ON THE MATHEMATICAL THEORY OF FLUIDS. 245 



pressure in the interior of liquids is a function of the density, 

 (at least at distances from their surfaces greater than the radius 

 of the spiiere of the molecular action). For admitting this to 

 be the case, it will be a simple analytical consequence, that the 

 small variations of pressure are proportional to the correspond- 

 ing variations of density, whatever be the form of the function 

 which connects the pressure and density together*. The know- 

 ledge of the degree of compressibility of water or of any other 

 liquid, furnishes the means of determining the velocity with 

 which sound is propagated in it. This application of the expe- 

 rimental determination of compression has been made by Dr. 

 Youngt and Laplace, who have each given a formula by which, 

 when the contraction is known for a given pressure, the velocity 

 of propagation can be calculated. Poisson has also given a de- 

 monstration of the formula in question^, which, it appears, applies 

 as well to solids as to liquids. If D be the density of the solid 

 or liquid, k the length of a cylindrical column of it under a 

 known pressure, e the small diminution of this length by a given 

 increase of pressure P, then the velocity of pi'opagatiou will be 



yP~k 

 -jj- . This formula has been put to the test by experiments 



made in the lake of Geneva by M. Colladon in 1826§. On ob- 

 serving that the sound of a bell struck a little below the surface 

 of the water was not audible out of the water at considerable 

 distances from the point of disturbance, but appeared to be de- 

 flected downwards when it fell very obliquely on the water sur- 

 face, it occurred to him to place a little below the surface a metallic 

 plate, with its plane vertical and perpendicular to the direction 

 of the sound, surmounted by a conical tube, to the end of which 

 when the ear was applied the sounds caught by the metal plate 

 were audible when they came from a distance of 13487 metres. 

 The sound traversed this distance in 9*4 seconds, consequently 

 the velocity was 1435 metres in a second. By calculating the 

 velocity given by the formula with due attention to all the cir- 

 cumstances that might affect the accuracy of the result, M. Col- 

 ladon finds 1428 metres. The difference between this and the 

 experimental value falls within the limits of the possible errors 

 of observation, and the accordance of the theory with fact may 



* Experiments on alcohol and sulphuric sether show a sensible diminution of 

 contraction for high pressures. See the Essay of MM. Colladon and Sturm, 

 An. de Chim. et de Phys., torn, xxxvi. p. 144 — 147. 



t Lectures on Natural Philosophy, vol. ii. p. 69. 



X Memoires de I'Inslitut, An 1819, j). 3'J6— 400. 



§ An. de Chim. et de Phys. lorn, xxxvi. p. 242, 



