434 THE THEORY OF TERRESTRIAL MAGNETISM. 



Assume + ^ 2) + ( ^ = + &C ' 



T pj- rf _ ~. _ 1 

 AJC U A/I w l j 



then > +r .a=i_. 0/.-i)(*-A 



for all values of 



Multiply by -~r and add to - - . 



X 1 X 1 



1 y l //, ( j/j 1 ) 



x _TI ~^~ (z 1) (x 2) (a; 1 ) (x 2) (x 



1 



&c 



x-1 (x-\}(x-y l -\} x-u-l' 



\ /\ i/ i / I/ 1 



1 y-l (y-l)(y-2) 1 



Or 7 "T" / 7V / 'V\~r/. -\/__ <-\/-- r\ i" OtC. " 



a; 1 (x i)(x 2) (* 1) (x Z) (x 6) x y 



Hence we have 



1 W, TO 1 



11 



"l / -i \ / r\ / r\ l" **** 



1 \1 / \ * /\1 7\i /\1 / 



J_ 



therefore the above factor reduces to m + 2m 2 =0, 



|_2mJ 



P f 1 



hence we get XX du. + Y"' Y du. = in all cases. 



J-i J-i 



22. In the series 



(2n 1)- -(2/1-3)7 



' n + m-l ' (n + m-l)(n + m-2) 



V / /^ i , 1 \ / i *, O\ /* i * O\ *^**l 



the alternate terms of which occur either in the development of (-X") 2 or 

 of (Y)\ each term may be divided into two parts, so that the series 



