Initiatives for female participation in the membership of certain clubs (for example, the Cosmos Club) seem to be advanced with increasing frequency, undoubtedly prompted by the steady progress of women's liberation. Such aspirations are understandable, but misdirected. What the initiators seem to overlook is the fact that clubs are by nature ex clusive. Persons who decide to form such associations have a perfect right to set up rules that suit them, and they should not be subjected to the challenge of their autonomy.

That women of today are seeking greater opportunities for participation in what is called "a man's world" is, of course, also understandable. But instead of knocking on the doors of exclusive clubs -- which want to maintain their status quo -- is it not more logical that women think in terms of entering in greater numbers such human associations in which they should be represented? To wit: the various branches of government.

There are more women than men in the United States; yet the female population seems to be content to be governed by men in their local councils, in their state legislatures and in their Congress. When it comes to eligibility for election, there is no difference between the sexes.

In a nation where the most precious legacy -- the children -- is largely entrusted to women teachers for guidance and early education, would it not make sense that greater female influence and participation be felt in the halls where the laws of this nation are forged -- that is, laws having to do with health, child care, welfare, schooling and good citizenship? FRED G. SIGERIST Washington

Members of the National Organization for Women are pushing in the wrong direction at the Cosmos Club. They should be rescuing the wives and children who are forced to go there for lunch or dinner. It's a deadly bore.