Properties of the Two New Fluids in Minerals. 123 



total reflection. This angle was 38° 42'. From the index of 

 the ordinary refraction of topaz, which is 1.620, I computed 

 the angle of refraction CDB to be 22° 42', and the angle of 

 total reflection 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 DA C and p the 

 angle of refraction CDB, we shall have x — ^L total reflection 

 -f- 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, a? = ^L Total Reflection + 9 . 



The goniometer remaining steady in its place, the divided 

 circle and the crystal were turned round, till the same ray 

 RD began to suffer total reflection from the refracting surface 

 of the expansible fluid and the topaz ; and the new angle of 

 incidence KDR', at which this took place, was found to be 

 26° 39'. The goniometer being turned still farther, the same 

 ray suffered total reflection, from the separating surface of the 

 second fluid MM and the topaz, when the angle of incidence 

 KD was 11° 52'. 



Now, if to is the index of refraction of any substance, the 

 sine of the angle at which light incident on its second surface 



suffers total reflection, will be — , and if any fluid is in con- 

 tra J 



tact with that surface, the sine of the angle of total reflection 



to' 

 will be — , the index of refraction of the fluid being- to', 

 to & 



Hence, 



to' = to X Sin. Angle of Total Reflection. 

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

 tion, to to', to" the indices of refraction for topaz, the expan- 

 sive fluid and the second fluid ; then we have sin p — ; 



TO 



P' — x — Angle of Total Reflection, and 



to' = to x Sin (p' — x) 

 m" = m x Sin (f — x) 



