ACCORDING TO THE UNDULATORY THEORY. 481 
through a system of waves of light after a lapse of the time é whose 
intensity is a and whose length of undulation is }, is expressed by the 
equation 
5 x 
=asin27 (#5) 
in which x stands for the distance of the particles from the centre of vi- 
bration. 
Let us use this formula to determine the velocities of undulation wu, 
Uy) Uo) Us...) Which the particle of ther acquires through the system 
of waves of light, whose intensities are: (1 —7)?a, r* (li-—r)? a, 
r4(1 —r)?a,7r°(1 —r)?a...., thus we have: 
x 
u=(1—r)a.sin 2x (¢—<) i 
=(1—r)*a.sin2r >) 
a+2b6 
IN 
“, =F? (1 ~r)a.sin2n (¢— 
=ri(1—r)?a [ sin 22 (¢— = oops re 
A nN 
— cos2r (: — ) sin 2727] 
oN r 
xr+46 
r 
u, =r (1—r)ta.sin 2 x (¢— 
=r+(l1—r)a [ sine = («—) cag 2 = aP 
— eos 2 (¢— 5) sin2. | 
; r N 
u; =7r°(1—r)*a.sin2r (¢ — a6") 
=r(l—r)*a [ sin Qn (« -<) cos. 220 
— eos 2x (¢ —§) sin 3 aed 
r IN 
er (1 —ra.sin 2x (¢— =") 
