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



quently vis viva will constantly be generated, till, as the waves 

 become extricated the one from the other, the vis viva will be, 

 what it will ever after remain, exactly what it was at first. 



Hence, if it were true, as Dr. Helmholtz assumes, that the 

 normal actions disappear from the equation of vis viva when we 

 consider the internal motions of continuous masses, that fact 

 alone would suffice to demonstrate the entire failure of his prin- 

 ciple of the conservation of force in cases of motion such as that 

 we have been considering. 



II. That the sum of the tensions does not in general vanish 

 when a wave traverses a medium may be seen as follows : — ■ 



Let x and y be the ordinates (measured parallel to the axis of 

 the tube) in the state of rest and at the time t of one surface of 

 an element made by planes perpendicular to the axis, p the 

 pressure at the same surface, D the density of equilibrium. 

 The equation of motion may be put under the form 



whence, multiplying hy -^-dt and integrating, we get for the equa- 

 tion of vis viva the following, viz. : — 



°-*Mf+W- 



dx d l°t 

 dtdx* 



the integration being effected between any limits we may fix 

 upon. 



Suppose that we have two waves of condensation, such as those 

 already described, travelling in opposite directions ; and [x and 

 y being measured^ parallel to cAC in the annexed figure) let 

 the ordinate perpendicular to c A C of the curve ABC represent 

 the condensation in the wave which moves towards the right, in 

 which direction we will suppose x and y measured positively; 

 while the corresponding ordinate of the curve a b c represents the 

 condensation in the wave which moves to the left. 



Assuming the truth of Boyle's law in cases of motion (which 



it will suffice to do for the purposes of this paper), if the wave 



corresponding to ABC (or, as for brevity I shall designate it 



dp ' 



the wave ABC) stood alone, we should have -f- positive through* 



dx 



