734 



or 



i 2 2.4 2.4.10 ) 



= 2.r-'k{U.vyi^\\- ^{l-x)---—{l-a^Y---—^ + const. 



9 ' 9.15' 9.15.21 



whence 



^ . I 2 2.4 2.4.10 



^' ■ 1 1.7 1.7.13 



+ 1.881 



or ' (5) 



^_ ,^ _ I 2 2.4 2.4.10 



^- • \ 9^ ' 9.15^ ^ 9.15.2r ^ 



The former series maj- be used when x is small, or /very large, 

 tlie latter holds for small ƒ, ./; being near unity. The additive con- 

 stant in the second series must be equal to 0, since for ^ = .rand/ 

 are both equal to 1. For the lii'st series the constant cannot be 

 determined by this condition: it was found by computing the value 

 of At for one and the same value of x from both series. 



By means of these series the time-function At was calculated for 

 a number of values of the expansion-factor /'. The temperature is 

 connected with /' by the relation 



Since the temperature changes according to this law throughout 

 the entire star, we are entitled to assume that the same law holds 

 for the effective temperature; the radiation per unit area then changes 

 proportionally to T*, i. e. to /~'''l< The surface itself changes a8/'^ 

 and thus the luminosity as /"""/s, hence 



log L — log L, = — '7^ log f. 

 or expressed in terms of classes of magnitude 



m — m^ = 7 log f. (6) 



The following table contains for a number of values of /' the 

 corresponding At and m — m^ 



