



-, from /, with the radius f<j, draw the arc g i; >' >j i 

 will b 



59). Let the curve bo 



.-. i-i'ii tlin liin-.s n ') mill d t and 



it into tivo equal parts; uiurk the HUCOI 



. upon 6 e dosoribu tho I'nuihit.-i-.il triangle b /, ami up..n 



scribe the equilateral I :/ .- fnuu /, with tho 



radiuH / b, draw tho arc l> c, and from <j, with tho radios g e, 



ho arc e d ; b c d will bo the cur\ 



Tln> pupil can draw an equilateral triangle upon a given lino 



th<> I. |..-t ' ' ( I !;.'. GO) bo tho lino upon 



i angle ia to bo described ; from a and 6 as centres, 



< radius l> a, describe two area intersecting each other 



point c; join c a and c b ; tho triangle a b c is an equi- 



trkmglo. (Seo Lessons in Geometry, VII., page 209.) 



' tlic Ogee (Fig. Gl). Let it be drawn between 

 the lines a b and c d; draw d e perpendicular to c d, and divide 

 it into four equal parts ; through the first from e namely, h 

 draw the lino h i g parallel to a 6, make h i equal to he; draw 

 the lino k i I parallel to e if, and from t, with the radiua i k, 



of a little help from goonwtry ; we advise him also to draw all 

 these lines of arrangement with a light hand, that they may be 

 more easily effaced when done with. 



To draw the pear (Fig. 63), we will fint draw a line to 

 represent the length or aiw, and from this line " offsets " oc 

 each aide as shown by dotted lines. The pupil may please him- 

 self M to the number of these " offsets " and their whereabouts ; 

 he will not be long before be finds that such lines are best 

 arranged opposite, and to meet, angles, and the greatest dis- 

 tance of curvature from the axis. He will then proceed to 

 draw the outline through the extremities of these offset*, 

 especially observing tho kind of line requisite between each 

 point: in some part* tho outline is more outwardly carved than 

 in others, in some it is nearly straight, in others the curve 

 ia inward. If the pupil will exercise his observation in this 

 way when looking at solids and natural objects, which be can 

 do at all times, whether he has a pencil in his hand or no^ 

 even when out for a walk, he will be not a little surprised 

 should he make this his general practice, to find how rapidly bt 

 will gain confidence and power, and be able to produce trutlls. 



draw the semicircle k g I , join I d, and upon it draw the equi- 

 lateral triangle I m d; from r,i as centre, with the distance 

 m d or m I as radius, draw tho arc cl n I ; the line d n I g k 

 will be tho curve required. By recommending the practice of 

 geometrical drawing, \vo only wish to direct the pupil where to 

 find further assistance in free-hand drawing ; we will now show, 

 by a few examples, how these principles .may be applied. An 

 oval or epg-shaped figure (Fig. 62) would be very difficult to 

 draw, if tho boundary line only were to bo attempted without 

 some assistance from geometry ; there would be a great deal of 

 rubbing out and alteration before it was finished. Let the pupil 

 try the figure in the following manner : first by the help of com- 

 passes, then by hand only. Draw the straight lino a b, and 

 divide it into two equal parts in tho point cZ. Through d draw 

 c d e at right angles to a b, and make d c equal to a d or d b. 

 Construct upon a b the equilateral triangle a e b, and take tho 

 point g at one-third of tho distance from e to b, and determine 

 tho point / in tho same way. Then from tho points /, g, draw 

 the lines fi,gh, perpendicular to a e and e b respectively, and 

 make each of them equal to one-half of c f or c g. After this 

 arrangement has been made, draw the semicircle a c b and tho 

 arcs 6 e and a e through h and t. It will bo necessary to repeat 

 it a few times, when the pupil wiH begin to see the advantage 



and useful drawings. We will give him another example 

 (Fig. 64), for which ho must arrange the scaffolding I : 

 with one exception, because it includes a principle which we 

 will merely allude to now, as we shall have better and more 

 frequent opportunities by-and-by to enlarge upon it. The 

 exceptional assistance we offer in this case, is that of the dotted 

 line which runs through the centre of the handle of the trowel, 

 and passes in a direct course to the point of the blade. V 

 may here observe that an implement of this kind, to be reallr 

 useful, ought to be so constructed ; and if we look at it with ar 

 artistic eye, the composition of lines which nrako np this vcr" 

 simple subject, must strike any one as being more symmetries, 

 than if the handle and the blade had been united at any otha 

 angle. This remark upon so insignificant an object as a garden, 

 trowel may appear trivial, but it ia the principle we contend for, 

 and which is, in reality, of the greatest importance. It is true 

 we might have selected a more noble object, but it would not 

 have better illustrated our moaning, or have made it mon> 

 evident, and at the same time have provided the pupil with a* 

 example for his practice more suited to the experience he has at 

 present attained as a draughtsman. Nature teaches us thia 

 lesson, and it ia evident everywhere that harmony of line and 

 proportion always accompany the greatest utility and strength. 



