ON THE CONDUCTIVE POWEES OF VAEIOUS SUBSTANCES. 
827 
, Ji^ h\ hvf 
d!^' h hy hr 
-'‘"i i+*;+-+i;+-- 
( 5 -) 
and if hr and h'r, be each large, according to our first hypothesis, we shall have 
and 
hf! 
ky! 
Jr 
kr 
kjj hy 
dx hr! 
~§~Jr 
d£ 
( 6 .) 
(^•) 
The first of these equations shows that, in the case before us, the quantity of heat trans- 
mitted will be in a ratio compounded of the ratios of the conductive powers, and the 
inverse ratio of the thicknesses ; and the second equation shows that the increase of 
tempeiutm-e in descending, or its decrease in ascending, will be inversely as the thickness 
of the strata, and independent of the conductive powers. 
In the second case, the numerator and denominator of the fraction on the right-hand 
side of equation (5.) may be considered independent of ky and J},^ on account of the 
H' 
comparative smallness of hy and Jy,. Hence, writing for the numerator ^ and for the 
denominator 
H 
K’ 
and 
k ^ 
’■ _ K H' 
,d^ K'’H’ 
dz’ 
dj 
^ _ K ^ C 
K''h'/c, 
dzd 
( 8 .) 
(9.) 
Hence, in this case, the quantities of heat transmitted will be independent of the con- 
ductive powers ; while the rate of increase of temperature descending through any two 
strata situated respectively in the two groups of strata, will be in the inverse ratio of the 
conductive powers. 
16. Let us now examine how far this investigation may apply to the case of the earth, 
assuming the actual terrestrial temperature to be due to the remains of a primitive heat. 
If the earth, considered spherical, were formed of matter of uniform conductive power, 
and the mean temperature at every point of its surface were the same, the surfaces of 
equal temperature would, after a sufficient lapse of time, be spherical surfaces concentric 
with the external surface ; and in the actual case, making due allowance for the differ- 
