( ; i :< >M i :TI; 1 i -A i , PERSPECTIVE. 



GEOMETRICAL PERSPECTIVE. II. 



IN thin course upon Geometrical Perspective we propose to 

 place before our pupils several methods of construction, and 

 show where they are applicable to special cases. The ground- 

 ]>tn,i ni.-t l.n'l is the most simple and general. The lineal method, 

 although it is equally useful, involves the necessity, in some 

 instances, of a greater number of lines ; but as this system 

 os with the use of a ground-plan, it may to some extent 

 curtail the amount of labour. Some of the problems will be 

 worked by both systems ; and with regard to the ground-plan 



it perpendicularly crer the plan a. It will be observed that 

 a cats the base of the picture, v l P 1 , in c, from which a per- 

 pendicular is drawn to moot the line K A in B, therefore B is 

 the perspective projection on the picture-plane of the point or 

 object, A. Wo give a similar representation of two points 

 (Fig. 6), which ore the extremities of the line A B. A is on 

 the ground, B is above the ground ; consequently the line 

 A B is inclined to the horizon. We need not enter into an 

 explanation of thin after that of Fig. 5, as it will be seen 

 by the working lines that c D is the perspective representation 

 of AB. 



Fig. 6. 



method, we shall introduce some modifications which we hope 

 will enable our pupils to understand it thoroughly. 



The station-point is sometimes determined by placing it at a also with the ground. 



We shall have to consider objects under various positions. 

 Case 1. When they ore parallel with the picture-plane, and 



given distance from the picture-plane, sometimes from the object 



represented by its ground-plan, the picture-plane intervening. 



In either case we must bear in mind that the visual rays from the 



two extremities of the object must not form an angle greater than 



60, meaning that the whole of the object must be included in 



that angle, because the full extent of vision each way, right and 



left, without moving the head, is not greater than 60. But 



even if we include the object within 60 only, we should be too 



near it to make a satisfactory and effective drawing ; therefore 



on angle of about 25 



or 30 at the outside 



is sufficiently large, 



as in Fig. 4, where the 



eye at E embraces tho 



line A B within on 



angle of 60, while at 



F the same line is in- 



cluded within an angle 



of 25. The latter 



point, F, is a better 



distance for viewing 



the object, A B. An 



explanation of the 



practical operations 



of perspective and 



their results 'may be 



Pic 



PP 



VP 



limited to that wliich 

 relates to a point, or 

 in the same way to 

 a series of points ; 



BP 



pel 



i- 



sp 



Case 2. When they are perpendicular to the picture-plane, 

 and parallel with the ground. 



Case 3. When they are perpendicular to the ground, and 

 parallel with the picture-plane. 



Cose 4. When they form an angle with the picture-plane, 

 and parallel with the ground. 



Cose 5. When they form an angle with the ground, and 

 parallel with the picture-plane. 



Cose 6. When they form an angle both with the picture- 



plane and the ground. 

 To illustrate the/irsl 

 position, place a rect- 

 angular table before 

 you, so that both ends 

 may be equally dis- 

 tant from the eye : 

 the front edge of the 

 table will be parallel 

 mth the picture-plane, 

 and the top will be pa- 

 rallel with the ground; 

 and at the same time 

 the retiring edges oi 

 the ends will be per- 

 pendicular to the pic- 

 ture-plane and parallel 

 with the ground. This, 

 answers to the second 

 case. The front of th 



HL 



Fig. 7. 





BASK OF PICTURE, OS FLAME OF PICTURE, BEOUGHT DOWH. 



table, from the top to 

 for as points are the extremities of straight lines, no matter j the ground, will explain the third case, bec&uae it is perpendicular 



their positions, it must be evident that if we can determine the 



to the ground, and parallel \rith the picture-plane. Now push 



position of one point upon the plane of projection, which we call one end of the table away from you, so as to cause the distance 

 tho picture-plane, we can do so of more, and thus determine j between the two ends from the eye to be different, then th* 

 tho extremities of lines. Let A (Fig. 5) be a point in space i front edge will be at an angle with the picture-plane, but the top 

 that is, somewhere in the air above the ground, and away from i will remain parallel with the ground. This illustrates the 

 the picture-plane, P P, P 1 p. The horizontal projection of this { fourth case. Bring the table back to its first position, and let 

 point in other words, its plan will be a. Let E be tho posi- one end be raised, then the top will form an angle with the 



tion of the eye, e will be the horizontal projection of the ey 

 that is, over where the eye is placed, otherwise called the 

 station-point, 8 p. Now if c and a are joined by a straight line, 

 the line ca will be the horizontal projection or plan of the 

 visual ray from the object, A, to the eye, E ; because A a and 

 K e are perpendicular lines, therefore every part of the line E A 

 41 N.K 



ground, and the front edge will be parallel with the picture-plane. 

 This answers to ihojifth case. The sixth case will be explained 

 if you push the raised end of the table away from you, as was 

 done in Case 4, then the front edge will be at an angle with the 

 picture-plane, and the top will be at an angle with the ground. 

 These positions might have been illustrated by a line only, but 



