232 



THE POPULAR EDUCATOR. 



lines express an idea with great force and power, but for a 

 learner to begin the art by sketching is altogether a mistake. 

 We once heard an eminent landscape painter say that " sketch- 

 ing is the ruin of hundreds of young artists ; it is beginning 

 at the wrong end; let them draw well first and secure the 

 power, then afterwards they may sketch." Sketches are clever 

 and valuable only when they are done by men who can really 

 draw well ; the unfortunate result of the habit of sketching by 

 an inexperienced hand may be compared to that of the very 

 objectionable system which compels schoolboys to write out 

 pages of Latin or English for punishment. There are many 

 who acknowledge in after years that their handwriting was 



under our notice, to draw which we shall be materially assisted 

 by principles borrowed from geometry. But though we cannot 

 employ compasses to draw the forms of flowers and leaves, 

 yet by the practice of geometry we easily associate lines, angles, 

 and centres with curves, although they are not visible upon the 

 object. Instruments are usually depended upon for drawing 

 architectural curves, mouldings, and the like, because they must 

 be constructed according to received proportions. We propose 

 now to place before our readers some examples of architectural 

 curves, with the rules for constructing them ; our reason for 

 doing so being simply to show the pupil a way of making his 

 eye familiar with the construction of curves on geometrical prin- 



63. 



spoiled by these "tasks" or "impositions," and who were 

 never able afterwards, with all their efforts, to write well. Let 

 the pupil therefore give up all idea of sketching, and seek 

 to draw well, if he at all hopes to make the art useful for 

 practical purposes, or to secure in its practice a pleasurable _ 

 resource in leisure hours. 



There is much to be said upon the advantage to be gained by 

 a knowledge of geometrical drawing, a branch which depends 

 for its accuracy upon the use of compasses, scales, and rulers. 

 We have already explained a method of drawing curves by 

 hand, that is, by previously placing points in the course of the 

 intended curve, and then drawing the line through these points. 

 There are innumerable instances of curves which may be better 

 drawn without the aid of instruments than with them. Leaves 

 and flowers, for instance, afford an inexhaustible supply of 

 curved lines, to copy which we usually depend entirely on the 

 eye and the hand ; while there are curves which frequently come 



ciples. From long experience we have found it to be the case 

 that they always make the best and quickest draughtsmen, 

 and do their work with the least labour, who have dipped 

 deeply into geometrical drawing and lineal perspective. In their 

 practice they have acquired a habit of precision, and have 

 learnt the means to arrive at it readily, and have become fully 

 impressed with its importance ; they know the reasons why in 

 such and such directions lines must be drawn ; the mind and 

 the eye have acquired a keener perception of the principles of 

 proportion ; a feeling for arrangement has grown from the use 

 of instruments in geometrical exercises, and then in the end the 

 hand readily takes up the practice. 



The curve called the Scotia (Fig. 58). Let a b and c d be the 

 two lines between which the curve is to be formed. Draw b d 

 perpendicular to c d, and divide it into three equal parts ; 

 through e draw the line g f parallel to a I; from e, with the 

 radius e b. draw the arc b g, and at the same time mark tho 



