78 Mr DAVIES on the Nature of the Hour-Lines 



tempted any mathematical proof that it is not a less circle. 

 His reasoning on this point, is not, even in form, any thing more 

 than an appeal to experiment, " it does not look like a less circle, 

 and therefore it is not one" " If," says he, " small circles, so placed, 

 be drawn on the sphere, or projected on a plane, it will be found 

 that their course deviates entirely from the course of the lines 

 bounding the hectemoria. The hectemorial lines, therefore, do 

 not coincide with small circles of the sphere, nor with conic sec- 

 tions on the central projection *." DELAMBRE himself, indis- 

 putably the highest authority of his age on every thing relative 

 to ancient astronomy, had always considered the hectemoria to 

 be rectilinear, till the appearance of Mr CADELL'S learned disser- 

 tation, when he discovered that his own equations indicated 

 their variation from straight lines f." Still he has not examined 

 what they really are : he has not shewn whether they be conic 

 sections, or lines of a higher order, nor even distinguished whether 

 they be algebraic or transcendental curves. Indeed, his equa- 

 tions were not calculated to shew the nature of the curves, 

 however well they might, by a little address, have been adapted 

 to the computation of the positions of isolated points in its course. 

 It may be remarked of Mr CADELL'S expressions ||, too, that they 

 are equally incapable of furnishing the properties of the hecte- 

 moria as a class of curves ; nor does it seem possible to extract 

 from them any decisive proof whether they are the representa- 

 tions of conic sections or not. Indeed, had it been so, there is 

 no doubt that Mr CADELL would have rendered them available 

 for that purpose, instead of substituting the mechanical test of 



* Edinburgh Transactions, vol. viii. p. 68. 

 J- Conn, des Temps, ubi sup. 

 J Histoire d'Astron. Ancien. torn. ii. p. 475. 

 |] Edin. Trans, ubi sup. p. 65. 



