408 DR BREWSTER on the Refractive Powers, and other 



the good fortune to meet with ; and one of the principal objects 

 of the present paper, is to give an account of the results which 

 it enabled me to obtain. 



To those who are acquainted with the doctrines of refraction, 

 it is scarcely necessary to state, that if m is the index of refrac- 

 tion of any substance, such as Topaz, the sine of the angle at 

 which light incident on the second surface of it will suffer total re- 



flexion, will be - , and if any fluid is in contact with that sui- 



m' 



face, the sine of the angle of total reflexion will be , the index 



nv 



of refraction of the fluid being m f . H ence 



m' m X Sin. Angle of Total Reflexion ; 



so that the index of refraction of the fluid is easily deducible 

 from the angle of total reflexion. 



When the surface of the cavity is parallel to a face of clea- 

 vage in the plate of Topaz which contains it, the angle of total 

 reflexion cannot be observed without cementing a prism upon one 

 of these faces ; but as this tended to make the experiment more 

 complicated, I sought for a cavity, the faces of which were in- 

 clined to the two parallel faces obtained by cleavage. This cavity, 

 shewn in Plate XIX. Fig. 1., consisted of a vacuity V; of a large 

 portion NN of the highly expansible fluid, and of a considerable 

 quantity MM of the second fluid, which suffered almost no 

 change by heat. The situation of this cavity in the specimen is 

 shewn in Fig. 2., where C is a section of the cavity perpendicu- 

 lar to its length MM, Fig. 1 ., and inclined to the parallel clea- 

 vage planes EF, GH of the Topaz. 



In a room where the temperature was about 60 of Fahren- 

 heit, I fixed this specimen upon a goniometer, and I measured 

 the angle of incidence at the surface EF, when the light of a 

 candle RD, incident on the vacuity, began to suffer total re- 



