While the cover blurb for Formula for Murder promises a "strikingly different kind of sleuth", vanMars (no first name given unless I missed it) is your typical Golden Age amateur; elegant, well-dressed, erudite, a New York City resident with friends in high places. Maybe not typical in all things. I don't recall Philo Vance ever ingesting magic mushrooms to help clarify his thoughts on a case as vanMars does in this novel...
Formula for Murder is a mystery involving suicide. Marcia Graham, a writer for Chic magazine (and presumably vanMars's love interest, although like many detectives he comes across as asexual and the relationship platonic) has been given the unusual assignment of authoring an article dealing with the study of a suicide. Unsure that she can do such a story well Marcia requests vanMars's help feeling that, with his background as a theoretical mathematician, his "scientific, detached attitude" will be a benefit to the writing of the article. Inquiring as to whether a case has been selected, Marcia replies that she'll be guided by circumstance. The next suicide story in the papers will be the one that she'll follow up.
Two days later Marcia has her story; Julian Hare, a former restaurant owner, has leaped from the Brooklyn Bridge in the early morning with two witnesses to his death. After getting the background of the case, Marcia is puzzled. "He wasn't really sick, he wasn't really broke, he wasn't really in any trouble." Even more puzzling is the link to another death. Julian's wife has been involved with an actor who was found murdered later that evening. How are the two deaths related?
Formula for Murder is a short yet solid mystery. vanMars lacks the obnoxiousness that characterizes many other gentleman detectives and the mystery plot, while obvious in some regards, is handled sufficiently well. The book takes its title from vanMars coming up with a formula for murder while in a trance state which, while novel, is basically nonsense.
Pictured is the author photo from the back cover. It's easy to visualize Bill S. Ballinger as vanMars.