468 NUMERICAL CALCULATION OF THE MAGNETIC FORCES 



For m = 3 and n=2r + 3, 



1.3.5...(2r-l)1.3.5...(2r+5) _ (2r-l)(2r + 5) ^ 



1.3.5 ...(4r + 5) (4r + 3)(4r + 5) "- 2> 



For m = 4 and n = 2r + 4, 



, _/ ,y L- 3 ' 5 - r^._. 

 1.3.5...(4r 



... (2r + 7) _ (2r-l) (2r + 7) ^ 4 



r + 7) (4r + 5)(4r + 



The law of formation of these quantities is evident, and their numerical 

 values for all values of m and n from to 10 have been determined from 

 these formulae. 



The numerical calculation of these functions from one another in suc- 

 cession is greatly simplified by putting n 1 = x, when we get the following 

 relations : 



r 2 I 



/nri _ l 



4cc 2 -l 



iLni*" 1 



X s - 9 



and generally 



2. Values of the Expressions for the Magnetic Forces at the Pole (p. 

 Here we have 



= ^L_ n G 



1 . 3. 5. ..(2?i-l) 2n-l "-" 



n- 1 (+!)! n+l ri 



n n -I OK In i~\ Q T" -l ' 



G! = 



2 

 2 2 1 . 2 f. 3. 5 ..."(2n-l) ~ 2n- 1 "-*' 



