RADIATION IN ABSOLUTE MEASURE AT VERY LOW TEMPERATURES. 367 
Method 2a. 
36. In some cases it was found desirable to use a fourth term, containing t 3 , in the 
expression for n', when the formula stopping with f did not give sufficient accuracy. 
This involved the finding of a fourth constant, 8. In this case n' — a + fit + yt 2 + St 3 . 
To calculate the emissivities the procedure is similar to that just described, except 
that four equations are formed for the determination of a, /3, y, 8 ; and by suitable 
modifications in the equations, p. 363, we find 
e = n~— {K + /3 + (2-yt + 3S^ 2 )} ; 
the time correction, instead of being a linear quantity, containing a squared term. In 
most cases 8 was negligible, and the first form of n' was found to be quite sufficient 
for our purpose. 
Discussion of Results. 
37. The following tables contain the results of our experiments on radiat ion of heat at 
low temperatures. The tables are divided into three groups. The first group, Tables I. 
to VI. and XI., gives the loss of heat from a copper globe covered with a very fine 
coating of soot, hung in a spherical copper shell, also sooted, and at the highest 
vacuum. In this group, therefore, we have probably the nearest practicable approach 
to the case of a perfectly black body cooling in vacuum at very low temperatures. 
38. In the second group, Tables VII. to X. and XII., all the circumstances are 
practically the same as in the first, except that the surface of the copper globe was 
covered with a coating of silver, polished to the highest degree to which we could attain. 
39. The third group, Tables XIII. to XV., gives the cooling of a sooted globe, and 
of a highly polished silvered globe, in the same enclosure as is specified above, but in 
air at about standard pressure, and all at very low temperatures. 
40. Tables I. and II. show the radiation from the sooted globe, at the highest 
vacuums we could reach, the temperature of the cooling globe being at the 
commencement about 10° C., and falling during the experiment, which lasted 2h hours, 
to —59° C., the envelope being maintained at the temperature of liquid air during the 
whole time. These two tables are placed side by side in order that it may be seen to 
what extent agreement was found between experiments made at different dates, the 
circumstances being, as far as possible, repeated. The comparison shows that the 
exactness of agreement leaves nothing to be desired. Whatever there is of difference 
between the numbers obtained for the emissivity is certainly to be attributed to 
difference in the condition as to vacuum. This will be seen from comparisons among 
themselves of experiments at different vacuums. 
41. It should he noted here that the vacuums attained in these experiments are 
certainly of a very much higher order than those obtained in Dr. Bottomley’s older 
