On the Conversion of Relief by Inverted Vision. 433 



quaquaversus light, like that of the sky. If the observer, 

 placed at a moderate distance, view these objects in the di- 

 rections E A, E' A', either with one or with both eyes, his 

 accurate appreciation of the distances E A, E' A', will prove 

 to him tliat 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 uncer- 

 tainty, that from causes which he cannot discover, they will 

 sometimes appear convex and sometimes concave. In this in- 

 determination of the judgement, a touch of A, A' by the finger, 

 or the introduction 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 di- 

 stinctly seen. 



Let us now look at A, A', at obliquities varying from 0° 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 0° 

 to the position E', fig. 2, the circular section of A' will ap- 

 pear an ellipse; but in passing from E' to 90°, the appear- 

 ance of A' will lose all resemblance to A. When the eye is 

 at ^, for example, the summit A' of the convexity will cover 

 the point a of the table, and am 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 con- 

 cavity A through the in- 

 verting eye-piece E G H, 

 the horizontal table M N 

 must obviously be inverted 

 as well as the hollow A; 

 but the apparent change, 

 produced by inversion, is "ST 

 very diflerent from the 

 real change. The surface -^ 



M N, out of which A is excavated, and upon which the ob- 

 server leans, and rests the lower end H of his inverting eye- 

 piece, appears to remain where it was, and still to look up- 

 wards, in place of appearing inverted, and looking downwards. 

 When 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 



ridl. Ma'i. S. 3. Vol. 30. No. 203. Jnne 1847. 2 G 



