87 



regions v it is equal fo s^ -\ — fr^, where s^ is the energy of a 



particle lying in a centre of a region v. / is an unknown function, 

 which for r = (i. e. in F) assumes the value unity, whereas in 

 the regions v it must satisfy the following equations: 



Sp + fy \ 



ƒ 



A 7nr^ Ne x ( ) ^^^'*' ^^'"*' '^"^^' '^''n dr^ drt 



vh 

 i 



2 



i 



Ne X ( ) dmr dins' dmt! dr,. dvg drt ^ i 



(15«) 



and a corresponding formula foi- the mean value of \ fvi?; and 

 . ^v + f'/ \ 



ƒ 



\ ?ns''^ Ne X ( ) d'ltr dms' dmt' dr,, dr^ drt | 



— ' = h^J I . . (156) 



ƒ 



f/> + ^q 



Ne ^ X ( ) dmr dms' dmt' dr,, dr^ drt 



and three corresponding formulae for the average values of ^ mt", 

 h/r/' and h frt'. 



In consequence of the formulae (156) we no doubt must assume, that 

 X is independent of s',t',rs and ?'^. If this is so we can divide in (15a) 



i m s" 



the numerator and the denominator by | e '^ dms' and by three 



corresponding integrals. We get therefore, if we add the two 

 equations (15a) : 



mr" -f-yV/ 



ƒ 



(^ mr^ + h fr,,^) e ^^ ^{r, r„, v) dmr dr,, 



vh 



mr" -i-fru" ^^ 



- 1 



(16) 



I e " X(r, r,,, v) dmrdr,, 



The integrations with respect to o should be extended between 

 and 00, properly speaking those with respect to r however only 

 between and R. If R and ƒ are sufficiently great and ^ sufficiently 

 small, it will be allowed to introduce also oo as superior limit for 

 the integration with respect to r. 



If we call the denominator of the left hand member of (16) J , 



dJ 

 then the numerator may be represented by ^" — . The equation may 



thei'efoi'e be written in the following form: 



