RADIATION AND ABSORPTION, 59 
since the coefficient m has been determined with great care by 
MM. Dulong and Petit, and found equal to 2°037 for a thermo- 
meter with glazed surface which was spherical, filled with mer- 
cury, and which was 6 centimetres in diameter. 
Assuming therefore 
we find B=1°'146. 
This result cannot be perfectly exact, both because the value 
of fis a little hypothetical, and because the true dimensions of 
the thermometer in question being wholly useless for the re- 
searches on cooling, MM. Dulong and Petit have only indicated 
them in a general manner: it is however certain that the error 
cannot be considerable, and we shall adopt the value of B as 
sufficiently near*. 
13. We may, indeed, demonstrate directly, in another way, 
that the values of the coefficient m are undoubtedly in a direct 
ratio to the surface and the emissive power of the bodies sub- 
jected to cooling, and in an inverse ratio to the weight of these 
bodies and their capacity for heat. 
In fact, admitting that the velocity of cooling in absolute cold 
is expressed as in the formula of MM. Dulong and Petit, by the 
relation t 
yv=ma, 
we obtain by integration the following formula: 
PY A Reet 
= a(S ), . . . . (3.) 
in which T represents the initial temperature of the body, and & 
the number of minutes which elapse whilst the body falls from 
the initial temperature T to any temperature ¢. 
Consequently, for the body to be lowered 1°is required a time 
expressed by 
ie (ies Vga 
~mla 
Now, if we represent the surface of the body by s, its weight 
by p, and its specific heat by c, it is evident that in falling 1° it 
* See Note 1, p. 85. 
