At the student bookstore of Goucher College, a few miles north of Baltimore, you can buy an ashtray that reproduces an old cartoon from The New Yorker. It shows three indignant matrons sitting in a restaurant, before a wall lined with pennants from colleges noted for their football prowess: Michigan, Georgia, UCLA, Iowa, Tulane, Tennessee, Mississippi. Pointing to the wall, one of the women accosts a passing waiter: "And where may I ask is Goucher?"

That punch line is about to lose its punch. Goucher isn't likely to line up with the intercollegiate football powers, but it is going to do the next best (or worst) thing: This century-old women's college has decided to admit men. As the result of a decision made last week by the school's board of trustees, in the fall of next year Goucher will no longer be a single-sex institution, reducing to 103 the number of American colleges that accept women only. At many of those 103 schools, administrators will be watching Goucher's transition with interest and apprehension, for as Goucher goes, so, too, may the rest of them go.

It's not that Goucher is the first or the most famous women's college to turn coeducational; since 1974 more than three dozen others have done so, the most notable being Vassar. But there are several reasons why Goucher's decision is disproportionately significant. First, its excellent academic reputation has up to now been sufficient for its survival as a women's college. Second, in recent years it has repeatedly declined to go coed, has rejected an overture to be swallowed up by Johns Hopkins University and has acquired a national reputation as a defender of single-sex education. Third, it is one of the top three or four women's colleges in Maryland, Pennsylvania and Virginia, which among them have a quarter of the nation's all-female colleges.

As all of this should suggest, Goucher's decision did not come easily and was not made with an excess of enthusiasm. Many people at Goucher, as at the surviving women's colleges, strongly believe that young women can learn and mature more effectively, as well as gain greater confidence in their capacity for leadership, in an atmosphere in which they do not have to compete with young men. Supporters of single-sex schools argue that their purpose is not to exclude men but to create an environment in which women, who are at a distinct disadvantage in many quarters of American society and economic life, can acquire the tools to attain genuine equality. In the coeducational colleges and universities, they argue, there are too many distractions for women, and men are permitted to capitalize on the advantages society confers upon them.

There is doubtless a great deal of truth to these arguments, and many at Goucher still believe them; in fact one of their most articulate advocates has been Goucher's remarkable president, Rhoda Dorsey, whose leadership has put that of most major-university presidents to shame. But they are arguments that, however justifiable and appealing, simply run counter to the altered realities of the day. Those realities, which the administrators and trustees of the 103 remaining women's schools know full well are staring them in the face, are:

*The finishing school is dead. With the exception of a few institutions in the South that still cater to the region's moonbeamed upper crust, women's schools are no longer expected merely to give students a veneer of genteel culture for their once-traditional roles as wives, mothers and hostesses. Women who go to college now expect just what men do: educations that will help prepare them for careers and, if they are serious students, for rewarding intellectual lives. That expectation has nothing whatever to do with finishing schools.

*With the baby boomers now matriculated, college enrollment is in a period of decline in which the smaller, less prosperous colleges are going to face dire prospects. Unfortunately, many such places are private women's colleges; Goucher, though scarcely impoverished thanks to an endowment of $45 million, has seen its enrollment drop more than 15 percent over six years, an alarming figure considering that its enrollment was small to begin with. The schools that survive will be those that can find ways to make themselves more attractive to more students; for women's colleges, one obvious recourse is to admit men.

*Coeducation is the order of the day. Fewer than 2 percent of girls now in high school are interested in attending women's schools, which is about as close to the bottom of the barrel as you can get and still keep those schools in business. It is quite possible that there is no longer a role for many of the women's colleges, in which case they should simply close their doors; but for those with good reputations, modern physical plants and strong faculties, coeducation is surely a more appealing fate than extinction.

*Like it or not, the longings of youthful sexuality are no longer sufficient reason to keep young men and women apart. The excesses of the '60s and '70s seem to be well in the past, thanks to the alarm caused by various sexual diseases and a slight trend back to a sterner morality, but students who want to do what they want to do have very little difficulty, these days, doing it. If anything, a good case can be made that single-sex schools heighten sexual tensions and appetites, thus intensifying students' desire to release them. Whatever the case, the women's college is no longer a nunnery, and only the nostalgic can hope to see it preserved as one.

All of this being true, it does not necessarily follow that when a women's college decides to admit men, the men will come flocking. A number of institutions that made the change have not had the desired results and are still fighting prejudice against them among men who "don't want to go to a girls' school." Goucher probably will have less trouble than others. Its long reciprocal relationship with Johns Hopkins has made men a familiar sight on campus for years, its proximity to the booming city of Baltimore makes it attractive to students of both sexes, it has a strong curriculum that has been intelligently reshaped to meet altered student demands without abandoning the higher-education basics, and its name carries no sexual overtones -- it was named, in fact, after a man.

Goucher is likely to make the transition with relative ease, not least because it has administrative and academic leadership of unusual distinction. But the transition must be lamented even as it is applauded. For a century Goucher College has stood for, and most effectively acted upon, the conviction that women are entitled to the best our educational system has to offer. It has stood not for separation of the sexes, but for equality. The new role it is about to assume is an important one, but so, too, was its old one.