IF DR. JOHNSON could turn sleuth, why not our own Dr. Ben Franklin?

Lillian de la Torre's elegant short tales of the detections of Dr. Sam: Johnson, with the Watson-like Boswell at his side, are one of the delightful finds in the mystery field. De la Torre sets a high standard, indeed. with her characterization, historical authenticity, and ingenious plots based on events that well could have happened.

Now Donald Zochert, a Chicago reporter, has attempted to do the same with Ben Franklin. Murder in the Hellfire Club (Holt, Rinehart and Winston, $8.95) is a charming first effort that brings back to life the bawdy 18th-century London of Hogarth.

It's set in 1757, when Franklin, already famous for his experiments with electricity and the lightning rod, comes to London on a business trip on behalf of the colony of Pennsylvania. One night he roisters with some old friends at the Vulture Tavern, a hangout for the Hellfire Club, a group of rakes drawn together for lechery, debauchery, and blasphemy. The next morning the unmarked body of the tavern porter, who turns out to have been a Hellfire Club member, is found dead in a locked room. Soon another brother goes to his hellfire, and Franklin's curiosity drives him to seek the answer to the murders. It doesn't take him long to discover the method (the first murder by electricity?) but he must track down the murderer and his motivation.

Franklin, that shrewd practical man with insatiable curiosity and a wandering eye, is a fine character for a dabbling amateur detective.Murder in the Hellfire Club is a lively period piece of detection marred only at the end, when the plot stumbles over a contrived last-message cryptogram.