Chapter Two of the Reagan administration's search for women to appoint to the federal judiciary takes us out to Ohio, where Alice Batchelder, a young, conservative lawyer, is being pitted against state Appeals Court Judge Sam Bell for a seat on the U.S. District Court for Northern Ohio. Both she and Judge Bell, not to mention the public, deserve better.

The story begins last March when, there being no Republican senator from Ohio, the state's Republican congressional delegation endorsed two men for two vacancies on the federal bench. The White House picked a former state Supreme Court justice for one vacancy and indicated it wanted to fill the second one with a woman. The Ohio delegation eventually sent Batchelder's name to the White House, along with Bell's, in case she did not pass muster. Two members of the delegation voted against the substitution and remained firmly in Bell's corner.

But Batchelder, 38, who has practiced law 11 years in Ohio, picked up considerable support from conservative leaders in Ohio where both she and her husband have been longtime Reagan supporters. She is a trustee and legal counsel for Birthcare, a group that provides women with alternatives to abortion, and was not opposed by any antiabortion groups. Her opponents, however, criticized her on the grounds that she has limited trial and no bench experience.

It appears now that her opposition has prevailed: an FBI check has begun on Judge Bell, and not on Batchelder, a clear indication that his name is the more likely to be nominated by the White House.

The Reagan administration's record on appointing women to the federal judiciary is nothing short of miserable. It has appointed 77 men to the federal judiciary and only four women, including Sandra Day O'Connor. The Carter administration appointed a total of 41 women to the federal judiciary, including 11 to the Circuit Courts of Appeal, the level just below the Supreme Court.

But what has happened with the Batchelder candidacy illustrates some of the difficulties the administration is running into. President Reagan is hampered by his commitment to appointing judicial conservatives, which, when combined with a sex requirement and experience requirements, severely limits his pool of talent. Further, the Carter administration had a large number of vacancies at one time as a result of the Omnibus Crime Bill, which added 152 new federal judgeships. This gave the administration bargaining room when dealing with Congress, which the Reagan administration does not have.

Early last year, the Reagan administration was considering appointing Judith Whittaker, a Republican lawyer from Kansas City, to the 8th U.S. Circuit Court of Appeals. Whittaker, who was deemed fully qualified by the American Bar Association, became the target of a smear campaign by antiabortionists and conservatives. Her name was swiftly dropped.

That episode increased pressure on the administration to appoint women, and the upshot of that is that both Batchelder and Judge Bell have been treated rather shabbily. Both have been subjected to months of uncertainty. Bell, by conventional standards fully qualified for such a post, found his name being set aside for a judgeship in an overloaded circuit in favor of a woman who has no experience on the bench.

Clearly, this is no way to do business. Assistant Attorney General Jonathan Rose, who has been intimately involved in judicial nominations, believes that part of the problem the administration is running into could be resolved if women's organizations brought the names of qualified women lawyers and judges to the attention of the appropriate members of Congress at the beginning of the nominating process.

It seems unfair, when Congress has such an important role in selecting judges, to place all of the blame for recent appointments solely on the administration. It would seem both Congress and the White House put too much emphasis on traditional political ties and qualifications and not enough on the need to create a diversified federal judicary. Surely, in the case of Judith Whittaker, it was a case of politics scoring a resounding triumph over commitment to women judges.

But, regrettably, no matter how committed Congress and the White House become, it may turn out that despite the surge of women into law schools in the '70s, there are still so few qualified female judicial conservatives that the federal bench under Reagan will continue a steady course of resegregation into a white male club.