and the Observed Velocity of Sound in Air and Gases. 13 



investigation, and has succeeded in proving that, during the 

 propagation of sound-waves in the atmosphere, the compressions 

 and expansions of the particles of the elastic fluid take place so 

 rapidly, that there is not time for any appreciable transmission 

 of heat between different particles; and that consequently the 

 variations of the pressure and density are related to each other 

 as they would be in a non-conducting vessel. In other words, he 

 has shown that Professor Challis's supposition, that the deve- 

 loped heat is lost by radiation, is untenable, and that Laplace's 

 view has a real physical foundation. 



Hence it follows that the momentary disengagement of heat 

 during the transmission of aerial sound-waves must be regarded 

 as a really existing cause, a vera causa, which must act to increase 

 the velocity above what it would be were there no such thermal 

 change produced by the changes of density. Under this point 

 of view, it is clear that any mathematical theory of sound which 

 fails to take cognizance of the development of heat in the propa- 

 gation of pulses in the atmosphere is, prima facie, defective and 

 imperfect. On this score, the formulae expressing the theoretical 

 velocity of sound in air, given by Cballis, by Potter, and by 

 Earnshaw, we fatally assailable. Perhaps the formula of Hera- 

 path is excluded from this category ; for it seems to have been 

 a deduction from his ingenious speculations on molecular physics, 

 the basis of which rests upon thermotic considerations. 



Looking upon Laplace's explanation as a vera causa acting in 

 the right direction, the rules of philosophizing will not justify us 

 in referring the observed effect to an unknown or imaginary 

 cause, when a real one is at hand adequate to account for the 

 whole effect. Consequently the onus probandi rests with those 

 who reject his explanation, to show that it is not adequate to ex- 

 plain the whole discrepancy between theory and fact. This aspect 

 of the question seems to have been partially recognized by Mr. 

 Earnshaw. He sets forth his reasons for discarding Laplace's 

 theory in the following words : — 



" I think I may say that the requisite value of the coefficient 

 (commonly denoted by k) is mucli greater than Dalton's experi- 

 ments warrant, and than what would have been conjectured a 

 priori to be its value. In looking also at the determinations of 

 its value, and also of the value of the velocity of sound, I am a 

 little suspicious that modern experimentalists have suffered them- 

 selves to be biased by a desire to make experiment and theory 

 agree. At any rate, if we compare experiments made since 

 1816, when Laplace announced his theorem for the correction of 

 Newton's result, with those previously made, it is impossible not 

 to notice a very sudden and startling change; and in the same 

 spirit the value of k has been gradually growing in the hands of 



