Illumination of small Arcs of the Horizon. 277 



It would, however, be better to grind one of the surfaces of 

 the lens above described into concave cylindric grooves instead 

 of convex cylindric prisms, thus making the lens of a meniscal 

 section with one surface spherical, and the other cylindric, as 

 shown in fig. 8.* A meniscus lens, having its different rings 

 cut out, or stepped on both sides, would also be preferable to 

 the plane convex form which is used in lighthouses, whether 

 for fixed or revolving lights, as the thickness of the glass 

 would be much decreased. My friend, Mr James M. Balfour, 

 has suggested to me that good curves might also be ob- 

 tained by placing the straight prisms horizontally on the 

 outer face, thus making the horizontal section plano-convex, 

 with such a curvature as to reduce the divergence to the re- 

 quired angle, while the vertical sections would be double con- 

 vex, the outer curve being such as to render parallel the 

 diverging rays as altered by the inner face. 



A like effect might also be produced by making double 

 cylindric a portion of one-half of the refractor which forms 

 the middle compartment of Fresnel's fixed apparatus. Let 

 us suppose a middle sector of this hoop of glass of such a num- 

 ber of degrees as the case may require, to be flanked on each 

 side by the supplementary sectors, having their convex sur- 

 faces next the flame, and their outer surfaces ground into 

 straight refracting and totally reflecting vertical prisms simi- 

 lar to those which I have already described for the outer face 

 of the annular lens. The inner face of this refracting hoop 

 will parallelize the rays in the vertical plane only, while the 

 outer surface will produce either such an amount of direct 

 divergence, or such an amount of convergence as will cause 

 them ultimately to diverge through the desired angle. The 

 same principle might be applied to the totally reflecting prisms 

 when they form part of the apparatus, but the construction 

 would probably be attended with too great difficulty, t 



Edinburgh, Feb. 12, 1855. 



* Mr Adie has lately made for me lenses of the forms shown at figs. 7 and 8. 



t The double cylindric refractor might be found serviceable for diminishing 

 the divergence of the light in the Davy lamp, as well as for use in lighthouses. 

 The effect would be increased by a back reflector of glazed earthenware or 

 zinc, both of which materials I have found give a good light, and require 

 almost no cleaning. 



