7T 



The Rev. S. Earnshaw on the Trip licit y of Sound. 189 



those of v for the ordinates. The curve 

 is evidently a parabola whose latus rectum 



is — ; it is represented by A B C in the 



A C is = V ; and A M, the maxi- 



The 



2tt 

 figure. 



mum value of kh, is equal to g . AC. 



magnitude of the parabola will vary for 

 different elastic media, but ABC will 

 always be a similar portion for all media. 

 In the case of the exponential type of 

 wave, the relation between k and v is ex- 

 pressed in terms of a by the equations (7 f ); 



and if a curve be constructed as in the former case, we shall find 

 it to be of the form C D, touching at C the line A C produced. 

 If A K be any abscissa, and K R be drawn parallel to A C, then 

 there will be three ordinates, K P, K Q, K R, representing the 

 three different velocities of the three corresponding waves. The 

 figure therefore represents to the eye the triplicity of sound. 



21. AM corresponds to the maximum value of k, which is 

 exceedingly enormous ; but in the case of all audible sounds k 

 does not much exceed 20,000, which is probably small in com- 

 parison with its maximum value. Hence the part of the curve 

 C B which corresponds to audible sounds lies close to C, where 

 it is obvious the ordinates are all nearly equal, which is the reason 

 why the velocity of transmission of all ordinary sounds is sen- 

 sibly the same. But since the curve C D has A C produced for 

 its tangent at C, the ordinates which lie near to C will differ 

 sensibly from A C in magnitude ; and hence a slight variation 

 of the value of k will be attended with a sensible variation in the 

 value of the velocity of transmission in this case ; and we may 

 therefore expect that the velocity of a thunder-clap will be greatly 

 different for small differences of intensity of the electrical dis- 

 charges. 



22. In considering the question of the intensity of sound, we 

 cannot but think it depends chiefly, perhaps entirely, upon the 

 whole momentum which reaches the ear in a given time ; and 

 this will chiefly depend in a given case upon the velocity of pro- 

 pagation. Hence the sounds which belong to the whole of the 

 curve A B, and to a large portion of C B lying near to B, would 

 probably be inaudible for want of sufficient momentum, even 

 were there no other reason. Oil the contrary, sounds belonging 

 to C D, with a usual amount of force in their genesis, will never 

 be inaudible from this cause. And hence if any method should 

 be found of simultaneously generating the three different sound- 

 waves corresponding to any value of k within the limits of audi- 



