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IV. On the Lines that divide each semidiurnal Arc into Six equal Parts
Published online by Cambridge University Press: 17 January 2013
Extract
The divisions of the day which different nations have employed, are denoted by hour-lines of various kinds on the sphere. Of these hour-lines, drawn on a supposition that neglects the inequalities of the Earth's motion, there are three kinds.
The first kind denotes hours counted from the meridian, equal to each other at all declinations of the sun. These lines are great circles on the sphere, passing through the poles of the equator, and every pair intercepting a similar arc on each of the parallels. Of this kind are the hour-lines of sidereal time, counted from the meridian, and the hour-lines of solar time, counted from the meridian.
- Type
- Research Article
- Information
- Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 8 , Issue 1 , 1818 , pp. 61 - 81
- Copyright
- Copyright © Royal Society of Edinburgh 1818
References
page 62 note * Ἑχℸημόςιον, sexta pars, sextarius, is used by Ptolomy. The lines that separate the hectemoria from each other are in this paper called hectemorial lines.
page 74 note * The passages from Clavius and Montucla are as follows:
Clavii Astrolabium lib. i. lemma 39. “Circuli maximi transeuntes per horas inæquales Æquatoris, et duorum parallelorum oppositorum, non necessario per horas inæquales parallelorum intermediorum transeunt in sphæra obliqua.” He gives a demonstration of this, and concludes, in the scholium, that in order to delineate the antique hours with strict accuracy, a considerable number of the semidiurnal arcs are to be divided into six parts, and the corresponding points of division joined.
Montucla, Hist. des Math. tom i. edition de 1758: “Les lignes de ces sortes d'heures [les heures antiques] ne sont point droites comme les precedentes, mais courbes, et meme d'une forme tres bizarre; de sorte qu'on ne peut les decrire qu'en determinant plusieurs points de chacune; la manière de les trouver se presentera facilement à tout geometre; c'est pourquoi nous ne nous y arretons pas.”
The circumstance mentioned in the beginning of the paragraph to which this note refers, has led the celebrated and profound astronomer Delambre to controvert the opinion of Montucla in the following words: “Montucla dit, en parlant des heures temporaires antiques, qu'elles sont courbes, et même d'une forme très bizarre, &c Hist, des Mathem. tom i. On ne conçoit pas comment une pareille inadvertance a pu echapper à un homme aussi instruit; car si la surface est spherique, ces lignes seront des grands cercles; et si la surface est plane, elles seront des lignes droites, puisqu'elles seront les intersections des plans de ces grands cercles avec le plan du cadran.” Delambre sur un cadran antique trouvé dans l'isle de Delos, et par occasion de la gnomonique des anciens; notice lue à la classe des Sciences Physiques et Mathematiques de l'Institut Royal de France, le 10 Octobre 1814.
page 76 note * Boissardi Antiquitates Romanæ.
page 77 note * Grævii Thesaurus Antiquitatum Romanarum.
page 77 note † Le Pitture antiche d'Erculano, tom. iii. Napoli 1762.
page 77 note ‡ Herodotus.
page 77 note ║ Diogenes Laertius.
page 78 note * Salmash Plinianæ Exercitationes.
page 78 note † Plinii Hist. Naturalis.