116 CH. vs on the Contractional Hypothesis. 
Assuming temperature to be dependent upon the value of 2, : 
the rate of variation would be expressed by the first differential 
coefficient sh whose value, acccording to Fourier, is 
‘ Crh 
ae 
ae nxt ae 
while the actual mets at that point would be 
5 
ere sala 
a= 
* 
iis of = and T, it is first necessary to assign some value 
to x, the = insti of conductivity. To find this Thomson 
vhich: expressed a “simple harmonic,” or vibration of. tempera- 
ture. By comparing the amplitudes of the annual vibrations 
at different depths, the value of the conductivity was deter- 
mined * for the materials experimented upon. For a mean 
value of », Thomson took 400 as the most probable one; the 
units being the foot, ee degree F°, and the year. This value, 
substituted in the first equation, gives 
ox 
dx 35-4" Rae 
It is also necessary to find some value for V, a matter of 
some difficulty. In the present case this will represent the 
maximum temperature of the interior at the beginning of the 
* That is, the value in terms of its specific heat. The <—ehe deter- 
mined by Regnanit from. blocks sent to him for that purpose. oe 
a2 
~~ 16008 
