The all-male Cosmos Club, whose members once included Supreme Court Justices Oliver Wendell Holmes and Louis D. Brandeis, is about to vote for the third time in its 110-year history on admitting women. But for the first time, the leadership of the club has unanimously endorsed the idea. Members of the club are scheduled to vote Saturday afternoon, and although no one will say for certain how the vote will come out, club President Tedson J. Meyers said the question of whether to admit women has become the main topic of conversation among members. Meyers, a lawyer and former member of the City Council in Washington, said that the club currently has about 3,000 to 3,100 members, down several hundred in the past few years. But Meyers denied that the vote on admitting women has anything to do with the decline in membership. ``Membership seems to go up and down,'' he said. Meyers also denied that the vote Saturday is a direct result of a ruling last fall by the Washington Human Rights Office that ``there is probable cause to believe'' that the club's men-only policy violates the city's anti-discrimination law. The office is ready to order public hearings on the case, which could result in the loss of all city licenses and permits, if the all-male policy stays in place. ``It's a matter the club would have taken up in any event,'' Meyers said, although he acknowledged that the Human Rights Office's action did act as a catalyst. And while Meyers confirmed that a Committee of Concerned Members, formed in 1980 to advocate the admission of ``distinguished women,'' still exists, he said that it was not the committee that had put forth the latest proposal to admit women. ``This is the first time the officers and the board of directors brought the proposal forward,'' Meyers said. ``They unanimously endorsed it. They always opposed the idea before.'' The club, located in a mansion on the city's so-called Embassy Row, first voted on whether to admit women in 1973, after 61 members signed a petition proposing that women be allowed to join. The proposal was killed by a 274-203 vote. Again, in 1974, 50 members called for a vote on admitting women. The vote in this round was 407-204 against the proposal. A two-thirds majority is needed to change the club's bylaws, Meyers said. He pointed out that women can, and do, use the club. Female guests of members, as well as wives and widows of members and former members, are allowed to dine in the downstairs dining rooms. But women are not allowed in the second-floor members dining room, except on Thursday and Friday evenings and weekends. Members of the club have included Cabinet members, Pulitzer Prize and Nobel Peace Prize winners. Supreme Court Justice Harry A. Blackmun was a member for 18 years, but resigned last winter. The club was founded by geologist John Wesley Powell in 1878 and originally met in Powell's living room. It now charges a $900 initiation fee and $900 in annual dues.