A third of the 3 million women who became mothers last year received - in a plain brown wrapping bearing a congressional frank - a free copy of the Department of Health, Education and Welfare's 72-page booklet, "Infant Care."

The infant care manual was mailed out through the good offices of Congress, each of whose members are entitled to send out 3,000 free copies annually. "Infant Care" sells for $1 to the public.

It is one of millions of government publications which members regularly mail gratis to their constituents, a practice which qualifies Congress as the nation's biggest and most unique book club.

It is also an example of the ever-growing cornucopia of Capitol Hill perquisites that give congressional incumbents and important advantage over their challengers at election time.

Another publication, which has a specific allocation of 3,000 copies per year per member, is "Your Child, 1-6." In 1976, some 643,902 copies of this 75-page booklet went out, according to a HEW official.

HEW aides say there is no way to break out of their overall printing costs - of some $30 billion - the specific expenses related to the congressional distributed publications.

At a House Appropriations Committee hearing earlier this year, a Government Printing Office witness said it cost $35,000 alone to distribute the HEW volumes - and that did not include mail costs, since they were sent out under the frank.

One thing is clear, however. The printing costs are not included in either the House or the Senate budget. Instead they are in the HEW appropriation.

Another agency since 1974 by law, bears the costs of printing and distributing publications that members of Congress send out free in the department of Agriculture.

Agriculture, however, has a specific account that ran over $1 million in 1976 to pay for its congressional gift books.

Heading the list in cost and popularity is the Agriculture Yearbook, a volume that will sell this year for $6.50 to the public. By law, Congress will send out 233,450 copies under a formula that gives each senator 550 free ones, each House member 400.

A 392-page, handsomely illustrated together, this year's copy is entitled "Gardening for Food and Fun." With printing completed in mid-October, free copies were being sent off from book that took more than a year to put Capitol Hill beginning last month to constituents in time for Christmas.

Last year's volume cost $443,221 to print according to Agriculture Department officials, who said a final total is not yet available for this year's book.

Along with the yearbook, Agriculture by law also makes available to members of Congress free copies of all the other pamphlets the department produces.

Each member is allocated 10,000 units, and every year some 3 to 5 million publications are sent out free under the program.

The department sends each member of Congress a list of the publications available and that list is mailed to lists of constituents. Each constituent then checks off what he wants, returns it to the member of Congress who passes is on to Agriculture as an order to be filled.

If a member uses up his allocation, he can borrow from a colleague - say from urban district - who has less demand for the farm publications. "Many such trades take place in a year," an official said recently.

Congress has not been shy in producing its own free publications when it wants to.

Each year, the House and Senate have the Government Printing Office turn out a wall calendar that members distribute free to constituents.

According to the 1977 House appropriations hearings, 198,000 calendars were to be produced this year, with each member authorized 2,000.

The cost, including printing and postage, according to a GPO official, was roughly $2 per calendar.

In 1970, the Congress, by concurrent resolution, approved printing of a slick-paper, coffeetable size color picture book entitled "Art in the U.S. Capitol."

At that time, 36,250 copies were produced at a cost of $205,000.

Under terms of the resolution, the Senate got 10,000 copies, the House 21,000 and the architect of the Capitol 4,000.

All those were to be given free to constituents and visitors.

The book proved so popular, illustrating as it did the works of art and other objects in the Capitol, that extra copies were run off and sold to the public for $12.55 each.

When Congress returns in January, a new resolution is planned to permit another printing of this book. Capitol Hill aides, who asked to remain anonymous, say it has yet to be determined how many copies will be authorized and thus how many each member will have available to give away.

"Remember," said one official in the printing office, "next year is an election year."

GPO also regularly turns out a series of small color pamphlets that members keep around the office to give visitors, including "The Capitol" (1,000 per member), "Our American Government" (1,000 per member) "The Working Congress" (998 per member) and "Our Flag" (500 per member).

Over the past few years, however, the appropriations committees in both houses, under pressure to cut congressional costs, have been reducing free volumes given to members.

An expensive, $44.31-per-volume Foreign Policy papers publications, produced by the State Department, was cut out. At one time, 3,000 copies were sent to Capitol Hill.

According to Hill aides, the House Appropriations Committee has asked the General Accounting Office in its annual review of the Government Printing Office to pay special attention to publications distributed free by Congress.

Cuts are expected, but chances are they will come in less popular volumes not the vote-getting baby and farm books.