﻿200 Mr. R. Moon on the Theory of Sound. 



It appears, therefore, that we have to choose between two things, 

 viz. on the one hand a diminished pressure where there is 

 throughout a tendency to expansion, and an increased pressure 

 where there is throughout a tendency to condensation ; or, on 

 the other hand, an increased pressure where there is throughout 

 a tendency to expansion, and a diminished pressure where there 

 is throughout a tendency to condensation. That this latter 

 alternative should be true appears incredible. We may with 

 safety conclude, therefore, that when the motion is to the right, 

 x being measured positively in that direction, the lower sign is 

 to be taken in (19), and vice versa. 



Applying this conclusion to the results previously obtained, it 

 follows that, when the motion is represented by (12), the par- 

 ticle-motion is to the left, and v is negative ; so that any disturb- 

 ance propagated to the right of the original disturbance will be 

 a rarefaction, and its velocity of propagation will be a(l+e); 

 while any disturbance propagated to the left must be a condensa- 

 tion, whose velocity of propagation will be «(1 —e). 



On the other hand, when the motion is represented by (18) 

 the particle-motion takes place to the right, i. e. v is positive; 

 so that any disturbance propagated to the right of the original 

 disturbance will in this case be a condensation, whose velocity of 

 propagation is a(l — e); while any disturbance propagated to 

 the left must be a rarefaction, and its velocity of propagation 

 will be a{\ +e). 



It results on the whole, therefore, that waves of condensation 

 are propagated with the velocity a(\~e), which is less than 

 what has hitherto been regarded as the calculated velocity apart 

 from temperature; while waves of rarefaction are propagated 

 with a velocity a(\+e), which is just as much greater than such 

 Calculated velocity. 



If it be asked whether is e so small that the difference between 

 these two velocities is imperceptible to the human ear under all 

 circumstances, or are two perceptibly distinct waves in fact pro- 

 pagated ? I answer that e is not so small as that the difference 

 between a(l +e) and#(l— e) cannot be distinctly appreciated. 

 Two waves will in fact be propagated, one of which (the slower) 

 the human ear is so constructed as to suppress. The proof of 

 this I reserve for a future communication. 



6 New Square, Lincoln's Inn, 

 February 16, 1869. 



