348 



to this remarkable result, that the velocity with which such 

 vibration spreads into those portions of the vibratory medium 

 which were previously undisturbed, is in general different from 

 the velocity of a passage of a given phase from one particle to 

 another within that portion of the medium which is already 

 fully agitated ; since we have 



velocity of transmission of phase =^ t, (A) 



but 



ds 

 velocity of propagation of vibratory motion = -77 , (B) 



aK 



if the rectangular components of the vibrations themselves 

 be represented by the formulae 



XAiCos(£+5^— A^a?), XA2 cos [i-^st—kx), XA3C0S {f\-st—kx), (C) 



t being the time, and x being the perpendicular distance of 

 the vibrating point from some determined plane. 



This result, which is believed to be new, includes as a 

 particular case that which was stated in a former communi- 

 cation to the Academy, on the 11th of February last, 

 (Proceedings, No. 15, page 269,) respecting the propa- 

 gation of transversal vibration along a row of equal 

 and equidistant particles, of which each attracts the two 

 that are immediately before and behind it ; in which par- 



k 

 ticular question s was — 2a sin-, and the velocity of pro- 



k 

 pagation of vibration was ■=. a cos -. Applied to the theory 



A) 



of light, it appears to show that if the phase of vibration 



in an ordinary dispersive medium be represented for some 



one colour by 



•+IC--')- «' 



so that X is the length of an undulation for that colour and 



