828 MR. G. A. SCHOTT ON THE REFLECTION AND REFRACTION OF LIGHT. 
The first term represents the refracted \v^ve, the second the pressural wave, which 
only exists close to the boundary x = d. 
ii is the angle of refraction, which obeys Snell’s law, sin = v — sin 
is a constant found to be + /yX (sin^ -^ 
s, s' are complex constants Se^^, S'e“^ ; S, S' are the amplitudes, cr,. a’ the retardations 
of phase, of the refracted and pressural waves. 
The pressure is proportional to 
^TT/^l 
S'. € 
2irfiiai 
~ 
{x - d) + ‘(-p2/ -;><) 
The signs of R, S are chosen so that at normal incidence v shall be + for each 
wave, as shown in the figure, when the signs of Pt, S are +. 
Variable Layer. 
It extends from x ■= 0 to x = d and is continuous with the media bounding it. 
The displacements and their first differential coefficients with respect to x must hiive 
tlie same values at the l^oundaries in the variable layer and in the media beyond, 
giving in all twelve boundary conditions, six of which determine the motion in the 
variable layer, and the remaining six determine the constants r, r, s, s' for vibrations 
parallel and perpendicular to the plane of incidence. 
We may write the displacements in the form u. 
^dio 
gv \ : write also 
nv 
+ A')= - 
01J ! A, 
then u. .V are functions of x alone, and 11 is proportional to the pressure, which 
vanishes for those theories which make m zero. 
The equations (II.) become 
Vibrations parallel to plane 
of incidence. 
27r fHI 2-771/ dv I-TT" , „ 
---t-— + „ (u'' — v^) u= 
\ dx \ dx ' >2 \r / 
— i 
Ttt" 
vU — t 
iTTV 
du d~v 
. -iTT” o 
+ • F 
V = 
