92 Mr DAVJES on the Nature of the Hour-Lines 



latitude of the point of contact, C of the sphere and plane. Draw BD, DP, 

 and prolong BP, in which take BE BD. With centre L and radius 

 EB describe a circle BLF, and draw the indefinite tangents at B and F. 

 With centre P and radius PD describe the circle DN, and upon CP 

 as a diameter describe the circle CHP. Make the angle BE A equal to 

 the longitude of the point of contact, and join AP. Take also E c E c' 

 = cot I = tangent of latitude of the place for which the dial is to be 

 made ; and draw the indefinite right lines c r, .c'r 1 parallel to the tangents 

 FI, BQ. 



Construction of Points in the Curves. Take any value of L as AEZ, 

 and join ZP, cutting the circle ICH in H. Repeat this angle (AEZ) n 

 times, beginning at B *, and let BL be this multiple. Draw the secant 

 EL, cutting c'r' in *'; make FI = E/; and join El cutting the circle 

 in 0. 



Again, draw CH, cutting the circle DN in N ; and make the angle 

 PNS = BE 0. The intersection X of PZ, NS is a point in the 

 curve. 



In the figure n is made =. 2, being adapted to the IX and III o'clock hour-lines. 



