Abstract
LONDON. Physical Society, December 8.—Prof. G. Carey Foster, F.R.S., Vice-President, in the chair.—Prof. S. P. Thompson read a paper on obliquely crossed cylindrical lenses. Any two cylindrical lenses crossed obliquely are optically equivalent to two other cylindrical lenses crossed rectangularly, and hence to a sphero-cylindrical lens. Owing to the difficulty of manufacturing cylindrical lenses with the axes of the opposite faces in different directions, it becomes of importance to the optician to be able to calculate the constants of the equivalent but more easily ground sphero-cylindrical lens. To a first approximation a surface of radius of curvature “r” will impress upon a plane wave a curvature of μ – 1/r where “μ” is the refractive index of the material. If we suppose an equiconvex cylindrical lens cut by two planes at right angles, the line of intersection of the planes passing normally through the centre of the lens, then the sections of the lens will in general be portions of ellipses. It is possible, therefore, to write down in terms of the angle which one of these planes makes with the axis, the convergivity which would be impressed by the lens upon plane waves travelling in these planes. The effect of a second lens crossing the first obliquely can also be written down with respect to the same two planes. The joint effect of the two lenses can then be resolved along any two lines at right angles. Differentiating the expressions for these effects and equating to zero, we get the directions of maximum and minimum cylindricity. These directions are at right angles, and represent two lenses crossed rectangularly, which are the optical equivalent of the original pair considered. The sphero-cylindrical lens is then easily obtained. From the mathematical expressions Prof. Thompson has deduced a graphical solution of the problem. The author exhibited a convenient combination of two cylindrical lenses for giving varying degrees of cylindricity. Let two lenses be ground, each being a mixed equi-cylinder consisting of a concave and convex ground at right angles to one another on the opposite faces of the glass. Two such mixed cylinders, if rotated with equal motion in opposite directions, will give a varying cylindricity of fixed direction in space. With the axes of positive cylindricity coincident they give the maximum; but when each is rotated 450, their resultant is zero. When rotated beyond 45°, the resultant axis of cylindricity is negative in the fixed direction in which it was formerly positive.—Mr. W. F. Blakesley read a paper on exact formulæ for lenses. In this paper the author makes use of the definition of focal length with respect to magnifying power, which he has described in the Proceedings of the Physical Society for November 1897. By this method the focal length of a lens combination is simply a line and not the distance between two definite points. Following the methods of his previous paper, Mr. Blakesley showed how it was possible to determine accurately the constants of lens combinations, and pointed out practical applications to the racking of telescopes for camera work, the determination of refractive indices of liquids, &c.—Prof. W. E. Dalby exhibited a friction dynamometer. The torque to be measured produces a twist in a spiral spring, and the object is to determine the amount of this twist. Side by side upon the shaft are two pulleys, one keyed to the shaft and the other fastened to the end of the spring. The lead of one pulley upon the other, therefore, measures the twist. Two other pulleys are mounted upon a slide, and are joined up to the first ones by means of a continuous band similar to a Weston's differential pulley block. When the shaft is at rest, the two pulleys on the slide are touching; but any motion of the shaft produces a twist in the spring, and therefore a lead of one of the shaft pulleys on the other. This produces a separation of the slide pulleys, which is proportional to the lead, and therefore to the torque, and so from a knowledge of the constants of the dynamometer and its number of revolutions per second the power transmitted is at once determined.—Prof. S. P. Thompson read a note on an organic compound of great double refraction. This substance is crystallised naphthaline, and it is 60 per cent, more doubly refracting than Iceland spar. It is exceedingly brittle, and therefore difficult to work into prisms. Any worked surface must be at once covered with glass to prevent sublimation.—The Society then adjourned until January 26, 1900.
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Societies and Academies . Nature 61, 164–168 (1899). https://doi.org/10.1038/061164b0
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DOI: https://doi.org/10.1038/061164b0