Another failing is the appearance of astigmatism, which, broadly, is due to a refracting or reflecting surface which is not a surface of revolution and therefore behaves differently for rays incident in different planes around its optical axis. In its commonest form the surface reflects or refracts more strongly along one plane than along another at right angles to it. Hence the two have different foci and there is no point focus at all, but two line foci at right angles. Figs. 163 and 164 illustrate this fault, the former being taken inside and the latter outside focus, under fairly high power. If a star image is oval and the major axis of this oval has turned through 90° when one passes to the other side of focus, astigmatism is somewhere present. As more than half of humanity is astigmatic, through fault of the eye, one should twist the axis of the eyes some 90° around the axis of the telescope and look again. If the axis of the oval has turned with the eyes a visit to the oculist is in order. If not, it is worth while rotating the ocular. If the oval does not turn with it that particular telescope requires reworking before it can be of much use. This astigmatism due to fault of figure must not be confused with the astigmatic difference of the image surfaces referred to in Chapter IV which is zero on the axis and not of material importance in ordinary telescopes. Astigmatism of figure on the contrary is bad everywhere and always. It should be especially looked out for in reflecting surfaces, curved or plane, since it is a common result of flexure. Passing on now from these simple tests for figure, chromatic aberration has to be examined. Nothing is better than an artificial star formed by the sun in daylight, for the preliminary investigation. At night Polaris is advantageous for this as for other tests. [Illustration: FIG. 162.—A Case of Zonal Aberration.] [Illustration: FIG. 163.—Astigmatism Inside Focus.] [Illustration: FIG. 164.—Astigmatism Outside Focus.] The achromatization curves, Fig. 163, really tell the whole story of what is to be seen. When the telescope is carefully focussed for the bright part of the spectrum, getting the sharpest star image attainable, the central disc, small and clean, should be yellowish white, seen under a power of 60 or 70 per inch of aperture. But the red and blue rays have a longer focus and hence rim the image with a narrow purplish circle varying slightly in hue according to the character of the achromatization. Pushing the ocular a little inside, focus, the red somewhat overbalances the blue and the purple shades toward the red. Pulling out the ocular very slightly one brings the deep red into focus as a minute central red point, just as the image begins to expand a little. Further outside focus a bluish or purplish flare fills the center of the field, while around it lies a greenish circle due to the rays from the middle of the secondary spectrum expanding from their shorter focus.