Motion of Solid and Fluid Bodies. 197 
If now, as in the former case, we designate by (9%, %, #5 9,» ?) the phases of 
the incident, transverse reflected, transverse refracted, normal reflected, and nor- 
mal refracted waves; and mark in a similar manner the other quantities in the 
problem, we shall obtain for the equations of condition (65), the following, 
(z=0, making ¢=¢,=9' = ¢, = ¢”, as before): 
Tcosa + 7,cosa, + 7,cosa, = 7’cosa’ + 7’cosa’’, 
scosy + 7,cosy, + 7,,cosy,, = 7’cosy’ + 7’’cosy”, 
(69) 
2ncosy 2n cosy, 1+ 2n?, ,2n'cosy’ , ,, 1+ 2n'”? 
a r a 7, A, a aT d,, =KkK (* nN SF cd Ne } 
{cosy + ncosa site Ucosy,+7,cosa, 21, ¥ Ucosy’+n'cosa’ 20’ 
> A 7 SZ KO MM ——_ 7 ——_ }; 
Xr f A, wt r,, Le N —- a ’ 
or substituting for J, 2, &c....a, y, &c., their values in terms of (@, 6,, 0’, @ 
6” ) 
which are all known quantities, we shall have, finally, 
Ti 
(7 +7,)cosd + 7,sin@,, = 7'cos6’ + 7’’sin6”, 
(7 —7,)siné + 7, cosé,, = 7’sind’ — 7’’cos0”, 
sin2@ 1+ 2cos°0, sin2@ 1+ 2cos*é\ 
=p, \ SS Sa es SS | SH = fe 70 
(7 fs) x Orr AG K (: WW se rn” (i ) 
cos20 sin26 cos2’ ,,sin26” 
nk a ami r “ax(? x Se X7 6 
“ 
: N 
K bemg equal to a 
ds 
These four equations determine completely, in terms of known quantities, 
the four unknown vibrations (7,, 7’, 7, 7’). 
To determine the actual position and magnitude of the two transversals in the 
present case, we must use the equations (67), which give for the first transversal 
the equations 
r 1 7 _— sin26 ee 
p ra td T° p+ Diem Ne v2 dQ; 
which show that it is situated in the bisection of the angle between 2 and — a. 
And for the second transversal, 
2anr 5 
g = Nr.cos26 sind. 
7" oO 
