ARE EMPLOYED IN THE THEORY OF TERRESTRIAL MAGNETISM. 251 



When m = n, the equation 



,7 Om + l 



- ).S"" = (see Art. 10) 



d m P 

 fails to give any value of S m or of ;ri7r> since the factor ii, m then 



vanishes. Hence we have 



7-H7> 



(1 - /i s ) B+1 - (/ , i+1 " = constant. 



This constant = 0, since P n is of the nth order. 



Also when m = n+l, the factor n m+1 vanishes and we have 



or 



nd P - 



dp." 



The value of c is given above in Art. 2. 



12. We have seen above that 



therefore by means of formulae (6) and (5) above, we get 



fH m ~ l P 



322 



