There is likewise a great difference in the average quality of seeing as between stars near the zenith and those toward the horizon, due again to the greater opportunity for atmospheric disturbances in the latter case. Pickering’s experiments (loc. cit.) show a difference of nearly 3 scale divisions between say 20° and 70° elevation. This difference, which is important, is well shown in Fig. 182, taken from his report. The three lower curves were from Cambridge observations, the others obtained at various Jamaica stations. They clearly show the systematic regional differences, as well as the rapid falling off in definition below altitude 40°, which points the importance of making provision for comfortable observing above this altitude. [Illustration: FIG. 182.—Variation of Seeing with Altitude.] [Illustration: FIG. 183.—Airy’s Diffraction Pattern.] The relation of the diffraction pattern as disclosed in the moments of best seeing to its theoretical form is a very interesting one. The diffraction through a theoretically perfect objective was worked out many years ago by Sir George Airy who calculated the exact distribution of the light in the central disc and the surrounding rings. This is shown from the centre outwards in Fig. 183, in which the ordinates of the curve represent relative intensities while the abscissæ represent to an arbitrary scale the distances from the axis. It will be at once noticed that the star image, brilliant at its centre, sinks, first rapidly and then more slowly, to a minimum and then very gradually rises to the maximum of the first bright ring, then as slowly sinks again to increase for the second ring and so on. [Illustration: FIG. 184.—Diffraction Solid for a Star.] For unity brightness in the centre of the star disc the maximum brightness of the first ring is 0.017, of the second 0.004 and the third 0.0016. The rings are equidistant and the star disc has a radius substantially equal to the distance between rings. One’s vision does not follow down to zero the intensities of the rings or of the margin of the disc, so that the latter has an apparent diameter materially less than the diameter to the first diffraction minimum, and the rings themselves look sharper and thinner than the figure would show, even were the horizontal scale much diminished. The eye does not descend in the presence of bright areas to its final threshold of perception. One gains a somewhat vivid idea of the situation by passing to three dimensions as in Fig. 184, the “diffraction solid” for a star, a conception due to M. André (Mem. de l’Acad. de Lyon =30=, 49). Here the solid represents in volume the whole light received and the height taken at any point, the intensity at that point.