Reversion of Power Series. 375 



(3) a? 3 - 2x* + 20#=2 



1 _ ___1_ 2 1 8 



10 ~* 10*^20* 



I 7 Jl h 1 



10' 1_ 10 ; ° 2 ~"~20 



*»0-1 + 0-001-0-00003-0-000002 = 0-100968. 



(4; ^=17 

 = .<«! + 2 

 ^ 4 + 8,/- 1 3 + 2W + 32^ = 1 

 1 3 . l 1 3 , 1 t 



C ""32 ; 6l ~""4 ; ^-"4 ; 63 -"~32' 



.r 1 = 0-0312500-0-0007324 + 0-0000266-0-0000011 



= 0-030513 #=2-030543. 



Substituting the original letters y, <« , a u a 2 , ... , and 

 arranging the terms with respect to the successive powers of 

 the a's, the general equation is * — 



a a « L a - a Jao a L «o 3 «o «o «oJ«o 

 + 11 — - 21 ^ ^ + 6 - - + 3 — 2 - -1 ^ - 



L « ° a 8 Oo a " a o 



+ ri32^!-330 ftl '-+120^ rt3 



<V\ a - a / a \ a a a / 



* See also "Inverse Interpolation by Means of a Reversed Series," this 

 Journal, May 1908. 



