THE AMERICAN HOUSE OF SAUD: The Secret Petrodollar Connection. By Steven Emerson. 450 pages. Franklin Watts. $18.95.

IN 1982, Steven Emerson, who had served as an aide on the Senate Foreign Relations Committee, wrote a series of articles for The New Republic to demonstrate that many American businesses were so enamored of their large contracts with Saudi Arabia that they had become unofficial, and unregistered, lobbyists for Saudi interests. Those articles have now been expanded into this book, a full-length compendium, which lists, in elaborate detail, the financial stake of many prominent American corporations, law firms, public-relations outfits and educational institutions in Saudi Arabia.

There is nothing illegal or even tawdry about American trade and support for Saudi Arabia since Saudi Arabia, after all, has been one of the United States' principal friends in the Arab world. But Mr. Emerson seems driven by a conviction that the Saudi connection bodes poorly for the United States, and that those who support the Saudis are somehow tainted by association.

The trouble with the book is that its premise of an all-powerful Saudi lobby in this country seems skewed. Mr. Emerson notes that ''the popular perception'' in Washington has been that ''the Arab lobby pales in significance when compared to the strength and effectiveness of its counterpart, the Israeli lobby - or the Jewish lobby as it is also called.'' He then sets out to show this premise is wrong by ''revealing'' the influence of the Saudis, often covered up by the lobbying of American businessmen who are not officially registered as foreign agents.

But sometimes truisms turn out to be true.

And in this case, I don't think there really is any doubt that Israel has the most efficient, most influential domestic lobby in this country. The Reagan Administration, for instance, never makes any move in the Middle East without consulting with the American Israel Public Affairs Committee, the chief pro-Israeli lobby, and many senators and Congressmen routinely look to that group for guidance on Middle East issues. This is not to say the Israeli lobby wins all the time. In 1981, it made an all-out effort to defeat the Administration's plans to sell Saudi Arabia five Awacs electronic surveillance planes, but failed by a narrow margin.

Mr. Emerson devotes a considerable section of the book to that 1981 vote, and his conclusion seems to be that the big money of the Saudi Arabians prevailed over the idealism of the Israeli supporters. But as one who helped cover that story, there never was much question that the chief reason the Awacs sale was consummated was not because of the Saudi pressure - although it contributed -but that President Reagan put the full weight of his office behind the sale. No arms sale to a foreign government had ever been rejected by Congress. And in 1981, the Republicans in the Senate were in the end not going to let the President down.

The discussion about the Awacs sale virtually ignores the President's impact on the decision. Likewise, in his desire to portray the Saudis as inherently suspect, Mr. Emerson seems to be writing only for the convinced - those who share his distrust of Arabs in general and the Saudis in particular. There is no effort to examine seriously why every American administration has sought to improve relations with the Saudis, and why the Saudis are viewed increasingly as strategically important to the United States. ---- ''The American House of Saud'' was reviewed in The Times Book Review on Sunday, June 23. A second review appears today because the original reviewer had been press secretary and special assistant to Senator J. W. Fulbright, who after leaving the Senate became counsel to a law firm representing the Saudi Government. The Times does not knowingly assign a reviewer who has had close ties with anyone prominently mentioned in the book being reviewed.

photo of Steven Emerson