264 



THE POPULAR EDUCATOR. 



nothing more ? But we hope that very few of our readers will 

 like to stop there. To draw from nature and the real thing, we 

 trust, is the ambition of every one who makes up his mind to go 

 through these lessons, that he may make the art of drawing 

 a useful and valuable auxiliary to his occupation as a means 

 of expressing himself, as well as a pleasing recreation for leisure 

 hours. Another reason why we recommend the pupil to study 

 our lessons in geometrical perspective is, as we have said before, 

 when treating upon drawing a simple outline from the flat (a 

 term used by draughtsmen when copying from a drawing), that 

 the practice of geometrical perspective assists the eye to under- 



panying barns, stables, strawyards, etc. etc. that we must 

 first make a measured plan of the whole, and go through 

 the drawing geometrically, before we can hope to make a 

 truthful picture. It would be as ridiculous to suppose that 

 when we write a letter or an essay, we ought to repeat all 

 the rules of syntax, so that the grammatical construction of the 

 sentences may be correct. Every educated man knows that the 

 right words flow naturally into their places in proper agree- 

 ment and sequence. The phrases harmonise without any effort 

 on his part, simply because he knows the rules, and experience 

 makes them easy to apply. 



PP 



Fig. 65. 



PS 



Fig. 68. 



PS 



------5^ 



Fig. 67. 



Fig. 66. 



HL 



\wm_L 



VP1 



HL 



-B. 



-VP2 



s 



stand and calculate more readily the proportions of retiring lines 

 and planes. As a practical illustration of this principle, we 

 meet with it repeatedly in the readiness with which an expe- 

 rienced carpenter will tell you the length of a board without 

 feeing the trouble to measure it. His eye is so accustomed 

 to the foot-rule, and the space a repeated number of measure- 

 ments will cover, that to him it is no difficulty to say within 

 a very close approximation how long the board is. It is the 

 repeated practice of geometrical perspective that enables a 

 draughtsman to decide upon the proportional length of a line 

 or plane as it retires, and to draw either correctly on his paper. 

 If we did not consider it in this way with regard to free-hand 

 drawing, it would be of very little use in the .practice of drawing 

 from nature. It would be absurd to expect, when we are seated 

 before a subject say a picturesque farmhouse, with the accom- 



We will now give a geometric method of representing two 

 walls meeting at an angle, as an illustration of what we have 

 stated. Let two lines, a b, a c (Fig. 65), forming an angle of 

 90 degrees, represent the plan of two walls meeting at the point 

 a, of which b a forms an angle of 40 degrees with the picture 

 plane. P P is the picture plane, H L the line of sight, B P base 

 of the picture, s P the station point, and v P 1 and v P 2 are 

 the vanishing points for the corresponding numbered lines of 

 the plan. First draw the picture plane, and then the line 6 a, 

 placing it at an angle of 40 degrees with the P P ; then from a 

 draw a c at an angle of 90 degrees that is, a right angle with 

 a b ; this will be the plan of the walls as they are placed before 

 our vision. Then mark s P to represent the supposed distance 

 we are from the angle of the walls. Find the vanishing points 

 for the two lines of the plane. We have already given the rule 



