N DRAWING. 



i. r 1, i> r _. .!<:: ; M . ' m e u will be a square in por- 



in which we drau uy hand as follows: The 



diagonals ( c and a m intersect each <>' 



a (see p. 138) ; through thin centre n draw the 



parallel to a c. Now observe where the lines from h h out 



Canals in , , , t; through thetie points, and also through 



draw bj hand the perspective circle as in the figiin U 



reoommond the pupil to draw this figure several times, as it re- 



auich pnwtii-f to draw the perspective circlo properly. 

 When this difficulty has been overcome, ho may try to draw 

 tho circlo without the geometrical perspective lines, aa follows 



DP'2. 



more underneath the eye than the top, he has a more enlarged 

 view of the base ; through k draw p r, the diameter of tho base, 

 equal to the diameter a 6 of the top, and mark the distance k n, 

 ; rom it* being lower to the eye than the distance oeal 

 the upper circle, the line k n will be somewhat longer. (Now 

 here, again, we should like to prove this by another geometrical 

 drawing, bat we decline it at present for reasons already stated; 

 but tho pupil may very easily, for his own satisfaction, draw 

 again Fig. 48, placing tho H L doable the height from the plan* 

 of the picture as therein shown, keeping DP! and D p 2 the 

 same distance from p M before ; the remit will show him 



(see Fig. 49) : First draw a b, according to the required width 

 or diameter of circle, say the top of a wine-glass ; through o, 

 the centre of a b, draw the perpendicular c d, mark the point e 

 from o (if the pupil has a glass before him, let him stretch a 

 piece of thread over the top of the glass to represent a l> ; he 

 will then perceive that the distance o e must be regulated ac- 

 cording to the view the object presents to the eye) ; make o h 

 equal to o c, and divide o h into three equal parts, add one of 

 these parts from 7i to/; then through o e b /draw, by hand, the 

 perspective view of the circle as in the copy. This, we allow, is 

 an approximation, but sufficiently near for practical purposes. 

 To complete the wine-glass, Fig. 50, continue the line c / to m 

 any length ; mark / i for the depth of the glass, and i k for the 

 length of the stem. If the pupil will ploco a wine-glass before 

 him on the table, he will notice that tho circular base, being 



that, when the circle is placed lower, the eye looks more upon 

 it.) Proceed with k //i and tho divisions as before, and draw by 

 hand the circle through the points p n r m. There is scarcely 

 anything more difficult for a beginner than the circle, under any 

 conditions ; therefore we earnestly recommend him to practise 

 it well from the foregoing instructions. Our reason for giving 

 the above simple geometrical problem for constructing the per- 

 spective view of a circle is to satisfy the mind of the pupil upon 

 the proportions and changes of its retiring dimensions, according 

 as it is seen nearer to or further below the level of the eye. 

 Let him raise the glass until the top is on a level with tho eye; 

 tho top will then present a straight line ; let him lower it gra- 

 dually, and he will see that the retiring diameter of the circle 

 seems to expand, until, when it is exactly under his eye (looking 

 down upon it), it then presents the true circle. 



