428 Mr green, ON THE DETERMINATION OF THE 



v= pe.e,......e..,.irp« f "^ , (47) 



a' 



and the equation (27), No 11, will give for the corresponding value of p', 



in - IN 



-m 



M-4-1 



K 



where P/, 9/, 62', &c. are the values which the functions P, 0i, 02, &c. 

 take when we change the unaccented variables fi, ^2, ^, into the cor- 

 responding accented ones ^/, ^/, f/, and 



p «-^ + l-w — ^ + 3 n — s + 2a}-l 



' ~ » + 2i + 2ft)-l .7^ + 2^ + 2(0 + 1 n + 2i + 4<w-3' 



or the value of P when p = 1 ; where as well as in what follows i 

 is written in the place of i'''. 



The differential equation which serves to determine H when we 

 introduce a instead of h as independent variable, may in the present 

 case be written under the form 



. = a=(a^-«'^) Vr + «M»«'-(*- !)•«"} ^ 

 ^ ' dcf * ' ada 



+ {?■(« + *- 2) a'' -(« + 2ft.)(« + 2a) + w-l)a'} H, 



and the particular integral here required is that which vanishes when 

 h is infinite. Moreover it is easy to prove, by expanding in series, that 

 this particular integral is 



*-l-n-2<o 



provided we make the variable r to which A" refers, vanish after all 

 the operations have been effected. 



But the constant k' may be determined by comparing the coefficient 

 of the highest power of a in the expansion of the last formula with 

 the like coefficient in that of the expression (46), and thus we have 



" yfc' = Kd'^"" (-\Y « + 2^' + 2a)-l.w + 2? + 2a> + l ?^ + 2^^ + 4a,^.-3 



^ ^ 2.4 . 6 2o) . 



