After a four day picketing action, waitresses at Cronin's Restaurant on Mt. Auburn St. have scored their first victory in recognition of their new union.

James E. Cronin, owner of the restaurant, agreed yesterday to recognize the Harvard Square Waitresses Organizing Committee (HSWOC) as the "sole and inclusive bargaining agent for purposes of collective bargaining with respect to wages, hours and other terms and conditions of employment."

Cronin declined comment last night except to say that he hoped for a rapid return to normalcy at his restaurant.

The waitresses employed by Cronin will submit formally the terms of their contract today. Negotiations between HSWOC and Cronin will begin at 1:30 p.m. Friday.

The group's demands include: a minimum wage of $1.35; a 15 per cent tip included in the bill; release from the responsibility for unpaid checks; sick pay; health insurance; overtime; a one week paid vacation for employees of one year or more; breaks; abolition of the uniform for which they pay; equal distribution of customers by number and protection by the management from harassment by customers.

Until Cronin's decision yesterday, the waitresses had urged a boycott of the restaurant. The union is now asking citizens to patronize Cronin's to demonstrate support for their demands. Patricia Welch, a waitress, said yesterday that Cronin expressed a willingness to work out a contract in response to their demands.

If however, negotiations are unsuccessful, the unionized waitresses may now legally strike. They will also be able to ask the teamsters union to halt deliveries to Cronin's.

It was Cambridge City Councilwoman Barbara S. Ackerman who contacted Cronin on Sunday and advised him to sit down and bargain with HSWOC. Members of HSWOC hope that both she and a prominent member of the National Organization of Woman (NOW), which has been serving the group in an advisory capacity, will become permanent board members of the new union.

Several waitresses at Cronin's said yesterday that they hope to bring other waitresses employed by restaurants around the square into the HSWOC. Kathee Allen and Stephen R. Domesick, attorneys who have aided the waitresses at Cronin's in their effort to unionize, said they have made themselves available to other waitresses for legal assistance.

The waitresses who founded HSWOC have not made clear why they chose to form their own union rather than join the appropriate AFL-CIO affiliate.