328 



THE POPULAB EDUCATOE. 



the wherefore will be the better educated man of the two, and 

 his information, though not so extensive as the other, will be 

 found in every way to be more serviceable to himself and to 

 those who errploy him. The latter can boast of possessing a 

 few coins of the true metal ; the larger stock of the former is 

 merely electro-plate. After the above remarks, we hope our 

 pupils will be anxious to accompany us into a little inquiry re- 

 specting the laws which regulate the disposition of shadows as 

 they occur under various circumstances. The extent of the 

 shadow is ruled by the position of the source of light. On any 



Figs. 76, 77, and 78 are intended to show the position of the 

 shadow of an object in three cases. In Fig. 76, the su 

 is parallel with our position, or with the picture plane, anfi 

 is on our right han-d, casting the shadow of the post at a b, 

 which is parallel with the horizontal line and picture plane. 

 In Fig. 77, when the sun is in front of the picture, or behind 

 us, the shadow is cast in a retiring position. In Fig. 78, 

 when the sun is behind the picture or before us, the shadow is 

 cast in advance of the object, or, in other words, approaches 

 us. We intend to give only a single geometrical example, 



Fig. 76. 



day at noon, when the sun is high in the heavens, the shadows 

 of our own figures are shorter than in the morning or evening, 

 when the sun is lower: this, then, suggests the consideration, 

 how are we to regulate or decide upon the extent of the shadow 

 of an object in a picture according to the sun's inclination. 

 This may be said to be the statement of the question relating to 

 all shadows under whatever conditions they may be found. We 

 propose now to take it up with reference to a few cases only, as 

 it will be more thoroughly answered in the lessons on Geometri- 

 cal Perspective. Sometimes the position of the sun may be 



Fig. 78. 



and that a very simple one, of the first of these positions, 

 and leave the pupil at present to take for granted much that 

 might be said, not only on this, but on the others also, as they 

 belong more especially to geometrical perspective. The position, 

 we have chosen is the parallel position, when the sun's rays are 

 in the picture. Let A, B (Fig. 79) represent two walls, forming a 

 right angle, one of which, A, is parallel to the picture plane,, 

 and the other, B, at a right angle, or perpendicular with the- 

 picture plane ; there is also a doorway in the wall B. Let the- 

 sun's rays be supposed to have an inclination of 45. The- 



Fig. 79. 



HL 



behind us, at other times before us, and again it may be, as it is 

 technically termed, " in the picture ;" that is, the sun is either 

 on our right hand or on our left, meaning by that neither 

 before us, nor behind us : consequently the rays are parallel 

 with the picture. Sometimes the source of light is a lamp or 

 candle, and although the rules for constructing the shadows 

 under this light are very much the same as those we employ for 

 shadows resulting from the effects of sunlight, yet there is this 

 characteristic difference : the sun's rays are always considered 

 to be parallel on account of its remote distance from the earth, 

 whilst the light from a lamp or candle radiates above, below, 

 and on all sides, and consequently the rays are not parallel. 



angle a b c (45) may be made anywhere on the ground line, 

 as it is only so placed for the purpose of drawing the dotted 

 lines, d e, f g, etc., parallel to a b, to ensure the given inclination 

 of the sun's rays, by which the extent of the shadows are deter- 

 mined. Our purpose then in introducing this problem is to 

 prove that the edges of the shadows of objects in a horizontal 

 position have the same vanishing point as the lines of the object 

 itself have when in parallel perspective. It wil-l be seen that 

 the shadow, g h, of the upper edge of the wall, B, as well as 

 the wall itself, are directed towards the point of sight, also the 

 shadow of the top of the doorway, and e i, of the end of the 

 wall A, are subject to the same rule. We should like to go 



