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to one another at various definite angles, the particulars of which I 

 shall presently explain, so that the outline of the unpolished sides is 

 of a trapezoid form. 



To the smallest face of the prism (which should form a square) 

 a plano-convex lens is cemented, and when in use it is through this 

 lens that the light emerges from the prism, and is condensed in the 

 focus of the lens, and immediately upon the object under examination. 



This will be more readily understood by reference to the figures. 



Fig. 1 represents the side view of a prism, without the lens, which 

 must be attached to the surface, d q. 



Fig. 2 represents an enlarged section of a prism, with its lens, 

 mounted in a metal fitting, the space not occupied by the glass being 

 filled with blackened cork. 



The rays of light (represented by three dotted lines) enter the base, 

 c b, of the prism, and as they fall on it perpendicularly, they suffer 

 no refraction, but pass directly, until they meet the inclined face, 

 c d, whence they are reflected internally, and fall on the face, q b, 

 from which they are again reflected internally, and emerge through 

 the square surface, d q, at right angles to it. 



The lens being cemented to the surface, d q, no light is lost by 

 reflection at that surface, and the rays are brought to a focus at e, 

 exactly in the same spot as would have been the case had the light 

 passed, without the intervention of a prism, through a lens fixed at 

 f d. There is, however, this important difference, that instead of 

 the mean direction of the rays being perpendicular to the object, it 

 is at a certain definite angle thereto, according to the construction of 

 the prism. 



Having made calculations to ascertain the relative angles and 

 dimensions of the sides, which will produce the best possible effect 

 for any given angle at which the bundle of rays is desired to fall on 

 the object, I find that the following formulae, which I have already 

 supplied to Messrs. Smith and Beck, for the purpose of constructing 

 the prism I have, will furnish all the particulars required. 



The surface, d q, should be a square, the side of which we will 

 call s. It is to this square surface that the lens is to be cemented. 

 The other surfaces, q d ,b c, and c d, are parallellograms, having 

 their short side = s. The long side of c d we will call = x. Then 

 let a = the angle at which the light is required to fall on the object. 



The angle q = 45°, whatever may be the value of a. 



Then the angle b = 135* 5 — the angle a. 



c = 45° + the angk « • 

 2 



