The fourth Lord Peter mystery.
It opens with a bit of unpleasantness indeed. At the club on Armistice Day, Lord Peter is one of the witnesses to the discovery that one member had died; his body had sat before the fireplace for certainly hours, Furthermore his grandson cracks up over it, which the younger members -- who had fought, like George, in World War I -- can take evenly, but it distresses the older ones.
Shortly thereafter, he learns that the man's sister had likewise died that morning -- and then that she had left a will where all turned on which had died first. Lord Peter is asked to help investigate the matter, informally and all that, given that investigating murders gives him some experience.
The plot unfolds from there. It involves a woman's painting with very poor skill, ductless glands, a quick engagement, the question of what the man had eaten before he died, a romantic story about a girl announcing over breakfast that she had gotten married that morning -- and when she was engaged to another man with the wedding date set, a man trying to influence his grandfather into thinking better of his younger brother, and much more.