ON THE ANTIQUE HOUR-LINES. 



19 



Explanation of the Figures. 



Central Projection of the Twelve Hour-lines, Figure 1st 4a 

 Figure 3d. 

 Figure 1st, Is a central or gnomonic projection of the hecte- 

 morial lines or antique hour-lines, on the inside of a plane 

 touching the sphere at the elevated pole of the equator. 

 This and all the other figures are drawn for the latitude 

 66° 30'. Each antique hour-line is marked with the Greek 

 numeral that belongs to it. 

 Figure 2d, Is a central projection of the summer portion of these 

 lines on the inside of a plane touching the sphere at the 

 depressed pole of the equator. 



The circle placed between figure 1st and figure 2d is a 

 great circle of that sphere from which all the projections 

 in these figures (except figure 9th) are formed. 

 Figure 3d, Is a central projection of the hectemorial lines on a 

 plane touching the sphere at the depressed intersection of 

 the meridian and the equator. 



Sections of the Jive undulated Cones zvhich contain the antique 

 hour-lines, by a plane at right angles to the axis, figure 4th 

 to figure 8th. 



Figure 4th, Is a section at right angles to the axis of the un- 

 dulated conical surface, which contains the first antique 

 hour-line A, and eleventh IA. In this and the other fi- 

 gures, the full lines are the section of one of the two op- 

 posite cones, and the dotted lines are the section of the 



other. 



