7 - The Case of the Cooling Cadaver—Solution

Summary

To: Inspector Vance McFrito

From: Math Iz Us

Subject: Calculation of the time of death of Lord Boddy

We present below our estimation of the time of death of Lord Boddy, who passed away sometime on the night of June 23-24, 20xy, as the result of a severe blow to the back of the head administered with a heavy brass candlestick. Since only one suspect failed to have an alibi at the time of death, we can therefore conclude who committed the murder.

We accuse Professor Prune of murdering Lord Boddy in the study with the candlestick at approximately 11:28 PM on June 23, 20xy. The reasoning that led us to this conclusion follows.

Let T denote the temperature of the study. (All temperatures will be measured in degrees Celsius.) According to evidence presented by Sherlock Marples, and because of the precautions taken to keep the study unoccupied throughout the investigation, we may assume that T remained constant throughout the period of the investigation.

Let t denote the number of hours elapsed from the time of the murder. Let a denote the number of hours from the time of the murder until 1:30 AM. Let C(t) denote the temperature of the corpse t hours after the time of the murder. Let y{t) denote the difference in temperature between corpse and study t hours after the murder.