152 



THE POPULAR EDUCATOR. 



Fig. 98. 



GEOMETRICAL PERSPECTIVE. XXL 



SHADOWS CAUSED BY ARTIFICIAL LIGHTS CONCLUSION. 



WE now intend to prescribe rules for projecting shadows 

 caused by an artificial light, as from a lamp or candle. If the 

 pupil has carefully studied the previous lessons upon shadows 

 projected by the sun, he will find the construction of those 

 caused by this light very 

 similar. The principal dif- 

 f erence between candle-light 

 shadows and sun shadows 

 is found to be in the posi- 

 tion of the luminary. A 

 candle placed on a table dif- 

 fuses its light in every direc- 

 tion, and consequently the 

 rays do not proceed as those 

 of the sun, which, from its 

 great distance from the 

 earth, are considered to be 

 parallel, although radiating 

 from one common centre; 

 besides, the source of light 

 being very near the objects, 

 when in a room, the sha- 

 dows for the most part 

 are much more extended, 

 and appear larger than the 

 objects which cause them. 

 However the forms and 

 positions of objects may 



vary, as well as the surfaces upon which the shadows are 

 cast, the principles that guide us in projecting them are the 

 same as those which belong to sun-shadows. The seat or 

 base of the source of light must be first determined, after- 

 wards the extent and direction of the shadows will be found 

 by drawing lines from the base of the light, which is upon the 

 ground, to intersect rays drawn from the luminary through the 

 angles and extremities of the object. This is the first 

 and most simple rule, and is illustrated by Fig. 98. 

 a is the source of light, and o is the horizontal pro- 

 jection or base of the light ; if rays are drawn from 

 the light through the angles of the table b, c, d, e, and 

 other lines drawn on the ground plane ,'\ 



from o, the foot of the light, the intersec- /'/, 



tions of these two sets of lines will give /';'/ 



the projection of the shadow at g, h, m, n. 

 Here we shall see that the extent of the 

 shadow is greater- 

 than the top of the ' 

 table which projects 

 it. This very simple 

 rule is the starting- 

 point for the rest, 

 and where the forms 

 and positions of ob- 

 jects vary we shall 

 find it necessary to 

 employ those rules 

 which guide us in 

 projecting sun sha- 

 dows, when again 

 the trace of the 

 plane of shade must be drawn 

 by ruling a, line through the 

 luminary, the vanishing point of 

 the plane receiving the shadow, 

 and the trace of the plane which casts the shadows. 



PROBLEM LX. (Fig. 99). A street lamp surrounded by an iron 

 'ence. Draw the perspective projection of a circle according to 

 the diameter a I; place the posts at pleasure (in the figure they 

 are situated upon the lines by which the circle is produced). 

 The post c d represents the given height of the whole, through 

 the top of which is drawn another perspective circle, in order to 

 obtain the proportionate heights of the remaining posts, and 

 the upper edge of the fence. From the foot of the lamp-post 

 lines are drawn outwardly to meet the rays drawn from the 

 light in the lamp at o, and through the top of each post as o f; 



/m 



e f is the shadow of the post e m. The same process is to be 

 observed with the rest ; tnrough the extremities of the shadows 

 of the posts draw another circle in perspective to represent the 

 shadow of the upper ring of the fence. The projection of the 

 shadow of the ring midway between the ground and the tops of 

 the posts is but a repetition of the upper one. 



PROBLEM LXI. (Fig. 100). Apole is leaning against a wall A, 



against which it casts part 

 of its shadow, and the re- 

 mainder upon another ivall 

 B, at right angles with A. 

 Let D be the source of light. . 

 Draw an indefinite perpen- 

 dicular line from PS. Draw 

 c e to represent the incli- 

 nation of the pole. From 

 the point d, at the intersec- 

 tion of c PS with the base 

 of the wall A, draw the per- 

 spective line d b ; cb will 

 be the representation of the 

 pole. Eule an indefinite line 

 from PS through the base m 

 of the luminary ; also a Hue, 

 the trace of the plane of 

 shade, from e, the VP of the 

 pole, through D to /. From 

 the point h, where the line 

 through the base of the 

 luminary vanishes at PS, 

 and intersects the base of 



the wall A, draw a perpendicular line to cut the trace of the 

 plane of shade in n ; draw from n through b to g on the inter- 

 section of the two walls ; through g, directed from e, draw g k ; 

 k will be found to meet a line drawn from / through c; c k g b 

 will be the shadow of the pole. 



PROBLEM LXII. (Fig. 101). A ladder leaning against a 

 wall casts Us shadow partly on the wall c ; it is continued upon 

 an open door, not perpendicular with its connecting 

 wall ; and lastly upon the ground. Project also the 

 shadow of the door. Let A be the source of light. 



After the last problem relating to the pole, it will 

 not be difficult to understand the shadow from the 

 ladder in this case ; the position of the 

 door will cause some difference in the 

 v ^. s course of the shadow which falls upon it. 



The method of projecting the shadow from 

 the top of the ladder at a on the opposite 

 wall c, is the same as 

 that of the pole; for 

 this portion VP 1 is 

 the vanishing point 

 on the trace of the 

 plane of shade ; VP 2 

 is the vanishing 

 point of the door 

 that is, for the lines 

 b c and d c. To 

 find the vanishing 

 point of the shadow 

 on the door, draw a 

 perpendicular line to 

 meet the trace of 

 the plane of shade from o, where 

 the vanishing line from the bot- 

 tom of the door intersects PS B ; 

 this will produce VP 4 ; lines 



drawn upon the door in continuation of those from a, and 

 directed by VP 4 , will be those of the shadow required. And 

 lastly, lines drawn from B through the foot of the ladder 

 will unite with those on the door at the base. To project 

 the shadows of the steps, draw lines from A, the luminary, 

 through the extremities of each step to meet the shadow lines 

 of the sides of the ladder between which the shadows will 

 be projected. To produce the shadow of the door on the 

 wall D to the left, let h n be the angle of the wall, and 

 h g its base. Draw / e, produced to k ; from k also an indefi- 

 nite perpendicular line through 3 ; the position of s will be 



