﻿in a Rectangular Bar by means of Polarized Light. 15 



outside. The case q< 0, V <0 does not occur. The three cases 

 just mentioned are illustrated by figs. 6, 7, and S respectively. 



Fig. 8. 

 H d F 



. (14) 

 . (15) 



u is a 



We have now to consider under what condition the points 

 P, P' are real. Clearly the greatest possible algebraical 

 value of rr{ is CQ 2 /4 = (7/ 2 sec 2 0')/4. If, then, P, P' are to 

 be real, we must have 



b' 2 sec 2 cf)' sin 2(i — <£') 



4 > + ~q£n~2i'~ ' 

 that is either 



ijb' 2 sin 2/>4 cos 2 tf> sin 2(z— </>') (?>0), 



or ^/ 2 sin 2z< 4 cos 2 </>' sin 2(i — (j) r ) (q<Q). 



Let us write ?j = 4cos 2 (/>' sin (2i — 2<f)') ; then 

 maximum or minimum when 



-tt\ = — 8 cos </>' cos (2i—3cj> f ) =0, 



which gives the values 



</> = — (maximum), w = 0, 



,, 2 . 7T. . . / 7r _9/\ 



9 = 7, * + 77 (minimum), w = — 4 sin 3 ( — 4 — ), 

 r o o \ 3 / 



,, 2 . 7T / . o/7T+2A 



9 — ^> z— /• (maximum), 7< = 4 snrl t> ) , 



, 2 . 7T , . . x 2i 



<£ = o z_ o (minimum), w = — 4 sin 3 ~ , 

 o ^ .5 



(j> = — - (maximum), « = ; 



z 



of these the second lies between <£' = i and <£' = -- , the third 

 between (f>' = i and <£'=i — y, the fourth between /— * and 



7T ^ 



Also corresponding to the values </>' = /, or 



77 



M =o. 



