THE RECIPROCAL ENERGY THEOREM 331 



discussing this subject states that the theorem holds for the current 

 w = \E -\- curl M. This cannot be true in general, however, because 

 from the foregoing in order that the theorem should hold for the 

 current w, it is clearly necessary that 



f{{F'-cm\ M") - (f"-curl M')]dv = 0. 



This is only true in the exceptional cases where the impressed force is 

 derivable from a potential; that is, curl Z' = 0, or else f = where 

 M ?^ 0. 



