"This club shall be composed of men . . . the by-laws read.

But if certain members of the Cosmos Club have their way, the signs that read "Members and male guests only" will have to be removed from the stairwell of the ornate stone mansion on Embassy Row where the 101-year-old men's society makes its home.

For the third time in the past decade, one of the nation's most prestigious clubs -- where judges, ambassadors, famous scholars and journalists dine and lounge beneath the portraits of Nobel Prize winners -- has fractured over the issue of admitting women as members.

To do that, all 16 living former presidents of the club proclaim, would lead to "the transformation of one of the world's distinguished men's clubs into a mere luncheon group."

"For a club that pretends to be based on accomplishment and achievement to bar women in this day and age is just bizarre," said one club member and supporter of women's admission. He declined to comment on the record because club rules mandate possible suspension of those who talk to the press.

Letters on both sides of the issue are swirling among the club's approximately 3,000 members, eliciting heated reactions. The club's board has refused to survey the membership on grounds that "its sponsorship of even the most objective poll concerning a 'change in the fundamental character of the club' would be seen by some members as advocacy of such a change," according to some of those who support the admission of women.

So, a group of members headed by John W. Gardner, one-time chairman of Common Cause, and former Supreme Court Justice Arthur J. Goldberg, has sent its own questionnaire to the club's members. Seven hundred people have responded in four days, but the responses remain unopened while the group waits to see if the club will agree to oversee its tabulation.

The insurgent group's efforts have led all 16 living former presidents of the club -- calling themselves "Past Presidents United to Preserve the Cosmos Club" -- to circulate a strongly worded, four-page letter attacking the pro-women forces as agitators and "ethical reformers".

The letter contends that the admission of women would lead to "costly and extensivive alterations of the clubhouse, massive resignations . . . (and) the prospect of epic confusion of male-member and spouse, female-member and spouse, and their guests."

According to the club's bylaws, female guests of male members, or members' widows, may use the club's facilities, and several hundred do, according to the club's general manager, James Lucas.

But the club only accepts as members men who show distinction in the arts, sciences, or public service. It is not illegal for private clubs to restrict membership.

Three U.S. presidents -- Herbert Hoover, William Howard Taft and Woodrow Wilson -- were members. There are photographs on the wall of all the club's members who have won Nobel and Pulitzer prizes, and those whose faces have appeared on postage stamps here and abroad.

The club has accommodations for live-in members, and some members feel an invasion of women would destroy their privacy.

Trying to allay such fears, the dissident group has noted in its letter to the membership that the Cosmos Club's bathrooms could be used by both sexes "in the same way as are those in motels and hotels in which not all rooms are equipped with bath and toilet. Europeans have survived such rigors for many decades."

The group supporting the admission of women includes U.S. Court of Appeals Chief Judge J. Skelly Wright, former Assistant Secretary of State Joseph J. Sisco, U.S. Secretary of Commerce Phillip M. Klutznick, and Alan K. Campbell, head of the U.S. Office of Personnel Management.

The group's letter says that Cosmos Club members "now associate with each other without consideration of race, national origin, age, religion, political affiliation, or other irrelevancies . . . (except) one consipicous criterion irrelevant in this final quarter of the 20th Century: a person's sex. Equity and expediency demand the elimination of this obsolete criterion."

The 16 past presidents retorted angrily in their letter, dated Nov. 3. "Once again we are told, for no clear purpose, that times have changed since the Club was founded . . . Once again our knees are expected to jerk simply because the buzz-words are uttered -- discrimination, exclusivism, eliticism, anti-feminism.

"It is all the old stuff -- with only the new ingredient of threat. . . On two previous occasions the cat did not jump. This time it is an even more supine feline."

The first controversy over the club's admission of women occured in 1973. After voting down a proposal to make women eligible, the Club instead approved an amendment that permitted women guests to use the front door of the Renaissance-style mansion. Previously, women had been restricted to a side entrance. In 1975, the membership refused again to admit women.