MR. Cr. A. SCHOTT ON THE REFLECTION AND REFRACTION OF LIGHT. 857 
Electromagnetic and Contractile Ether Theories :— 
K|| 
COS^ (t'o + \) 
COS^ {h — h) _ 
^ ^ sill sill cos cos h , g sill" sin 2 i-^ cos h cos h ”| 
cos ih ~ cos (^0 + h) 0Os2 (iy — -Ij) COs 2 (Iq + ^\)J 
tan (/oil) = Dcos^o 
tan (/o-L) — tan (pW) = E 
sill" cos tg 
cos (Iq — ?’j) cos (Iq + h) 
tan {pE — /o 11) = 
E sin2 cos h 
cos (h — ij) cos (h + h) + E 
^ XL 
These expressions are true as far as order d^jX^, provided X/27rd > greatest value 
of p. occurring in the variable layer. 
Except in the neighbourhood of the polarizing angle, tan (pX — pll) reduces to 
E siid h cos 
cos (^0 - h) cos (h + h) * 
Elastic Solid Theory. 
Here Ave introduce subsidiary angles defined by the equations 
2 2 
tan a =: M tan + b) tan /8 = M tan (ff, — q), where M = 
Mr + M(i~ 
Then we have 
RAy_ cos® /S. cos® {\ + q) 
Ell/ cos® a . COS® (h — q) 
cos cos 
^ ^ cos® a. cos® /S. sin® q sin® q 
cos® (q — q) cos® (q + q) 
tan (p 11) = D . cos 7 q 
tan (p X) — tan (p 11) z=: tan (a -I- ;S). [1 + D cos q. tan (« + m 
tan (p X — p 11) = 
cot (« + /3) -I D cos q 
y. (xii.) 
cot® {ci + yt?) (1 + D® cos® q) + D cos q cot (a + yd) + D® cos® q 
or 
, / , ,,, 1^0 cos® q. cosec® (« + /3) 
cot (pX — p II) = cot (a + m -L D®- — 
^ ' \ I I cot (« + y8) + D cos q 
* The expression for tan {fiL — ^)ll) inclusive of terms involving (27rfZ/\)® is of the form 
E sin2 q cos q 
cos (q — q) cos (q I- q) (1 + a sin®fQ + h singly + ..)+ a' + h' sin® v'o + . . ’ 
a, b, . . . a', h’, . . . being constants of .order ( 297 -d/\) 2 . Since tan {i>l. — />!!) is large only in the 
neighbourhood of the polarizing angle I, we may put z= I in the small terms, thus obtaining the 
expression in the text. Then 
— 2« ~ ~ '“d + 
pi _ _ /n® — /<o® _ 277-d^ ^ P _ _ a + b' sin® I b . . . 
1 + asin^I f 6 sin'll H- . . X 1 + a sin® I + h sin'll + . . . 
MDCCCXCIV.-A. 5 E 
