H. R. CARLETON. 



LXXXIX. 



prisms are right lines, but in the process of grinding the prisms, 

 it is found convenient for the workmen to give a curved form to 

 the refracting sides, the one being made convex and the other 

 concave '; so that both being ground to the same radius (about 

 four metres), the convergence of the rays produced by the first 

 shall be neutralized by the divergence caused by the second. 

 The author has also obtained an expression for the direction of the 

 tangent to the curve at any point in the case of the piano convex 

 lens, but so far has been unable to integrate this expression, and 

 he asks those members of the section interested in the subject to 

 assist him. 



Prob. 1. 



To find the section of a refracting zone or straight prism. 



ofs.-.^-ri- 



APPROXIMATE SOLUTION. 



ACDG is the section ; F, the radiant point; FX a perpen- 

 dicular to the side CA. produced. 



OD,OE, normals to the circular arc bounding the prism, 

 and making the angles if/ and <£ with FX. 



a and p the angles of incidence and refraction at A. 



ft and o- „ „ „ B. 



FM =/'; CD = t; AC = b ; 



and b =f (tan ft — tan a ) + 1 tan <r. 



p. sin p = sin a 



p. sin a — sin ft 



