RADIATION AND TEMPERATURE. 



247 



perature of the enclosure being marked on each curve. Now the heights 

 of these curves are in a constant ratio to each other, each being 1*16 

 times as high as the preceding. Then if we have obtained the rate of 

 cooling for a given temperature of the enclosure, when we raise that 

 temperature by 20 we must multiply the ordinate of the curve by 1'16, 

 when we raise it 40, by 1-16 2 , when we raise it 60", by T16 3 , and so 

 on. Then for a difference of 1 we should multiply by 1'ld*, or by 

 1-0077, and for a difference of n by 1-0077". Taking curve I., where the 

 enclosure is at 0, if we multiply the ordinates. by 1'0077~ 278 ='123 

 we shall obtain the curve of cooling when the enclosure is at absolute, 

 and this is the radiation curve on the assumption that the results 

 obtained between C. and 300 C. allow us to extrapolate. 



We have already shown that the cooling curves are successive pieces 

 of the radiation curve, and if we break the radiation curve up into suc- 

 cessive 1 steps, beginning at the absolute zero, as in Fig. 142, the height 



0abs 



I' 2" 3' 



FlG. 142. Eadiation Curve broken up into Cooling Curves. 



of each step above the last is, by Dulong and Petit's result, 1 '0077 times" 

 the preceding height, or B6= 1-0077 Aa ; Gc = 1-0077 B6, and so on. 



But these 1 steps up are each - - for the radiation curve so that 



dv 



^~ is multiplied by the factor 1'0077 for each step of 1, and at 6 we 



dB 



shall have 



^=1-0077" Aa 

 dv 



where Aa is the height of the first step. Integrating we get 



R = 7(l-0077'-l) 



where m is a constant for the radiating body. 



For a long time this result was supposed to represent the radiation 

 curve, at least within the range of the experiments, but there is no 



