A notice appears on every table in the main cocktail lounge of the Harvard Club of New York: "The transaction of business requiring a conspicuous display of papers and documents is not in keeping with the purpose for which the Club's public rooms are maintained."

Since 1865, the Harvard Club of New York has served, as its charter states, "to promote social intercourse among ourselves and others, our associates and our successors, who have been connected to Harvard University." "Conspicuous displays" of paper or anything else are out of order at this musty, but strong New York institution, one of the more venerable of the many Harvard clubs across the country.

Membership in the club is open to anyone who has graduated from or spent one academic year at Harvard, and, as of 1973, Radcliffe College. People who have received a degree from any Harvard graduate program as well as faculty and officers of the University may also join. About 7200 people, the second highest total in the Club's history, now enjoy membership privileges at the elegant red brick building on 44th St., just west of Fifth Avenue.

Clubs in New York serve a variety of purposes. Many, like the Union and Knickerbocker Clubs, are primarily social clubs serving the Social Register set. They are exclusive enclaves, mostly old fashioned, and, some say, outmoded. Admission to these clubs is difficult and usually requires that the applicant know the "right" people.

The Harvard Club may once have been one of these "social" clubs, but it no longer is. While the admissions committee still rigorously adheres to the nominating procedure, requiring a nominator, a seconder and two letters of recommendation, just about any Harvard graduate who wants to join the club may do so. The ambience of prosperity and old-world decorum has not completely disappeared, however, despite the relative egalitarianism.

People usually say they have joined the club for its reasonably priced facilities and convenient location, rather than for its social pretensions. There are eight squash courts, a small gymnasium, banquet facilities, meeting rooms, a library, a restaurant, several rooms for overnight accommodations, as well as Harvard Hall and the Grill Room, two large rooms filled with comfortable leather chairs where one can sip cocktails at any hour or just take a snooze in the wood-paneled serenity.

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"My father went to Princeton and he told me the only reason he could think of to go to Harvard was the Harvard Club, which was the nicest club in New York," Walter N. Rothschild Jr. '42, president of the Harvard Club in 1978, says.

Rothschild says he did not go to Harvard because of the club, but he still readily concurs with his father's evaluation. From his office less than one block away from the club, where he works for a variety of businesses and charities, the former president of the Abraham and Straus department store chain views the club as primarily a service facility for people who have a common Harvard background.

"The club has a social purpose basically, and it does maintain ties with people to the College and University, which many of the members seek. I think they rather like the idea that it is a club of Harvard people. People just like it, it's got a long tradition, it's a nice building and it has always had quite a lot of character," he says.

The club's "character" is most evident on the ground floor of the seven-story building. The exterior is modest, consisting of a simple brick facade with the flags of the United States and Harvard flying side by side. The front is an inadequate preparation for the imposing interior spaces that loom therein.

In the entrance foyer, there is a prominent reminder that men should be "properly attired in necktie and jacket at all times," and women should limit their wardrobe to "dresses, pant suits or skirt suits."

"We have trouble policing the dress code, especially among the younger members," Duane Chenier, executive assistant manager, says, but violators seem few and far between.

Straight back from the entrance is the Grill Room, the main cocktail lounge. Rich wood paneling surrounds a room filled with leather chairs, backgammon sets and muted conversation. Brooks Brothers and J. Press (both stores are about a block away) seemed to have clothed every patron of this dignified enclave.

Harvard Hall, the building's most magnificent room, lies just to the rear of the Grill Room. During the day, huge bay windows provide dramatic illumination to the hall, which is used for speeches, receptions and large dinners. Harvard Hall is the unmistakable work of late-19th century architect Stanford White, who also designed the Freshman Union. The hall is remarkably similar in style and scale to the main dining hall of the Union, but in atmosphere the two couldn't be more different. An immense elephant head watches over the dour solemnity of Harvard Hall, silently observing a room where time seems to have stood still around the turn of the century.