74 Mr. Gwyther oji a 



2/2 = the expression we should obtain by writing 

 {71 - i){?i - 2%,x''-^ for c,,x''-^ 

 (n.[ii - i)a,^ + 2b^x"~^ for a^x"" 

 {n - 2){fi - -^b^x"--^ for b,,x]''-'^ 

 21^ = the expression we should obtain by writing 

 {n - I )- - -{71 - d,)c^x'^-'^ for r„aj"- ^ 

 {7t..-{7i- 3)«„ + d,{n -2){n- 3)^„]*'"-^ for a,{f]' 



{n - 2)- --in - s)b„x"'-^ for b,^x"--^, and so on. 

 Then our integral will take the form 



where 



TI -^ 



?/2 71(71 +l)Uo 



2r 



»i+i 



U^ {fl - \)7m<i (714- l)-- -(tZ + 2)Uo 



U-i = g-;r^2 ^y^ + g;:M^2 5 etc., 



and the integral between the proper limits is 



^.[{5->-}»{|-/!"4] 



and 



u^ = -3 Vo 



dr 



^ ^?'- dr 



In differentiating with regard to r, we must bear in mind 



that 



dx _ r dy _ r{x + c) 



■Jk c dr cy 



