The First Aplanatic Object Glass

TLDR: Herschel's analysis concluded with a set of tables, "set down for the convenience of those who may be inclined to make trial of this construction" as mentioned in this paper, which is the basis for a planar achromatic doublet.

Abstract: It has not unfrequently of late been made a subject of reproach to mathematicians who have occupied themselves with the theory of the refracting telescope, that the practical benefit derived from their speculations has been by no means commensurate to the expenditure of analytical skill and labour they have called for, and that for all the abstruse researches of Clairaut, Euler, D'Alembert, and other celebrated geometers, nothing hitherto has resulted beyond a mass of complicated formulae, which, though confessedly exact in theory, have never yet been made the basis of construction of a single good instrument, and remain therefore totally inapplicable, or at least unapplied, in practice.' Thus John Herschel introduced his mathematical account of \"the aberrations of compound lenses and object glasses\" in 1821. His aim was a genuinely useful result, since previous attempts to derive conditions for an aplanatic achromatic doublet had yielded formulae too complex to be handled by a practical optician and had used data irrelevant to his methods and materials. Herschel's analysis concluded with a set of tables, \"set down for the convenience of those who may be inclined to make trial of this construction't.s of radii of curvature and focal lengths of the lenses of a compound object glass-an achromatic doublet that would be free from spherical aberration, both for celestial objects and for terrestrial objects situated on the axis of the telescope. The values could easily be adjusted for any required focal length. During the 1820s Charles Tulley was one of the leading English opticians. He was in business with his sons William and Thomas and was engaged, for example, by the Royal Astronomical Society, to conduct experiments on large object glasses.\" Sir James South commissioned him to make an objective of 31in. aperture and 45 in. focal length according to Herschel's prescription, and in 1822 South published some observations of close double stars made with Tulley's telescope, in order to show that \"what, therefore, Mr Herschel's theory told him would be good, Mr Tulley's practice has declared SO\".4 This telescope has been described in subsequent literature,\" but until now there has been no evidence that the instrument itself had survived. William Pearson, in his Introduction to practical astronomy (London, 1829), says that Tulley made a 3-!in. aperture, 45 in. focal length object glass according to Herschel's design, which \"turned out so good, that it was competent to separate double stars of the first class, and to exhibit minute objects very distinctly\". Pearson does not mention South, but says that \"The telescope is now in the possession of a Mr Moore of Lincoln\".\" However in the following year, 1830, there appeared John Herschel's article on \"Light\" in the Encyclopaedia metropolitana. Here he deals once again with his account of an aplanatic object glass, and says that the telescope belonging to Moore is the one made for South: