From the outside, Yale's Payne-Whitney Gymnasium looks like a cathedral. On the first floor it resembles the great hall of a medieval castle, and on the second floor there is a trophy room that looks like the grand council chamber in a movie version of Hamlet. The only thing which gives Payne-Whitney away as a place of athletics is the faint odor of perspiration which pervades the whole place.

Probably the best way to find out why Payne-Whitney is the greatest gymnasium in the country is to take an elevator to the top of its neo-Gothic tower and then work down.

The tenth and highest floor is a solarium. It is set under a system of skylights and is bounded on four sides by the complicated masonry which inevitably goes with Gothic architecture.

Two consecutive floors below are devoted to boxing enthusiasts. The ninth level contains a punching bag room and by the eight floor, the tower has widened enough to allow space for five boxing rings. Pictures of greats of pugilism surround the rings, perhaps for aesthetic reasons, or perhaps for inspiration.

The seventh floor is a court for fencers and the sixth floor is a wrestling room. None of these facilities is anything any big university gym does not have. Payne-Whitney just has more of them.

A fifth floor, the last in the tower, harbors an exercise room with mats, ropes, swedish boxes, and all sorts of other gymnastic equipment. It isn't until the fourth floor that the gym widens out and shows what its got that other gymns don't have. The fourth and third levels contain squash courts, three swimming pools, exercise rooms, steam rooms, and every conceivable gymnastic device that athletic directors at Yale have been able to think of.

The gym even has a vault like door on every floor that opens up to chute for soiled towels. A lady visitor to the gym once said to her date, when she first spotted one of the towel disposal doors, "What is this, another secret society?"

When it was abuilding in the 30's, Payne-Whitney cost Yale about $5,000,000 unequipped. Now the cost of building a similar gym would run to about $18,000,000.

Its three pools provide swimming facilities for about 200 men each day according to Hob Kiphuth, Yale's swimming coach and former director of athletics. One of the three pools is an exhibition pool set in an amphitheater whose almost verticle rows of seats accommodate about 2200. A movable concert partition between the two practice pools allows adjusting of their lengths.

The gym can hold about 1500 people at a time though this limit is never reached. During the winter, however, 45 percent of Yale undergraduates exercise there three times a week and during other seasons, 35 percent make use of the stone wonder.

So ample are the facilities in Payne-Whitney that New Haven's citizenry are permitted to use it as a place to exercise. All freshmen generally use the gym between Thanksgiving and spring vacation when they have to fulfill their physical training requirements.

Probably the only objection that Yale undergraduates can muster toward their gym is that it has only three-basketball courts, far too few in comparison with the abundance of everything else.