166, 167.] §14. Monochromatic Aberrations 195 at 6; but between b and q it will be elliptical with the major axis of the ellipse perpendicular to the plane of the diagram. The ellipse gets smaller and more elongated, the nearer the cross section is to q ; and at q the cross section of the bundle of rays is a horizontal straight line perpendicular to the plane of the diagram. Beyond this point the cross section is again an ellipse with its major axis perpendicular to the plane of the diagram, which soon becomes more and more round and is actually circular about midway between q and s; then it becomes an ellipse again with its major axis in the plane of the diagram, which collapses into a vertical line at s. Beyond this point it gradually gets broader again and becomes more and more circular. The results are similar when a narrow bundle of incident rays encounters a spherical refracting surface obliquely. Suppose that the curve bch in Fig. 76 is the section of a spherical surface and that the straight line pc represents a ray incident on it at a finite angle of in¬ cidence. We know (cf. Fig. 32) that rays proceeding in the plane of the diagram and incident on the surface in the immediate vicinity of the point c do not intersect each other in a point on the axis pq after refraction, but at a point off the axis which lies on the caustic surface. Suppose t is this point. Conceive now that the whole figure is rotated around ap as an axis; so that the ray pc will come in succession into the positions of all rays from p that cross the axis at the same angle. The corresponding refracted ray cq will also describe a ray-cone with its vertex at the point q. Consequently, whereas the rays immediately adjacent to pc in the plane of the diagram intersect it at t, those ad¬ jacent to it on either side of that plane intersect at it q. Finally, it may be added that other adjacent rays do not intersect pc at all. Another question to be asked about this subject is, What is the effect of diffraction of light at the edge of the pupil on the monochro¬ matic aberrations? And this suggests a further question as to whether the star-like form of the small blurred patterns may not be due to the minute indentations in the edge of the pupil. In fact, if a luminous point is viewed through an opening smaller than the pupil, the edge of which is not perfectly smooth, a more extensive star-shaped figure will be seen; although, as a rule, such patterns consist rather of very fine hair-like brightly coloured rays, similar to the hair corona of the eye which was described above and which is seen around any brilliant point-source even without using an artificial opening. When the opening is rotated around its centre, the entire corona turns with it; which shows that the effect is due to the contour of the aperture. The writer could not be sure of perceiving in his own eye the indica¬ tion of any diffraction of light due to the fine fibrous structure of the crystalline lens. When a small luminous point is observed through a