No Wind of Blame by Georgette Heyer.
Georgette Heyer was an English novelist and short-story writer, in both the Regency romance and detective fiction genres. Her writing career began in 1921, when she turned a story conceived for her ailing younger brother into the novel The Black Moth.

The Plot
Tragedy befalls the Carter family following an eventful visit from a Russian prince and a scandalous blackmail letter. The murder of Wally Carter generates a bewildering mystery – how does one shoot a man crossing a narrow bridge without being near the murder weapon when it is fired? The superlatively analytical Inspector Hemingway reveals his unnerving talent for solving a fiendish problem.
No Wind of Blame is available from
Amazon at https://amzn.to/4qD2q7s
Waterstones at https://tidd.ly/4qHHSee
City Adventurers Solve The Murder at https://uk.bookshop.org/a/3668/9780099493679
The Black Moth: Gossip, scandal and an unforgettable Regency romance is also available from Amazon https://amzn.to/4jlsNfC