514 Sir G. Greenlrill on t+e 



The generalisation was made in the ' Quarterly Journal ' 

 by replacing Laplace's assumption 



4-7r>' 4 dp 7 



M 



.and then 



J^bvi-p)". . . . . ; (9 



dr a 2 " \a' v 



. T Aira^dp r/M \.ttol h d 2 p 47r(>i — 4) dp . '„ 



\1 = — - = i — = A-trr z o 



i-"-* dr' dr r"-* dr 2 r"' 6 dr p ' 



. . . (10) 



^g_ ( „_-4)4%fry P =o,. . . . (id 



dr dp \aj 



q differential equation of a. form (5) § 5 considered here 

 before ; and then putting 



fr\ l ndr dx ' 



r ll f=n,^, **? + P & = »«(.**$ + **Y . (13) 

 dr <lx dv dr \ dx- dx! 



the equation becomes 



and no change need be made in the dependent variable p to 

 bring the equation into the Bessel form. 

 Next, with 



dM ' 1 dM nM 



-=4^, P = 4?rr2 ^, .... (15) 



dp_ 1 d 2 M 1 dM_ M 



d?' 477?'* d?' 2 27T?' 3 rfr 47T?' 4 



dr- 



r/ 2 M r/M /r » 



dr \a / 



/r\ n 

 s in (9) § 9, changing with I - ) = n 2 x into 



* *™ + ( l _ .i? \ ^ + ,, M = 0, M - C 3 <» = x"C s (x) .(18) 

 a A'" V ?i / dx -- 



