658 



SIR DAVID BREWSTER ON THE 



one or with both eyes, his accurate appreciation of the distances E A, E'A', will 

 prove to him that A is a concavity, and A' a convexity ; but if E A, E' A' approach 

 to equality, either from the distance of the observer, or from the shallowness of 

 A, or the slight elevation of A', he will cease to recognise any difference in the 

 distances E A, E' A', and will be unable to tell which is the convexity, and which 

 the concavity. So great, indeed, is this uncertainty, that, from causes which he 

 cannot discover, they will sometimes appear convex and sometimes concave. In 

 this indetermination of the judgment, a touch of A, A' by the finger, or the intro- 

 duction of a shadow, will remove or confirm the illusion, whatever it may be. 

 The same result will be obtained, if we view A and A' vertically, with an erect 

 or inverting eye-piece. In all these cases, we suppose that the circular, or 

 rather the elliptical, base of the convexity or concavity is distinctly seen. 



Let us now look at A, A', at obliquities varying from to 90. In Fig. 1 the 

 concavity A will have an elliptical section at all obliquities, till, at 90, it appears 

 a straight line; but in the convexity the effect is very different. In passing 

 from to the position E', Fig. 2, the circular section of A' will appear an ellipse ; 

 but in passing from E' to 90, the appearance of A' will lose all resemblance to 

 A. When the eye is at e', for example, the summit A' of the convexity will cover 

 the point a of the table, and a m will be invisible ; and near 90, the convexity A 

 will eclipse the whole surface of the table m M, however extended it may be, and 

 will rise above it. 



Let us now suppose that the eye at E, Fig. 3, views the concavity A through 

 the inverting eye-piece E G H, the hori- 

 zontal table M N must obviously be in- 

 verted as well as the hollow A ; but the 

 apparent change, produced by inversion, 

 is very different from the real change. 

 The surface M N, out of which A is ex- 

 cavated, and upon Avhich the observer 

 leans, and rests the lower end H of his 

 inverting eye-piece, appears to remain where it was, and still to look upwards, in 

 place of appearing inverted, and looking downwards. AVhen he strikes the table 

 with the end H of the eye-piece through which he looks, he believes that it is the 

 lower end of the field of view that strikes the table, and rests upon it. With 

 these convictions, he sees what is re- rig. 4. 



presented in Fig. 4. The concavity 

 mAn, Fig. 3, appears inverted ; and as 

 the visible part of the concavity A m, 

 Fig. 3, is nearest the eye in Fig. 4, and 

 the invisible part A n, Fig. 3, farthest 

 from the eye in Fig. 4, m A n must ap- 



Fig. 3. 



