Mr. Ivory's Tlieory oj the Velociti/ of Soiind. 253 



a parcel of air agitated in an aerial undulation, there is no 

 extraneous heat, and t = : the foregoing equation, therefore, 

 will become, 



ji \ -\- a.6 — tti 



j' 1 + a ^ + /3 i * 



And, bv exterminating i, 



This equation expresses the relation between the elasticity and 

 density in the circumstances supposed, and it is that which 

 must be employed in the investigation of the velocity of sound 



in place of the equation ^ = A, resulting from the law of 

 Boyle and Mariotte, and forming the basis of Newton's for- 

 mula. 



In the Philosophical Magazine for June 1825, p. 12, the 

 following equation is obtained in considering the motion of a 

 line of air, viz. 



-i. = 1 - ^: 



g ax 



Substitute, now, this value in equat. (D) ; thus 



and if we put k = I -\- -^, and go through the rest of the 

 calculation as at the place cited, we shall obtain, 



ddz , v' ddz 



dT"^ f dx" 



The true velocity of sound is therefore ^ ^ ^ ~j'- ^ut the 

 Newtonian velocity, deduced from the law of Bo^'le and Ma- 

 riotte, is /— : and these two formula contain the demon- 

 stration of Laplace's theorem. 



The theory we have attempted to give of the combination 

 of heat with elastic fluids is founded on acknowledged facts. 

 It is general, extending as far as experience has enabled us 

 to reiluce the effects of heat to precise rules. It follows from 

 it that the quantity k, on which the velocity of sound depends, 

 has the same value for air and all the gases ; and likewise that 

 it remains constiint in every diversity of pressure and density: 

 all which consequences arc known to be consonant to obser- 

 vation. 



Ihc 



