378 Mr. R. Moon's Remarks on Helmholtz's 



that "the principle of the conservation of vis viva" holds. (Tay- 

 lor's Scient. Mem. 1853, p. 127.) 



Now in order to establish the truth of the conservation of force 

 as that principle is propounded by Dr. Helmholtz — in other words, 

 in order to show that the constancy of " the sum of the tensions 

 and vires vivce " holds in the above or any other instance, it is ob- 

 viously necessary that we should derive by independent methods 

 values for the vis viva and " the sum of the tensions " — equivalent 

 to the kinetic and potential energies of a more modern nomencla- 

 ture, — and that we should then show that the sum of the expres- 

 sions so arising is always constant. 



As Dr. Helmholtz, while attempting to prove that the con- 

 servation of force holds in the case of a train of waves traversing 

 a medium, confines all his efforts to establishing the constancy 

 of the vis viva, taking not the smallest notice of " the sum of 

 the tensions/' I am led to conclude that he regards the latter 

 as always vanishing in cases of motion of the kind in question. 

 It is to be regretted that so important a step should have been 

 passsd over in silence*. In the mean time I assume that the 

 author relies on the principle — which I have seen and heard 

 enunciated — that the mutual normal actions between elements 

 in contact may be neglected in forming the equation of vis viva. 



The method of estimating the vis viva adopted by Dr. Helm- 

 holtz in the case we are considering, I believe to be utterly erro- 

 neous and misleading. At present, however, I do not desire to 

 dwell upon this point, but shall proceed to show, as I hope to do 

 strictly : — 



I. That if it were true that when waves traverse a medium 

 the sum of the tensions disappears from, or is constant in, the 

 equation of vis viva, that fact would be fatal to the theory of the 

 conservation of force proposed by Dr. Helmholtz. 



II. That it is not true that the sum of the tensions in general 

 vanishes under the circumstances supposed. 



III. That the principle of vis viva, and therefore the principle 

 of the conservation of force as propounded by Dr. Helmholtz, 

 does not hold in the case of waves traversing a medium. 



I. It is well known that a wave in which the vibration is 

 normal to the front may be propagated in a cylindrical tube filled 

 with air in a direction parallel to the axis, without undergoing 

 any change in its length, or in the mode in which the con- 

 densation and particle-velocity are distributed throughout it, 



* Clausius makes upon Helmholtz's memoir the following remark : — 

 " It is to be regretted that the author of this ingenious essay has not en- 

 tered more fully into the details of his subject. From this cause certain 

 portions appear to me to be incorrect." — Taylor's Scientific Memoirs, Nov. 

 1852, p. 6, note. 



