THERE WAS a story in the Style section of The Post the other day about the arrival of the freshman class at Brown University. That isn't the sort of thing that's usually covered by out-of-town papers, but in this case the class includes Amy Carter, daughter of the former president; Cosima von Bulow, whose father was recently acquitted in a famous trial; Laura Zaccaro, daughter of Geraldine Ferraro, and Vanessa Vadim, daughter of Jane Fonda.

A spokesman for the university, asked how Brown had the good fortune to have attracted four such well-known freshmen, replied: "The obvious reason is that this is a good school. There are 13,500 others who apply to this place and are equally enthusiastic." Not all 13,500 are celebrities, of course, but Miss Fonda put it well when she said Brown is "getting to be a hotter and hotter campus." In other words, it's the place to be this year.

But with the lifespan of the average American trend being somewhere between six hours and six months, will it be the place to be next year, or will the focus have moved on to Harvard, the University of Minnesota and then perhaps to some tiny and suddenly overcrowded normal school on the western plains where socially prominent young men and women will have to fight their way to class through howling sandstorms? Probably so.

In the meantime, this year's freshmen will be left behind to complete their four-year course of study in a place that has become a social wasteland. The only alternative would be for them to transfer every semester or so to whatever campus is currently fashionable, acquiring along the way a smattering of knowledge in such areas as mining, agriculture, oceanography and French literature, along with -- should one of the service academies be briefly in favor -- an obligation to serve five years in the Navy.

This is the sort of thing that happens when colleges begin bragging about the number of celebrities they enroll. It makes us wonder: whatever happened to football teams as the measure of a great university?