of Air and the Gases, and the Velocity of Sound. 1 1 



determine the velocity of sound in the atmosphere. Newton 

 led the way in this research. But the part of the Principia 

 which treats of the nature and velocity of the aerial pulses is 

 confessedly obscure, and the soundness of the reasoning has 

 been called in question by philosophers of the first rank. 

 Without attempting the discussion of a point on which it is 

 certainly very difficult to form an opinion entirely free from 

 objections, all are agreed that the velocity of sound assigned 

 by Newton is just and accurate if we admit the law of elasti- 

 city on which his investigation proceeds. His results has 

 been confirmed by every philosopher who makes the elastic 

 force vary in the same proportion with the density. Yet when 

 we appeal to experience, a great discordance is found between 

 the fact and the theory. The velocity of sound determined 

 by experiment is greater by a sixth part of the whole than the 

 quantity computed by Newton's formula. No admissible ex- 

 planation of this great difference was found, till Laplace hap- 

 pily conjectured that the true account of it was to be sought 

 for in the law of Boyle and Mariotte. That law is exact only 

 when the temperature remains unchanged. But a series of 

 aerial pulses is a succession of condensations and rarefactions, 

 accompanied with the disengagement and absorption of heat, 

 and consequently with an increase of the air's elasticity. It 

 is true that the variations of temperature are equalized and 

 brought to the common standard in a short moment of time 

 by the transference of heat between the atmosphere and the 

 air in motion. But a sensible time is required to produce 

 this effect; and the elastic force is exerted instantaneously, and 

 while the agitated air retains all its heat of combination. 

 Therefore, in the investigation of the velocity of sound, we 

 ought not to adopt the law of Boyle and Mariotte, which sup- 

 poses that the agitated air has the same temperature with the 

 atmosphere : we ought to employ the elastic force of air, which 

 changes its volume while it retains the whole of its absolute 

 heat. When this ingenious explanation of Laplace is attended 

 to, the difference between the theory and observation disap- 

 pears, or is reduced to minute quantities that may reasonably 

 be ascribed to unavoidable errors. 



Conceive a slender horizontal tube of an indefinite length 

 containing air in a state of equilibrium ; and let x, reckoned 

 from a fixed point in the axis of the tube, be the distance of 

 a small cylinder of air within the tube, the thickness of which 

 is equal to dx. Suppose now that the cylinder is pushed 

 forward by some force to the distance x + z from the fixed 

 point, and that it occupies the length dx -\r dz in the axis. It 

 is to be observed that d x is invariably of the same magnitude, 

 B 2 whatovtr 



