184 Dioptrics of the Eye [156, 157. difference between curve A and curve B is that the latter becomes perpendicular to the Æ-axis at the point /, corresponding to the actual position of the boundary. That is, for x = 0, the derivative dH db 2 Bb N{N-1) 2 vV2 —x2+log nat P | r |_r+ Vr-xzj ) (9) becomes infinite. This sudden drop in intensity enables the eye to recognize the position of the edge, even if some light does extend beyond it. In the case represented by curve A, however, the falling off is more gradual, so that there is nothing to indicate exactly where the edge is. If it were possible to take into account the diminishing brightness of the colours towards the ends of the spectrum, the curve B would be found to follow more nearly the dotted line drawn adjacent to it. That is, the intensity would approach its normal maximum value more rapidly inside the edge, and would fall off more rapidly outside, than curve B indicates. It will be clear from these considerations why the distinctness of visual images is so little affected by chromatic aberration. A combina¬ tion of lenses intended to correct the chromatic aberration of the eye does not produce any appreciable improvement of the visual acuity, according to the writer’s experience. A concave flint glass lens of 15.4 mm focal length, taken from the objective of a microscope, was found suitable for this purpose. It was combined with convex crown glass lenses so as to produce a system with a negative focal length of about 2.6 ft; which was adapted for the writer’s eye so that he could discern distant objects through it clearly. On looking through this arrangement with half of the pupil covered, no coloured fringes ap¬ peared at the boundary between light and dark. The same was true even with the eye imperfectly accommodated; so that the lenses evidently rendered the eye practically achromatic. There was, how¬ ever, no apparent improvement in definition. The chromatic aberration in the eye was known to Newton, who mentions the coloured fringes that appear when the pupil is half covered.1 Newton made the mistake of supposing that the dispersion of all transparent media is proportional to their refraction; and hence he concluded that an achromatic combination of lenses was impossible. Curiously enough, Euler,2 starting from the false premise that the eye is achromatic, argued that Newton must have been wrong as to his theory of dispersion and thence deduced the correct conclusion that an achromatic combination of lenses was possible. d’Alambert3 took exception to this reasoning, by pointing out that the chromatic aberration may not necessarily become noticeable in the 1 Optics. Lib. I. P. II. Prop. VIII. 2 Journal Encyclop. 1765. II. p. 146. — Mém. de VAcad. de Berlin. 1747. 3 Mém. de VAcad. de Paris. 1767. p. 81.