Refracted Rays of Light in Cry da line Media. 273 



passing from one to the other ; so i£ the surface cuts the 

 locus in three points each must give a real solution. Let the 

 refractive index of this medium be l/d r = l/b and let a = 75°, 

 then 



0-26194 sin 8 0!— 0*56635 sin 6 L -f 0*36460 sin 4 L 



-0-05986 sin 2 ^ + 0*0000321 = 0. 



The roots are 0/=76° 40', 1 /, = 29° 56' 30", 0/"=-79° 15'. 

 The fluids which most nearly agree with this condition are 

 those of the bromo-naphthaline group. Since the above 

 rays are not deviated, we may consider them to be the rays 

 in the crystal and find the corresponding rays in the medium, 

 substituting naphthaline, by the sine law, as they obey the 

 ordinary law of refraction. 



Medium, — a mono-bromo-naphthaline. Walter gives 1/d 

 = 1-65820 at 20°. As 1/6= 1-68157, 0' = 8O° 39' 57", 0" = 

 30° -24' 30", 0"'=-85°4' 3". 



Medium, — j3 mono-bromo-naphthaline. 1/^ = 1*66138 

 (Gladstone) ; 0'=79° 33' 28", 6" = 30° 17' 40", 0"'=-83° 

 11' 20". 



2nd Case. — Circle within ellipse (tig. 3). The equation of 

 the locus is the same as in the first case except that the 

 symbols b and c, y and z are interchanged. 



With a bounding medium of carbon bisulphide and a = 77°, 



0-32965 sin 8 0-0-7 L619 sin 6 + 045578 sin 4 



- 0-06980 sin 2 + 0*000029 = 0. 



The roots are, 0' = 73° 48', 0"=28° 10'; 0" is imaginary. 



3rd Case. — Ellipse within circle (fig. 4). No calculations 

 were made for this section, as even for aragonite, which has 

 a relatively large difference between the three refractive 

 indices, the elliptic wave-front is practically a circle. So 

 that there is little that is characteristic for this section. 



The asymptotes of the envelope, when the crystal is spar, are 



z=.+ ~ =+0-31797. 



a + o ~ 



w= ±b = ±0-60297 ; 2= + , 2 , ,.^ = +0*44901. 



The real points on the axes are 



ab 

 {a*Tb')i 



The asymptotes for aragonite are, as given earlier in the 

 paper, 



\i# 4 + \ 3 a? 2 H-X 3 = 0, 



;m 4 + 2^ + ^=0. 



