372 PEOFESSOE BTJNSEX DE. H. E. EOSCOE’S PHOTO-CHEAHCAL EESEAECHE3. 
The excess of temperature of the gas over that of the suiTOunding medium was 
therefore, for the time , Wq— Wj — ; and if a represents the cool- 
ing velocity for the thermometric unit and this difference of temperature, we have 
du 
-7,= —au. 
dt 
The integral of this differential equation is log natw=— const., and according to 
definition of log nat Wo= const., and log nat Wi= —afj-f- const. Hence 
log nat Mq— log nat u■^ 
The values of calculated from the experiments according to this formula, are as follow : 
Exp. 1 . . 
a. 
. 0-630 
Difference. 
-0-047 
Exp. 2 . . 
. 0-567 
-0-110 
Exp. 3 . . 
. 0-806 
-i-0-129 
Exp. 4 . . 
. 0-578 
-0-099 
Exp. 5 . . 
. 0-806 
+0-129 
Mean . 
. 0-677 
Although the difference between each value of a and the mean is considerable, yet in the 
calculation of the temperature this variation has very little infiuence, a difference of OTl 
m the value of a causing an error of only a few hundi’edths of a centesimal degree. 
If the difference of temperature between the gas and the surrounding medium at the 
moment of exclusion of light is (Wo — W„), measured in centesimal degrees, the cooling- 
velocity immediately after darkening is a (Wo — W„). If, further, the volume in cub. cent, 
of the gaseous mixture at the moment of closing is called Vo, its specific gravity s, the 
pressure to which it is subject P, its temperature Wo, and its specific heat by constant 
pressure compared with water c ; and if the weight of the platinum in the vessel is 
and its specific heat Ci, the decrease of temperature in the unit of time during the cooling, 
expressed in units of heat representing the amount required to raise one cub. cent, of 
water one degree Centigrade, is found from the expression 
{076 (1+0-00366 Wo) *773 O^'o— «)• 
As the amount of heat evolved by combustion is equal to that lost by radiation, we have 
Si P RC_| 
773 '076 (1+0-00366 Wo) 2 1 
sc 
773 0-76 (1 + 0-00366 Wo) 
Vo-fc.i)U(W„-W„). 
x\s the values of Wo and W„ differ only by a few hundredths of a degree Centigrade, it 
is possible to replace the value (l-J- 0-00366 W„) for (1-f 0-00366 Wo) without exceeding 
the limits of the errors of observation. 
^ scP 
■^""773.0-76 (1 + 0-00366 WJ’ 
Hence if A= 
SiPC 
2.773.0-76 (1+ 0-00366 WJ’ 
and 
