51, 52] RECIPROCAL RELATIONS. 191 



la. In an adiabatic motion if an increase in one positional co- 

 ordinate q r causes an increase in the impressed force P s belonging 

 to another positional coordinate q s at a certain rate, then an increase 

 in the positional coordinate q s causes an increase in the impressed 

 force P r at the same rate. For 



190) * 



C<l r 



Ib. In an isocyclic motion we have the same property as 

 above. For 



8p 



II a. If in any motion an increase of any cyclic momentum p r , 

 the positional coordinates being unchanged, causes an increase in a 

 cyclic velocity qj at a certain rate, then an increase in the momentum j?,,,, 

 the positional coordinates being unchanged, causes an increase in the 

 velocity q r ' at the same rate. For 



192) 



r rs s 



lib. If in any motion an increase in any cyclic velocity q r ' f the 

 positional coordinates being unchanged, causes an increase in a cyclic 

 momentum p s , then an increase in the velocity qj causes an increase 

 in the momentum p r at the same rate. For 



193) 



Ilia. If an increase in one of the cyclic momenta p r , the posi- 

 tional coordinates being unchanged, causes an increase in the impressed 

 force P s necessary to be applied to one of the positional coordinates q s 

 (in order to prevent its changing), then an adiabatic increase of the 

 positional coordinate q s will cause the cyclic velocity q r ' to increase 

 at the same rate. For 



Illb. If an increase in one of the cyclic velocities q r ', the posi- 

 tional coordinates being unchanged, causes an increase in the impressed 

 force P s necessary to be applied to one of the positional coordinates q s 

 (in order to prevent its changing), then an isocyclic increase of the 

 positional coordinate q s will cause the cyclic momentum p r to decrease 

 at the same rate. For 



dP 

 195) 



0<l 



