If we agree to consider as positive the type of aberration which results the most often from the disproportionate extension of spherical surfaces, then we will denote as negative the aberration in the opposite direction which results from an exaggerated or inopportune correction of a spherical figure. But, if we only consider the ray bundle as a whole independent of the apparatus that makes it converge, we can agree to denote as a positive aberration the arrangement of a bundle of rays wherein the central ones converge last of all. In this case the caustic (see figure 10) formed by the series of crossing rays has its vertex turned towards the side where the light is heading. By contrast, we will call a
negative aberration the opposite arrangement, wherein the central parts of the ray bundle converge first, and wherein the caustic has a vertex pointing towards the mirror, as in figure 11.|
| Let us suppose, for example, that a spherical surface is examined in circumstances where it should present an ellipsoidal figure. That is to say that instead of the correct figure s (shown in figure 12) we substitute figure s' which is not correctly figured. To have an idea of the appearance which should result from this, let us put the circle and the ellipse on the same set of coordinates, and then let us construct the curve given by the changes in the differences in the y-coordinates corresponding to the same x-coordinates. This curve, which is of the fourth degree, is in fact the one which, if we imagine it rotated around the y-axis, would generate a surface that matches what we see in black-and-white shadows (figures 13 or 14) on a mirror that is examined by the third method, and when this mirror has a central zone that is a conic section, and when it has been verified as being outside the conditions defined by the positions of its own foci.
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