358 
DR. J. T. BOTTOMLEY AND MR. F. A. KING ON THERMAL 
centre may be different from that of the surface .* This objection was completely 
answered by numerical calculations founded on the dimensions and conductivities of 
the globes in question ; and, in an interesting appendix, the whole question is discussed 
in ‘ Hoy. Soc. Proc.,’ June 10, 1875.f 
23. In the above formula the coefficient e corresponds to the emissivity ; it is the 
quantity of heat lost per second, per square centimetre of surface, per degree 
centigrade of difference of temperatures of radiating surface and surroundings. This 
formula is commonly taken to be a representation of the “ law of cooling,” whether 
in air or in any other gas, or in vacuum, the range of temperature dealt with being 
moderate. The numerical value of e depends on the circumstances under which the 
cooling takes place, and, when air is present, on the dimensions and shape of the 
cooling body. 
24. One way of dealing with the matter, from an experimental point of view, is to 
solve the equation above as though e were constant—which is, of course, approximately 
true if the difference of temperatures is small—and then to determine numerically the 
value of e at different places in the temperature scale, taking an exact account of the 
circumstances. When a sufficiently large number of such values have been obtained, 
a basis for a wider theory will have been laid. 
Taking, then, the equation 
eS {v-V), 
and its solution 
log e 
v-V 
where v 0 is the temperature of the cooling globe when l — 0, and V the temperature 
of the enclosure, we have for the numerical calculation of e, using common logarithms, 
M being their modulus, 
« = ||{log(«>.-V)-log(*-V)}. 
Here t 1 = 300, the interval of time used in our experiments being 5 minutes; 
c = 25'482, and S — 50'26, to which we must add a small quantity which we roughly 
estimate at about 0'6 per cent.—the correction applied for the carrying away of heat 
by the thermojunction.wires. This we calculate, assuming that the emissivity of the 
surface of the conducting wires is much the same as that of a tolerably clean silvered 
surface. 
* To find experimentally how long it would take for a wave of heat to travel from the surface to the 
centre of the copper globe, a spirit flame was applied to the outside of the globe, and the instant of 
application was taken with a stop-watch. The flame was kept under the globe for 2 seconds, and in 
6 seconds the zero of the galvanometer scale was seen to be moving rapidly across the field of the observing 
telescope. The maximum deflection was obtained in less than 20 seconds from the time of applying the 
spirit flame. 
t Republished in Lord Kelvin’s ‘ Collected Papers,’ vol. 3, p. 245. 
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