Formulation of the Principle of Huygens. 265 



general term vanishes. The integrand is 



dr i [ >i + ro) n njn + rpr- 1 ! _ dr, V (n + nO" n (r, +r ) M - 1 -| 

 dn 1_ r 2 rQ rir>o J da L r^ ? » iro J 



, n(n-l-)( n-2)(,-2) „_ 4 n(n-l) „_ 8 .itf -1 ! 



+ ~ 1.2.3 n n — o~ r ° + ^J 





•7 r ,«-2 



„( n _l)( n _2)(-2) M _ 4 n(n-l) ft _ 3 



17273 n r ° — F7T n 



which may be written 



1 d n _ 1 „_! d 1 1 d n _, u _! rf 1 



r cm d/i ?' ?']_ dn dn r t 



d 71-2 . d »_2 

 dn dn 



n(n-l) f d ... »_3^ -| 



1.2 L°to ri " ?1 57 J 



n(n-l)(/i-2 ) r 2 ^ „„ 4 n _ 4 ^ 2 l 

 1.2.3 L ?0 ^ ri " n ^J 



+ H2T3 l n dn ro - ro 57 J 



- . . . . + 



- . . . . + 



Remembering that VV l -n(« + l)}' B " 2 , we see that the 

 subject of integration of the equivalent volume integral is 



n(n-l)^ n{n-l)^—-n(n-l)(n-2)(rr*-rr 4 ) 



?'i r Q 



^L>[(n-2) ( n-3)^r 5 -2!|l 3 J 



