upon the Antique Dials. 97 



XIV. 



Conical Hectemoria. 



In the second volume of STUART and REVETT'S Antiquities of Athens, 

 page 29, there is given a side and front delineation of a dial traced upon a 

 conical surface, whose vertex is in the prolongation of the axis of the gene- 

 rating sphere. The lines traced upon this are, by Mr CADELL, considered 

 to belong to the temporary system. Without anticipating what I have to 

 say concerning this and some other specimens of ancient dials commonly re- 

 ferred to this class, I shall here investigate the equation and characters of a 

 hectemorial conical dial, whose contact with the sphere is a circle parallel to 

 the equator. 



Let H be the vertex of the cone, G one of 

 the points of contact of the cone and sphere. 

 Let *. = latitude and L = longitude of G, 

 reckoned from the meridian of the place; 

 D = declination of one of the points of the 

 spherical hectemoria corresponding to L, such 

 that its value fulfils the equation 



tan D = tan I cosec L. 



Let Q be the point upon the cone into which D is projected. The ob- 

 ject, then, which we have in view, requires the value of the line HQ in 

 terms of L, D, *. ; or rather of L and x, since D is a known function of L ; 

 we have, 



-^HOD = 90 D 



= 90 V 



= D >.'. 



