OP DIALING. 345 



hour-lines of XI, X, IX, VIII, and VII ; and because LECT. 



the sun sets not before eight in the evening on the ^^^^ 



longest days, continue the hour-lines of VII and VIII in 



the forenoon, through the center a, to VII and VIII in 



the afternoon ; and all the hour-lines will be finished on 



this dial ; to which the hours may be set, as in the 



figure. 



Lastly, through 51j degrees of either quadrant, and 

 from its center, draw the right line ag for the hypothe- 

 nuse or axis of the gnomon agi; and from g let fall the 

 perpendicular gi, upon the meridian line ai, and there 

 will be a triangle made, whose sides are ag, gi, and ia. 

 If a plate similar to this triangle be made as thick as the 

 distance between the lines ac and bd, and set upright 

 between them, touching at a and b, its hypothenuse ag 

 will be parallel to the axis of the world, when the dial 

 is truly set ; and will cast a shadow on the hour of the 

 day. 



N. B. The trouble of dividing the two quadrants 1 * 

 may be saved, if you have a scale with a line of chords 

 upon it, such as that on the right hand of the plate : for 

 if you extend the compasses from to 60 degrees of the 

 line of chords, and with that extent, as a radius, de- 

 scribe the two quadrants upon their respective centers, 

 the above distances may be taken with the compasses 

 upon the line, and set off upon the quadrants. 



To make an erect direct south dial. Elevate the pole to TO con- 

 the co-latitude of your place, and proceed in all respects strucl an 

 as above taught for the Horizontal dial, from VI in the dial. 

 morning to VI in the afternoon, only the hours must be 

 reversed, as in the figure ; and the hypotlienuse ag, of 

 the gnomon ag f, must make an angle with the dial- 



yote 107. The trouble of dividing the two quadrants is obviously 

 unnecessary. It is sufficient to divide one, as f h; and, taking the dis- 

 tances from / to the points where the hour-lines of I, II, III, Sec. in- 

 tersect the quadrant fh in tbe compasses, to set them off from e on the 

 quadrant i g-: the lines drawn from the center a, to the points thus 

 found, will be the forenoon hour lines, XI, X, IX. kc. 



