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III. An Inquiry into the Geometrical Character of the Hour-Lines upon the Antique Sun-Dials
Published online by Cambridge University Press: 17 January 2013
Extract
Il resterait à résoudre une problème plus générale, à trouver la courbe hectémoreale sur la sphère même, et sur un cadran quelconque.
Delambre, Conn. des Temps, an. 1820, p. 341.
The nature of these lines, though a subject of repeated investigation, has never been accurately determined. The loci of the points which divide the semi-diurnal arc into n equal parts, have almost invariably been considered as great circles, and their projections upon a plane, which are the dial-lines in question, in consequence viewed as straight lines. Clavius was the first to point out, and to prove, the error of this opinion; and Montucla (or rather Lalande) not only denied that they were circles at all, but affirmed they were curves of a very fantastical kind—“tres bizarre.” This latter opinion, which is partly true and partly false, seems rather to have been inconsiderately hazarded, than derived from any satisfactory course of reasoning. They are not great circles, it is true; but, as Delambre has replied, “il y a beaucoup d'exageration à donner une forme tres bizarre à des lignes qui, dans aucun des cadrons qu'on a tracées de cette manière, n'ont jamais pas s'ecarter sensiblement de la ligne droite.”
- Type
- Research Article
- Information
- Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 12 , Issue 1 , 1834 , pp. 77 - 122
- Copyright
- Copyright © Royal Society of Edinburgh 1834
References
page 77 note * Conn, des Temps, pour l'an. 1820.—Mem. de l'Inst. tom. xiv. p. xxxi.
page 78 note * Edinburgh Transactions, vol. viii. p. 68.
page 78 note † Conn des Temps, ubi sup.
page 78 note ‡ Histoire d'Astron. Ancien. tom. ii. p. 475.
page 78 note ∥ Edin. Trans. ubi sup. p. 65.
page 92 note * In the figure n is made = 2, being, adapted to the IX and III o'clock hour-lines.
page 100 note * For, in this case, 
.
page 105 note * Journal de l'Ecole Polytechnique, cah. xiv. pp. 182–190.
page 109 note * It would have been more conformable to the commom usage to have designated these dials by names diametrically opposite upon the compass; but if, in all cases, we imagine the dial plane, after the hectemoria are traced, to be revolved upon its intersection with the horizon through 180°, and the gnomon to be a continuation of the radius of the sphere and equal thereto, the extremity of it will be the gnomonic point to the dial as it is now placed. The reasons for this departure from common usage cannot be conveniently explained here: nor is it of importance that it should be, a bare indication of the fact being sufficient to prevent misapprehension.
page 111 note * Erroneously stated in the ‘Memoranda of Lord Elgin‘s pursuits in Greece,’ to be from the Temple of Bacchus. Mr Kinnaird saw the dial in the Temple of Bacchus in its original position in 1818. See his Notes to the new edition of Stuart's Athens. In the present arrangement of the Elgin Gallery, in the British Museum, this dial stands opposite the stairs, in the angle of the room.
page 111 note † Edinburgh Transactions, vol. viii. p. 79, and the corresponding plates.
page 113 note * Stuart, vol. i. pl. 10.
page 116 note * That is, a dial which touches the hectemorial sphere at the intersection of the equator and maridian of the place for which it is made.
page 116 note † Plate II. fig. 3. of the Memoir already referred to.
page 115 note ‡ Art. XIII.
page 121 note * Tome ii., at the end of the Table of Contents.