Properties of the Two New Fluids in Minerals. 409 



flexion. This angle was 38 42'. From the index of the ordi- 

 nary refraction of Topaz, which is 1.620, I computed the angle 

 of refraction CDB to be 22 42' and the angle of total reflexion 

 DCP to be 37 38' 35". Hence the angle ADC was 67 18' ; the 

 angle ACD 52 21', and DAC, the inclination of the face of the 

 cavity to the refracting surface EF, was therefore 60 21'. 



Calling x the inclination of AB to EF, or DAC and <p the 

 angle of refraction CDB, we shah 1 have x~^ total reflexion + <p. 

 For in the similar triangles ADB, CPB right angled at D and 

 C, we have CAD = CPB. But CPB = DPQ = CDB + DCP, 

 that is x ^ Total Reflexion -f- <p. 



The goniometer remaining steady in its place, the divided circle 

 and the crystal were turned round, tiU the same ray RD began to 

 suffer total reflexion from the refracting surface of the expan- 

 sible fluid NN Fig. 1. and the Topaz ; and the new angle of in- 

 cidence KDR', at which this took place, was found to be 26 39'. 

 The goniometer being turned still farther, the same ray suffered 

 total reflexion, from the separating surface of the second fluid 

 MM and the Topaz, when the angle of incidence KD was 11 

 &. 



These results obviously enable us to determine with accuracy 

 the refractive power of the Two New Fluids. 



Calling 6 the angle of incidence, <p, <p' the angles of refrac- 

 tion, m m', m" the indices of refraction for Topaz, the expan- 

 sive fluid and the second fluid ; then we have sin -^ ; 

 , m 



9 oc Angle of Total Reflexion, and 



m' = m X Sin (tf act) 



m" =. m X Sin (<p" a?) 



Hence we have the indices of refraction as follows 



m = 1.620 Topaz, 



m" - 1.2946 Second Fluid. 



m' 1.1311 Expansible Fluid. 



SF2 



