Motion of Solid and Fluid Bodies. 193 
dy 
==a() =NnN— 
N ’ 5 ee 
== (oh n= 0, (59) 
a0) — gals 
dx 
from which it is evident that the equations of condition at the limits (57) will be 
reduced to the following, 
y= 4; N——- = 
(60) 
recollecting that the condition, z = 0, is implicitly supposed in these latter equa- 
tions, as they belong only to the limits. The equations of condition at the limits 
are thus reduced to ¢wo, which is exactly the number required ; for as all the mo- 
tion is perpendicular to the plane of incidence, there will be no normal reflected 
or refracted wave, but only one reflected and one refracted wave, whose vibrations 
are transversal and perpendicular to the plane of incidence, and whose intensities 
are the ¢wo unknown quantities in the problem. The equations (59) also prove 
that the first transversal is zero, and that the second lies in the plane of inci- 
dence. 
As there are two waves in the first body, and one in the second, we shall have 
a = tcosh + 7 cos, ay’ = cos’ ; 
7,7, 7 being the incident, reflected, and refracted vibration respectively, and 
on on on , , 
= (lx + nz—vt), o, = x le +nz—vt), ¢ = x (Ve+n'z—v't); 
/ 
l, X, v belonging to the incident wave, J, A,, v, to the reflected, and /’, X’, v’ to 
the refracted. 
Substituting these values in (59), and proceeding as in (42), we obtain 
Page Pe hae Ap Dreiser a atc? 
7 5 (= sing + x sing, —.f"=N & sing : 
Qa fe ses al * 7 hy . Qa J eee ET al! . ] 
pil == IN Gaing + ee sing), za IN (F sings) 
: bod r in 
but sinceJ=/1, v=v, ASA, n= —7N,, and since 7 = 7 = = a where 
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