310 
Proceedings of the Royal Society 
If an infinite plate be kept permanently heated in layers, each of 
equal temperature throughout — the temperature rising gradually 
from one side to the other — the hypothesis is made that the tem- 
peratures of any three contiguous layers (of equal thickness) so 
adjust themselves that the least possible energy can be restored 
from the system of three. From this it immediately follows that 
if x x be the thickness of the plate, t 0 and t x the (absolute) tempera- 
tures of its sides ; and if the specific heat be the same for all tem- 
peratures between t 0 and t x : the temperature t at a distance x from 
the side at t 0 will be 
—log. h. 
t = * 0 e *1 t 0 
But if k be the conductivity of the substance, at temperature t , 
we have for the flux of heat 
/ = 
k^ oc kt. 
ax 
This must be the same throughout the plate, because there is 
equilibrium of temperature, and therefore 
k oc 
t 
The only published experiments, so far as I am aware, by which 
this result can be tested, are the very valuable series by Forbes 
{Trans. Roy. Soc., Edin. 1864), which are, unfortunately, confined 
to iron. They agree uncommonly well with the above theoretical 
result, as the following short table shows : — 
t 
k 
kt 
290° C. 
0*0164 
4-76 
330° 
0-0130 
4-24 
400° 
0-0110 
4-40 
440° 
0-0105 
4-58 
476° 
o-oioo 
4*76 
561° 
0-0090 
5-04 
No account has, in this abstract, been taken of the alteration of 
specific heat with temperature, which is as yet only approximately 
known, but which is applied in the paper to account completely for 
the increase of kt with temperature. As to the increase of kt at 
