xxii Historical Sketch of the Physical Sciences, 1818. 
or it would correspond with the Newtonian law. The reason 
why it deviates from this law is the quantity of heat which it 
receives by radiation during the process of cooling. This quan- 
tity must be constant if we suppose the temperature of the 
surrounding surface to be constant. Hence the reason of the 
constant quantity by which the geometrical series must be dimi- 
nished. The reader will see by turning to the Annals of 
Philosophy, xii. 245, how well the formula deduced from this 
law of cooling in vacuo agrees with the results of the experi- 
ments made by our authors on this subject. 
Having thus determined the law of cooling in vacuo, or by 
simple radiation, the next subject of investigation was the law of 
cooling in air, or any other elastic fluid. Jt is obvious that the 
cooling in such cases is a complicated process. Part of the 
heat radiates from the body, just as it does in vacuo, and another 
portion of it is carried off by the conducting power of the elastic 
fhud. ‘The effect of this last in cooling the body is easily deter- 
mined by subtracting from the rate of cooling in the elastic fluid 
the rate of cooling in vacuo. The remainder obviously gives 
the heat carried off by the conducting power of the elastic fluids. 
This last quantity is not affected by the nature of the surface of 
the hot body, which is known to have so great an eflect upon 
radiation. Our authors tried the cooling of one of their thermo- 
meters in air and in hydrogen gas, both when the surface of the 
bulb was glass, and when it was silver. The portion of heat lost 
by conduction was in both cases the same, 
By another set of experiments, they have established that the 
rate of cooling, due to the conduction of elastic fluids alone, 
remains the same while the elasticity of the elastic fluid conti- 
nues unaltered for the same differences of temperature between 
the hot body and the elastic fluid, whether the initial tempera- 
ture of the elastic fluid be high or low. This law they have 
expressed in the following manner: 
“‘ The velocity of cooling of a body, due to the sole contact 
of a gas, depends, for the same excess of temperature, on the 
density and temperature of the fluid; but this dependance is 
such that the velocity of cooling remains the same, if the density 
and the temperature of the gas change so that the elasticity 
remains constant.” 
The effect of yariations in the elasticity of the gas was then 
tried by cooling the thermometer in air and other gases of the 
elasticities 1,2, 1,4, 1. From these experiments our authors 
have drawn the following conclusions : 
“1. The law according to which the velocity of cooling by 
the contact of elastic fluids varies with the excesses of tempera- 
ture remains the same, whatever be the elasticity of the air.” 
“<2. If the elasticity of the elastic fluid varies in a geometrical 
progression, its cooling power changes likewise in a geometrical 
progression ; so that when the ratio of the first progression is 2, 
