Abstract
LONDON. Optical Society, December 12.—Prof. F. J. Cheshire, president, in the chair. —Instructor-Com. T. Y. Baker and Major L. N. G. Filon: An empirical formula for the longitudinal aberration of a ray through a thick lens. The authors showed that the development of the longitudinal aberration as a power series is frequently illegitimate owing to its divergence for comparatively slight inclinations of the rays. Instead of such development of the form al2 + bt1+ …, where t is the tangent of the inclination of the ray, they proposed a formula At2/(1 + Bt2), and determined A and B numerically from the values of the aberration of particular rays calculated trigonometrically through a lens. This was done for a whole series of image positions and for a whole series of lenses of different shapes but of the same focal length. The numerical values of A and B so obtained were then analysed, and an endeavour was made to obtain approximate general formulæ for them in terms of the image position and the lens shape. The authors decided that in all cases the value A in their empirical formula and the value a in the power series were practically identical. The value of a was given by the authors in a paper read before the society in May. The value of B can be expressed as a cubic in M, the linear magnification of the image. Thus B = B0 + B1M + B2M2+ B3M3, in which the four coefficients B0, B1, B2, and B3 are all quadratic functions of the mean curvature of the lens faces.—Major E. O. Henrici: Spirit-levels. The best bubble tubes for spirit-levels hare been made in Germany; it seems desirable that an investigation should be made of the factors necessary for producing satisfactory tubes. The advantage of a long air-bubble, as regards both the accuracy and rapidity with which the bubble comes to rest when displaced, was pointed out, and also the advantage of a short radius of curvature as regards the latter point. The radius of curvature (in other words, the sensitiveness) must, however, be sufficiently great for the bubble to move noticeably with the smallest angular tilt of the tube which it is desired to indicate. If the bubble be too sensitive, time is lost; if it be not sufficiently sensitive, a spurious idea of accuracy is given; the sensitiveness of every bubble tube for accurate work should be marked. The methods of mounting, illuminating, and viewing the bubble tube frequently leave much to be desired, and improvements in these matters lead to increased accuracy for a given sensitiveness. Several methods of viewing by means of prisms were described, the most satisfactory known to the author being one placed on the market by Zeiss. The accuracy of shaping the surface required in a sensitive bubble is very great. If a tube has a corrugated surface, the corrugations having an amplitude of 1/2000 mm. and a period of 10 mm., the angle of tilt to move the bubble 1 mm. may vary 38 per cent, from its nominal value in the case of a bubble with a sensitiveness of 10 seconds per mm., the bubble being 35 mm. long. A similar corrugation with a 2-second bubble will make it almost useless for any purpose. Further investigation is required into the effect of the following factors on the performance of the bubble:— Quality, polish, and cleanliness of the glass; quality and purity of the liquid and vapour in the tube, and the best methods of mounting and viewing.
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Societies and Academies . Nature 102, 359–360 (1919). https://doi.org/10.1038/102359a0
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DOI: https://doi.org/10.1038/102359a0