62 ON THE ANTIQUE HOUR-LINES. 



different points of the parallel which passes through the ze- 

 nith. The Italian hours counted from sunset, and the Ba- 

 bylonian hours counted from sunrise, are denoted by lines of 

 this kind. 



The third kind of hour-line, and of which it is proposed to 

 speak more particularly here, denotes hours varying in length 

 as the declination of the sun varies, each hour beino- one-sixth 

 part of the semidiurnal arc, whether that arc be a smaller por- 

 tion of the circumference, as in winter, or a greater, as it is in 

 summer. On the oblique sphere these lines are not great cir- 

 cles, and each adjacent pair intercepts a dissimilar arc on each 

 semidiurnal arc. This kind comprehends the hour-lines of the 

 ancient Greeks and Romans, which denote hours called hecte^ 

 moria *, that is, sixth parts of the semidiurnal arc. 



The curvature of these lines is visible when they are drawn 

 on a globe ; it is likewise seen in their gnomonic projection, in 

 the following manner. 



Figure 1st is a perspective view of the lines which intercept 

 one-sixth part of each semidiurnal arc ; the point of sight is the 

 centre of the sphere ; the plane of projection touches the sphere 

 at the pole of the equator, and is therefore parallel to the equa- 

 tor ; the latitude is 66° 30' ; at this latitude the whole of each 

 hectemoFial hour-line is gone over by the sun in a year. This 

 perspective view is the same as the central or gnomonic pro- 

 jection of the sphere on the inside of a plane which touches the 

 sphere at the pole of the equator ; it forms an inferior equi- 

 noxial dial for the latitude 66° 30', when placed parallel to the 

 equator, with its inscribed surface downwards, and the point 

 xxiv. elevated. 



In 



* 'E*I»i|tteg«iv, sexta pars, sextarius, is used by Ptolomy. The lines that separate 

 the hectemoria from each other are in this paper called hectemorial lines. 



