## Über Interpolation.

Berlin: Königlichen Akademie der Wissenschaften, 1828.

First printing of what is now called the Gauss-Newton interpolation formula; which enables one to predict the value of a quantity given a finite number of observations. Gauss had lectured on the interpolation formula at Göttingen in 1812; his then student Encke attended Gauss’s lectures, and published his notes on them in the present paper almost two decades later. Gauss’s interest in interpolation formulas derived from their obvious application to predicting the present position of a celestial body given several observations of its position in the past. Gauss had become famous by correctly predicting the position of the minor planet Ceres, discovered by G. Piazzi on 1 January 1801, on 7 December 1801 after its orbit had taken it behind the Sun. Although Gauss published nothing on the interpolation formula during his lifetime, a manuscript discussing it entitled ‘Theoria Interpolationis Methodo Nova Tractata’ was found in his *Nachlass* and published in *Werke*, vol. III, pp. 265-327.

Encke (1791-1865) is now principally remembered for his work on comets. He predicted the orbit of a comet discovered in 1818 and when this was confirmed by observation the comet was named after him. His work brought him the Gold Medal of the Royal Astronomical Society. In 1825 he became professor at the Berlin Academy of Sciences and director of the Berlin Observatory. “After his appointment at Berlin, [he] undertook the editing of the *Berliner Astronomisches Jahrbuch*... With the support of his assistants... he issued the yearbooks for 1830-1866... Its issuance was a private matter, supported by the state, but not without economic risk. The opportunity to publish made possible the appearance of Encke’s treatises in the yearbooks, dealing particularly with orbit determinations and perturbation computations” (DSB). In the present volume, the first of the yearbooks issued by Encke, the first section (pp. 1-235) is taken up with tables of ephemerides, while the second section (pp. 239-308) is taken up with five papers by Encke on the calculation of stellar occultations, on a stellar sextant, etc., as well as the paper on the interpolation formula.

Provennace: Contemporary engraved bookplate of (third) Earl of Dunraven on front paste-down. Edwin Quin, third Earl of Dunraven, was educated at Eton where he showed a strong taste for astronomy; and afterwards spent three years at the Dublin Observatory under Sir William Rowan Hamilton. While the natural sciences occupied much of his attention; he was also deeply interested in the study of Irish antiquities, and was a prominent member of the Royal Irish Academy, the Celtic Society, and several archaeological associations. His *Notes on Irish Architecture* (two volumes, London: 1875-77) were published after his death in 1871.

In: Berliner Astronomisches Jahrbuch für 1830... herausgegeben von J. F. Encke, pp. 265-284. The complete volume offered here: 8vo, pp. xii, 308, with one engraved plate of diagrams. Contemporary dark blue-green half-calf and marbled boards, smooth spine panelled by broad gilt rolled bands, one panel directly lettered in gilt, other panels with large gilt tool in centres, edges speckled green. A fine and clean copy.

Item #2983

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Price:
$850.00
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