ON THE CONDUCTIVE POWEES OF VAEIOUS SUBSTANCES. 
811 
with reference to mercury, on account of its being the substance from which the radia- 
tion took place in all my experiments. The increase of radiation indicated by the 
above expeiiments is in general accordance with the law of Dulong and Petit, but it 
is smaller in amount. 
6. Effect of Biscmitinuity. 
In all the preceding cases the substances experimented on were in unbroken con- 
tinuous small masses. It is important to inquire how far their conductivity is atfected 
by a breach of this perfect continuity. Several experiments were made for this purpose ; 
but before I proceed to state these experimental results, it may be better (as in art. 1) 
to deduce the theoretical results with which they must be compared for the purpose of 
determining the additional coethcient, or constant, which must be introduced on the 
hypothesis that the discontinuity in the conducting substance produces a discontinuity in 
the law according to which the temperature decreases as the heat passes from one 
bounding surface to the other. These sm’faces being supposed parallel and of indefinite 
extent, as before, for a mass of one substance (A), conceive another mass (B) of different 
conductivity, and bounded also by parallel plane surfaces, to be placed upon the former. 
Let ifi denote the constant temperature at which the lower y. 
surface of A (fig. 1) is maintained; that of its upper ^ 
surface ; the temperature of the lower surface of B in 
contact with the upper surface of A ; that of the upper 
surface of B; and r that of surrounding space. I shall 
assume that the quantity of heat which flows through a 
unit of area of the surfaces of junction, in a unit of time. 
^2 
4 
B 
^2 
A 
where q is independent of and Then, since the same quantity of heat when the 
temperature is steady, must pass through each parallel surface, we must have 
( 1 .) 
p being the radiating power of the upper surface of B. We have also (art. 1.) 
and therefore 
C— 
C— 
and 

where A, = thickness of A. 
In like manner we obtain 
h{t, — Q=p{t'^—r)h^, 
where ^ 2 = thickness of B. 
( 2 .) 
(3.) 
