Representation of a Circle. 4-23 



The construction of a sun-dial is a very simple problem in 

 perspective. In fact, if OE and KCOG (fig. 5.) are perpendi- 

 cular to each other, if OE = the height of the style ; OEG the 

 angle which the polar axis makes with the style, which, when 

 the dial is hoi'izontal, is the colatitude of the place ; CK = EC, 

 the nih hour-line or GV„ is found by making the angle 

 CKV„ = 7ixlB°, and joining GV„. The curve which the 

 extremity of the sun's shadow describes may be thus found : 



Draw AGB (fig. 5.) perpendicular to OG. Make GD in 

 GC = GE, and let ADG = BDG = sun's codeclination. 



Let 



CKV's = 7° 30' 

 CKV'4=22°30' 

 CKV'3=37°30' 



CKV'„= {n-5) \5° + 1° 30'. 



CKVs = 75^ 

 CKV4 = 60° 

 CKV3 = 45° 



CKV„ = 11X15° 

 Join BV, cutting GV, in P, 



P„_i, P„ cutting GV„ in P„, 



Pi, P2 , &c. P„ are points in the curve. 



The problem is the same 

 as to represent on the dial a 

 circle situate in a plane of 

 which VCV is the vanishing 

 line; EO the height of the 

 style, being the distance of the 

 picture, and the circle such 

 that a perpendicular from the 

 eye of the spectator meets the 

 circle to be represented in its 

 centre. This circle is in fact 

 the circle described in the 

 heavens by a sun whose right 

 ascension and declination are 

 those of the real sun +180°. 



The extent which a picture 

 ought to take in, must of course 

 be regulated by the field of 

 view. Objects are not seen 

 distinctly by the human eye, 

 which subtend an angle greater 

 than 45° with the visual axis; 

 therefore the limit of the picture should be such that it does 

 not contain the vanishing point of any line which makes an 

 angle greater than 45° with the axis of vision. If objects are 

 dehneatcd wliich are beyond this buundarv, the perspective 

 becomes dislorli'd, and does not convey to the n)ind an accurate 

 idea of tlie object wliich is to be represented. In representing 



the 



