H. R. CARLETON. XCV. 



It remains, therefore, to determine the form of the outer surface, 



so that all rays emerging from the glass shall be bent into a 



horizontal or any other required direction. 



a (/x — 1) 



The equation to this curve is r = - n where r = the 



^ fM — cos v 



radius vector, a, the value of r, when 6 = o, 6 the vectorial 



angle, and jx the index of refraction. 



Description of Path of Rays in Dioptric Apparatus. 



In the dioptric apparatus the path of a ray issuing from the 

 light through the central lens is twice refracted, and, generally 

 speaking, emerges in a direction parallel to the optical axis. The 

 same occurs on the passage of a ray through the annular zones, 

 which are merely portions of a larger lens with the central 

 portion cut away to reduce the thickness of the glass. The path 

 of a ray through the triangular prisms is first refracted, then 

 reflected, and then again refracted in such a manner as to emerge 

 in a direction parallel to the optical axis. The paths are illustra- 

 ted on the diagram. In holophotal lights the rays which emerge 

 to the back of the focus are reflected back again through the 

 focus by prisms having their inner faces normal to the outward 

 and backward rays, and their outer surfaces constructed to such 

 curves as to cause the rays to be twice reflected and thrown back 

 through the focus on to the forward lenses and triangular prisms. 



If the section shewn on the diagram revolve round a vertical 

 axis passing through the focus, it will generate the cage which is 

 used in a fixed light, and if the same section revolve round a 

 horizontal axis passing through the focus it will generate the 

 apparatus used in revolving lights, but the extent of the revolution 

 in this case is governed by the number of sides it is intended the 

 cage shall have. 



Comparison of Dioptric and Catoptric Systems. 



The superiority of the dioptric over the catopric system is, of 

 course, well established, but the following, taken from Stevenson's 

 work, gives a measure of their relative values: — ''From experi- 



