) 



Mr. J. J. Waterston on the Theory of Sound. 489 



Mariotte's law, Dalton and Gay-Lussac's law, aud the velocity 

 of sound are represented by the statical hypothesis, we have 

 still Dalton and Graham's law of diffusion and diffusive velo- 

 city ; Gay-Lussac's law of volumes ; Dulong and Petit's law 

 of specific heat, extended to, the tnpre simple gaseous bodies 

 by Haycraft and the French phy.sicists j the law of latent heat 

 partially discovered by Gay-Lussac aod Welter's experiments ; 

 also the diminution of temperatrffe -jn ascending the atmo- 

 sphere, — all as yet undeduced from -spiy' statical theory of elastic 

 fluids. It may be that additions t^xthe mathematical hypo- 

 theses of Laplace will be attempted wifh .]the view of extending, 

 their capacity, as indeed there seems to 'be '-no hmit to this arti- 

 ficial and barren system of procedure, 'which is as far removed 

 from the simplicity of nature as the hiddous epicycles of Ptolemy. 



There is another mode by which pulses may be conceived to 

 be transiiiitted, which admits of being set forth in a popular way. 



Suppose we range a number of ivoi'y balls in a straight line 

 upon a billiard table, and strike the first of the row upon the 

 second, the initial velocity will be carried forward from one ball 

 to the next adjacent, and so will make its appearance in the last 

 — supposing perfect elasticity and no resistance in rolling — 

 undiminished as if the motion of the first ball had continued, 

 and the impulse had been carried by it alone, and not trans- 

 ferred by impact through others. These balls, confined to one 

 line, are supposed to be in motion among themselves, so that 

 those adjacent alternately strike against each other in opposite 

 directions ; the end ones being reflected from the cushions, and 

 then back again after striking the next adjacent ball, the vis viva 

 in one direction being at all times equal to the vis viva in the 

 opposite. 



If we now suppose one cushion to move forward with compa- 

 ratively slow velocity, each time the adjacent ball strikes it it 

 will be reflected with a velocity greater than that with which 

 it impinged. This increment of velocity it transfers to the 

 next ball, and so on ; and the velocity with which the impulse is 

 transferred along the line is equal to the common velocity with 

 which the balls move. We may suppose the line extended inde- 

 finitely, and the motion of the cushion to be alternately forwards 

 and backwards. While the adjacent ball impinges many times 

 during each advance and retreat — during the former carrying 

 forward a succession of small increments of vis viva, during the 

 latter a succession of small decrements of vis viva — a pulse is 

 formed, the intensity and duration of which depends on the 

 motion of the cushion, but the velocity of propagation upon the 

 motions of the balls, upon their common vehx-ity. 



