- Philo Vance, dilettante detective
- John F. X. Markham, district attorney
- Professor Bertrand Dillard, physicist
- Belle Dillard, his niece
- Sigurd Arnesson. his adopted son, professor of mathematics
- Adolph Drukker, scientist, author, and hunchback
- Mrs. Otto Drukker, his mother
- John Pardee, mathematician and chess expert
- J. C. Robin, archer
- Raymond Sperling, civil engineer
- John E. Sprigg, college student
- Madeleine Moffat, a little girl
Locale: New York City
Synopsis: Philo Vance and D. A. Markham are called out to a report of murder on a long narrow archery range, sandwiched between the Dillard home and the Drukker home. The deceased is J. Cochrane "Cock" Robin, and immediate suspicion falls on Raymond Sperling who was present. It is noted that "Sperling" means "sparrow", and the murder follows the nursery rhyme of "Who killed Cock Robin?"
The Dillard house and the Drukker house back up to one another. Professor Dillard lives with his daughter Belle (here is a love triangle, both Sigurd Arnesson and John Pardee enamored of her). Adolph Drukker is a strange sort who prefers to spend his days playing games with the neighborhood kids, and lives with his mother who may have seen the murder.
Other murders follow, with nursery rhyme tie-ins. After each, a note is sent to the newspapers signed "The Bishop".
This is my third read, and each time I like it better. There is a small cast of characters, so it is easy to keep track of the players.
The description of the houses/archery range plan in Chapter 2 cries out for the customary S. S. Van Dine crime scene map. It is even mentioned as being "attached" on p. 28 but it is not there. In my hardcover Collier spiderweb edition it finally appears in Chapter 18 (p. 241). So if you are just starting the book, check ahead to Chapter 18 to see if you have a crime scene map.
The book is heavy with higher mathematics and chess references, but still understandable even if you are neither a mathematician nor a chess player. You can skip the mathematics/chess/footnotes and not lose any of the story; in fact, eliminate them and this could be an Agatha Christie or Ellery Queen plot.
As usual, plenty of irrelevant footnotes take up valuable space. Several times while reading Van Dine I have thought "this footnote can't be real", and looked up some of his references; to find they are factual. If he had left these additional research bits out, he likely could have written several more books!
Chapter XXI ("Mathematics and Murder") can be skipped entirely if you are not into space-time continuums, as it is a lecture on that subject. The only relevant piece is the last sentence.
The dénouement is enjoyable, fooling the reader by seeming to point at one person after another, with a surprise twist on each.
Vance's method of dealing with the killer at the end is an eyebrow-raiser, certainly out of bounds today; but S. S. Van Dine readers are used to the killer never making it to an arrest.