( i I .< M 1 a'lUCAL PERSPECTIVE. 





Fig. 71 



the 



tag to the angle of inclination, to whore it out* a perpendicular 



:.iwn through thovp*; thus we find it* vani-mng ]>"int, 



wh'-ther its inclination be downward* <>r upward-; t; 



draw u lino from DVP*, at an angle of 50 with the HL, cutting 



i-pemliculiir from vi- at vi j , tlio vani-hiiix' point. \?i< 



.undo tliu nearest corner of the window 2 feet to the 



: the eye, represented by the distance i to I: a lino from 



t> must ho ruled to PS, 



upi'ii which we wish to out /"~ 



feet to find a, the 

 nit within; a lino 

 from c, which is 4 feet from 

 /', must be drawn to i>i:', 

 and where it outs the lino 

 in K is the point re- 

 quired. Draw the perpen- 

 dicular a h m. Draw from 

 through a to p ; make 

 iu.il to the width of 

 window. Draw back 

 again from r, cutting 

 DVP I in s; draw the per- 

 .i.'iiliir si; the base 

 of the window is drawn 

 from /, on the line of 

 contact, 5 feet from the 

 ground, to the vp 1 

 height of the window, 

 4 feet 3 inches, is 

 marked from / to e ; 

 a lino from e to vp 1 , 

 cutting the perpendi- 

 culars from a and s in 

 m and t, will give the 

 top of the window. 

 The opening of the 

 window is m t h n. 

 Now we must draw 

 the shutter ; the cor- 

 ner nearest us is v, 

 consequently it in- 

 clines upivard towards 

 ike icall, but down- 

 wards from it ; there- 

 fore, the vp for the 

 shutter must bo above 

 the HL, which we 

 have explained. To 

 measure or set off the 

 length of the shutter, 

 we have raised a line 

 of contact for that 

 purpose from o, found 

 by drawing from vp 2 

 through s to meet the 

 ground-line. From t 

 directed f romvp 3 draw 

 a line through w; this 

 will be the further 

 Bide of the shutter ; its 

 Jength must be deter- 

 mined thus : From 

 t directed from DVP* 

 draw a line to the 

 line of contact, meet- 

 ing it in y ; make y a 

 equal to the length of the shutter, the same as the length of the 

 window ; draw from x back again to DVI>, cutting t w in w ; 

 draw w v, directed by vp 1 , and v m directed by VP J . 



We will now draw the shutter at the same angle with the 

 wall, but inclined upwards from it (Fig. 70). The important 

 iifference in working the problem under these conditions arises 

 from the upward inclination of the shutter from the wall, but 

 inclined downward* to meet the watt. This last view of the 

 position of the shutter is the proper one for our purpose, because 

 after a little consideration we shall perceive that it is a retiring 

 plane, but downwards ; therefore its VP is below the eye or HL. 

 fin the former case the shutter was a retiring plane, but up- 



wards, establishing its VP above the eye or HL.) Consequently, 

 we most draw the vanishing line for the vH downward* from 

 DVP 8 . The sides of the shutter, t w and m v, mu*t be drawn 

 in the direction of VP*, and cut off from DVP*, first by drawing 

 a line through t to y ; make y x equal to the length of the 

 shutter ; draw from z to DVP*, producing w. All the early 

 part of the problem, relating to the wall and window*, 



and the remaining line* 

 w v and t m, will be but 

 a repetition of the butter 

 under the first position. 

 Wo can prove the truth of 

 this method of drawing the 

 perspective inclination of a 

 plane by another method. 

 Draw the right angle 

 cad (Fig. 68) ; make a b 

 equal to the length of the 

 shutter, and at an angle 

 of 40 with o c or 50 a 

 with ad; draw b c pa- 

 rallel to a d ; a c will be 

 equal to the height of b 

 above a. This mast now 

 bo applied to Fig. 70. 

 Draw a line from VP* 

 through t to e on the line 

 of contact ; make e / 

 equal to the height of 

 b above a, viz., c a 

 (Fig. 68). Draw from 

 / back to vp 2 ; it will 

 be found to cat the 

 corner of the shatter 

 in to, proving by both 

 methods that t v> is 

 the perspective length 

 of the further side of 

 the shutter. 



A plan of a build- 

 ing may be made, 

 having all its propor- 

 tions, angles, and 

 other measurements 

 arranged and noted, 

 yet nothing may be 

 said as to its position 

 with the picture- 

 plane, and from this 

 plan several perspec- 

 tive elevations maybe 

 raised. When such is 

 the case, all that is 

 necessary will be to> 

 draw a PP across the 

 paper in such a posi- 

 tion with the plan, 

 that by drawing visual 

 rays.the picture-plane 

 we have chosen may 

 receive the view we- 

 wish to take of it 

 Suppose A (Fig. 71) is 

 the plan of a build- 

 ing, and we wished to 

 have two views of it 



one taken with an end and front in sight, the other with a 

 view of the front and the opposite side we should then place- 

 the PP at such an angle with the side or front as might be 

 considered to be the best for our purpose. PP' would receive 

 the visual rays from the front and the end B ; PP 2 would re- 

 ceive those from the front and the end c. In short, any line- 

 may be drawn which represents the PP at any angle with the> 

 plan, or opposite any side we may wish to project. This will 

 give a very useful illustration of the way to treat a subject 

 when its proportions are given, as is frequently the case, with- 

 out any reference to the view to be taken of it ; in other words, 

 the angle it forms with the picture-plane. 



