ARE EMPLOYED IN THE THEORY OF TERRESTRIAL MAGNETISM. 261 



The same values for 6r'" and 6r, when /A = and n m = 2r, may also 

 be obtained from equation (18), thus 



r , / ,y. l(2m+l) 3 (2m + 3) (2r- 1) (2m + 2r- 1) 



m+2r ^ ' (2ra+l)(2wi + 3) ' (2ra + 5)(2m+7)""(2m+4r-3)(2m+4r-l) 



_ , _ }r 1.3. 5...(2r-l){(2m+l)(2m + 3)...( 

 (2m+l)(2m + 3)...(2m + 4r- 



'7" 1.3.5. . .(M- ?/i - 1)_. 1 . 3. 5... 

 ~ " ~ 



23. We have seen above (in Art. 16) that 



and 

 therefore 



a/A 



is. sJm-1 



But (1 - /*') - - 2m/, + (n + m) (n -m + 1) " = 0, 



therefore 



Combining these equations, we see that 



