and the Observed Velocity of Sound in Air and Gases. 23 



modern and more accurate experiments before him, it is difficult 

 to imagine why he should adopt Dr. Young's estimate, " that 

 the true velocity of sound is about 1 130 feet (344*42 metres) per 

 second." Assuredly it will scarcely be maintained that this is 

 the best-determined value for the velocity of sound at the standard 

 temperature of melting ice ! And yet, after the warning he has 

 given experimentalists, it might be hazardous to suppose that 

 the mathematician has suffered himself " to be biased by a 

 desire to make experiment and theory agree." 



I now proceed to the consideration of evidence bearing on 

 this question derived from quite a different quarter. The deve- 

 lopment and experimental verification of the u Dynamical Theory 

 of Heat" has furnished an unexpected and independent confirma- 

 tion of the truth as well as the adequacy of Laplace's explanation 

 to account for the whole excess of the observed above the New- 

 tonian velocity of sound. A few words will, I hope, place this 

 in a clear light. 



According to the experiments of Regnault*, the coefficient of 

 dilatation of pure air under a constant pressure of 0*760 metre 



of mercury and at 0° Centigrade is equal to 0*00367 = Q 



of its volume for an increase of one degree Centigrade in tempe- 

 rature. Let us suppose a cylinder, the area of whose cross sec- 

 tion equals one square foot, filled to the height of 272*4795 feet 

 with a homogeneous column of pure air, under the conditions of 

 pressure and temperature above indicated. The volume of air 

 contained in the cylinder being 272*4795 cubic feet, its weight 

 will be 272*4795 x 0-0807288 = 21*99694 lbs. avoirdupois. If 

 the temperature of this column of air be raised from 0° to 1° C. 



it will expand of its volume, and will consequently 



me in the cylinder through a space of one foot. In this expan- 

 sion it will lift the weight of the entire atmosphere pressing on 

 one square foot (or 2116-268 lbs. avoirdupois) through this dis- 

 tance, namely one foot. Again, according to the experiments of 

 Regnault f, the specific heat of pure air under constant pressure 

 is 0*2379 in relation to the specific heat of an equal weight of 

 water. Hence the amount of heat required to increase the tem- 

 perature of 21*99694 lbs. of air from 0° to 1° C. equals the 

 quantity of heat necessary to raise the temperature of 21*99694 

 x 0*2379 = 5*233074 lbs. of water from 0° to 1° C. Of this 

 amount (according to the dynamical theory of heat) a part is 



* Memoires de VAcademie des Sciences, vol. xxi. p. 73. Paris, 1847. 

 t Comptes Rendus for April 18, 1853; also Phil. Mag. S. 4. vol. v. 

 pp.481 (1853). 



