65 
of Edinburgh , Session 1872-73. 
reached ; accordingly the ice was then scraped off from the 
bottom of the flat dish, and the time noted. An experiment 
usually lasted about one hour. The thickness of the substance 
was measured and also that of the ice formed. 
Let 0 1 be the temperature of the ice-cold water, 0 o that of the 
freezing mixture, and 0 that of the boundary between the substance 
examined and the ice formed. 
Let x = the thickness of ice formed, 
a = „ substance examined, 
h = conductivity of ice, 
,, the other substance. 
Then the flux of heat being F, 
F = k a = k 
a 
0,-0 
x 
0, - go S0_ 
a x ~ a x 
k + \ l + k. 
Also, adopting the same notation as before, 
F = — ■ S.L. 
dt 
. SO dx 
a x ~ dt 
ic + h x 
tSO __ a 
sx. = i x + w, 
k = 
ax 
tSO x?_ 
SX. “ 2 A 
The last term in the denominator is always small for a non- 
conductor, and if ever it becomes large, we may be sure that this 
mode of experimenting is not available, since the temperature will , 
not be in a permanent state. 
In examining solid bodies, it is well to immerse the solid body 
itself in the water. Moreover, in this case I employed a convenient 
vessel to contain the freezing mixture, consisting of a funnel-shaped 
