NO THE ANTIQUE HOUR-LINES- 81 



Sections of the Jive undulated Conical Surfaces by a Cylindri- 

 cal Surface, figures 10th to l^th. 



Figure 10th, Is the section of the undulated cone which con- 

 tains the first antique hour-line A, and eleventh IA, by a 

 cylindrical surface touching the sphere at the equator. 

 To avoid intricacy in this figure, the section of only one 

 of the two opposite cones is drawn. Figure 4th is the 

 right section of the two opposite surfaces. 



Figure 1 1th, Is the section of the undulated cone which con- 

 tains the second antique hour-line B, and tenth I, by a cy- 

 lindrical surface. The full line is the section of one of 

 the two opposite cones ; the dotted line is the section 

 of the other. Fig. 5. is the right section of this surface. 



Figure 12th, Is the section of the two opposite surfaces which 

 contain the third antique hour-line r, and ninth 0, by a 

 cylindrical surface.. Their right section is figure 6th ; and 

 one of these two opposite surfaces is represented in peiv 

 spective, and shaded at figure 9th. 



Figure 13th, Is the section of the undulated cone which con- 

 tains the fourth antique hour-line A, and eighth H, by a 

 cylindrical surface. In this undulated cone, the two op- 

 posite conical surfaces coincide in one : there are therefore 

 no dotted lines, neither on this figure, nor on figure 7th, 

 which is the right section of this undulated cone. 



Figure 14.th, Is the section of the undulated cone which con- 

 tains the fifth antique hour-line E, and seventh Z, by a cy- 

 lindrical surface. Figure 8th, is the right section of the 

 same. 



Vol. VIII. P. I, L V. 



