﻿by Vibrations of the Air. 285 



titled to be called a science. For a long time I admitted the 

 possibility of the propagation of a solitary wave, and consistently 

 therewith maintained that the condensation varied inversely as 

 the square of the distance. But I have recently become aware 

 that that admission is contradicted by results of my hydrody- 

 namical researches which, I have reason to say, are well esta- 

 blished. The contradiction I refer to will be understood from 

 the following explanation. 



A general law of free vibratory motion parallel and transverse 

 to an axis, and of uniform propagation of such motion in the 

 direction of the axis, having been arrived at antecedently to the 

 consideration of any cause of disturbance of the fluid, it seems 

 necessary to conclude that motions produced by given arbitrary 

 disturbances are actually composed of such spontaneous motions 

 due exclusively to properties of the fluid. (I need not here 

 refer more particularly to these views, further than to say that 

 the arguments by which they are maintained were fully given in 

 the pages of this Journal.) Now a solitary wave of condensa- 

 tion or rarefaction cannot be composed in this manner, because 

 the result of such composition must be both condensation and 

 rarefaction. It seems, therefore, that on these principles, when 

 a disturbance tends to produce condensation only, the conden- 

 sation is resolved into a series of alternate condensations and 

 rarefactions, arranged in a manner depending on the disturbance 

 on each side of a maximum condensation, and diminishing by 

 gradations in both directions from this, in such manner that the 

 excess of condensation is equal to that impressed by the disturb- 

 ance. A solitary wave of rarefaction would be similarly resolved. 

 Also like resolutions would take place at an abrupt beginning, 

 and at an abrupt ending, of a regular series of plane-waves. 

 Similar considerations may be applied to account for resolutions 

 into series of transverse vibrations caused by abrupt lateral dis- 

 turbances. 



According to these views, the condensation in waves propa- > 

 gated from a centre, however they may have originated, will vary / 

 inversely as the distance. For, as I have elsewhere proved, 

 and in fact may easily be shown, by reason of the part of the 



velocity expressed by the term — ^ ^ > tne rate of dimi- 

 nution of the condensation or rarefaction with distance from the 

 centre will be continually changed from the law of the inverse 

 square of the distance to that of the simple irfverse of the dis- k 

 tance, provided there be alternate condensations and rarefactions. / 

 For in that case the above-mentioned velocity gives rise to a con- 

 tinual flow from the rarefied into the condensed parts, and just in 

 the proportion required for altering the law of diminution with 



