806 
ME. W. HOPKDs'S’S EXPEEBIEXTAE EESEAECHES 
denote the temperature at the distance z from the lower surface, when the temperature 
has become steady. The ditferential equation for the determination of ^ will then be 
£ 
dz 
(!•) 
7 dt 
a constant. 
(2-) 
Jy 
The expression measures the quantity of heat which passes thi-ough a unit of area 
parallel to either bounding surface, in a unit of time. We may conceixe k to be a 
function of ^ or z, but it is here considered constant. It is the quantity which is 
always taken to measure the conductivity, or conductive jyower, of the mass through which 
the heat is transmitted, and which can only be determined for different substances by 
experiment. 
Again, let 4 be the temperature of the upper bounding suifface ; then will the quan- 
tity of heat which radiates from a unit of area of that surface in a unit of time be 
p being constant, and independent of the temperatures 4 and r, at least for considerable 
ranges of those temperatures. It measures the radiating 'power of the upper suifface 
of the mass*. Now since the same quantity of heat must pass through a unit of the 
upper surface as through any unit of area parallel to that surface in the interior of the 
mass, equation (2.) will become 
Integrating again 
and since when z=0, 
and since ^=^2 when z=h, 
( 3 .) 
Kii — 0=Pit2-r)z; (4.) 
If A be known and the temperatures t^ and t be observed, this equation -uill determine 
k . 
-, the ratio of the conductivity of the substance to the radiating power of its suifface, 
which is very different for different substances. If, hoAvever, the upper suifface be 
covered by a thin stratum of any other matter which will assume the temperature of the 
upper surface of the transmitting mass, p will then be the radiating power of this super- 
* I have adopted the approximate law of radiation, as much more simple and convenient than the more 
exact law of Dulong and Petit, and sufficiently accurate for my purpose. All the experiments described 
in this paper aim only at comparative results, and most of them have been made under nearly tlie same 
thermal conditions. Those requiring any considerable accuracy have been made in the form of differential 
experiments. Hence the use of the approximate law of radiation can lead to no error of any importance in 
the experimental results. 
