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An Inquiry into the Geometrical Character of the Hour-Lines up- 

 on the Antique Sun-Dials. By T. S. DAVIES, Esq. F. R.S.ED. 

 F.R.A.S. 



II resterait a resoudre une probl&me plus generate, a trouver la courbe hectemoreale 

 sur la sphere menu 1 , et sur un cadran quelconque. 



DELAMBRE, Conn, des Temps, an. 1820, p. 341. 



(ReadZlst Feb. 1831.; 



THE nature of these lines, though a subject of repeated investi- 

 gation, 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 pro- 

 jections 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 MON- 

 TUCLA (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 ha- 

 zarded, 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 a donner une forme tres 

 bizarre a des lignes qui, dans aucun des cadrons qu'on a tracees 

 de cette maniere, n'ont jamais pas s'ecarter sensiblement de la 

 ligne droite*." Mr CADELL, the last author, except DELAMBRE, 

 who has attended to this subject, very clearly shews that the 

 curve on the sphere is not a great circle ; but he has not at- 



* Conn, des Temps, pour Tan. 1820. Mem. de Tlnst. torn. xiv. p. xxxi. 

 VOL. XII. PART I. L 



