THE CALCULUS OF CSI
Estimating Time of Death
By: Catherine Lipford
The Factors in Estimating Time of Death
 Rigor Mortis– The gradual muscle stiffening that spreads over
the body in the hours after death then fades as gradual as it
started.
 Algor Mortis– The slow cooling of a warm-blooded corpse as it
equilibrates with the temperature or its surroundings.
 Livor Mortis– The dark blue or red discoloration of the skin
caused by the pooling of blood due to gravity. This begins the
moment blood pressure plummets to zero.
**Anywhere from 24 to 48 hours after death, lividity reaches its peak,
the body reaches room temperature, and rigor mortis disappears.
Therefore, estimating the time of death is more accurate within the
24 hours after death. Anywhere from 2 days or more these factors
are no longer valuable in the investigation.
Methods for Estimating Time of Death…..
 The Concurrence Method: Comparing the occurrence of events which
took place at known times with the estimated time of death. Examples
include: a wrist watch stopped by a blow during an assault or the extent
of digestion of the last know meal.
 The Rate Method: Measuring the change produced by a process taking
place at a known rate that was either initiated or stopped by death.
Examples include: the amount and distribution of rigor mortis, change
in body temperature, and degree of decomposition of the body.
Dr. Harry Rainy
 Rainy was Second Regius Professor of Forensic
Medicine at the University of Glasgow.
 He was the first to find and relate a formula for
estimating time of death in the mid 1800’s
 He was also criticized for his lack of knowledge and
understanding in Forensics outside of the medicine
field.
 However, due to the formula having such strict
stipulations, such as, the environmental temperature
had to be a constant 98 degrees, the formula was not
considered further.
Newton’s Law of Cooling
Newton’s Law of
Cooling:
The original formula for Newton’s Law
of Cooling is……
 The rate of change in
the temperature of an
object is proportional
to the difference
between the object’s
temperature and the
temperature of the
surrounding medium.
By using this formula, one can solve for
t which is time, by using
integration. After solving for t, the
equation will be….
Algor Mortis with Newton’s Law
 Newton’s Law of Cooling was
originally applied to smaller
masses with known starting
temperatures, but after deriving
another formula from the
integrated original, one can
apply Newton’s Law with body
temperature to estimate the
body’s cooling rate.
The derivation formula that is
specific for estimating the time
of death of a body is as stated
below.
= time in hours
= Body temperature (°F)
= Room temperature (°F)
The Case of the Murdered Accountant
After a busy evening of income
calculations an accountant was
found dead in his office. At 10:00 a.m. the coroner
measured the body temperature to be 85.6 °F, then again at
12:00 p.m. it was 82.6 °F.
The room temperature was measured to be a constant 70 °F.
*Assuming the body temperature at death was 98.6 °F,
what would the estimated time of death be to the nearest
minute?
Solution…
10hrs – 6.061hrs = 3.93hrs = 3:56
a.m.
12hrs – 8.197hrs = 3.80hrs = 3:48
a.m.
At 10:00a.m. :
Time of death interval:
3:48 a.m. to 3:56 a.m.
Estimated time of death: 3:52a.m.
At 12:00p.m. :
Why Time of Death?
Estimating the time of death is of great importance
to the police investigators working on a murder
case and/or finding a hidden cause of death. It
gives a time interval in which further investigation
is needed. It also allows investigators to rule out a
suspect due to a legitimate alibi during that time
interval. Therefore, the estimation of the time of
death is ranked very high on the to-do list of crime
investigation.
Works Cited

http://webpages.csus.edu/~sac46677/process.htm

http://www.pstcc.edu/facstaff/tlcrossl/1730_4_5.pdf

http://regentsprep.org/Regents/math/algtrig/ATE9/logsResource.htm

http://www.thenewdetective.com/Resources/eZine.html

Snyder Sach, Jessica. Corpse: Nature, Forensic Science, and the Struggle to Pinpoint Time
of Death. New York: Da Capo Press, 2001.

Axelrod, Alan, and Guy Antinozzi. The Complete Idiot’s Guide to Criminal Investigation.
Indianapolis: Alpha Books, 2003.