FOE DETEEMINING THE EADIATING POWEES OF SUEFACES IN AIE. 393 
Hence 
Q a 
breadth of the annulus 
rad. of radiating surf. 
Hence taking Qi as before, 
The expression above obtained for will only be accurately true when /3 is indefinitely 
small, as is easily seen from the limits which have been taken for 6 and ^ in the integra- 
tion. If (3 be small but finite, as in our actual case, the above value of g will be approxi- 
mately true, but somewhat too large. 
It may be doubted whether the above investigation is strictly applicable to the whole 
o:^ the heat which emanates from the heated surface or to that part only which may 
be conceived to radiate through the air to the bottom of the calorimeter, in contra- 
distinction to that which must be borne away by the air from the heated surface by con- 
vection or conduction. As the efiect, however, produced on the narrow annulus must be 
of the same kind, there is probably little error in the correction, by supposing it of the 
same magnitude. 
11. There is another error, which would seem perhaps to be inherent in any experi- 
mental determination of the quantity of heat radiating from one surface and falling on 
another. It arises from the fact of one of these surfaces (as the base of the calorimeter 
in my experiments, and the internal surface of the surrounding globe in those of Du- 
LOXG and Petit) not being ggerfectly absorbent, as assumed in the results, which ought, 
therefore, in the follo'wdng experiments, to be increased in the proportion which the heat 
reflected from the blackened surface of the calorimeter bears to the heat absorbed by it. 
This ratio is probably very small, but I am not aware of any attempt to determine it. 
Numerous experiments were made before the calorimeter assumed exactly the form 
above described ; for it was only by a careful observation of the anomalies presented by 
the earlier experiments that I became fully aware of the importance which attached to 
different points in the construction of the instrument, and the mode of conducting the 
experiments. I shall give a few of the later experiments, on which some of my prin- 
cipal results are founded, in full detail, to enable the rqader the better to judge of the 
confidence to which they may be entiUed. The following experiments on a glass disc 
were made for the determination of m (art. 3). 
12. Let T,= temperature of the radiating surface when the experiment begins; 
T 2 = ditto when it ends ; 
Pi= reading of the thermometer of the calorimeter at the beginning of the 
experiment ; 
Il 2 = ditto at the end of it ; 
6 G 
MDCCCLX. 
