The Case of the Cooling Corpse

The main details

THE VICTIM

• Found in his study
• Initial body temperature was 88 degrees Fahrenheit at 4:30am
• liked his room warm and usually had the study at a temperature of 76 degrees Fahrenheit
• Two hours after the first reading the victims body temperature was 85.8 degrees Fahrenheit

• wife: left theater at 10:30pm and got home at 11pm
• butler: left pub at 10pm got home at 10:05pm
• partner: got home at 10:30pm after a evening at the office
• the room temp was 76 degrees
• the initial temp was 88 degrees
• the temp after 2 hours was 85.8 degrees
• body temp at the time of death would probably be around 98.6 degrees
• the equation we will use to find the amount of time that has passed since his death would be T-Ts=(To-Ts)e^-r2

Finding The Time Of Death

• first we fill in the numbers to find r ,the rate at which the body cooled, in the equation using the initial and second temp reading of the victim

85.8-76=(88-76)e^-r2

• now we simplify it a bit

9.8/12=12/12e^-r2

.817=e^-r2

• now we use natural log to separate the -r2

ln.817=-r2 lne (natural log of e is one so it can basically be canceled out)

-0.2021/-2=-r2/-2

0.10105=r

Conclusion

The initial temp was taken at 4:30am

so that means the victim died at 10:15pm so that instantly points to the partner because the butler was home by 10:05pm and the wife left the theater at 10:30pm. the partner must have snuck into the victims home on his way back from the office and murdered him and left to arrive home by 10:30pm

• now that we have the rate we can find the time in between from when the body was at 98.6 to 88 degrees son now we just plug in 98.6 as the initial and 88 as the second and we can plug in the rate and find time so same concept different numbers

88-76=(98.6-76)e^-0.10105t

12/22.6=22.6/22.6e^-0.10105t

ln0.5310=-0.10105t(lne)

-0.6330/-0.10105=-0.10105t/-0.10105

6.26=t

• now we have to convert the decimal to minutes so i cross multiplied and found that it was 15 minutes
• so that means the murder occurred 6 hours and 15 minutes before the initial temp was taken

It was a dark and stormy night . Holmes and Watson were called to the scene of the murder by Inspector Lestrade of the police. The victim was a wealthy but cruel man. He had many enemies.

THE SUSPECTS

The most likely suspects are the wife, the business partner, and the butler. Each has an equally strong motive. Each also has an alibi.

The wife claims to have spent the entire evening at the theater across town. She was seen leaving the theater at 10:30pm and returned home at 11:30 going straight up to her bedroom. Her return was verified by the upstairs maid.

The business partner claims to have spent the evening working on papers at the office. His wife and household staff verified that he returned home at 10:30 p.m.

The butler was on his night off. He claims to have been at the local pub until 10:00 p.m. The butler returned to his quarters above the carriage house at 10:05 p.m. and did not leave. This was verified by the other servants.

The Case of the Cooling Corpse