the resemblance referred to is merely accidental, or whether it expresses an affinity involved in the nature of the problem. But the latter seems the more probable explanation. The numerical values of the radii in his system, computed for a special case,* are here transcribed from his original memoir, after reducing them to a focal length, for the two lenses combined, of twenty-one French feet, for the sake of comparison with the large Munich refractors. I. Gauss's Curves. 1st surface of the crown lens, convex, radius= ft. +2.535 In No. 1289 of the Astronomische Nachrichten Oudeman has given the following measurements of an object-glass made by Frauenhofer for the Equatorial of the Observatory åt Utrecht. The numbers have been reduced to the same unit as before, assuming the focal length from Astr. Nach. 1281. II. Frauenhofer's Curves. 1st surface of the crown lens, convex, radius, = ft. レ +25.945 = 21.00 Another of his object-glasses, probably computed from a similar formula, but for glass of slightly different refractive and dispersive powers, has values of the radii as follows: †This number has been corrected to accord with the erratum noticed at the end of the volume cited. Zeitschrift für Astron., IV. 352. These numbers we will now compare with the two solutions of Herschel's equations, using the notation l, r and r', to denote the reciprocals of the compound focal length and of the radii of the front surfaces of the two lenses. The substitution of the values of the indices of refraction and of the dispersive powers which have been used by Gauss for computing the system I. gives the relations*: 21.31 r59.57 12 +3.5792 l r' · 1.4233/2 With these radii the figures in the accompanying Plate have been constructed, representing sections of the different object-glasses, each having a focal length of two feet, and an aperture of nearly four * In the equation (2) Phil. Trans. 1821, p. 258, the coefficient of has been corrected from 2μl + 1 3 μ+1 Vide Article on Light, Encyc. Met., p. 424. to inches. The ratio of the aperture to the focal length has een taken larger than can be adopted in practice, in order to exaggerate the amount of curvature. It will be seen that the curves in the systems of Gauss and Frauenhofer may be nearly represented by the two solutions of Herschel's equations.* It follows that Gauss's form, originally designed to secure a more complete elimination of the chromatic dispersion, must be also rather favorable than otherwise as regards the correction of the aberration of figures. It may be remarked, further, that his investigation, neglecting the thickness and distance of the lenses, leads to an equation of the fourth degree, which has no solution corresponding to V., nor to the above values of the radii used by Frauenhofer. On the other hand, if the curves in III. and V. have been derived from substantially the same theory, which seems a probable inference, it is scarcely possible that Frauenhofer should not have had at some time under consideration the system represented by the other solution of the equations, which would have conducted to forms approximating very nearly to the system of Gauss. Five hundred and twenty-seventh Meeting. November 11, 1863. STATUTE MEETING. The PRESIDENT in the chair. Professor Cooke reported that no purchases of books for the Library had been made since the annual meeting. The Academy voted to continue without change the list of periodicals. The President presented the following report from the Council: * The refractive and dispersive powers in III., and probably in II., differ by small amounts from those used in computing IV. and V.; moreover, in the latter, the effect of the thickness of the lenses and of their distance from each other has not been included, so that the numbers to be strictly comparable would require a small correction. The values V., computed with the elements of refraction and dispersion used for III., neglecting only the correction for thickness, become ft. + 14.212 + 6.349 6.488 + 25.375 21.00 |