3ii8 Mr. Challis's General Co?isideratwfis respecting 

 Combining these equations with (A), we arrive at, 



= p + 6^-^?--^'(0; (B) 



and ip(/), which is the value of v when g = 1, may be sup- 

 posed to be nothing or constant, so that <^' {t) = 0. First, let 



P = 0. Then — 7^ = — ^, and p being a function of 0, 



must be equal b" g. This is the only relation between jo and p 

 by which uniform propagation can obtain, when no force is 

 impressed on the fluid. 



As the velocity of aerial propagation is not found to be that 

 which would be deduced theoretically from the relation be- 

 tween p and p, which experiments on air at rest make known, 

 some additional force, which is latent in the quiescent state of 

 the particles, must be called into play by their motion. In 



Laplace's theory P ='— Fa^ —7^, and b = a \/ I + k^. Hence 

 from (B), 4- = (i^- Fa'^) _1^ = i^, 



^" jdi ^ ' ^dx fax 



and consequently p = a^ p, which ought to be the case. Hence 

 this theory, which every thing tends to confirm, is not restricted 

 to small motions. 



Up = a^-p' + \ P = («V"(l + «)-^0 ^'^quan- 



tily which, when p is nearly 1, and b = a\/l + 71, is veiy 

 small. Consequently, when the motions are small, the velo- 

 city of propagation may be very approximately deduced from 



the law, p := a^. p ' '', without supposing any additional force 

 to act. But if this law really obtained in nature, the type of 

 a series of undulations would not be constant during their 

 propagation. 



To take another instance of propagated motion, let us con- 

 sider the passage of light through transparent bodies according 

 to the undulatory hypothesis. It has been usual to suppose the 

 diminished velocity of the propagation of light in the interior 

 of mediums, to be accounted for by the existence of a less 

 elastic force of the aether in their interior than exterior to them. 

 But this supposition leaves out of consideration the obstacle to 

 the free motion of the particles of the aether, which nuist be 

 presented by the material particles of the medium. Let us 

 suppose that p — a^ p both out of the medium and in it; and 

 as the velocity of propagation in the medium is uniform and 



less than a, let P = — -j~' Then by reason of the equation 

 (B), b =a v/T^^. If — = — , P = 1 - —. The re- 



* '' am' m^ 



tardinff 



