18 



W. Ferret — Lew of Thermal Radiation. 



since the value of e is now different in the numerators and 

 denominators in the expression. For the same reason (8) be- 

 comes 



(19) R = A(X--l) in which (20) A=^-^ 

 v ; \r^ K j \ > q 27ge 



or in the case of a spherical cooling body 

 (20') A= -2- 



"With the expression of e in (17) substituted in (19) such val- 

 ues of the constants A, e and c should be found, if the assump- 

 tion of (IT) is correct, as will make (19) represent, at least 

 within the limits of possible errors of observation, the observed 

 values of R. In the expression of e above, however, the two 

 terms are somewhat complementary, so that by increasing e 

 and decreasing c correspondingly, and vice versa, through a con- 

 siderable range the expression of (18) represents the observed 

 values of R nearly as well through a considerable range of 

 temperature. But with different assumed values of e and 

 corresponding changes of c different values of A are required, 

 and so there is the same uncertainty here with regard to the 

 value of this constant, and consequently by (20) or (20'), in the 

 value of ?n, which we have found elsewhere. The value of 

 e which is found in general to satisfy observations' best is 

 about 3"0, though if it be changed to 2 - 9 or 3'1 or even made 

 to vary considerably more, if the value of c is changed accord- 

 ingly, the residuals are nearly as satisfactory. 



19. Slightly different values of c in (17) seem to be required 

 for different radiating surfaces, which is to be expected from 

 theoretical considerations, and seem to be indicated by Schleir- 

 macher's experiments as pointed out in § 15. If we put 



(21] 



e=3-0 + 0-00038r 



we get from (18) with A=0"905 and T =273°, the values of R 

 in the second column of the following table corresponding to 

 the values of T in the first column : 



T 



R 



o-c 



T 



R 



O-C 

 -1-4 



T 



R 



O-C 



353 



1-43 



+ •05 



329-6 



11-4 



393 



2-21 



-•02 



373 



1-98 



— •02 



369-6 



30-5 



-1-0 



413 



3-91 



+ •05 



393 



2-64 



— •04 



389-6 



42-6 



+ 0-2 



1 433 



3-74 



-■01 



413 



3-41 



-•03 



409-6 



56-8 



-1-8 



| 453 



4-69 



-•03 



433 



4-31 



•00 



429-6 



73-4 



-0-9 



473 



5-90 



-•06 



453 



5-37 



+ •06 



449-6 



92-5 



-1-0 



493 



7-04 



+ •07 



473 



6-60 



+ •04 



469-6 



114-7 



+ 2-0 









493 



8-02 



-•07 



489-6 



140-0 



+ 1-9 









513 



9-67 



+ ■07 



509-6 

 529-6 

 5496 

 569-6 



169-1 

 202-6 

 240-5 

 284-0 



+ 0-4 

 + 1-4 

 — 1-0 

 -0-5 









