1878.] 



The Magic Mirror of Japan. 



139 



screen be held very near to the mirror, the apparent reflection of the 

 back, the magical property in fact, onght to become invisible. And 

 this, also, is exactly what happens when we make the screen almost 

 touch the polished surface. 



We have, therefore, strong reasons for favouring the " inequality of 

 curvature " theory. In order, however, to make the explanation 

 quite certain, we have had made a small concavity and a small con- 

 vexity on the face of one of the mirrors, by hammering with a blunt 

 tool, carefully protected with a soft cushion to avoid scratching the 

 polished surface, and, as is seen on trying the experiment, the con- 

 cavity reflects a bright image and the convexity a dark one when the 

 screen is in the position DF, but when the screen is shifted to D'F', it 

 is the convexity which appears as the bright spot, and the concavity 

 as the dark one. 



And not only do we think that the thicker portions of the convex 

 mirror are flatter than the remainder, but the existence of a focus for 

 a divergent pencil (as evidenced by a best position of the screen in 

 fig. 2) leads to the conclusion that, in some instances at any rate, the 

 thicker portion is actually concave, and is found to have a radius of 

 about three to four metres. ^ 



In the account of the Chinese Magic mirror, given by Ou-tseu-hing 

 at the end of the thirteenth century, he mentions that the wall or 

 screen on which the shadow is cast should be near, an instruction 

 which people have usually found it necessary to follow in order to see 

 the phenomenon clearly. But this condition of proximity of the 

 screen to the mirror is necessary, simply because the sunlight falling 

 on the mirror neither forms a parallel beam, nor one diverging from, 

 nor converging to, a single point, but consists, of course, of an 

 enormous number of slightly diverging beams. Consequently, on any 

 one point of the mirror there fall rays of light, each making a slightly 

 different angle with the surface. Now, as these, after reflection, pro- 

 ceed in slightly different directions, they will illuminate different 

 points of the screen, and, therefore, make a well-defined image impos- 

 sible, unless the screen be held near. If ordinary sunlight then be 

 employed, the screen, as previously explained, must be held not so near 

 the mirror that the inequalities of the surface are unable to produce 

 any decided displacement of the rays before they strike the screen, 

 and in addition, as we now see, not so far from the mirror that the 

 different rays falling on the same point are perceptibly separated before 

 they reach the screen ; or, putting the above conditions into more pre- 

 cise mathematical language, the screen mast not be held so near the 

 mirror that the product of this distance into the angle between the 

 normals to two adjacent parts of the surface is too small, and not so 

 far from the mirror that the product of this distance into the angular 

 diameter of the sun is too large. 



