THE THEORY OF FISHER. 185 



then pQ from (37) and finally ,5' from (38). The values of /9/ and p^' 

 as functions of ^^ are given in table 3 below. The former were obtained 

 by interpolation from an extended table giving CjB and CfB^ as functions 

 of j9. To trace the positions of interior particles at different distances and 

 different epochs would require a double-entry table, which could be supplied 

 by equation (38) after p^' has been computed. 



The specific energy of impact, or Icinetic energy of a unit-mass falling 

 from infinity to the surface of a nucleus of mass m^ and radius r/ is, then, 



e-=^ (41) 



W.=^^. 



where by (26) the attracting mass is 



The values of e^ are given in table 4, in terms of ^g, which determines the 

 ultimate position of the particle. 



The total energy transformed by impact is, then, 



E,=^7t I p, • -^ ■ r,Hr, 



t/o * 



which, since p^^p^B^, is equivalent to 





But by equation (40) 

 whence 



Use of this relation to transform the variable of integration from ^^ to 

 /?/ gives 



where the integrand is expressed entirely in terms of ^J, the upper limit 

 of^the integral being unchanged according to (40). The result of the inte- 

 gration is 



\Qk%p,'B,' r (l -/?, cot /?,)=^ l -Acot/9, /3,n 

 q^ ^'V 2 + 2 ej 



which may be written: 



E,=^AV.{^'-^-^^^^ff^+feos'A-|j (43) 



