ON THE ANTIQUE HOUR-LINES. 67 
in which the curves are contained, are the ninth and fifteenth 
astronomical hour-line counted from midnight. 
From figure Ist it may be collected, that the asymptotes of 
each hectemorial line are as follows : 
(! 
The equicrural curvilinear branch, | has for asymptoles the astro- | which compre- | 
composed of the hectemorial lines nomical howr-/ines, counted | hend an angle 
From midnight, of 
First A,and Eleventh IA,) VII. and XVII. 150° 
Second B,andtenth I,} VILL. and XVI. 120° 
Third Tr, and ninth ©,)  IX.and XV. 90° | 
Fourth A, and eighth 4, X. and XIV. 60° 
Fifth, E, and seventh Z, XI. and XIII. 30° “aoe 
Figure 1st represents the portions of the day hectemorial 
lines which touch the greatest invisible parallel for the latitude 
66° 30’; these are the winter portions. In-order to delineate 
the portions which touch the greatest wholly visible parallel, 
or the summer portions, the projection is made on the plane 
which touches the sphere ‘at the depressed pole ; this projec- 
tion is exhibited in figure 2d, which contains portions of 
curves, each of which is similar and equal to the curve of the 
sane hour in figure Ist, but differently placed. It forms a su- 
perior equinoxial dial for 66° 30’, when placed parallel to the 
equator, with the inscribed surface upwards, and the a XXxiv. 
elevated. Th tia 
- However extended the plane of projection touching the 
sphere at the pole be, still it will not contain the portions of 
the hectemorial lines that are near the equator. To have these, 
the plane of projection is taken at right angles to the equator, 
in touching thie Saaunig at the depressed intersection of the 
ms Tern 12 equator 
