( 146 ) 



2. This relation was tlie following:') 



.^•(l-.^•)ö=' 



{l—2.v)v—ó.v{l — .c)i3 



J^l/a{c-br 



S,tii-.v)0{6—^[/a)-\- 



-\-a{v-h){v—db) 



= 



(1) 



In this &= cw—? ]/a = (b, Va^—h^ Va,) + « [v—li) ; a = \/a^—Va, 

 and /? = 1\ — ^i- 



In the derivation it was only assumed that a^^ = y/a^n^ might be 



I\ 2 

 (1 X) |/«i + ^^' K«2 • 



This is the only simplifying assumption. 



We now proceed to make the above given expression homogeneous 

 in the Avay of p. 35 et. seq. of my last paper. (These Proc. June 1905). 

 By considering oiily the case b^ = b^ more closely (which was 

 sufficient for our purpose), we simplified this expression considerably 

 in the paper mentioned, but now we shall put the quantity /? not 

 = 0, so that a new variable quantity must be introduced. 



Let us put as before: 



[/a. 



= 9 



V 



But now also: 

 then we get: 



— m — =1 «O) 



V V 



[/a 



= ^ + A- ; 



= to (1 + ''•^') • 



Hence after division by x{l — ,T)a\'' (1) passes successively into 



+ 

 and 





0, 



.r (1 — w) 



fl — nvi {<p + wU \{l — 2.f) — S.V (1 — w) na)\-\- 

 -f {(f + .^0 (l — a)(l + n.r) J Fs fl - no){(p-\-w)\ (l — 2nü)(y + a-) J-f 

 {(p + (vf f 1 — CO (1 + nw)] ( 1 — 3to (1 + mvU 



+ 



w{l — w) 



0. 



1) 1. c. p. 33, formula (2). Gf. for the derivation: These Proc. of April 1905, 



