Double Refraction of Quartz. 99 



sma + <ji. w-k. cos a + <p.x +sin a + <j).y + cos " + g = o ^ 



sin a + <p. x +k. cos a + (p.w+ sin u + <p.x - COSa + y _ o ^ 



ft 



By the solution of these equations 



c 



w = 



j^-pCOS a + <p, 



k . 



k 2 



V- Y^rjf c - C0Sa +<P> 



~ = ~rTF c - sina+ ^ 



And hence the expressions for the vibrations are (omitting the 



common factor ■ c ,„ ^: 

 1 + k-J 



In Oo,, cos a + <p. sin -^(vt-x) + k. sin a + <{>. cos — (vt-x) 



■\ \ vv w f ■ ■*••*«* w-ry/.vuo — — 



In o l0o V. sin a + <p. sin -^(vt-x)-k.cos7?$. cos — (vt-x). 



In Ee„ V-cos <* + <}>. sin-?- (vt-x)-k.sin7+$. cos— {vt-x). 



to e ie 2 , sin a + 0. sin ^ (»*-#)+£. cos <T+0. cos — (»*-«). 



After emerging from the crystal, x must be diminished, in the 

 two latter expressions, by 9. (e is in fact negative for quartz, 

 but that circumstance makes no difference in our investigations 

 or conclusions). 



N2 



