250 Mr. Ivory's Theory of the Velocity of Sound. 



the small parcel of air is less than in the quiescent state, 

 the elasticity will be greater on the second supposition than 

 on the first, on account of the extrication of heat ; but, when- 

 ever the bulk is greater than in the quiescent state, the elasti- 

 city will be less on the second supposition than on the first, 

 on account of the cold produced by the absorption of heat. 

 Now the accelerating forces of the aerial particles are the dif- 

 ferences between their actual elasticity and the elasticity of 

 the quiescent medium ; and as these forces are always greater 

 on the second supposition than on the first, the velocity of 

 the undulation must be swifter in that case than in this. The 

 formula of Newton, being deduced from the law of Boyle and 

 Mariotte, is consonant to the first supposition ; and there is 

 undoubtedly in the second supposition a tendency to diminish 

 the difference between theory and experiment, by increasing 

 the estimate of the velocity of sound. One circumstance how- 

 ever, it may be alleged, must in some degree modify the effect 

 of the variations of heat in the agitated air ; namely, the ra- 

 pidity with which the small increments and decrements of free 

 heat would be equalized to the temperature of the surrounding 

 medium. But the whole time of an aerial vibration is ex- 

 tremely short; and we may safely consider every change of 

 volume that takes place during its progress, and every varia- 

 tion of free heat, as enduring only for an indivisible instant of 

 time. Every parcel of air as it is successively agitated retains 

 the whole of its absolute heat ; and the rapid evolution and 

 absorption of free heat have no other effect than to increase 

 the elasticity. 



The principle suggested by Laplace, having a real exist- 

 ence in fact, and being adequate at least in a certain degree 

 to reconcile the theory with experiment, it became important 

 to ascertain the exact increase of velocity deducible from it. 

 But here a difficulty occurred. It was known that heat was 

 extricated from air when it is condensed, but there was no 

 measure of the effect. It even seemed very difficult, if not 

 impossible, to arrive at any tolerably precise estimation by 

 direct experiment. MM. Biot and Poisson therefore reversed 

 the question, and inquired in what degree the elasticity com- 

 puted by the law of Boyle and Mariotte must be increased ; 

 or, which is the same thing, in what proportion the free heat 

 must vary with respect to the volume ; in order to bring out 

 the true velocity of sound. By this means we might at least 

 be able to judge whether the assigned cause would alone ac- 

 count for the observed deficiency. And, admitting that the 

 effect fell within the limits of probability, there can be no 

 doubt that the just rules of philosophizing would be nowise 



infringed 



