FOE DETEEJMTN'INa THE EADIATING POWEES OF SURFACES IN AIE. 
389 
which, therefore, in the area occupied by it, the radiation took place instead of the 
radiation from the surface of the disc itself. It will be necessary to examine whether our 
experimental results were sensibly affected by the difference of radiation in these cases 
from the mercury and that from an equal extent of the discs made use of. Thus let 
f*= radius of the radiating disc ; 
g= radius of the centi-al portion where the radiation takes place from mercury ; 
T= temperature of the radiating surface; 
K= reading of the thermometer of the calorimeter, i. e. the temperature of its lower 
smfface, on which the radiating heat falls ; 
then will 
c(T — E) and zit(T — E) 
express the quantities of heat which emanate in air from a superficial unit of the 
respective surfaces of mercury and glass. The coefficients c and ra- may be considered 
approximately as constant for variations of T — E which are not too large, but their ratio 
(which alone is required for the correction) is easily deduced from the experiments to be 
given in the sequel, for comparatively large values of T — E. Then if Qj be the observed 
quantity of heat which emanates from the disc in a given time, 
Qi='3 'rV(T — E) — 157 — c)(T— E) 
or if Q=the quantity of heat which would emanate from the whole disc without the 
central orifice. 
very nearly. The second term, ^2^1 — correction required. In my experi- 
ments this quantity is always small, but in some of them it is sensible. 
9. Again, when discs of glass and metal were used, it was the temperature of the 
mercury on which they rested that was observed, ^. e. the temperature of the lower sur- 
face of the disc. It becomes necessary, therefore, to examine what correction ought to 
be applied to this observed temperature, in order to obtain that of the upper or radiating 
surface. Now if be the temperature of the lower surface of the plate, that of its 
upper surface, r that of surrounding space, or of a surface (like the lower one of the 
calorimeter) on which the radiation takes place, h the thickness of the plate, k its con- 
ducting power, and to- the radiating power of its surface in air, we have the approximate 
formula used in my last memoir (where the symbol^ was used instead of cj), 
"CT t ^ ^2 
