322 Dr. C. Burton on Plane and Spherical 



case of § 3 (fig. 2) : and first, concerning the nature of the 

 analogy, it should be noticed that the individual spheres are 

 not the analogues of the separate gaseous molecules, but that 

 when both spheres and molecules are very small and very 

 numerous, the apparently continuous properties of the system 

 of spheres correspond to similar properties of the gas. The 

 connecting springs represent the elasticity of the gas, iso- 

 thermal or adiabatic as the case may be, and the energy of 

 relative motion and unequal relative displacement amongst 

 the disturbed spheres suggests that there is a production of 

 heat over and above that which would be due to the (iso- 

 thermal or adiabatic) change of density : that is, a dissipative 

 production of heat. The motion considered in the last section 

 properly corresponds to the case where there is no conduction 

 of heat, so that the connecting springs are the representatives 

 of adiabatic elasticity, and the additional heat generated 

 remains wholly within the more condensed part of the air. 

 If we make the somewhat violent assumption that the tempe- 

 rature of the air remains constant throughout, the additional 

 heat generated will be conducted away isothermally, and the 

 equivalent energy will be, for our purposes, entirely lost. 

 To represent this case by means of our spheres we should 

 have to regard the connecting springs as representing iso- 

 thermal elasticity; while the energy of relative motion and 

 unequal relative displacement among the disturbed spheres, 

 as fast as it is produced, is to be consumed in doing work 

 against suitable internal forces. 



6. The mechanical system of spheres and springs, having 

 suggested a solution, has served its purpose, and it now 

 remains for us more closely to consider the aerial problem in 

 the light of this suggestion. We may take, first, the case 

 where the temperature is supposed to be invariable ; for 

 although such a supposition is necessarily far removed from 

 the truth, it leads to very simple results, which indicate well 

 enough the general character of the motion. Let the piston 

 A (fig. 4) be moving to the 

 right with constant velocity j^ 4 



v (which may be either less 

 or greater than a, the velo- 

 city of feeble sounds in air). 

 Assume all the air between 

 A and a parallel plane sur- 

 face B to have the velocity v 



and density p x , while all the air to the right of B is at rest 

 and has the density p . Let the plane B move to the right 

 with velocity V. Then the invariability of mass between A 



