W. Ferret — Law of Thermal Radiation. 21 



We get from (18) by differentiation and substituting for e 

 and dT(=dz) their values from (17), 



in which M is the modulus of common logarithms. The last 

 two terms within the parenthesis depend upon the variation of 

 e and the whole parenthesis is equivalent to an increased value 

 of e. By taking the differential of (18) regarding e as a con- 

 stant we get 



dU T- 1 



dT =m 273< e 



These two expressions become equal by putting 



T lo<* T 



(28) e=e + CT + c--^- 



But by satisfying this condition we simply make the two func- 

 tions of T increase at the same rate at some given temperature 

 T at the middle point or elsewhere of some given temperature 

 range. If the condition is satisfied for the middle point of the 

 range the two functions may agree approximately through the 

 whole range, but the satisfying of this condition does not 

 generally give the best agreement. 



For the middle of the range in the preceding table in which 

 T = 323°, we get from (28) in the case of a lampblack surface 

 in which we have found c=O00032, 



6 = 3-0 + 0-00032X50 + 0-597=3-6 13 



But we have found by a tentative process that the value 

 6=3*833 gives the best agreement of the two functions through- 

 out the whole range of 100°. The preceding value of e would 

 simply make the rate of increase of the two functions the same 

 at the temperature of 50°. But by comparing the difference 

 of successive values in the second and third columns of the 

 preceding table it is seen that the increased value of e makes 

 them a little greater in the latter column in the middle of the 

 range. This furnishes an explanation of the increased value 

 of e required when regarded as a constant. Up at the temper- 

 ature of 160°, or T=433°, which is the middle temperature of 

 the range in Dulong and Petit's experiments and also very 

 nearly that in Rosetti's experiments, putting c= 0*00038 in this 

 case, we get from (28) <?=4'06. The value of e=4'2 was found 

 to satisfy best the observations through the whole range. 

 With e=0-00032 (28) would give a still smaller value in the 

 case of Rosetti's experiments, but the value 4*2 was found in 

 this case also to be the best ; but as has been remarked before, 

 a considerable change in the value of e does not greatly affect 

 the residuals in comparing with observation. 



