SMITH".  That command
will effectively  prevent mail  from the  History of  Technology discussion
group from  reaching my  e-mail account;  to get  it back,  I would have to
subscribe again.
   Our list  of discussion  groups is highly compressed, and cannot do more
than give  a hint  of the vast resources available on the INTERNET.  Should
you desire  a more  complete list  of  discussion  groups,  you  have  many
alternatives.   A BITNET list of all public LISTSERV groups can be obtained
by sending  an e-mail  message to  the addresses  LISTSERV@NCSUVM.BITNET or
LISTSERV@VM1.NODAK.EDU; the  body of  the letter  should read  simply "LIST
GLOBAL".   You should  soon receive  an e-mail  letter  containing  a  more
substantial list than that presented here.  Diane Kovacs has written a list
of scholarly  electronic conferences; it may be retrieved by connecting via
ftp to   Once there,  you can  get in by using the login:
"anonymous".   The  lists  may  be  found  by  changing  to  the  /library/
directory, using the cd command: "cd library".  Once there, you will find a
group of ACADLISTS which cover scholarly conferences alphabetically, and by
subject area.   The same lists may be received through conventional e-mail:
just  send   a  letter   containing  the   command  "GET   "   to
   A combined bibliography of INTERNET groups and BITNET lists, compiled by
David Avery, can be retrieved via ftp from; just use
the standard  "login:  anonymous"  instruction,  and  change  directory  to
/siglists.   Then use  the "get"  command to get the list you want.  Again,
the  same   lists  are  available  by  sending  the  following  message  on
conventional  e-mail  to  LISTSERV@DARTCMS1;  "INDEX  SIGLISTS"  and   then
"SEND ".Marty Hoag's "list of lists" is available using
e-mail from LISTSERV@VM1.NODAK.EDU or LISTSERV@NDSUMVM1. The message is the
same for both locations: "GET LISTS OF LISTS".
   Finally, should  you want  the complete  "list of lists" from which this
article was  compiled, it  can be retrieved using ftp as well.  To get this
list (which covers all electronic mailing lists and interest groups, on all
systems, scholarly  or otherwise),  simply connect  via  anonymous  ftp  to and  enter using  the login  "anonymous".    Once  on  the
system, go  to the  directory netinfo  (just change directory by typing "cd
netinfo").   In that  directory, a complete list of all interest-groups and
mailing lists  can be  found under the name "interest-groups"; a compressed
version is  in the same directory under the name "interest-groups.Z".  This
list is  updated regularly,  and is  arranged in alphabetical order; simply
scroll through to the discussion group you want.  The list will give you an
address for  subscription,  a  description  of  permitted  topics,  posting
guidelines  and   list  etiquette,   list   owners,   locations   of   back
correspondence, and ways to "unsubscribe" from the list.
  To get your own copy of this document, type "get interest-groups" or "get
interest-groups.Z"; you  would  be  well  advised  to  get  the  compressed
version, as  the full  text runs  to several  hundred pages  and  has  full
details on an enormous number of mailing lists!
   Our list  below is arranged alphabetically by subject.  The entry at the
left gives  the name  of the  discussion group; the central entry gives the
network address (or LISTSERVER group) of the conference; and the right-hand
entry briefly  tells you  what the list's topics are.  Again, more complete
information on  these lists  may be  found in  the "lists  of lists" above.
Happy hunting!

AIBI-L           AIBI-L@ACADVM1.UOTTAWA.CA L'Association Internat. Bible
NT-GREEK         NT-GREEK@VIRGINIA.EDU Greek New Testament

BEE-L            BEE-L@ALBNYVM1    Discussion of Bee Biology
BIO-DOST         BIO-DOST@TREARN   Biyolojik Bilimlerde Calisan Turk
BIOCIS-L         BIOCIS-L@SIVM     BIOCIS-L Biology Curriculum Innovation
BIOESR-L         BIOESR-L@MIZZOU1  Applications of Electron Spin Res.
BIOMCH-L         BIOMCH-L@HEARN    Biomechanics and Movement Science
BIOMED-L         BIOMED-L@MCGILL1  Assoc. of Biomedical Communications
                 BIOMED-L@NDSUVM1  BIOMED-L Biomedical Ethics
BIOPI-L          BIOPI-L@KSUVM     Secondary Biology Teacher Enhancement
BIOSPH-L         BIOSPH-L@UBVM     Biosphere, ecology, Discussion
BIOTECH          BIOTECH@UMDD      Biotechnology Discussion List
CONSLINK         CONSLINK@SIVM     Discussion on Biological Conservation
EMBINFO          EMBINFO@IBACSATA  EMBNet (European Molecular Biology Net).
FORUMBIO         FORUMBIO@BNANDP11 Forum on molecular biology
GNOME+PR         GNOME+PR@IRLEARN  Human Genome Project
HYPERMED         HYPERMED@UMAB     Biomedical Hypermedia Instructional
INFO-GCG         INFO-GCG-L@UTORONTO Genetics Computer Group Software
                                   (Computer Aided Molecular Biology)
LACTACID         LACTACID-L@SEARN.SUNET.SE  Lactic Acid Bacteria list
LCC-L            LCC-L@BRUFMG      Lista para intercambio de informacoes
MARINE-L         MARINE-L@UOGUELP.CA Marine biology
MEDSEA-L         MEDSEA-L@AEARN    Marine Biology of the Adriatic Sea
MORPHMET         MORPHMET@CUNYVM   Biological Morphometrics Mailing List
ORCHIDS          ORCHIDS@SCU.BITNET Orchid Growing
OXYGEN-L         OXYGEN-L@MIZZOU1  Oxygen Free Radical Biology and Medicine
POP-BIO          POP-BIO-L@IRLEARN Population Biology
PROFEE-L         PROFEE-L@BRUFMG   Lista para intercambio professores
RBMI             RBMI@FRORS13      Groupe de Recherche Biologie Moleculaire
                 RBMI@FRULM11      Groupe de Recherche Biologie Moleculaire

CHEMCONF         CHEMCONF@UMDD     Conferences on Chem. Research and Ed.
CHEMED-L         CHEMED-L@UWF      Chemistry Education Discussion List
CHEMIC-L         CHEMIC-L@TAUNIVM  Chemistry in Israel List
CHEM11-L         CHEM11-L@MIZZOU1  Chemistry 11 Discussion

AGRIC-L          AGRIC-L@UGA       Agriculture.
ASEH-L           ASEH-L@TTUVM1     Amer. Soc. of Environmental
BEE-L            BEE-L@ALBNYVM1    Bee Biology.
CONSLINK         CONSLINK@SIVM     Biological Conservation.
ECONET           ECONET@MIAMIU     Ecological and Environmental Studies.
ENERGY-L         ENERGY-L@TAUNIVM  Energy List.
ENVST-L          ENVST-L@BROWNVM   Environmental Studies.
ITRDBFOR         ITRDBFOR@ASUACAD  Dendrochronology Forum.
POP-BIO          POP-BIO@IRLEARN   Population Biology
SFER-L           SFER-L@UCF1VM     South Florida Environmental
UNCEDGEN         UNCEDGEN@UFRJ     Public Discussion of
                                   Environmental Issues

INGRAFX          INGRAFX-L@PSUVM.PSU.EDU Cartography & Computer Graphics

GEOLOGY          GEOLOGY@PTEARN    Geology Discussion List
GEOREN-L         GEOREN-L@EMUVM1   Geology Building Renovation
QUAKE-L          QUAKE-L@NDSUMVM1  Earthquakes (Help/Assistance)

AFRICA-L         AFRICA-L@VTVM2.CC.VT Forum Pan-Africa.
TUNISNET         TUNISNET@PSUVM    Tunisia Network.

ANCIEN-L         ANCIEN-L@ULKYVM   Ancient Mediterranean Studies.
                 ANCIEN-L@ULKYVM.LOUISVILLE.EDU  (peer)
ANTHRO-L         ANTHRO-L@UBVM.BITNET Anthropology,Anglo-Saxon ruins,
                                   cemeteries, villages.
ARCH-L           ARCH-L@EARN.DGOGWDG1 Archaeology
CONTEX-L         CONTEX-L@UOTTAWA  Ancient Texts
CLASSICS         CLASSICS@UWAVM    Classics & Latin discussion.
ELLHNIKA         ELLHNIKA@DHDURZ1.BITNET Classical/Modern Greek TeX.
HELLAS           HELLAS@AUVM       Hellenic List
IOUDAIOS         IOUDAIOS@YORKVM1  First Century Judaism

EXLIBRIS         EXLIBRIS@RUTVM1   Rare Books and Special Collections.
GUTNBERG         GUTNBERG@UIUCVMD  Machine Readable Texts.
LITERA-L         LITERA-L@TECMTYVM Literature in English & Spanish.
SHARP-L          SHARP-L@IUBVM     History of the Printed Word/Authorship.

BALT-L           BALT-L@UBVM       Baltic Republics.
HUNGARY          HUNGARY@UCSBVM    Hungarian Discussion List
MIDEUR-L         MIDEUR-L@UBVM     Middle European Topics.
POLAND-L         POLAND-L@UBVM     Discussion of Polish Culture
SEELANGS         SEELANGS@CUNYVM   Slavic & East European
                                   Language and Literature
SLOVAK-L         SLOVAK-L@UBVM     Slovak Issues.

AJBS-L           AJBS-L@NCSUVM     Association Japanese Business Studies
CHINA            CHINA@PUCC        Chinese Studies.
CHINANET         CHINANET@TAMVM1   Networking In China
CSA-DATA         CSA-DATA@UICVM    Chinese Statistical Archive.
EMEDCH-L         EMEDCH-L@USCVM    Early Medieval China (3rd-6th C. AD).
J-FOOD-L         J-FOOD-L@JPNKNU10 Japanese Food & Culture
JAPAN            JAPAN@FINHUTC     Info-Japan
JPINFO-L         JPINFO-L@JPNSUT00 Information About Japan
JTEM-L           JTEM-L@UGA        Japanese Through Electronic Media
TWUNIV-L         TWUNIV-L@TWNMOE10 Chinese Scholars and Students.
SCC-L            MD48@CMUCCVMA     soc.culture.china (Bitnet Distribution)

RUSHIST          RUSHIST@USCVM     Russian History 1462-1917
                 RUSHIST@VM.USC.EDU (peer) Russian History
                 RUSHIST@DOSUNI1   (peer) Russian History
                 RUSHIST@CSEARN    (peer) Russian History
RUSSIA           RUSSIA@INDYCMS    Russia and Her Neighbors
RUSSIAN          RUSSIAN@ASUACAD   Russian Language Issues
SCS-L            SCS-L@INDYCMS     soc.culture.soviet via ListServ
SOVHIST          SOVHIST@USCVM     Soviet History 1917-1991
                 SOVHIST@VM.USC.EDU (peer) Soviet History
                 SOVHIST@DOSUNI1   (peer) Soviet History
                 SOVHIST@CSEARN    (peer) Soviet History
TPS-L            TPS-L@INDYCMS     talk.politics.soviet via Bitnet
                 or UKRAINE@INDYCMS.IUPI.EDU Ukraine Discussion

ALBION-L         ALBION-L@UCSBVM   British History
ESPORA-L         ESPORA-L@UKANVM   Spanish/Portuguese Studies
FRANCEHS         FRANCEHS@UWAVM    French Historical Studies
GRMNHIST         GRMNHIST@USCVM    German History from 800 AD
                 GRMNHIST@DGOGWDG1 (peered) German History
HABSBURG         HABSBURG@PURCCVM  Austrian History since 1500
                 or LISTSERV@IRLEARN.BITNET Current Irish politics
                 or LISTSERV@IRLEARN.UCD.IE Welsh Language Bulletin Board

ASTR-L           ASTR-L@UIUCVMD    Theater History Discussion
CONSIM-L         CONSIM-L@VM.UCS.UALBERTA.CA  Historical Conflict
                                   Simulation Games, Military History
DANCE-L          DANCE-L@HEARN     Folkdance/Traditional Dance
HISTORY          HISTORY@CSEARN    (peered) History
HISTORY          HISTORY@DGOGWDG1  (peered) History
HISTORY          HISTORY@FINHUTC   (peered) History
HISTORY          HISTORY@IRLEARN   (peered) History
HISTORY          HISTORY@RUTVM1    (peered) History
HISTORY          HISTORY@UBVM      (peered) History
HISTORY          HISTORY@UMRVMB    (peered) History Discussion
HISTORYA         HISTORYA@UWAVM    HISTORYA History Department
HISLAW-L         HISLAW-L@ULKYVM   Law History (Feudal/Common/Canon)
                 HISLAW-L@ULKYVM.LOUISVILLE.EDU (peer)
HIST-L           HIST-L@UKANVM     General History
MILHST-L         MILHST-L@UKANVM   Military History
NATIVE-L         NATIVE-L@TAMVM1   Aboriginal Peoples
PEACE            PEACE@INDYCMS     Peace studies.
POLI-SCI         POLI-SCI@RUTVM1   Political Science Digest
SOCHIST          SOCHIST@UCBVM     New Social History
WMST-L           WMST-L@UMDD       Women's Studies.
WORLD-L          WORLD-L@UBVM      Non-Eurocentric World History
WWII-L           WWII-L@UBVM       World War II.

BUDDHIST         BUDDHIST@JPNTOHOK Indian and Buddhist Studies
INDIA            INDIA@PCCVM       India List
INDIA-D          INDIA-D@TEMPLEVM  India Interest Group
INDIA-L          INDIA-L@TEMPLEVM  India News Network
PAKISTAN         PAKISTAN@ASUACAD  Pakistan News Service
TAMIL-L          TAMIL-L@DHDURZ1   Tamil Studies.

E-HUG            E-HUG@DARTCMS1    Electronic Hebrew Users Newsletter
IOUDAIOS         IOUDAIOS@YORKVM1  First Century Judaism.
HEBREW-L         HEBREW-L@UMINN1   Jewish & Near Eastern Studies
JEM              JEM@MITVMA        Jewish Electronic Mail Conference
JUDAICA          JUDAICA@TAUNIVM   (Peered) Judaic Studies Newsletter
MENDELE          LISTSERV@YALEVM   Yiddish Literature and Language

BORIKEN          BORIKEN@ENLACE    Cultura y Sociedad de Puerto Rico
BRAS-CON         BRAS-CON@FRORS12  Brasnet na Europa Continental
BRAS-NET         BRAS-NET@BRUFMG   Brasileiros no Exterior
CDSBC-L          CDSBC-L@UFRJ      Conselho da Sociedade Brasileira.
CENTAM-L         CENTAM-L@UBVM     Central America.
CH-LADB          CH-LADB@UNMVM     Latin America Data Base
CHILE-L          CHILE-L@PURCCVM   Chile.
LALA-L           LALA-L@UGA        Latin Americanist Librarians.
MEXICO           MEXICO@VMTECMEX   Mexico.
MEXICO-L         MEXICO-L@TECMTYVM Knowing Mexico: people, culture.
NAHUAT-L         NAHUAT-L@FAUVAX.BITNET Aztec Studies. Subscribe to
NOTICOL          NOTICOL@ANDESCOL  Noticias de Colombia
POLITICA         POLITICA@UFRJ     Politica Brasileira
SM-LADB          SM-LADB@UNMVM     SM-LADB - Latin America Data Base
UP-LADB          UP-LADB@UNMVM     UP-LADB - Latin America Data Base

ANSAX-L          ANSAX-L@WVNVM     Anglo-Saxon England
CAMELOT          CAMELOT@CASTLE.ED.AC.UK Arthurian Discussion
                                   List.  Subscribe to:
CELTIC-L         CELTIC-L@IRLEARN  Celtic Culture.
CLASSM-L         CLASS-L@BROWNVM.BROWN.EDU Classical Music (Gregorian
                                   Chant to George Crumb)
EARLYM-L         EARLYM-L@AEARN    Early Music (Medieval+) List.
FICINO           FICINO@UTORONTO   Renaissance and Reformation
MEDFEM-L         MEDFEM-L@INDYCMS  Feminist Medieval History
GAELIC-L         GAELIC-L@IRLEARN  Irish/Scots Gaelic Language.
GERLINGL         GERLINGL@UIUCVMD  Germanic languages to 1500
LITURGY          LITURGY@MAILBASE.AC.UK Liturgical studies.
MEDIEV-L         MEDIEV-L@UKANVM   Medieval History (283-1500 AD)
MEDTEXTL         MEDTEXTL@UIUCVMD  Medieval Textual Studies
REED-L           REED-L@UTORONTO   Records of Early English Drama
RENAIS-L         RENAIS-L@ULKYVM   History of the Renaissance.
                 RENAIS-L@ULKYVM.LOUISVILLE.EDU (peer)
TML-L            TML-L@IUBVM       Thesaurus Musicarum Latinarum
VW5EARN          VW5EARN@AWIWUW11.BITNET Medieval/Renaissance Music

CAAH             CAAH@PUCC         Art and Architectural History
HISTOWNR         HISTOWNR@UBVM     List for Owners of History Lists
IMIGNET          IMIGNET@SUVM      Interdisciplinary Multi - Cultural.
INTLBU-L         INTLBU-L@TEMPLEVM International Business
KUHIST-L         KUHIST-L@UKANVM   History at the University of Kansas
MUSEUM-L         MUSEUM-L@UNMVM    Museum Discussion List
MUSIC            MUSIC@FINHUTC     Music-Research
OPERA            OPERA@VM1.NODAK.EDU Opera
ROOTS-L          ROOTS-L@NDSUVM1   Genealogy List
SCA              SCA-REQUEST@MC.LCS.MIT.EDU Society Creative Anachronism
SIIN-L           SIIN-L@UNBVM1     UPEI Inst. of Small Island Studies
SQSP             SQSP@UQUEBEC      Soc. quebecoise science politique
TEL              TEL@USCVM         The Turkish Electronic Mail List
URBAREG          URBAREG@UQUEBEC   Etudes urbaines et regionales
XCULT-L          XCULT-L@PSUVM     International Intercultural Newsletter

9NOV89-L         9NOV89-L@DB0TUI11 Events around the Berlin Wall
CLASSM-L         CLASSM-L@BROWNVM  Classical Music List
C18-L            C18-L@PSUVM       18th Century Discussion
AUSTEN-L         AUSTEN-L@VM1.MCGILL.CA Austen, Burney, Wollstonecraft
                                   Literature and their time
EMHIST-L         EMHIST-L@RUTVM1   Early Modern History Forum
                 EMHIST-L@USCVM    (peer)
GWDG-NEU         GWDG-NEU@DGOGWDG1 Mitteilungen der GWDG
HEGEL            HEGEL@VILLVM      The HEGEL Society.
HESSE-L          HESSE-L@UCSBVM    Hermann Hesse Life/Work
INMYLIFE         INMYLIFE@WKUVX1.BITNET Popular Culture 1962-1974
MILTON-L         MILTON-L@URVAX    Milton Scholarship
MODBRITS         MODBRITS@KENTVM   British/Irish Literarure 1895-1955
SHAKSPER         SHAKSPER@UTORONTO Shakespeare Electronic Conference
TWAIN            TWAIN-L@VM1.YORKU.CA Mark Twain Life and Times

AFAM-L           AFAM-L@MIZZOU1    African-American Research
AFAS-L           AFAS-L@KENTVM     Afro-American Studies
AMLIT-L          AMLIT-L@UMCVMB    American Literature
                 AMLIT-L@UMCVMB.MISSOURI.EDU (peer)
AMWEST-H         AMWEST-H@DOSUNI1  History of American West,1809-1890
                 AMWEST-H@USCVM    (peer)
                 AMWEST-H@UMRVMB   (peer)
FRANKLIN         FRANKLIN@NCSUVM   Benjamin Franklin Scholars
GOVDOCS-L        GOVDOCS-L@PSUVM   US/UN Government Documents
INMYLIFE         INMYLIFE@WKUVX1   Popular Culture, 1962-1974
LABOR-L          LABOR-L@YORKVM1   Labor in the North American Economy
L-CHA            L-CHA@UQAM        Canad. Hist. Assoc. Conference
MCLR-L           MCLR-L@MSU        Midwest Consortium, Latino Research
PNWCSC           PNWCSC@UWAVM      Pacific Northwest Canadian Studies
VWAR-L           VWAR-L@UBVM       Viet Nam War.

APNET-L          APNET-L@JPNSUT00  Asia Pacific Network
CURRENTS         CURRENTS@PCCVM    South Asian News and Culture Magazine
PACARC-L         PACARC-L@WSUVM1   Pacific Rim Archaeology
PACIFIC          PACIFIC@BRUFPB    Pacific Ocean & Islands Forum
SEANET-L         NUSVM             Southeast Asian Studies

AHC-L            AHC-L@DGOGWDG1    Association for History & Computing
CHUG-L           CHUG-L@BROWNVM    Brown University Computing in Humanities
HCFNET           HCFNET@UCSBVM     Humanities Computing Facilities Network
HSTNET-L         HSTNET-L@UKANVM   Organizing Committee for HistNet
HISTOWNR         HISTOWNR@UBVM     For owners of history-related lists
HUMANIST         HUMANIST@BROWNVM  Humanities Computing
HUMSPC-L         HUMSPC-L@BROWNVM  Humanist Special List
SHOTHC-L         SHOTHC-L@SIVM     History of Computing Issues.
SIGPAST          SIGPAST@LIST.KEAN.EDU History of Computers

AMERCATH         AMERCATH@UKCC     History of American Catholicism.
BELIEF-L         BELIEF-L@BROWNVM  Personal Ideologies Discussion List
BUDDHA-L         BUDDHA-L@ULKYVM.BITNET Buddhist Studies
BUDDHIST         BUDDHIST@JPNTOHOK Indian and Buddhist Studies
                 BUDDHIST@JPNTUVM0 (peer)
ELENCHUS         ELENCHUS@UOTTAWA  Christian Thought and Literature
                 ELENCHUS@ACADVM1.UOTTAWA.CA  in Late Antiquity
EOCHR            EOCHR@QUEENSU.CA  Eastern Orthodox Christianity
HISTEC-L         HISTEC-L@UKANVM   History, Evangelical Christianity
ISLAM-L          ISLAM-L@ULKYVM    The History of Islam
RELIGCOM         RELIGCOM@UKCC     Discussion forum.
SHAKER           SHAKER@UKCC       United Society of Believers.

CADUCEUS         CADUCEUS@Beach.Gal.UTexas.EDU
                 Not LISTSERV;     Subscribe to addresses above
HPSST-L          HPSST-L@QUCDN     History/Philosophy of Science
HTECH-L          HTECH-L@SIVM      History of Technology
HOPOS-L          HOPOS-L@UKCC.UKY.EDU History of Philosophy of Science
L-ARTECH         L-ARTECH@UQAM     Les Arts et les nouvelles
SCIFRAUD         SCIFRAUD@ALBNYVM1 Fraud in Science.
SHOTHC-L         SHOTHC-L@SIVM     History of Technology on Computer (SHOT)
TEXTILES         TEXTILES@TREARN   Textiles & Clothing Studies
78-L             78-L@CORNELL.EDU  History of Phonographs, Records.

ALLIANCE         ALLIANCE@NCSUVM   North Carolina Science and Math Alliance
CEM-L            CEM-L@UTDALLAS    UTD Center for Engineering Mathematics
CRYPTO-L         CRYPTO-L@JPNTUVM0 Forum on Cryptology and Related Math
EWM              EWM@ICNUCEVM      EWM European Women in Mathematics
MATHDEPT         MATHDEPT@TECHNION MATHDEPT - Technion Mathematics Net
TECHMATH         TECHMATH@TECHNION TECHMATH - Technion Mathematics Net
UICMATH          UICMATH@UICVM     UIC Mathematics
UICMATHS         UICMATHS@UICVM    UIC Mathematics Majors

AIDS             AIDS@EBCESCA1     (Peered) Sci.Med.AIDS Newsgroup
                 AIDS@RUTVM1       (Peered) Sci.Med.AIDS Newsgroup
                 AIDS@USCVM        (Peered) Sci.Med.AIDS Newsgroup
AMIED-L          AMIED-L@MCGILL1   American Medical Informatics Assoc.
BIOMED-L         BIOMED-L@MCGILL1  Assoc. of Biomedical Communications
                 BIOMED-L@NDSUVM1  BIOMED-L Biomedical Ethics
CMEDSSOC         CMEDSSOC@UTORONTO Canadian Medical Student Societies
COCAMED          COCAMED@UTORONTO  Computers in Canadian Medical Education
COMPMED          COMPMED@WUVMD     Comparative Medicine List
CONFLIST         CONFLIST@UCSFVM   School of Medicine Conference List
CROMED-L         CROMED-L@AEARN    CROatian MEDical List
EMFLDS-L         EMFLDS-L@UBVM     Electromagnetics in Medicine/Science
FAMILY-L         FAMILY-L@MIZZOU1  Delivery of Family Practice and Clinical
HEALTHCO         HEALTHCO@RPIECS   Communication in health/medical context
HERB             HERB@TREARN       Medicinal and Aromatic Plants
HYPBAR-L         HYPBAR-L@TECHNION HyperBaric & Diving Medicine List
HYPERMED         HYPERMED@UMAB     Biomedical Hypermedia Instructional
JMEDCLUB         JMEDCLUB@BROWNVM  Medical Journal Discussion Club
LASMED-L         LASMED-L@TAUNIVM  Laser Medicine
MEDCONS          MEDCONS@FINHUTC   Medcons (Medical consulting)
MEDFORUM         MEDFORUM@ARIZVM1  Med Student Organization/Policy Forum
MEDIMAGE         MEDIMAGE@POLYVM   Medical Imaging Discussion List
MEDLIB-L         MEDLIB-L@UBVM     Medical Libraries Discussion List
MEDNETS          MEDNETS@NDSUVM1   MEDNETS Medical telecommunications Net
MEDNEWS          MEDNEWS@ASUACAD   MEDNEWS - Health Info-Com Network News
MEDSEA-L         MEDSEA-L@AEARN    Marine Biology of the Adriatic Sea
MEDSTU-L         MEDSTU-L@UNMVMA   Medical student discussion list
OXYGEN-L         OXYGEN-L@MIZZOU1  Oxygen Free Radical Biology and Medicine
PANET-L          PANET-L@YALEVM    Medical Education and Health Information
PRION            PRION-REQUEST@ACC.STOLAF.EDU Prion/Slow Virus Infection
SMDM-L           SMDM-L@DARTCMS1   Medical Decision Making List
TELEMED          TELEMED@FRMOP11   Network for the TELEMED project
THPHYSIO         THPHYSIO-L@FRMOP11 Thermal Physiology
VETLIB-L         VETLIB-L@VTVM2    Veterinary Medicine Library issues
VETMED-L         VETMED-L@UGA      (Peered) Veterinary Medicine
                 VETMED-L@VTVM2    (Peered) Veterinary Medicine
WHSCAB-L         WHSCAB-L@EMUVM1   Medical Administration network
WU-AIDS          AIDS@WUVMD        Sci.Med.AIDS Newsgroup

WX-TALK          WX-TALK-L@UIUCVMD Weather News
WX-SPOT          WX-SPOT-L@UIUCVMD Storm Spotting

ANIMAL-RIGHTS    Animal-Rights-Request@XANTH.CS.ODU.EDU  Animal
AYN-RAND         AYN-RAND@IUBVM    (Moderated) Objectivist Philosophy
BIOMED-L         BIOMED-L@NDSUVM1  Biomedical Ethics
BIOSPH-L         BIOSPH-L@UBVM.BITNET Biosphere, Pollution, Ecology
ETHICS-L         ETHICS-L@MARIST.BITNET Ethics in Computing
FEMSEM           FEMSEM@SBCCVM     Stony Brook Feminist Philosophy
HPSST-L          HPSST-L@QUCDN     History and Philosophy of Science
INTUDM-L         INTUDM-L@UTEPA.BITNET Intuition in Decision Making
LITSCI-L         LITSCI-L@UIUCVMD  Soc. Literature/Science-Philosophy
NSP-L            NSP-L@RPIECS      Noble Savage Philosphers mailing list
PHILCOMM         PHILCOMM@RPIECS   Philosophy of Communication
PHILOSOP         PHILOSOP@YORKVM1  Philosophy Discussion Forum
PHILRELSOC       PHILRELSOC@MITVMA.MIT.EDU Philosophy/Religion/Sociology
SWIP-L           SWIP-L@CFRVM      Society for Women in Philosophy
TIPS             TIPS-L@FRE.FSU.UMD.EDU Teaching in Psychology

ALPHA-L          ALPHA-L@LEPICS    L3 Alpha physics block analysis diagram
ASTRO-PL         ASTRO-PL@JPNYITP  Preprint server for Astrophysics
FUSION           FUSION@NDSUVM1    Fusion - sci.physics.fusion
OPTICS           OPTICS@TOWSONVX   Optical Research
PHYS-L           PHYS-L@UWF        Forum for Physics Teachers
PHYS-STU         PHYS-STU@UWF      Physics Student Discussion List
PHYSHARE         PHYSHARE@PSUVM    Sharing resources: high school physics
PHYSIC-L         PHYSIC-L@TAUNIVM  Physics List
PHYSICS          PHYSICS@MARIST    (Peered) Physics Discussion
                 PHYSICS@RICEVM1   (Peered) Physics Discussion
                 PHYSICS@UBVM      (Peered) Physics Discussion
PHYSICS          PHYSICS@UNIX.SRI.COM Physics discussion list
PHYSJOB          PHYSJOB@WAYNEST1  Physics Jobs Discussion List
POLYMERP         POLYMERP@HEARN    (Peered) Polymer Physics discussions
                 POLYMERP@RUTVM1   (Peered) Polymer Physics discussions
SPACE            SPACE-L@UGA       Space News

APASD-L          APASD-L@VTVM2     APA Research Psychology Network
APSSCNET         APSSCNET@MCGILL1  American Psychological Society Students
IAPSY-L          IAPSY-L@ALBNYVM1  Interamerican Psychologists (SIPNET)
IOOB-L           IOOB-L@UGA        Industrial Psychology
IOOBF-L          IOOBF-L@UGA       Industrial Psychology Forum
MPSYCH-L         MPSYCH-L@BROWNVM  Society for Mathematical Psychology
PSI-L            PSI-L@RPIECS      Parapsychology Discussion Forum
PSYC             PSYC@PUCC         PSYCOLOQUY: Refereed Electronic Journal
PSYCGRAD         PSYCGRAD@UOTTAWA  Psychology Graduate Students
PSYCH-L          PSYCH-L@EMUVM1    Psychology Building Renovation Project
                 PSYCH-L@UOTTAWA   UOTTAWA chool of Psychology
PSYSTS-L         PSYSTS-L@MIZZOU1  Psychology Statistics Discussion
SPORTPSY         SPORTPSY@TEMPLEVM Exercise and Sports Psychology

ALLIANCE         ALLIANCE@NCSUVM   North Carolina Science & Math. Alliance
ASCD-SCI         ASCD-SCI@PSUVM    Alliance for Teaching of Science
BIOMCH-L         BIOMCH-L@HEARN    Biomechanics and Movement Science
C-ALERTL         C-ALERTL@JPNYITP  CONTENTS-Alert by Elsevier Science Pub.
CCS              CCS@UKCC          Center for Computational Sciences
CSEMLIST         CSEMLIST@HASARA11 List of Society of Computer Science
EMFLDS-L         EMFLDS-L@UBVM     Electromagnetics in Medicine & Science
FAMLYSCI         FAMLYSCI@UKCC     Family Science Network
GEONET-L         GEONET-L@IUBVM    GEONET-L Geoscience Librarians
GLSWICHE         GLSWICHE@ARIZVM1  Library Science Conference
HIT              HIT@UFRJ          Highly Imaginative Tech and Science
HPSST-L          HPSST-L@QUCDN     History and Philosophy of Science
LIBRES           LIBRES@KENTVM     Library and Information Science
LITSCI-L         LITSCI-L@UIUCVMD  Society for Literature and Science
METHO            METHO@UQUEBEC     Methodologie quantitative, science
MGSFAC           MGSFAC@UBVM       UB Management Science Faculty List
MGSGRAD          MGSGRAD@UBVM      UB Management Science Grad Students
MGSNEWS          MGSNEWS@UBVM      UB Management Science Discussion List
NCPRSE-L         NCPRSE-L@ECUVM1   Reform discussion list for Science Ed.
NEUCHILE         NEUCHILE@CUNYVM   NEUCHILE: Chilean Neuroscience
NEURO1-L         NEURO1-L@UICVM    Neuroscience Information Forum
NEUS582          NEUS582@UICVM     Methods in Modern Neuroscience
ORCS-L           ORCS-L@OSUVM1     Operations Research/Computer Science
POLCAN           POLCAN@YORKVM1    POLCAN Canadian Political Science
POLI-SCI         POLI-SCI@RUTVM1   Political Science Digest
PSRT-L           PSRT-L@MIZZOU1    Political Science Research & Teaching
QUALRS-L         QUALRS-L@UGA      Qualitative Research for Human Sciences
RQSS             RQSS@UQUEBEC      Regroupement quebecois des sci. soc.
SAIS-L           SAIS-L@UNBVM1     Science Awareness and Promotion
SCIFRAUD         SCIFRAUD@ALBNYVM1 Discussion of Fraud in Science
SCIMAT-L         SCIMAT-L@UAFSYSB  Arkansas Science and Math Education
SCIMIN           SCIMIN@MCGILL1    Minutes for Faculty of Science
SCSE             SCSE@UQUEBEC      Societe canadienne de science economique
SOS-DATA         SOS-DATA@UNCVM1   Social Science Data List.
SQSP             SQSP@UQUEBEC      Societe quebecoise de science politique
SRSA-L           SRSA-L@WVNVM      Southern Regional Science Association
STAT-GEO         STAT-GEO@UFRJ     Forum of Quantitative Methods, Geosci.
SYSCI-L          SYSCI-L@UOTTAWA   System Science Discussion List
                 THEORYNT@UICVM    Computer Science Theory Net
TURKSCI          TURKSCI@TRITU     Turkish Science and Technology Policy
T321-L           T321-L@MIZZOU1    Teaching Science in Elementary Schools
USTC85-L         USTC85-L@RICEVM1  Discussion for Univ of Science & Tech.
UVHINF-L         UVHINF-L@UVVM     UVic Health Info Science Bulletins
WISENET          WISENET@UICVM     Women In Science and Engineering NET
WVNCSF-L         WVNCSF-L@WVNVM    WVNET Computer Science Faculty List
XXI              XXI@UCHCECVM      XXI Ciencia & Tecnologia.

AISTFTBM         AISTFTBM@CUVMC    AIS Task Force Technology Business
ARMS-L           ARMS-L@BUACCA.BU.EDU Peace, War, Arms Control
BIOTECH          BIOTECH@UMDD      Biotechnology Discussion List
CAAH             CAAH@PUCC         Art and Architectural History
CATV             CATV-REQUEST@QUACK.SAC.CA.US Cable TV Technology, History
CIT$P            CIT$P@PLEARN      Cracow Institute of Technology private
CIT$W            CIT$W@PLEARN      Cracow Institute of Technology open
DEVEL-L          DEVEL-L@AUVM      Technology Transfer
EDTECH           EDTECH@OHSTVMA    EDTECH: Educational Technology
EEC-L            EEC-L@AUVM        European Training and Technology List
EUITLIST         EUITLIST@BITNIC   Educational Uses of Information Tech.
FACT-L           FACT-L@UBVM       SUNY Faculty Access to Computing Tech.
FACTCOM          FACTCOM@UBVM      SUNY Faculty Access to Computing Tech.
HIT              HIT@UFRJ          Highly Imaginative (SF) Technology
HOMESAT          HOMESAT@NDSUVM1   HOMESAT - Home Satellite Technology
INTECH-L         INTECH-L@ULKYVM   Instructional Technology Discussion
IPCT-L           IPCT-L@GUVM       Interpersonal Computing and Technology
JTE-L            JTE-L@VTVM1       Journal of Technology Education
L-HCAP           L-HCAP@NDSUVM1    Technology for Disabled
LLTI             LLTI@DARTCMS1     Language Learning and Technology Int.
MILITARY         MILITARY@ATT.ATT.COM Military Technology
NOVOPS           NOVOPS@SUVM       Novell Technology Operations List
NOVTTP           NOVTTP@SUVM       Novell Technology Transfer Partners
PHOTO-L          PHOTO-L@BUACCA    Photographic technology
SCAPCOM          SCAPCOM@UBVM      SUNY Student Access to Computing Tech.
SCUBA-L          SCUBA-L@BROWNVM.BITNET Scuba Diving & its History
SHOTHC-L         SHOTHC-L@SIVM     Society for History of Technology
TECHNO-L         TECHNO-L@MITVMA   Issues In Technology Licensing
TURKSCI          TURKSCI@TRITU     Turkish Science and Technology Policy
USTC85-L         USTC85-L@RICEVM1  Discussion for Univ of Science & Tech.
UTS-ITC          UTS-ITC@UTXVM     UT System Information Technology Council
WMTS-L           WMTS-L@WMVM1      William and Mary Technology Support
WVUVTC-L         WVUVTC-L@WVNVM    WVU Video Technology Coordinating


                 Using "Newsgroups" through BITNET/INTERNET
                            By Julian A. Smith
                               May 30, 1993.

   Newgroups are  an enjoyable  "sideline" to  the historian's  use of  the
INTERNET   for scholarly  and academic purposes.  Newgroups are essentially
informal conferences  for discussion  or debate, rather like LISTSERV  news
or   letter groups,  but much  less predictable.   There  are   hundreds of
newsgroups, each  one devoted  to a  specific topic;   you      can    join
newsgroups   ranging   through  history, philosophy and  the sciences,  all
the   way to   Star  Trek,   Elvis Presley  and Ham  Radio.   Whatever your
interest, you  are likely  to find  a  newgroup somewhere  on the  INTERNET
that  deals with it.  Some are  moderated, but  most are not; and this lack
of central control leads to a surprisingly diverse range of discussion.
   Newsgroups are  useful for  several reasons.  To begin with, they are an
excellent resource for students with questions on specific topics.  If, for
example, you   want  to  know  about  available materials for  a particular
research project,  chances are  good that there  is a  newsgroup with  some
"resident experts"  in  that  area.  Secondly,  technical  questions  about
various computer  tools of  interest  to historians,  as well  as questions
on software  or hardware problems, may be directed to one of  the  numerous
computer newsgroups;  no matter  what your problem, there is likely another
computer user  on the INTERNET familiar with it.  Thirdly, newsgroups often
announce   new   employment   opportunities,   available   jobs,   upcoming
conferences, calls  for papers,  journal announcements,  and other  news of
professional interest.  Finally, newsgroups are often just plain fun!
  Newsgroups are open to any BITNET/INTERNET user;and their content depends
largely upon  the fluid  mixture of  subscribers  from  day  to  day.  Some
"peered"  or "moderated"  newsgroups are quite formal and academic in tone;
for others, it's "anything goes!"
   How does  one join  a newsgroup?   Procedures  vary from  university  to
university; but the method at the University of Toronto's EPAS system is  a
typical   one (check your local systems administrator for local  variants).
At the  UNIX %  prompt, simply  type "rn"  and return  to "read  news". The
system will tell you to "get" or "subscribe" to a newsgroup by entering the
command: g.   So,  for  example,  if  you  wished  to  join  the
"bit.listserv.history" newsgroup, you would type "gbit.listserv.history".
    So  how  do you  find out  what newsgroups  are available?  The easiest
way is  just to  type in that letter "g", but without a particular request;
a complete   list  of all  newsgroups will  then be  returned to  you.   Be
warned; the   print-out   of   this   list  occupies over  50 pages!  While
scrolling through  this, it is easy to find out if it contains a particular
topic of  interest; simply use the  standard search character "/".  So, for
instance, if  you wanted  to    find  all  "radio"  newsgroups,  just  type
"/radio", and the current radio newsgroups will be shown.
    Let's  suppose that  you have  found the  newsgroups you want, and have
subscribed to  them using  that "get"  command.  When you enter "rn" at the
UNIX % prompt, you will see a screen looking somewhat like this:

Unread news in                 17 articles
Unread news in bit.listserv.history           12 articles
Unread news in sci.astro                      23 articles
Unread news in epas.phil.general               2 articles
Unread news in bit.listserv.ethics-l           8 articles

******** 17 unread articles in now? [ynq]

    You have  several choices at this point.  If you say q (quit), you will
leave the newsgroup program, and be returned to the UNIX % prompt.  If  you
say  n (no),  you will  be sent  to the next newsgroup in your subscription
list (in  our example  above, this  would be bit.listserv.history).  But if
you say  y (yes), you will begin to  scroll, one  by one,  through those 17
unread messages.   You  can also  get (or  subscribe to) a new newsgroup at
this point, by entering the familiar "g" command; for instance, the command
ginfo-academic.freedom would add that newsgroup to your list.  Once you say
yes, you will begin to read these 17 messages.  The "message header" at the
top of the screen will tell you where  the post came from, who sent it, and
when it  was sent,  along  with  subject  headings  and  other    pertinent
information.   It will also show you  as much  of the  text of  the message
as   your  screen permits.   The spacebar will continue the message, giving
you the  following screen;   but if  you enter  a "n"  (for next), you will
immediately advance   to the  subsequent post (this allows you to skip over
irrelevant or   uninteresting  messages).    All messages are
the end of the post, you should see a line that looks somewhat like this:

End of article 5683 (of 5687)---what next? [npq]

  As you would expect, "n" gives you the next message (5684), and "p" gives
you the previous one (what you have already seen).  The "q" (quit)  command
moves you  to the  next newsgroup  (in our  example, bit.listserv.history).
If   you wish,  you can  also jump  forward or  backward  to  a  particular
message; just   enter   the number of  the message  you want.  If  you read
a  particularly important or memorable article, it can also be saved into a
file; simply  enter   "s" (save)   at  the  prompt.   The newsgroup program
will save  that message into a default file, but you can enter any filename
you wish.
    As  newsgroups  transfer an  enormous amount  of mail, it may sometimes
turn   out that  you simply  do not  have time to read them all; if so, you
can always   mark  all   the messages as "read" by using the "c" (catch-up)
command  at  the  "what  next?  [npq]" prompt.   If you  enter "c"  at this
place, you will receive the following instruction:

Do you really want to mark everything as read? [yn]

   If you  say "n"  (no), you  will be returned back to your familiar "what
next?  [npq]" prompt.   But  if you  say "y" (yes), all the letters (up  to
5687)   will be   marked  as "read",  and you  will be instantly marked  as
being "up-to-date"; in other words, when you log in and read news again, it
will start at 5687 and beyond.
    If you  are ever away from your electronic mail account for an extended
period   (say, a   vacation),  it  is strongly  recommended that you  "turn
off"  your newsgroups;  otherwise, your newsgroup box will be flooded  with
a veritable  torrent of  articles.   This is  done simply by using the  "u"
(unsubscribe) command.  If you enter this command at the "what next? [npq]"
prompt, you  will be "unsubscribed" from  this newsgroup;  you will not see
it in  your list  of   newsgroups anymore,    and  will  have  to  get  (or
subscribe) to it to receive mail from it again.
    After  reading the  newsgroup's articles for a few days, you may decide
you  want to  contribute something  yourself.   So let us suppose you  have
read   an   article   by   John Smith,  requesting information on Ptolemaic
astronomy.  There are two ways to answer this posting; you can  either send
a private  reply directly to John Smith,  or you can post a public reply to
all the readers of that newsgroup.  To post a private reply, enter "r"; for
a public  forwarding of information, enter "f".  Both choices will take you
into a  text editor,  not unlike the standard E-Mail text editor, where you
can write  your answer to Smith's message.  You will be asked if you have a
"prepared file  to include" with your message; the program  basically wants
to know   if  you   have an already-prepared letter  to add  to your reply,
and if so, you can enter its filename here.
   The E-mail  text editor works precisely like the elm mail editor most of
us are   used  to;  you may write your comments exactly as you would in any
word processing  program; F3  saves your work, and gives you  the choice of
sending ("s"), copying ("c") or aborting (forgetting, "f")  your work.   If
you are  satisfied with  your answer to  John Smith, just enter "s" at this
point, and you will have made your first contribution to the newsgroup.
    This  all  sounds rather  complex, but  it is  actually  fairly simple.
If you  ever get stuck, you can always enter a "h" (help) at any  newsgroup
prompt;   that will   give  you a  complete list  of  commands  (much  more
extensive than the restricted list of options described here).
   Although newsgroups  are in  a continual  state of  flux,  the following
is   a partial   list of newsgroups of potential interest to historians and
philosophers   of science   and  technology.   Our listing  is arranged  by
subject heading, but will soon be out of date; newsgroups start up and shut
down all the time.  You can see if your system supports a newsgroup in your
own particular  field of  interest by  using the "l" or "list" command.  To
use this, simply  type "l" at the "what next? [npq]" prompt.   For example,
if   I wanted all the newsgroups dealing with the subject of radio, I would
enter "lradio";  I would  then be  given a list of all the radio newsgroups
then available.   Good  luck  in  your  own  choices,  and  happy  INTERNET

   TOPIC                  NEWSGROUP(S)


ANTHROPOLOGY:         sci.anthropology

ARCHAEOLOGY:          sci.archaeology

ARCHITECTURE:         alt.architecture

ASTROLOGY:            alt.astrology

ASTRONOMY:            alt.sci.astro.aips


AVIATION:             rec.aviation

BIOLOGY:              bionet.agroforestry


CHEMISTRY:            sci.chem

COMPUTERS:            alt.cyb-sys

CONSCIOUSNESS:        alt.consciousness



FEMINISM:             comp.society.women

GEOLOGY:              sci.geo.geology

GREEK:                bit.listserv.hellas

HISTORY:              bit.listserv.history

MATHEMATICS:          sci.fractals

MEDICINE:             bit.listserv.medlib-l


MILITARY:             alt.military.cadet

MYTHOLOGY:            alt.mythology

PHILOSOPHY:           alt.philosophy.objectivism


PHYSICS:              alt.sci.physics.acoustics

PSYCHOLOGY:           sci.psychology




                           |   Book Reviews   |


        Storms of Controversy: The Secret Avro Arrow Files Revealed
                            by Palmiro Campagna

   On February 20, 1959, the newly elected Conservative government of Prime
Minister John  George Diefenbaker (1895-1979) cancelled the Avro Arrow, one
of the  most unusual  aircraft ever  built in  Canada.  Almost overnight an
entire industry  was dismantled  and exported  to  the  United  States  and
Europe; over  30,000 people  lost their  jobs, plans and technical drawings
were shredded,  and the  five completed Arrows were quickly blowtorched and
sold for  scrap.   All that  remains is  a nose  cone, now  on  display  in
Ottawa's National Museum of Science and Technology.
   The reasons for this abrupt cancellation have fascinated historians ever
since.   After all, the Arrow was easily the most advanced fighter aircraft
of its  day; many  aviation historians  considered it to have been at least
ten or  twenty years  ahead of  its time.   It  was  probably  the  fastest
aircraft yet  built (clocked  at 1400 mph during test flights with inferior
engines), and it had attracted considerable interest from European military
planners.   Moreover, a  thriving  Canadian  aerospace  industry  had  been
assembled around  the Avro  project; and when it was closed down on the eve
of its greatest triumph, its many technicians, designers and engineers went
on to productive careers with the American NASA program, and other European
aerospace industries.
  Historians have blamed the demise of the Arrow on a multitude of reasons.
Some have argued that Diefenbaker himself was primarily responsible, seeing
the Arrow  as a  Liberal initiative,  of benefit  only to  Central  Canada.
Others have  suggested economics, claiming that even before the Diefenbaker
landslide of  March, 1958, the Liberals were on the verge of cancelling the
Arrow due  to its enormous cost overruns.  Still others have pointed to the
growing "missile  threat"; by  1959, according  to this  line of reasoning,
American and Soviet ICBMs had already rendered the Avro Arrow obsolete.
  Now Canadian Department of National Defense engineer Palmiro Campagna has
developed another  theory.   Storms of  Controversy: The  Secret Avro Arrow
Files Revealed  (Toronto: Stoddart  Publishing, 1992), is based on a series
of newly  discovered Avro  documents, that weave a complex web of political
intrigues involving  Canadian and American governments, military officials,
and intelligence agents.  Campagna suggests that the Arrow was sacrified to
appease the  three-fold demands  of the United States government.  To begin
with, Campagna says, the Americans felt that the Arrow represented a threat
to U.S.  security.   A fast  high-altitude interceptor, it was probably the
only aircraft  that could  shoot down  the Americans'  top secret  U-2  spy
plane.   And that  plane was vital for US overflights of the largely hidden
Soviet Union.
   Secondly, the  Arrow contained highly advanced aerospace technology, and
the presence of Soviet spies in Canada led to American fears that sensitive
military data  would fall  into enemy hands.  "It may sound like paranoia",
Campagna admits,  "but the country was in the midst of the cold war and the
RCMP was  knowingly allowing  secrets to  pass behind  the Americans' back.
Everything, then,  would have  to be the existing climate of
the day,  one simply  could not  risk having this information fall into the
wrong hands."
   Finally, Campagna  argues, the  high-tech industry surrounding the Arrow
represented a  competitive threat to the American aerospace program.  North
America simply was not big enough for two aviation industries; and if there
was to  be a  single aerospace  program, it  would have  to  be  owned  and
controlled by the United States, not Canada.
   Storms of  Controversy develops  these three  themes with  elegance  and
verve.   "Dreams" describes  the pre-history  of  the  Arrow  project:  the
successful  CF-100   Canuck  "Clunk"  and  the  daring  CF-102  "Jetliner".
Campagna notes  the considerable  "U.K. and  U.S. Interest"  in Avro,  then
covers the  surprisingly advanced  design of the Arrow, noting how elements
of its  construction resurfaced  in modern  American planes  like the SR-71
Blackbird and  B-2 Stealth Bomber.  But the bulk of Campagna's narrative is
devoted to  the underlying  political developments surrounding the program.
Campagna rejects the anti-Liberal "Diefenbaker emnity" hypothesis; in fact,
he shows  the order  to reduce the Arrow to scrap originated with Air Staff
Chief Hugh Campbell, not Diefenbaker, and further suggests that Diefenbaker
may not  even have seen the order (his argument is weakest here).  Campagna
also criticizes  the economic arguments against the Arrow, such as those of
John McLin in Canada's Changing Defence Policy, 1957-1963 (Baltimore: Johns
Hopkins, 1967).   Campagna  argues that  Canadian Ministers  of Defence and
Economics, as  well as  Chiefs of  Staff, unanimously  believed the Arrow's
costs were  reasonable; and  that costs  were declining, not rising, as the
Arrow was  being produced.   He also disputes the official "missile threat"
argument, pointing  out that  it was  advanced only  because  "the  average
Canadian would  be unable  to dispute  it in  the  absence  of  any  secret
intelligence information."  Such information was available, Campagna notes,
but it was ignored.
   Campagna concludes  with a  very interesting  collection of 18 myths and
misconceptions about  the Arrow, ranging from the popular belief in company
mismanagement to  the tantalizing rumour that "One Arrow got away" from the
cutting torch.   There  is also  a useful appendix, consisting of facsimile
reprints  of   critical  documents   in  Campagna's  case.    There  is  no
bibliography, but  the notes  and index  are adequate.   Yet  the  book  is
deceptive in  one respect; already short (at 202 pages), it is printed with
extremely large  type (less  than 300  words to  the page).  It can be read
very quickly, and indeed is more like a lengthy article or monograph than a
full-length book.
   Conspiracy theories,  by their very nature, often invite skepticism from
their readers;  but Campagna's  arguments are  clearly explained  and  well
documented.   Whether you agree with the more extreme suggestions of Soviet
spies and  CIA involvement  is not  really that important, for Campagna has
certainly given  historians a fresh approach to the Avro Arrow problem, and
for that the profession owes him their gratitude.



           The People's Railway: A History of Canadian National
                             By Donald MacKay

   The development  of steam-powered railways revolutionized transportation
in nineteenth  century Europe and the United States, but nowhere were their
effects more  dramatic than in Canada.  An enormous country with poor roads
and frozen  waterways five  months every year, Canada had much to gain from
railroad construction;  and during  the century  after 1830  her  "Railroad
Boom" left  the country  with more railroad miles per capita than any other
nation in  the world.   But  this flurry of railroad construction exacted a
heavy toll; as Canadian railroad mileage proliferated between 1890-1914, so
did government financial assistance to often-fledgling companies.  And when
World War  I stopped  both the flow of both immigrants and British capital,
Canada's railroads  found themselves in desperate financial straits.  Prime
Minister Robert  Bordon soon  called a Royal Commission into the railroads,
which recommended  their nationalization in May, 1917; and out of the ashes
of fiscal  collapse arose  the phoenix of the Canadian National Railroad in
1919, as Canada's first Crown Corporation.
   The construction  of Canada's  first transcontinental railroad line, the
Canadian Pacific,  between 1880-1885,  has  become  one  of  our  "national
epics"; and  this mammoth  undertaking has  inspired a  host of historians,
ranging from  W. K. Lamb and J. Lorne Macdougall to Pierre Berton.  But the
history of  Canadian  Pacific's  arch-rival,  the  Canadian  National,  has
remained much  more obscure.  This comparative neglect is partly because CN
was formed  out of already existing rail lines; so its history is much more
that of  the legislative  chamber and  the boardroom  than the  wilderness,
mountains and  prairie.   But CN's  history is  no less interesting for its
emphasis on  business and  finance.   CN's history  is a  tangled story  of
continual struggle  between political  dreams of  national development  and
economic demands to reduce its enormous inherited debt.  And this story has
recently been well told by Montreal historian Donald Mackay (1925-).
   Mackay is  no stranger  to either  railroad or  economic history.    His
earlier work,  The Asian  Dream: the  Pacific  Rim  and  Canada's  National
Railway (Vancouver: Douglas and McIntyre, 1986), dramatically interwove the
stories of  Canada's  Chinese  and  Japanese  immigrant  workers  alongside
histories of  both CN   and  the Canadian Merchant Marine.  Mackay has also
written a  good business  history of  the  forestry  giant,  the  MacMillan
Bloedel Company, entitled Empire of Wood (Vancouver: Douglas and McIntryre,
1982), along  with several  other books  on logging  and forest management.
And Mackay  has recently  completed an  interesting account  of  the  early
history of  the tightly-knit Montreal business community, called The Square
Mile: Merchant Princes of Montreal (Vancouver: Douglas and McIntyre, 1987).
His experience in economic and business history has been put to good use in
his latest  book, The  People's Railway:  A History  of  Canadian  National
(Vancouver: Douglas and McIntyre, 1992).
  The People's Railway begins with Mackay's account of "Boom and Bust", the
late 19th century building of a plethora of fiscally-shaky railroads, whose
economic weakness  ultimately led  to CN's  establishment in  1919.  Mackay
concentrates primarily  on the  period after 1920, and this is probably the
book's most  significant flaw;  a more  detailed history  of the enormously
complex web  of companies  that were  to amalgamate  into Canadian National
would have  been most  helpful.   Readers seeking  more information on CN's
"prehistory" should  consult  the  much  more  detailed  Canadian  National
Railways, 1-2, by G. R. Stevens (Toronto: Clarke, Irwin and Company, 1960),
which deals with this period in depth.
   Mackay does  excel, however,  in bringing  the otherwise  dry and  dusty
economic history  of CN  after 1920  to life.    He  covers  the  political
machinations of  Prime Minister  Mackenzie  King  (1874-1950)  and  railway
official  Henry   Thornton  (1871-1933)   with  dramatic   flair;  and   is
particularly impressive  in his treatment of CN during the Great Depression
of 1929-39  ("A Colossus Fallen" and "Hard Times") and World War II ("CN at
War").   Mackay takes  us behind  the scenes, showing us not only the power
struggles of  important business executives and political leaders, but also
the   day-to-day  experiences  of  the  lesser-known  members  of  CN:  the
engineers, firemen, brakemen, track workers, and many more.  On the way the
reader is  favourably impressed  with the  high  standards  of  comfort  on
Canadian trains;  on page  73, for  example, we  read that  early CN trains
offered diner  and parlour  cars, sleepers,  buffet  cars,  solarium  cars,
lounges, and  coaches.   In 1924  the Toronto service stop on the Montreal-
Chicago line  lasted a  mere 15 minutes, and in 1927 CN could take you from
Montreal to  Vancouver in  only 4.5  days (those  statistics are surprising
even by today's standards).  Mackay follows the growth of CN all the way to
the  1970s   and  1980s,   where  successive   governments  "downsize"  and
"privatize" the company to a shadow of its former self.
   The People's  Railway includes  several photographs of CN's innovations,
including the  truck "piggyback" service of 1952 and the revolutionary 1969
Turbo; but  this is  not a technical history.  Mackay spends much more time
emphasizing the  social, political  and economic  consequences  surrounding
these changes.  There are several helpful maps, and the apendices include a
year-by-year chronology  of company highlights, a page of company logos and
heralds, and  several graphs.   There  is also  a table  of Canadian  Prime
Ministers alongside  their Railway  Ministers; but  oddly enough, the table
gives the  terms of the former, but not the latter (often there are several
Railway Ministers in the course of a single Prime Minister's office).
  The People's Railway is a solid, capable history of the Canadian National
Railway Corporation.   Admittedly,  it is  a business history rather than a
history of  railway technology,  but its continual emphasis on the lives of
CN workers  successfully prevents  it from  becoming dry,  tedious or dull.
Statistics  are   presented,  but  their  appearance  is  usually  low-key.
Documentation is  adequate, and  all notes  are placed  at the end to avoid
distraction; unfortunately, the publishers have adopted the modern irritant
of referring to sources by brief quotations rather than footnotes.  But all
in all,  this is  an excellent  volume,  well  supplementing  and  updating
Stevens' 1960  book, his  more recent History of Canadian National Railways
(New York:  1973), or  T.D. Regehr's  Canadian Northern  Railway  (Toronto:


                         The American Way of Birth
                            By Jessica Mitford

  Thirty years ago, Jessica Mitford published a devastating critique of the
American funeral  industry.   Entitled The American Way of Death (New York:
Simon and  Schuster, 1963), Mitford's controversial bestseller dramatically
exposed the  crass cynicism,  corrupt business  practices and naked avarice
that surrounded  much of  the American  funeral home industry, and made her
famous.  Now Mitford has returned with a companion volume, The American Way
of Birth  (New York: Dutton, 1992), which promises to be no less explosive.
Mitford examines  the social, economic and political issues involved in the
American "birthing  industry", and reaches some disturbing conclusions.  To
begin with,  her comparative  study of  "champagne birthing suites" for the
well-to-do, and  the utter lack of pre-natal care for the poor, lead her to
condemn the  modern American health care system as inefficient, ineffective
and discriminatory.   Mitford argues that misogyny has coloured physicians'
attitudes to  pregnancy and  birth, and  that  women  have  been  cynically
manipulated by  the medical  profession's obsessive drives for money, power
and control.   Finally,  she points  to a  way out of the current morass of
high health  care  costs  and  rising  infant  mortality;  a  rejection  of
technological "birthing  fashions" and  "caesareans to order", and a return
to qualified female midwives and supervised home births.
   Mitford's book  is well-written,  interesting and  capably  argued;  her
principal contention,  that Americans should be allowed to choose their own
methods of giving birth (home versus hospitals, or doctors versus midwives)
seems both  reasonable and justified.  And Mitford provides enough evidence
of medical  and political  complicity  in  restricting  patient  choice  to
justify sweeping  reforms in  the American  health care  system.   But  The
American Way  of Birth  is not  without its  flaws.   There are  four  main
problems with  the book:   the  too-frequent replacement  of  argument  and
analysis by irrelevant personal opinion, the parroting of outmoded feminist
rhetoric, the  efforts to  gain laughs with "humour" of questionable taste,
and her silence on one of the biggest American reproductive "industries" of
   Mitford's   tendency  to  inject  irrelevant  personal  experiences  and
opinions into everything she studies gives the work a annoyingly subjective
character; at  times, they  read more like Mitford's diaries than objective
critiques of  American business.    For  example,  when  she  examines  the
successful Alabama-based  "Gift of  Life" program,  which supplies superior
hospital and  pre-natal care to thousands of poor, black Medicaid patients,
she cannot  resist telling us that she almost forgot she was in the "Cradle
of the  Confederacy" until she heard "a prototypically racist spiel" from a
pediatric nurse  about the pregnant teenagers the program serves (page 90).
Should it  really surprise  us that  some of  the  people  she  interviewed
happened to  harbour  objectionable  personal  views?    I  would  be  more
surprised if  they did  not!   Even by  her own  admission, the doctors and
nurses of  the "Gift of Life" program provide excellent health care to both
black and white patients, and are almost universally supported by community
leaders of both races.  So why inject the divisive issue of racism where it
is not relevant?
   Another example  comes in her discussion of modern birth fashions, where
she writes  to economist  John Kenneth Galbraith (1908-) about her upcoming
book, and  Galbraith replies  that he  "had not  previously given more than
three minutes'  thought" to the subject (page 68).  So what?  Well, Mitford
goes on  to explore  why Galbraith  had not  thought  more  about  it,  the
solitary struggles  of his wife in labour, and a suggested "reenactment" of
the scene  where Galbraith  is pulled  "off the  world stage  and into  his
wife's delivery chamber."  Colorful, yes; but relevant, no!
   A second  major problem  with the text is its knee-jerk use of hackneyed
feminist cliches.   While  studying the  Friedman Curve (a 1978 statistical
analysis of  the durations  of the  various stages  of  labour  by  Harvard
Medical School  obstetrics professor Emmanuel Friedman), Mitford scathingly
concludes (page  143) that  "Only a man could have thought that up!"  I had
hoped that  modern feminism had progressed further than this sort of gender
stereotyping; indeed,  I thought  that its entire raison d'etre was to deny
differences in thinking between men and women altogether.
   Care for  another?   Her study  of midwives  and physicians in Victorian
England (page  37-8) repeats  the hoary  old feminist  myth that the former
were "thoroughly  familiar with  the ins  and outs of the female body", but
the latter  "felt woefully  inadequate to  the task  at hand."    Her  sole
evidence:  an  1848  physicians'  manual  stressing  the  importance  of  a
confident and  self-assured bedside  manner.   Are we  to believe that male
physicians learned  nothing of  female anatomy  from literally thousands of
patient examinations?   Mitford is in deep waters here, but things are much
more complicated  during her  brief study  of the  Medieval and Renaissance
periods; one  doubts, for  example, that childbirth forceps inventors Peter
Chamberlin I,  the Elder  (1560-1631) and  Peter Chamberlin  II (1572-1626)
were really  nothing more  than "grasping tightwads, bent only on their own
enrichment" (page 25) for keeping their creations secret.  On the contrary;
virtually all  Renaissance scientists and inventors shared this passion for
secrecy to  some degree, for varied and complex reasons, including priority
of discovery, insurance against competition, and many more.
  A third difficulty with the book is its frequent descent into poor humour
at the  expense of  good taste.   While  discussing the Anita Hill-Clarence
Thomas sexual  harrassment case,  Thomas is  reviled as  "Long Dong Silver,
with a  pubic hair atop his can of coke".  Regardless of one's own personal
views on  this highly  controversial topic,  these types  of  comments  are
unnecessary and  unprofessional; indeed, they are no better than the gender
stereotyping done by male doctors that Mitford so adamantly condemns.   How
about another?  While acknowledging the  many contributions of her literary
representative, Hollywood  lawyer  and  entertainment  writer  Renee  Wayne
Golden, she  jokes that  the book may be sold as a Broadway musical comedy,
with titles  like "Les  Mids?  Oh Cal Cut Her! (in which Dr. Cal performs a
caesarean to  the background  music of  'I've got  you under  my skin...')?
[or] A  Chorus Line  (featuring the  top  brass  of  the  American  Medical
association singing  "Oh no, You can't take that away from me").  Mitford's
account would  be far  more compelling  and persuasive if it could restrain
itself from such bad taste.
   The final  problem with The American Way of Birth is its almost complete
silence on  the controversial  question of  birth and  abortion.  Since the
1973 Roe  vs. Wade decision legalized abortion on demand in America, almost
20 million  unborn (a  third of  all pregnancies)  have been  aborted;  and
indeed an  entire "abortion  industry" has  been established  in the United
States, with  its own  devotion to profit-seeking, power and the control of
womens' bodies.  Ignoring this industry, whose frequently unsafe, unhygenic
and corrupt  medical and  business practices  prove Mitford's  arguments of
female exploitation far better than most American hospitals, in surprising;
indeed, the  "abortion clinic"  poses a  greater threat  to the  mother and
child than  any dispute over home versus hospital birthing techniques.  And
regardless of  one's personal  view on  this bitterly  divisive issue, both
pro-choicers and  pro-lifers agree  that the exponential growth of abortion
as a  common solution to unwanted pregnancy is a sad commentary on American
society.    But  Mitford's  devotion to  a  particular   feminist  ideology
prevents her from taking the same hard-nosed, critical view of the abortion
clinic as she does of the hospital delivery room.
   Apart from  these flaws,  however, The  American  Way  of  Birth  is  an
interesting and  timely book.   Useful  appendices  give  various  position
statements on  midwives from  the California  Medical Organization, and the
World Health  Organization.   There is  no bibliography,  but  the  "Source
Notes" at  the book's  end give  enough detail to locate the works cited in
the text  (but like  so many other recent works, it unfortunately uses page
quotations rather  than  footnotes  to  identify  materials).    Perhaps  a
subsequent edition  will correct  these problems;  but even if it does not,
The American Way of Birth is still well worth reading.



      Loss of Eden: A Biography of Charles and Anne Morrow Lindbergh:
                              By Joyce Milton

   Almost everyone  knows the  essential  facts  of  U.S.  aviator  Charles
Augustus Lindbergh's  (1902-1974) life.   The principal symbol of the early
years of aviation, Lindbergh made the first solo flight (33.5 hours) across
the Atlantic Ocean in his Ryan monoplane, the Spirit of St. Louis.  He left
from Roosevelt  Field, New  York on May 20, 1927, and arrived the following
day at Le Bourget airport near Paris, France to a hero's welcome.  Formerly
an  obscure   airmail  pilot  and  carnival  aviator,  Lindbergh  became  a
celebrity; he  was given  the Congressional  Medal of Honour and many other
international awards.   But  tragedy struck Lindbergh.  In 1932, his infant
son Charles was kidnapped and killed; and the subsequent investigation into
the crime,  largely handled by Lindbergh, became the most publicized police
case of  the 1930s.   Lindbergh  eventually moved to England (1935-1939) to
escape the  intense media  publicity surrounding  both  the  case  and  the
subsequent capture  and  trial  of  the  suspected  killer,  Bruno  Richard
Hauptmann.   After a long and bitterly-contested trial, Hauptmann was found
guilty and executed.
   Meanwhile, Lindbergh  created great  controversy in the United States by
touring Nazi  Germany and accepting awards from their government (1938); he
also attracted  criticism by  his  isolationist  "America  First"  speeches
(1940-1941) and  his anti-Semitic remarks.  But he largely redeemed himself
in the public eye through his exemplary service for the US Air Force during
World War  II, serving  as a  civilian technician  and flying  more than 50
combat missions  in the Pacific Ocean.  After 1945, Lindbergh was appointed
a government  advisor and  brigardier-general in  the Air Force Reserve; he
also became  active in  environmental and  conservation  work.    His  1953
autobiography, the  Spirit of St. Louis (New York: Charles Scribners' Sons,
1953), won him a Pulitzer Prize.  Lindbergh died of cancer in Hawaii in the
spring of 1974.
   Lindbergh was  the most  recognized aviator  of  his  age,  and  he  has
consequently been  the subject  of a virtual flood of newspaper stories and
magazine articles;  the interested reader is referred to Perry D. Luckett's
Charles A. Lindbergh: A Bio-Bibliography (New York: Greenwood, 1986).  Book
length  biographies   have  also  been  completed  by  several  historians,
including Walter  S. Ross's The Last Hero (New York: Harper and Row, 1968),
Leonard Mosley's  Lindbergh: A Biography (Garden City: Doubleday, 1976) and
Brendan Gill's Lindbergh Alone (New York: Harcourt Brace Jovanovich, 1977).
So what is the need for a new biography in 1993?
   Joyce Milton's  Loss of  Eden: A  Biography of  Charles and  Anne Morrow
Lindbergh (New York: Harper Collins, 1993) differs from its predecessors in
several important  respects.   Milton is  a Brooklyn,  New York  author and
historian, who  has published several engaging books on 20th century social
history; previous  efforts include  The Yellow Kids: Foreign Correspondents
in the  Heyday of  Yellow Journalism, and The Rosenberg File.  Loss of Eden
brings the same thoughtful, spirited and engrossing approach to Lindbergh's
life.   But Loss  of Eden  is much  more than  just an  entertaining  read.
Milton breaks  ground through  her in-depth  look at  Lindbergh's wife, the
fellow aviator  Anne Morrow  (1906-); in  fact, Loss  of Eden  is really  a
"parallel biography"  of both aviators and their respective families.  This
sometimes leads  to some confusing leaps forward and backwards in time, but
overall, the  technique sheds  light on  many little-known  aspects of  the
Lindberghs and  their era.   We see, for example, a particularly insightful
analysis of  Anne's long  literary career,  which saw  the  publication  of
several works  of poetry,  romance, travel  literature and more, as well as
her famous  bestselling book  on the  role of women in modern society, Gift
from the Sea (1961).  This "deceptively graceful book", Morrow says, though
ignored by  feminists and  professors of womens' studies alike, was central
to her philosophy, and more importantly, conveyed a revolutionary "feminist
message" of self-renewal to millions of American women.
   Unlike many  previous biographies,  Milton does  not make  the 1927 solo
transatlantic flight  the principal  event of  Lindbergh's life.   Instead,
Loss of  Eden devotes  its central  focus to  the  1932  abduction  of  the
Lindberghs' 20  month old  son, Charles.   Milton  persuasively argues that
this tragic kidnapping changed the course of the Lindberghs' lives forever,
replacing Charles' basic optimism and utopian philosophies of aviation with
a profound  skepticism, despair  and pessimism  about  the  future  of  the
western world.   Milton  also differs from several other Lindbergh books in
her dispassionate  and critical  look at  this  kidnapping;  she  does  not
attempt to  exculpate Hauptmann  (other books have erected a dizzying array
of alternate  hypotheses and  conspiracy theories),  but rather focuses her
interest in  Lindbergh's own  long-term administration  of the  case, which
eventually became a personal obsession.
  Loss of Eden portrays Lindbergh as a moral and principled man, whose high
idealism and  faith in  aviation as a bridge between cultures was cynically
manipulated by his friends and betrayed by his advisors.  It is Lindbergh's
ultimate  disillusionment   with  American   democracy  that   prompts  his
"flirtation" with  Nazi ideologies,  says Milton;  and, she  argues, it  is
press misrepresentation  and media  distortion that  lead  to  the  popular
perception that  he was  a notorious  racist and  anti-Semite.  Milton does
quote from Lindbergh's pre-war speeches (pages 382, 400), but suggests that
his comments  must be  appreciated in  the context of the endemic nature of
prejudice within  the Lindberghs'  social circle.   Lindbergh reflected the
troubled and  unsettled nature  of his times; and Loss of Eden is the first
biography to effectively link Lindbergh's early populism and air-mindedness
to his postwar New Age thinking and despair at a world gone mad.
   Milton alludes  to the  many myths  surrounding Lindbergh  and aviation,
particularly with her mention of the "alti-man" of Alfred Lawson (page 49).
But she  does not  develop any  of these flying myths in detail; and a more
extended analysis of the aviation mythologies of the period, especially the
"flying ace"  and "intrepid birman" so thoroughly studied by Joseph J. Corn
in The Winged Gospel: America's Romance with Aviation, 1900-1950 (New York:
Oxford University Press, 1983), would certainly be instructive here.
   On the  whole, however,  Loss of  Eden is  an excellent  updating of the
Lindbergh story.   While  the critical  reader might  quibble with Milton's
occasional lapses  [how, for  instance, can  we be  so sure  Anne's written
reaction to  Lindbergh's flight  was "unconsciously  sexual" (page 153), or
that one  of Charles'  early letters  to his  parents "reeks  of suppressed
resentment"? (page  34)], there is no doubt that Loss of Eden is a triumph.
Lindbergh may  well have  been a  solitary "lone  wolf"  to  the  tabloids,
dependent on  no one;  but Milton  painstakingly traces  his complex social
network, and  the many  disparate influences  that made him the man he was.
For this difficult accomplishment, her readers will be grateful.



                      The Art of Medieval Technology
                            By Richard W. Ungur

   Richard W. Unger, known principally for his earlier book on _The Ship in
the  Medieval   Economy,  600-1600_,   here  tackles   the  more  difficult
methodological question:  what can  artistic representations  tell us about
actual technological  practices?   In the  preface to  _The Art of Medieval
Technology_ (New Brunswick, New Jersey: Rutgers University Press, 1991), he
states that  he was  not trained as an art historian and therefore finds it
hard to  replicate their  methods.  This is certainly true: as a sourcebook
of art  history and  detailed analysis  the book  falls short,  but  as  an
example of  a relatively  untouched technique  of  historical  inquiry,  it
serves admirably.  His subject matter, and indeed the subtitle of the book,
is "Images  of Noah  the Shipbuilder".    In  short,  Unger  seeks  to  use
pictorial representations  of the construction of Noah's ark to divine what
role the  "shipbuilder" played in the middle ages and to see to what extent
artists looked to their local shipyards for inspiration.
   In the iconography of Noah he finds an evolution of the shipbuilder from
the craftsman in the eleventh century to a naval architect in the sixteenth
and seventeenth centuries.  Additionally, he finds that artists did to some
extent look to their local builders to create their images.  The particular
types of  ships used  in the  Mediterranean and  the Baltic/North  Atlantic
regions  are  indeed  reflected  in  the  northern  and  southern  European
iconographies.  It is interesting to find that in a few cases, knowledge of
one region's  shipbuilding techniques was transmitted to the other region's
artists.   Unger occasionally  errs in  his  interpretation  of  particular
details of  the art  historical sources,  in  the  feasibility  of  certain
practices, in  leaving the  reader without  a reference  or a  summary (for
example, the  use of  axes and  drilling technologies).   Nevertheless, the
methodology he  uses in  this book  is invaluable: historians of technology
should use artistic sources in addition to textual and archaeological ones.
   The book  is brief  and is  meant as a companion not a substitute of his
earlier works; in any case, these should be consulted for more rigorous and
complete details.   The  copious plates are grouped at the end of the book,
which makes  comparison easy, but flipping back and forth from the text can
be distracting.   _The Art of Medieval Technology_ is worth reading for its
fresh methodological approach, although historians of naval architecture or
Diluvian iconography are advised to move on quickly.

                                               Reviewed by Steven A. Walton


          Hidden Attraction: The Mystery and History of Magnetism
                           By Gerrit L. Verschuur

   Gerrit L. Verschuur, a research professor of astronomy at Rhodes College
in Memphis,  Tennessee, is  both an  author of  popular books  on  physical
science and  a contributing  editor to Air and Space magazine; he has hence
become  quite   experienced  at  interpreting  highly  abstract  scientific
concepts to  lay audiences.  After successfully explaining the mysteries of
complex topics like radio astronomy in The Invisible Universe Revealed (New
York: Springer-Verlag,  1987), Verschuur  has since turned his attention to
more down-to-earth  topics.   Hidden Attraction: The History and Mystery of
Magnetism (New  York: Oxford University Press, 1993), is his latest effort;
it gives  a popular  history of  magnetism, beginning  with  Ancient  Roman
observations of  magnetic lodestones  and continuing  to  the  most  recent
discoveries in astronomy and physics.
   Overall, Verschuur's  account of the growth and development of magnetism
is clear,  easy to  follow and  well-written.   However, it  is not without
difficulties.   The most  significant is  the lack  of  research  into  the
lodestone in  non-Western cultures;  to be  precise, there is no mention of
Chinese magnetic  theory.   The indefatigable  labours  of  Joseph  Needham
(Science and  Civilization in  China) have  shown that Chinese work in this
area was unparalleled in its elegance and sophistication, several centuries
before comparable  European research;  and some  cross-cultural comparisons
would have  been quite  helpful in  explaining the  influence  of  magnetic
discoveries in the two cultures.
   However, Verschuur has written a good account of magnetic history in the
West.    His  treatment  of  18th  and  19th  century  electromagnetism  is
excellent; and his discussion of 17th century magnetical theory is likewise
lucid and easy to follow.  Unfortunately, his discussion of earlier periods
is less satisfactory.
   The most problematic of these areas is the Medieval era.  Verschuur is a
modern  astronomer  and  not  a  Medieval  historian,  so  he  follows  the
traditional pattern  of interpreting  the 1269 Epistola de Magnete of Peter
Peregrinus (fl.1261-1269)  as the  essential beginning  of magnetic science
(pages  9-12).     Recent  research  has  shown  that  although  Peregrinus
essentially summarized  the magnetic knowledge of the time, he added little
to it  that was  original; indeed there were many precursors to Peregrinus,
ranging from  Alexander Neckam  (1157-1217) to Roger Bacon (c.1213-c.1292).
Verschuur's ommissions  are partly  because he based this section of Hidden
Attraction largely  on secondary  sources like the Dictionary of Scientific
Biography, the  Encyclopaedia Britannica,  and Park Benjamin's 1898 History
of Electricity, rather than primary documents.
   His account  of Renaissance magnetic theory is better, as here Verschuur
uses the  important primary  materials of  the English magnetic scientists;
particularly Robert  Norman's (fl.1576-1590)  The Newe  Attractive of 1581,
William Gilbert's  (1544-1603) De Magnete of 1600, and William Barlow's (?-
1625) Magneticall Advertisements of 1618.  But he still repeats many of the
standard  "magnetical   myths",  including   the  beliefs  that  (page  13)
Christopher Columbus  (1451-1506)  unknowingly  passed  the  line  of  zero
magnetic declination  (in fact,  he was well aware that declination changed
over the  earth's surface,  and noted  its variations in his journals), and
that  Robert  Norman  discovered  magnetic  inclination  in  1576  (whereas
Nurnburg vicar  George Hartmann (1489-1564) noted the same effect in 1544).
There are  some editorial  oddities as  well; for instance, Verschuur gives
dates for all of his principal characters (an admirable trait!), but in the
case of  Niccolo Cabeo  (1586-1650),  the  dates  come  during  the  second
discussion of his work (page 39), not the first (page 28).
  Verschuur then traces the development of magnetism and electricity in the
18th and  19th centuries.   This  portion of  Hidden Attraction is careful,
clear and  surprisingly easy  to understand;  and  this  is  all  the  more
remarkable when we  realize  the enormous mathematical complexity of topics
like field theory  and electrodynamics.   It  would  have been easy to lose
his readers in a dense theoretical thicket, but Verschuur manages to convey
the essentials  of Andre-Marie  Ampere (1775-1836),  Michael Faraday (1791-
1867) and  James Clerk  Maxwell (1831-1879) in non-technical language.  But
in all  fairness, it  would have been helpful to include more illustrations
of those  sophisticated mechanical  field theory  models, particularly  for
   Hidden Attraction  is at  its best  when it  deals with modern theories;
Verschuur particularly shines when he deals with origins of magnetic rocks,
explaining the  remarkable discovery  that lodestones are made by bacteria!
A sediment  organism  (GL-15)  eats  iron  and  converts  ferric  oxide  to
magnetite which,  over billions of years, forms layers of magnetite in iron
formations (pages  169-174).    Verschuur's  description  of  this  complex
process is a delight.
  Hidden Attraction has no bibliography; but substantial notes are included
at the  end of each chapter.  There is also a large appendix, "The Patterns
of Progress"  (pages 233-249)  which  includes  Verschuur's  own  six-phase
theory of  scientific progress,  based partially on the work of philosopher
of science  Thomas Kuhn's  Structure of Scientific Revolutions (1962).  But
Verschuur, unlike  Kuhn, supposes  that scientific  "paradigm shifts"  soon
allow the  convergence and eventual synthesis of several specialized fields
of knowledge  into wide-ranging  "theories of  everything"; for  the  first
time, he  suggests, scientists  are well  on the  way to  "significant  and
possibly complete  understanding of  the nature  of the physical universe."
Such scientific "optimism" has historically always been proven to have been
misplaced; as  Verschuur himself  notes, late  19th century physicists were
virtually certain  that the completion of classical Newtonian mechanics was
inevitable when  the twin  discoveries of  relativity and quantum mechanics
radically altered  their world-view  at the turn of the century (page 184).
Verschuur's model  of scientific progress also does not seem to account for
the persistence  of rival  schools of scientific thought after the erection
of a new paradigm (such as Cartesian physics after Newton); but to be fair,
Kuhn's theories  are far  from complete here as well.  Even so, Verschuur's
six-stage theory is both intriguing and useful.
  Verschuur's work is a welcome addition to the comparatively few treatises
on the  history of  magnetism now  available.   There are  some  historical
simplifications, to  be sure,  but on  the whole  Hidden  Attraction  is  a
capable, competent  and clear history of a very difficult topic.  Verschuur
is to  be congratulated  for his  attempt to  erect a  theory of scientific
progress alongside  his history; this will no doubt provoke much discussion
from the profession.


          Gates: How Microsoft's Mogul Reinvented an Industry---
                And Made Himself the Richest Man in America
                     By Stephen Manes and Paul Andrews

   Virtually everyone who uses computers is familiar with the controversial
software programming  genius William  Henry Gates  (1955-). As  the head of
MicroSoft Systems,  and the  originator and  developer of  both MS-DOS  and
MicroSoft Windows,  Bill Gates  is arguably the most important and powerful
man in  the entire  computer industry.  He is  also the  youngest self-made
billionaire in American business history; but his astonishing ten-year rise
to the  pinnacle of the software industry of the United States has prompted
enormous criticisms  of his  business and  corporate styles.  Alternatively
idolized, hated,  envied and  feared, Gates  is truly a paradoxical figure;
and in  an industry where form is as important as content, an understanding
of this figure is critical for any history of the computing industry.
   There has  been no  shortage of  news stories,  magazine articles and TV
features about  Bill Gates  and his MicroSoft Corporation; but much of what
has been  printed about  Gates is  more  properly  the  stuff  of  legends.
Histories of  MicroSoft and  its president  also exist  in  profusion,  but
almost all  have a  particular ideological axe to grind; they either lavish
praise on  Gates and  his MicroSofties  for creating the standard operating
system for  over 100  million personal computers, or they heap criticism on
him for  his alleged  theft of  rival technologies,  monopolistic  business
practices, and  ruthless disregard for alternative visions of the future of
the computer.
   Gates was  co-written by  two experts  on  Microsoft  and  the  Personal
Computer: Stephen  Manes and Paul Andrews. Manes has explained the computer
industry to  its users  for more  than a  decade, serving  as columnist and
contributing editor  to both  PC Magazine  and PC/Computing.  He  has  also
written more  than 30 books. His colleague, Paul Andrews, is a reporter for
the Seattle Times newspaper, covering the technology and computer "beat" in
his weekly  column. Gates  began as  an "unauthorized"  biography in March,
1991; but  by July  both Gates and MicroSoft were actively participating in
the project, granting a series of in-depth interviews and permitting access
to MicroSoft's enormous internal archives and files.
 The  result is  a tour-de-force.  Manes and Andrews carefully document the
rise of  Gates and  MicroSoft from their humble beginnings with the Traf-O-
Data traffic  analyzer and  Altair 8800  computer of the 1970s, all the way
through the stunning triumphs of MS-DOS and MicroSoft Windows in the 1980s,
to Gates'  future plans  for multimedia, biotechnology, and the information
revolution. Gates intends far more than just a "computer in every home"; he
hopes to transform the very ways we live, work and play.
   But Gates'  visions of  an  eventual  technological  utopia  have  their
critics.  Manes   and  Andrews   painstakingly   document   the   byzantine
relationships between  rival software  companies, and  the  maze  of  legal
battles and  judicial decisions  surrounding them.  They show  that  Gates'
monolithic and  highly centralized  control of  MicroSoft is far from being
the competitive "free for all" that characterizes its advertising and press
releases. Yet  on the  whole, they  chalk most  of Gates'  failings down to
youth and  inexperience rather  than maliciousness.  Gates has  an  uncanny
knack for  transforming product  delays and  software  bugs  into  business
success; and  in an  industry which  is littered  with the  wrecks of rival
firms, the  authors reject  the heroic "lone inventor" myths, and show that
Gates' magic has been based on good luck as much as programming wizardry.
   About the  only place  where Gates  fails is  in its  rather rudimentary
account of  the early  history of  the  computer.  Manes  and  Andrews  are
understandably concerned  with computing  technology during  the late 1960s
and early  1970s, when  the young  Bill Gates begins serious programming on
his school's  computers; but  they tell  us very  little about  the  rather
arcane world  of computing  before then.  Clearly the mainframes that Gates
used to  "cut his  programming teeth"  did not  spring  into  existence  ex
nihilo; and  a more  detailed account  of their development, along with the
software used  to operate  them,  would  have  been  both  interesting  and
  Gates   is  sometimes  quite  technical;  when  discussing  the  internal
architecture of  a  particular  piece  of  software,  it  often  assumes  a
considerable prior  knowledge of  computers.  Yet  even  if  one  does  not
understand all the details, the overall picture is almost always clear, and
for this Manes and Andrews are to be commended; this could very easily have
become an  advanced technical handbook on rival operating systems, or a dry
company history (for in a very real sense Bill Gates is MicroSoft, and vice
versa). But the authors' regular appeal to humourous anecdotes illustrating
the enormous  stresses underlying  Gates' workaholism,  and the  strains of
life under  the MicroSoft  whip, ensure that the final product, while often
complex, is never boring.
   Gates is both entertaining and well written. The text includes extensive
endnotes (again,  replacing  standard  footnotes  by  that  depressing  and
irritating "quotations  attached to  pages" style which is all too frequent
today). Yet  the authors  are  to  be  commended  for  at  least  including
sufficient documentation  to allow  readers to easily locate their sources;
and that  is especially  important in  a study like this, where many of the
documents are  in company  archives, or other locations which are difficult
to access.  There is  also a  helpful bibliography  of printed  books;  and
despite  the   limited  "shelf-life"   of  most   computer  books,  such  a
bibliography is  at least  a useful  orientation to the field. The index is
also very detailed.
   Gates is  an excellent  biography of  the most  significant contemporary
figure in  the American  computer industry.  But  Manes  and  Andrews  have
succeeded in  giving us  not only  a  first-class  biography,  but  also  a
carefully-crafted economic and business history, alongside a good technical
primer of  personal computing  software and  hardware. For this the authors
deserve our gratitude and respect.


      The Hacker Crackdown: Law and Disorder on the Electronic Frontier
                               By Bruce Sterling

   The explosive  growth of  personal computer  use in  the last decade has
opened up  a new universe of research, teaching, learning and communication
in a  brave new  world world  known as  "cyberspace"; an  almost completely
unregulated universe  of "virtual  space"  consisting  of  home  computers,
telephone lines, and connecting mainframe computers.  Cyberspace is growing
at an  exponential rate,  as more  and more  institutions, governments  and
organizations get  "on-line"; even  long-term cyberspace  residents can  no
longer keep  up with  the rapid  advance  of  this  "electronic  frontier".
Formerly a  primitive "meeting  place" for research scientists and computer
programmers, cyberspace  has grown  to embrace  doctors, lawyers,  artists,
writers, and many more.
   But with  all the  many positive  aspects of  the "electronic  frontier"
(including, we  hope, this  journal!), there  have  arisen  the  disturbing
parallel trends  of computer viruses, hackers, "phone phreakers", and other
computer outlaws.   Although  "computer crime"  has been widely reported in
the media,  it is  still very  poorly understood by the general public.  In
part this  is because  of the  enormous technical  complexities of  many of
these computer  crimes; but  it is  also partially  due to  our  persistent
misunderstandings of the social milieu in which computer criminals live and
work.   Most of us do not understand UNIX TCP/IP protocols, to be sure; but
we also  canot conceive  of just  why these "systems invasions" take place.
If hackers  do not  steal anything, just what do they gain by breaking into
computer systems?   Should  we be  concerned if  a hacker  "looks around" a
system but alters nothing?  And if so, what should we do?
  Bruce Sterling (1954-) has attempted to answer some of these questions in
his latest  work, The  Hacker Crackdown: Law and Disorder on the Electronic
Frontier (New York: Bantam Books, November, 1992).  Sterling's expertise in
the world  of cyberspace  is  well  known.    A  self-described  cyberpunk,
Sterling is  a Texas-based  science  fiction  writer  and  popular  science
journalist, and  has been  personally involved  with many  of the principal
figures in  the "electronic  frontier".   Sterling  edited  the  definitive
fictional anthology  of  the  new  movement,  Mirrorshades:  The  Cyberpunk
Anthology, and  was a co-author, with cyberpunk novelist William Gibson, of
The Difference Engine (1990).  Sterling's experience has been well employed
in his latest book.
   The Hacker  Crackdown  deals  ostensibly  with  the  massive  May,  1990
crackdown on  computer pirates  known as  "Operation  Sundevil",  in  which
American law  enforcement agents seized 40 computers, closed down scores of
bulletin boards, and arrested four computer operators.  Sterling tells this
story from  several different  perspectives, describing the high-tech world
of computer  cyberspace as  seen by  not just  hackers, but  also  science-
fiction writers,  lawyers, civil libertarians, politicians and police.  But
the hacker  raids of  1990 are  at best  only a  small part  of this story;
Sterling excels  in showing  us the  arcane, hidden  world of  the computer
hacker, carefully  explaining his  or her  methods, motivations,  styles of
interaction, and  group behaviour.   This  is  not  as  "how-to"  book  for
hackers; it  is better  described as  a social map of the hacker hierarchy,
showing how  members change  from one  subculture to  another, and  how one
"moves up"  the scale  from simple  telephone  fraud  to  complex  computer
network espionage.  Sterling also deals with telephone and computer network
problems based on internal system flaws, not hacker interference; the 1990-
91 failures  of AT&T  are perhaps  the best examples.  The Hacker Crackdown
explains these  rather  mystifying  network  "glitches"  with  clarity  and
   Sterling is at his best when he deals with the underlying motivations of
the computer hacker.  Though they may go to extraordinary efforts to "break
into" computer  systems, theft  is usually not their motive; most are after
information, and  their forged  access codes and copied passwords represent
"bragger's  rights"   more  than   "stolen  goods".    Sterling  is  to  be
congratulated for  explaining so  clearly how  hackers ply their trade, and
how the successful practice of one type of computer fraud leads to another.
Sterling even  provides  a  chilling  "personal  example"  of  the  typical
hacker's approach  to life;  while waiting  outside  a  closed  meeting  of
computer security  workers, he  raids a  company trash can and reconstructs
from discarded receipts and torn letters an elaborate "personal history" of
his intended victim (pages 197-201).
  Sterling's book is really a history of the "hacker mentality" in the last
ten years; he sometimes reaches further back, but the results are usually a
bit disappointing.   Sterling  is, after  all, a science fiction writer and
journalist, not  a historian.   The  Hacker Crackdown  begins, for example,
with a  short history  of the  invention of  the telephone  (pages 4-9)  by
Canadian-American inventor  Alexander Graham  Bell (1847-1922).   There  is
only a  brief discussion  of the  enormous technical,  social and  economic
problems Bell  and his backers overcame in developing a workable "telephone
system"; and  there is  no mention at all of the telephones being developed
by rivals.   One  of these,  the American inventor Elisha Gray (1835-1901),
filed a  caveat on  his telephone  the very  same day Bell filed his patent
(February 14,  1876), and  is often considered to be the co-inventor of the
telephone system;  but Sterling says nothing about him, or indeed about any
other rivals.   His  own "Chronology  of the Hacker Crackdown" has a single
entry for  Bell (1876),  one for  telephone restrictions (1878), and then a
yawning gulf of six decades to his next entry: the Futurians of 1939.
   The "Futurians"  were a  literary group of science fiction afficionados,
whose membership  included such leading figures as Isaac Asimov (1920-1991)
and Frederick  Pohl (1919-).  In 1939 the Futurians were raided by the U.S.
Secret Service,  who suspected  that their mimeographs and private printing
presses were  being  used  to  do  more  than  just  print  science-fiction
magazines; rather,  they were  suspected to  be counterfeiting  money.  The
raid was  a disaster;  no forged  currency was  found,  and,  according  to
Sterling, the Futurian House was subsequently left alone (page 150).
   Sterling is interested in this case because he feels it parallels the US
Secret Service  1990 hacker crackdown of science fiction publishing company
Steve Jackson  Games.  Both were misunderstood innocents, Sterling charges,
whose dabbling  in  the  "fringes"  of  publishing  technology,  and  their
connections with  disreputable science-fiction  writers, ultimately  led to
their legal problems.  Sterling tells us little about the Futurians, but it
is clear  that they  were involved in another type of "forbidden scientific
knowledge" that  was understandably  of  great  interest  to  the  American
government: atomic energy.
   Had Sterling  probed deeper  into this  part of his story, he would have
found a  great deal  of evidence  to further  his  belief  that  government
attacks on unregulated and technically literate groups like science fiction
writers frequently approach paranoia.  He would have seen that the American
government employed  extraordinary  means  to  restrict  public  access  to
knowledge about  nuclear energy  in the  period 1939-45,  to the  point  of
closing down  science fiction  magazines, pulling  technical journals  from
library shelves,  asking librarians  to report citizens who requested them,
and censoring  magazines, newspapers and radio, forbidding the use of words
like fission,  uranium, atomic power, and so on.  There are many historical
parallels between  institutional efforts to control atomic knowledge in the
1940s and  computer knowledge  in the  1990s; but  this story has yet to be
   Sterling also  briefly glances at the United States' Secret Service, and
its role in stopping computer crime; here, he argues that there are uncanny
resemblances between  its handling  of 19th century counterfeiters and 20th
century hackers  (pages 173-176).  Sterling recalls that in 1865, before US
treasury bills became standardized, there were over 1600 different types of
paper currency,  all issued  by local  banks; in  essence,  there  were  no
standards, and it was very difficult to spot faked bills, as counterfeiters
were often  "technically skilled  printers" who  had previously  worked  in
legitimate banknote  companies.   "Like a  badly guarded node in a computer
network," Sterling  says, "badly designed bills were easy to fake and posed
a security  hazard for  the  entire  monetary  system"  (page  173).    But
centralizing the  money supply  by instituting  one currency  only made the
problem worse;  crooks  soon  learned  to  counterfeit  the  US  Treasury's
"greenbacks", and the race between cop and crook was on again.
   The Secret  Service responded,  Sterling says, in much the same way they
successfully prosecuted  computer hackers  in 1990's  "Operation Sundevil";
making many  arrests,  working  informally  and  outside  the  bureaucratic
regulation  of   local  police   departments,  and  driving  the  criminals
underground.     This  is   the  most  competently  handled  of  Sterling's
"historical asides",  but one  might  well  question  (1)  whether  network
centralization has  made computer fraud worse, or just more publicized, and
(2) if there is really that much resemblance between the enormous number of
800 "boodling" (counterfeiting) arrests made between 1865-69 and the hacker
arrests made in 1990?  Only time will tell; but recent police crackdowns on
hackers do not seem to have the momentum of the 1865-69 campaign.
   Sterling's The  Hacker Crackdown is an admirable attempt to document the
very complex  world of  the electronic  outlaw.   It  is  written  for  the
interested lay  reader, rather  than the  computer specialist;  so there is
very little  "computerese" or  technical jargon,  and  no  bibliography  or
endnotes.  Still, Sterling more than makes up for this by supplementing his
account  with   his  considerable   "inside  knowledge"   of  the  computer
underground, and  provides  many  "personal  touches"  that  make  this  an
enjoyable (albeit  scary) book  to read.   You will probably not agree with
all of Sterling's arguments, but one thing is certain; you will never be as
complacent about computer security again.


                         Information for Authors:

   The HOST Journal welcomes submissions from researchers in all aspects of
the history  of science and technology.  We publish articles, book reviews,
bibliographies, works  in progress and news of general interest to those in
the profession.   The HOST Journal is published twice a year (Spring/Summer
and Fall/Winter),  and  appears  in  both  printed  and  electronic  forms.
Contributions are  welcome in either English or French; all research papers
will be refereed.
   Contributors may  submit their  work in either print or electronic form.
Printed manuscripts  must be  typed, double-spaced with inch margins, on A4
paper (8+  X 11");  figures must  preferably be provided as 8 X 10" prints.
The original  must be  submitted along  with two  photocopies.   Electronic
submissions on  disk (in  duplicate) may use either IBM, Apple or Macintosh
formats; they may be in either Word Perfect, Microsoft Word, or ASCII text.
  All research articles must include an abstract, in 250 words or less, and
a short  (under 200 words) author biography.  Printed submissions should be
sent to the editors, at the following address:

     Institute for the History and Philosophy of Science and Technology
     Room 316, 73 Queen's Park Crescent, Victoria College,
     University of Toronto, Toronto, Ontario, Canada           M5S 1K7.

  Electronic contributions may be either mailed, or submitted by Electronic
Mail through INTERNET, at the following addresses:


   Submissions should  follow the  style of the Canadian Historical Review,
and the spelling of either the Oxford English Dictionary or Le Dictionnaire
Francais  Larousse.     All  correspondence  concerning  papers  should  be
addressed to the editors.  Manuscripts will not be returned, but copyrights
remain with the authors.

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