308 Royal Society : — 



gradual longitudinal disturbance to convert itself by degrees into a 

 wave of sudden disturbance. But although suddenness of disturb- 

 ance may be approximated to, it cannot be absolutely and permanently 

 realized ; whence it follows that the propagation of waves of longitu- 

 dinal disturbance of absolutely permanent type for an indefinite dis- 

 tance 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 d(f>=0 ; 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 compressed 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 conse- 

 quently that the respective velocities with which the plane of greatest 

 compression gains upon and the plane of greatest rarefaction falls 

 behind the plane of undisturbed 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 indefinitely small, to the well-known value of the velocity 



vm- 



of sound, viz. \/ J i L the relation between P and S being de- 



termined by the condition d(f> = 0. 



Supplement. 



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

 investigations on waves of finite longitudinal disturbance by the fol- 

 lowing authors : — 



Poisson, 'Journal de l'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 identical with those of the above-mentioned previous researches ; 

 and he claims the following results as new: — The conditions as to 

 transfer and transformation of heat which must be fulfilled in order 

 that permanence of type may be realized, exactly or approximately, 

 in a wave of finite longitudinal disturbance in any elastic medium ; 

 the types of wave which enable such conditions to be fulfilled with 

 a given law of the conduction of heat ; the velocity of advance of such 

 waves ; and some special results as to the rate of change of type in 



