OF DIALING. 375 



line E Q, cutting the substilar line at rifht angles in K; LECT. 

 and from K make K R perpendicular to the axis C R P. '^^-^ 

 Then K G (=K R) being made radius, that is, equal to 

 the chord of 60 or tangent of 45 on a good sector, 

 take 42 52* (the difference of longitude of the places Z 

 and D) from the tangents, and having set it from K to 

 M, draw C M for the hour-line of XII. Take A' X 

 equal to the tangent of an angle less by 15 degrees than 

 KM; that is, the tangent 27 52*.; and through the 

 point Xdraw C Xfor the hour-line of I. The tangent 

 of 12 5% (which is 15 less than 27 52') set off the 

 same way, will give a point between K and N, through 

 which the hour-line of II is to be drawn. The tangent 

 of 2 8* (the difference between 45 and 42 52") placed 

 on the other side of C L, will determine the point 

 through which the hour line of III is to be drawn : to 

 which 2 5 8', if the tangent of 15 be added, it will make 

 17 8' ; and this set off from K towards Q on the line 

 E Q, will give the point for the hour-line of IV : and so 

 of the rest. The forenoon hour-lines are drawn the 

 same way, by the continual addition of the tangents 15, 

 30, 45, &c* to 42 52* (= the tangent of A' M ) for the 

 hours of XI, X, IX, &c. as far as necessary ; that is, 

 until there be five hours on each side of the substile. 

 The sixth hour, accounted from that hour or part of the 

 hour on which the substile falls, will be always in a line 

 perpendicular to the substile, and drawn through the 

 center C. 



4. In all erect dials, C M, the hour-line of XII, is 

 perpendicular to the horizon of the place for which the 

 dial is to serve : for that line is the intersection of a 

 vertical plane with the plane of the meridian of the 

 place, both which are perpendicular to the plane of the 

 horizon: and any line HO, or ho, perpendicular to 

 C M, will be a horizontal line on the plane of the dial, 

 along which line the hours may be numbered ; and C M 



