WHEN HE was appointed in March as independent counsel to investigate the HUD scandals, Arlin Adams said that he accepted the job with the understanding that the investigation could be undertaken and completed in a matter of months. Since then, the probe has been expanded at the request of Attorney General Thornburgh so that three HUD programs, instead of one, will be probed and the number of people at HUD and other agencies who will be investigated greatly increased. On Tuesday, the housing subcommittee of the House Government Operations Committee asked Mr. Adams to broaden the inquiry yet again, and chances that the investigation will -- or should be -- completed this year, are fading.

The subcommittee request demands attention. It was signed by every member of the panel -- five Democrats and three Republicans -- each of whom has been deeply involved in the congressional aspect of the HUD investigation for more than a year. They have asked Mr. Adams to consider charges in three specific areas: possible perjury by former secretary Sam Pierce in his testimony before the subcommittee; Mr. Pierce's dealings with his former law firm while he was secretary and HUD's management of a coinsurance program that may cost the taxpayers $1 billion. The subcommittee's letter is detailed and supported by documentary evidence.

Mr. Adams can ignore this request, or he can go to the special federal court that appointed him to ask for expanded authority. Clearly, this is the course he should follow. He will need the support of the attorney general to make his case, since, in practice, the court does not authorize an expanded inquiry over the objection of the Justice Department. The point of the law establishing procedures for independent counsel is to remove political influence and bias from criminal cases involving high administration officials. It is an effective mechanism not only when an official is indicted and tried but also when he is cleared of wrongdoing, since absolution from a completely independent investigator is far more persuasive to the public than a clean bill of health bestowed by a Cabinet colleague.

Public confidence is eroded if a probe is less than complete or if it is limited at the request of a politically appointed official. Mr. Adams's investigation, if it is to be thorough and credible, should include these new and serious allegations, and he should have the support of Attorney General Thornburgh in asking the court for expanded authority.