66 Sir 1). Brewster's Explanation of an Optical Illusion. 



had a much simpler origin than my correspondent supposed ; 

 that they were not images derived optically from the real sil- 

 houettes, but were only phenomena arising from the union of 

 penumbral shadows of bodies held at different distances from the 

 eye, and seen indistinctly by persons with every variety of sight. 



When a finger of each hand, A and B, is held up near the 

 eye against a luminous ground, so that the nearest A does not 

 eclipse the remotest B, and that both are seen very indistinctly 

 with a penumbral shadow, then if we bring the two fingers 

 together, the most prominent part of B seems to swell outivards 

 till it meets A. Now if we suppose the edge of the finger A to 

 be a silhouette, or a notched line like a saw, then it is obvious 

 that when the straight edge of B comes near it, a part of this 

 edge opposite the nose of the profile, will swell out and meet it, 

 whereas the notch below the nose will not. In like manner the 

 parts opposite the two projecting lips of the chin will swell out 

 till the straight edge of the finger has prominences exactly like 

 those of the silhouette or profile, and we shall have the appear- 

 ance of two silhouettes, a phantom one and a real one, looking 

 at each other. 



If we next suppose the edge of the finger B to be a silhouette, 

 the projecting parts of the profile will swell out when they ap- 

 proach the edge of the finger A, and a phantom silhouette will 

 thus appear to rise out of the other, and looking in the same 

 direction as described by my correspondent. 



In some long-sighted eyes, where the crystalline lens has begun 

 to decay, and to give slightly double images of objects, the phan- 

 tom silhouette emerging from the real one will seem to be 

 slightly separated from it ; but in good eyes the prominence of 

 the projecting features is merely increased, that is, the nose, the 

 two lips, the chin of the former swell out, and give the appear- 

 ance of a phantom silhouette coming out of the real one. 



All these phenomena may be produced merely by receiving 

 upon a white ground the shadows of a silhouette and a straight 

 edge, so that they have penumbras analogous to those which 

 they have when seen directly by the eye. 



As there can be no doubt that the phantom silhouettes are 

 produced by the swelling of the penumbral shadows, in the 

 manner I have described, we have only now to refer the reader 

 to an explanation of the cause of this swelling. 



The swelling of shadows seems to have been long ago observed 

 by optical writers, and was erroneously ascribed by some to the 

 inflexion of light. Our countryman Mr. Melville, however, 

 nearly 100 years ago, gave the true explanation of it*, which is 



* Essavs and Observations, Physical and Literary. 3 vols. Edinburgh. 

 1754. ' 



