upon the Antique Dials. 91 



able ; that is, they do not pass through the same point on the surface of the 

 sphere. The hectemorial chords will not, therefore, pass through the same 

 point on the dial itself. 



It is worthy of remark, too, that the tangents (Eq. 2.) intersect in current 

 points whose ordinate L is independent of I. Hence the tangents to all 

 the hour-circles which pass through the same points of the equator, will, 

 taken two and two, and adapted to equal values of I, always intersect on the 

 same meridian of the sphere. 



XL 



We have now given the spherical equation, and examined a few of its 

 properties, and shall proceed, in the next place, to give a gnomonic projec- 

 tion of these hectemoria upon any tangent plane. 



GNOMONIC PROJECTION OF THE HECTEMORIA UPON A GIVEN 



TANGENT PLANE. 



General Preparation of the Dial. Let CD be the radius of the 

 sphere upon which the hectemorial curves are traced ; C the point of con- 



tact of the sphere and plane, BC, CP the tangent and cotangent of the 



