ON THE CONDUCTIVE POWEES OF VAEIOUS SUBSTANCES. 
815 
when H=^ 4 -^i+^^ 3 + • • ; and writing fj— r— r) for — \ we have 
fH+^- 
P ti 
q tf^-r 
-1 
Let K be the required conductivity of a mass whose thickness is H, and of which the 
extreme temperatures are and as in the divided mass. Then, since the radiating 
power [p) is also the same, 
(art. 1), 
and therefore 
/I i\ p \ 
k — k’ p k 1 
k’ 
and therefore. 
qpYV 
k’ 
k' 
P k 
1 
q pB. 
( 6 .) 
T) • 
As an example of this formula, let us take^=i^ as determined in case (3.) of art. 7 ; 
k . 
and - = -52 (its value for the sandstone used in the experiments), the unit of length being 
one foot. Then 
k' 1 
k' 
1 + 
20 H 
Suppose H = 100 feet, and that there are 100 discontinuities, 
k' 1 
k' 
1 -L 
^•20 
r=l— ^ nearly; 
so that with a discontinuity on the average for every foot, the effect would only be 
equivalent to a diminution of -^th of the conductive power ; and a discontinuity every 
6 inches would be equivalent to a diminution of about iijth of that power, in the parti- 
cular case now selected for illustration. 
9. In the practical application of these researches to the case of the earth’s crust, 
(equation 6.) (art. 8} is so important that it may be worth while to verify it by a some- 
what different process. It appears by equation (4.) that the temperature is entirely 
independent of or Ag? the distances of the plane of discontinuity from the terminal 
planes, since the equation only involves the sum of A, and or A. We may therefore 
conceive the plane of discontinuity indefinitely near to the terminal plane of which the 
temperature is In like manner we may suppose all the planes of discontinuity, in the 
5o 2 
