and the Observed Velocity of Sound in Air and Gases. 15 



be abundantly evident in the sequel, when the results of theory 

 are compared with those of the most reliable experiments. 4. 

 While Mr. Earnshaw denies the sufficiency of Laplace's sugges- 

 tion, he admits that it is a vera causa, and yet he obtains a 

 formula which professes to give accurately the velocity of sound, 

 without taking cognizance of this vera causa, this development of 

 heat during the transmission of aerial pulses ! Assuredly, if 

 this disengagement of heat is a real cause tending to augment 

 the velocity of sound-waves (however inadequate to account for 

 the whole discrepancy between theory and fact), it should cer- 

 tainly have constituted an essential element in his mathematical 

 investigation. As far as I am able to understand, the whole 

 excess of velocity given by his formula above that of Newton is 

 exclusively ascribed to the circumstance that he has discarded 

 the assumption of continuity in the medium, and substituted in 

 its place the hypothesis of " particles separated by finite inter- 

 vals." The thermic changes taking place during the propagation 

 of aerial pulses are entirely excluded from the investigation. 

 Hence he concludes, " Thus we see that the error committed in 

 calculating the velocity of sound was not the leaving out the 

 consideration of the development of heat, but the supposing the 

 medium of air to be continuous" 



I now proceed to the consideration of the adequacy of the 

 various formulas which have been devised for computing the 

 velocity of sound, by a comparison of their results with those of 

 the best experimental determinations. The Newtonian formula 

 forms the basis of every expression for the theoretic velocity of 

 sound which the ingenuity of mathematicians has elicited. 

 Without exception, they all concur that Newton's velocity must 

 be multiplied by the square root of a certain factor. And the 

 question is, What is the true value of this factor ? Hence it is 

 evident that, in order to a correct comparison of the numerical 

 results given by the several formula? with experiment, it is neces- 

 sary, as a preliminary step, to determine the true value of the 

 quantity vgh, expressing the Newtonian velocity of sound in 

 air. As both g and h are determinable solely by experiment, 

 let us see what are their best-determined values. 



And first, in relation to the value of h, or the height of a 

 homogeneous atmosphere. According to the admirable experi- 

 ments of M. Regnault*, one litre of mercury at Paris, 60 metres 

 above the sea, at the temperature of zero Centigrade, weighs 

 13595*93 grammes. According to the same experimenter \, 

 as corrected by M. Hitter J for a slight error of computation, 



* Memoires de VAcademie des Sciences, vol. xxi. p. 162. Paris, 1847. 

 t Ibid. p. 157. Paris, 1847. 



% Mimoires de la Societe de Physique et d'Histoire Naturelle de Geneve, 

 vol. xiii. p. 361. 



