Anna Katharine Green 
Mystery of the Hasty Arrow 

An intriguing mystery from the start. A girl dies in a museum, shot in the heart by an arrow from one of the displays. It is such a mystery that it takes Bryce and Stillwater days of painstaking work to find the clues. When they believe they have discovered who did such a thing, they do not trust their own instincts. So many questions that must be answered to the finest detail because if they are wrong it would be a great public embarrassment. Bryce is over 80 in this book and finds the case to be an overwhelming physical and emotional strain almost too much to bear. (Goodreads)