120 Mr. K. Moon on Helmholtz's Memoir on 



the distances B and r," is in fact the sum of the following 



products, viz. of the tensions acting (say) at the beginning of 

 each of an indefinite number of equal intervals dt, into which 

 the interval T t (corresponding to the distances 11 and r) is 

 divided, each multiplied by the velocity of the particle at the 

 same instant and the short interval dt, during which the ten- 

 sion and the velocity may be considered uniform. 



It is thus evident that the term in the equation of vis viva 

 which Dr. Helmhoitz offers to our notice as depending solely 

 on the tensions, does in fact depend on the tensions and velo- 

 cities combined ; from which it results that the interpretation 

 of the equation of vis viva which forms the basis of Dr. 

 Helmholtz's theory, viz. that the energy of a system consists 

 of two separable constituents, one depending solely on the 

 motion existing in the system, the other depending solely on 

 the forces exerted by the particles on one another, has no foun- 

 dation in fact. 



Who shall say how far the acceptance so widely accorded 

 to Helmholz's theory is not due to this palpable, though no 

 doubt unconscious, misrepresentation of the true import of the 

 equation of vis viva ? 



The later disciples of Dr. Helmhoitz, while altering his 

 nomenclature, have not attempted to eliminate from it its 

 misleading character. 



" The kinetic energy of a body is the energy which it has 

 in virtue of being in motion, and .... its value may be found 

 by multiplying the mass .... and half the square of its velo- 

 city." (Maxwell's ' Theory of Heat,' p. 90.) 



This is a plain assertion that half the product of the mass 

 and the square of the velocity represents the whole of the 

 energy which the body has by virtue of being in motion, which, 

 it is manifest from what has preceded, is not the case. 



The epithet " potential," as characterizing a kind of energy 

 different from the kinetic, is open to the same objection as 

 Dr. Helmholtz's expression "sum of the tensions;" that is, 

 that it states or necessarily implies what is not the fact, viz. 

 that the quantity which it is intended to designate is inde- 

 pendent of the velocities existing in the system. 



III. A like confusion of language, and one equally misleading, 

 occurs in a passage to be found in the next page of Prof. 

 Maxwell's Treatise, the consideration of which will serve to ex- 

 hibit in a striking manner the degree of care and judgment 

 with which the foundations of the theory have been laid, and 

 the amount of discrimination displayed in the criticism which 

 has been bestowed upon it. 



After being told that " the energy of a system of bodies 



