ARE EMPLOYED IN THE THEORY OF TERRESTRIAL MAGNETISM. 247 



6. A very short and simple proof connects the relations expressed by 

 equations (l) and (2) 



Dividing by 2" +1 .(n+l)! we get from equation (2) 



where \P n dfi vanishes when p. = \. 



But we have also by Leibnitz' theorem 



Equating the above expressions for 



and omitting the term common to both sides, we get 



- M-= 



r /P C 



Hence (/* a - 1 ) f " = w (n + 1 ) 



ap. j 



or differentiating 



From the above equations we also obtain 



=1 



which also is a simple and elegant formula. 



