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 being 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 @ 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 Ist 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 
hectemorial 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 
xxiy. elevated. 
In 
* ‘Exlnudgio, sexta pars, sextarius, is used by Protomy. The lines that separate. 
the hectemoria from each other are in this paper called hectemorial lines, 
