162 M. V. Regnault on the Velocity of the 



(2) That its elasticity is not affected by surrounding objects. 

 But my experiments on the propagation of waves in tubes show 

 that the walls of the tubes exert a very notable influence. 



(3) That the gas does not oppose any inertia to the transmis- 

 sion of the wave. Now my experiments show that the emission 

 of a strong wave always causes a true displacement [veritable 

 transport) of the first gaseous layers, which displacement consi- 

 derably increases the velocity of the wave's propagation, espe- 

 cially through the first portion of its course. 



(4) In order to make allowance for the acceleration produced 

 by the sudden disengagement of heat which takes place at the 

 moment of the wave's passage, Poisson's law is introduced into 

 the calculation. But this law is only exact if the gas has per- 

 fect elasticity, if it obeys Mariotte's law, &c. 



Finally, the theoretical calculation assumes that the excess of 

 compression which exists in the wave is infinitely small com- 

 pared with the barometric pressure supported by the gas. But 

 the experiments made to determine the rate of sound in free air 

 have been hitherto made by means of a cannon, and the wave 

 has been reckoned from its source, namely the cannon's mouth. 

 Now this wave as it leaves the cannon is under enormous com- 

 pression — a compression, it is true, which diminishes very ra- 

 pidly as the wave spreads spherically through space ; but during 

 the first part of its course it cannot be supposed that its com- 

 pression is infinitely small. 



When the excess of compression in the wave is a sensible 

 fraction of the compression of the gaseous medium at rest, we 

 can no longer employ Laplace's formula, but must have recourse 

 to a more complex formula embracing the true elements of the 

 problem. Even the formula which I have given in my Memoir 

 is only an approximation; for it implicitly admits Mariotte's law 

 and all its consequences. 



In short, the mathematical theory has as yet only touched 

 upon the propagation of waves in a perfect gas — that is to say, in 

 an ideal fluid possessing all the properties which had been intro- 

 duced hypothetically into the calculation. It is therefore not 

 surprising that the results of my experiments often disagree from 

 theory. 



I. According to theory, a plane wave in a straight cylindrical 

 tube should advance to an indefinite distance with a constant 

 velocity. My experiments show that the intensity of such a 

 wave continually diminishes, and this the more quickly the less 

 the section of the tube employed. 



In order to establish this fact conclusively, I created waves of 

 equal intensity by discharging one gramme of gunpowder from 

 the same pistol at the orifices of conducting tubes of very differ- 

 ent sectional areas, and I endeavoured to ascertain the length 



