After agonizing for two weeks, the House ethics committee finally did the right thing by deciding today to investigate possible misconduct by House Speaker Jim Wright.

Though the investigation could be embarrassing at a time when Wright is about to preside over the Democratic National Convention next month, the probe should be less awkward for Wright and the Democrats than no investigation at all.The need for an investigation should be clear from the fact that questions about Wright's conduct are being raised not just by his political enemies but by Common Cause, a non-profit liberal group that pushes for tighter standards of ethics in government.

While it's much too soon for the public to pass judgment on Wright, at this point the case against him looks damaging.

By using a member of his congressional staff to help him write a book, Wright may have violated the law as well as House rules. Those rules forbid compensating employees from public funds to perform non-official, personal, or campaign activities on behalf of a member. Beyond that is the question of possible public fraud when an employee whose salary comes from tax funds is diverted from his regular duties to work on a project involving personal financial gain.

Questions about the book also center on the unusually high royalty - 55 percent, which is four to five times the normal fee to authors. The book was published by one of Wright's friends, who was paid more than $250,000 by the Speaker's campaign committee for re-election services performed during 1985-86. Under the circumstances, there's room for wondering if the deal was a scheme to convert campaign gifts into personal income.

Moreover, by helping two oil companies, Wright may have broken a House rule barring members from improperly using their political influence for financial gain.

Anyway, the decision by the House ethics committee marks the first ethics probe of a House Speaker in this century. But a worse precedent would have been set if the committee had avoided investigating someone under as big and dark a cloud as the one hanging over Jim Wright.