upon the Antique Dials. 95 



and, finally, make the angle R'NX = BE 9. The intersection of NX, 

 Z H' will give X, as before, a point in the curve. 



3. When the latitude of the point of contact of the sphere and plane 

 is considerable. By similar triangles, 



B D (= B E) : B P : : D C : C P : : rad : cosec x, 

 (*. denoting the latitude of the point of contact) ; and hence, if, on any 



ficale we take B'E' : E'P' : : rad : cosec x, we may proceed with the sub- 

 sidiary operations for finding B'E'O' as before, upon this new figure. The 

 same relation will obviously subsist between A'E'8' and its projection 

 A' P' Z', as between the corresponding angles upon the dial which we are 

 constructing. We have, then, merely for any longitude L = A' E' Z' to 

 find A' P Z' ; to make APZ = A'P'Z' ; and, finally, by the general pro- 

 cess find PN, and make the angle PNX = A'E' 6'. We thus get X. 



4. Wlien * = 90, or the point of contact in the pole of the equator. 

 In this case P, C, H coincide, and we have only to draw 

 CN at right angles to CZ, and equal to the radius of the ge- 

 nerating sphere ; then making CNX = B' E' V. We get X 

 a point in the curve. 



We might have supposed the coalescence of A and B in 

 this last construction, since the pole may be deemed of any 

 longitude. 



N 2 



