82 



On the Thermodynamic Theory of Waves. [Recess, 



Tn applying this equation to particular cases, <p and t are to be ex- 

 pressed in terms of p and s. 



It is shown to be probable that the only longitudinal disturbance which 

 can be propagated with absolute permanence of type is a sudden disturb- 

 ance ; and that the consequence of the non-fulfilment of the condition of 

 permanence of type is a tendency for every wave of gradual longitudinal 

 disturbance to convert itself by degrees into a wave of sudden disturbance. 

 But although suddenness of disturbance may be approximated to, it cannot 

 be absolutely and permanently realized ; whence it follows that the propa- 

 gation of waves of longitudinal disturbance of absolutely permanent type 

 for an indefinite distance is impossible ; and this may be the cause of the 

 absence of longitudinal vibrations from rays of light. 



The laws of the advance of adiabatic waves are investigated ; that is, 

 waves of longitudinal disturbance in which there is no transfer of heat, and 

 in which consequently d0=O ; and it is shown, by the aid of the equation 

 marked (B) in this abstract, that the compressed parts of those waves tend 

 to gain upon and at last overtake the rarefied parts, just as the crests of 

 rolling waves in shallow water gain upon and at last break into the troughs, 

 the consequence being a gradual conversion of the adiabatic waves into 

 waves of sudden disturbance, followed by a mutual interference of the com- 

 pressed with the rarefied parts which leads to the energy of the waves 

 being spent in molecular agitation. 



It is also shown that the extreme values of the pressure and of the 

 bulkiness are constant during the change of type ; and consequently that 

 the respective velocities with which the plane of greatest compression gains 

 upon and the plane of greatest rarefaction falls behind the plane of undis- 

 turbed density are uniform. 



The values of the linear velocity of advance, mS, found for various modes 

 of finite disturbance, all approximate, when the disturbance becomes inde- 

 finitely small, to the well-known value of the velocity of sound, viz. 



, the relation between P and S being determined by the 



condition d(p = 0. 



Supplement. Received October ], 1869. 

 (Abstract.) 



In this supplement the author of the paper refers to the previous inves- 

 tigations on waves of finite longitudinal disturbance by the following 

 authors : — 



Poisson, 'Journal del'Ecole Poly technique,' vol. vii. cahier 14, p. 319 

 Stokes, Philosophical Magazine, Nov. 1848, S. 3. vol. xxxiii. p. 349. 

 Airy, Philosophical Magazine, June 1849, S. 3. vol. xxxiv. p. 401. 

 Earnshaw, Philosophical Transactions, 1860, p. 133. 

 He points out to what extent the results arrived at in his own paper are 



