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 
> (A) 
velocity of transmission of phase = 
m1 
but 
(B) 
velocity of propagation of vibratory motion = oe 
if the rectangular components of the vibrations themselves 
be represented by the formule 
XA, Cos(e4st—hkx), X Ao cos (e+st—ha), xA3cos (e+-st—ha), (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- 
: ; Nie 5 
ticular question s was = 2a sin 5° and the velocity of pro- 
: a k : 
pagation of vibration was = a cos 3° Applied to the theory 
of light, it appears to show that if the phase of vibration 
in an ordinary dispersive medium be represented for some 
one colour by 
+3 (t-2), (C)’ 
so that A is the length of an undulation for that colour and 
