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On a Varying Cylindrical Lens, [Dec. 16, 



II. " On a Varying Cylindrical Lens." By TEMPEST ANDERSON, 

 M.D., B.Sc. Communicated by Professor A. W. Williamson, 

 For. Sec. R.S. Received November 18, 1886. 



A cylindrical lens of continuously varying power has long been a 

 desideratum, and one was constructed and described by Professor 

 Stokes, at page 10 of the Report of the British Association for 1849 

 (Transactions of the Sections). He points out that — 



" If two piano-cylindrical lenses of equal radius, one concave and 

 the other convex, be fixed, one in the lid and the other in the body of a 

 small round wooden box, with a hole in the top and bottom, so as to be 

 as nearly as possible in contact, the lenses will neutralise each other 

 when the axes of the surfaces are parallel ; and by merely turning 

 the lid round an astigmatic lens may be formed, of a power varying 

 continuously from zero to twice the astigmatic power of either lens." 



This very beautiful optical contrivance has the disadvantage that 

 the refraction varies from zero in both directions at once, the refraction 

 at any given position of the lenses being positive in one meridian, and 

 negative or concave to an equal degree in a meridian at right angles to 

 the first ; moreover, there is no fixed axis in which the refraction is 

 either zero or any other constant amount. It has in consequence 

 never come into extensive use in the determination of the degree of 

 astigmatism. The author has planned a cylindrical lens in which the 

 axis remains constant in direction and amount of refraction, while the 

 refraction in the meridian at right angles to this varies continuously. 



A cone may be regarded as a succession of cylinders of different 

 diameters graduating into one another by exceedingly small steps, so 

 so that if a short enough portion be considered, its curvature at any 

 point may be regarded as cylindrical. A lens with one side plane 

 and the other ground on a conical tool is therefore a concave 

 cylindrical lens varying in concavity at different parts according to 

 the diameter of the cone at the corresponding part. Two such 

 lenses mounted with axes parallel and with curvatures varying in 

 opposite directions produce a compound cylindrical lens, whose refrac- 

 tion in the direction of the axes is zero, and whose refraction in the 

 meridian at right angles, to this is at any point the sum of the refrac- 

 tions of the two lenses. This sum is nearly constant for a con- 

 siderable distance along the axis so long as the same position of the 

 lenses is maintained. If the lenses be slid one over the other in the 

 direction of their axes, this sum changes, and we have a varying 

 cylindrical lens. The lens is graduated by marking on the frame the 

 relative position of the lenses when cylindrical lenses of known power 

 are neutralised. 



