On Helmholtz's Memoir on the Conservation of Force. 377 



and Z (fig. 15) ; in X take K to represent the resistance, 

 and in Y take M so that the area of the rectangle K M 

 represents the electromotive force, and therefore M the 

 strength of the current. Similarly, take ON in Z also to 

 represent the strength of the current. Then the heat generated 

 in unit of time is proportional to the contents of the rectangular 

 parallelopiped O P, constructed upon the lines OK, M, and 

 N. The locus of P is the intersection of two equal and similar 

 hyperbolic cylinders, whose equations are respectively xy = con- 

 stant = electromotive force, and < r,2' = constant = electromotive 

 force, and is itself a rectangular hyperbola in the plane of X and 

 Q, and having these lines for asymptotes. If K' represent 

 the internal resistance of a battery, and K' K the external resis- 

 tance, the heat generated inside the battery is represented by 

 the parallelopiped P', and that generated in the external con- 

 ductor by the parallelopiped "KJ P. 



XLIII. Remarks on Helmholtz's Memoir on the Conservation of 

 Force. By Robert Moon, M.A., Honorary Fellow of Queen's 

 College, Cambridge*. 



THE following observations are offered on'the assumption that 

 Helmholtz's memoir iC Ueber die Erhaltung der Kraft " 

 (Berlin, bei G. Reimer, 1847), the original of which I have not 

 had an opportunity of examining, is correctly represented by 

 Professor Tyndall's translation contained in Taylor's Scientific 

 Memoirs for 1853. 



I pass by for the present the introductory matter and the dis- 

 quisition on the conservation of vis viva contained in the memoir; 

 nor shall I now discuss the grounds upon which the author rests 

 his primary induction that the constancy of " the sum of the 

 tensions and vires viva" (which undoubtedly holds u in all cases 

 of the motion of free material points under the influence of their 

 attractive and repulsive forces, whose intensity depends solely on 

 the distance ") represents a general law of nature. 



I come to the author's " special application w of the principle, 

 or to what would be morecorrectly designated as his attempts to 

 demonstrate its truth in cases of motion where we do not deal 

 with " material particles under the influence of their attractive 

 and repulsive forces/' but with continuous masses the different 

 portions of which act upon each other otherwise than by attrac- 

 tion or repulsion ; and of these cases of motion I shall confine 

 myself to one, viz. where " a medium ... is traversed by a train 

 of waves M — a case in which Dr. Helmholtz evidently considers 



* Communicated by the Author. 



