But the photographic summation may be done at any slant instead of only in the vertical, and therefore the sensitive plate may be made to summate these curves through a long range of periods. In order to get a long range of periods, the diagram was mounted on an axis with clock-work and slowly rotated in front of a camera with a cylindrical lens for objective, a horizontal slit in the focal plane, and a sensitive plate passing slowly downward across the slit by clock mechanism. In this way a full range of possible periods come under the summing process, and when a real period is vertical the crests of the curves form vertical lines which come down as a series of dots or beads in the slit. When no period is in the vertical the light coming through the slit is uniform. Of course, there is a practical limit to the different angles at which the diagram may be viewed. An angle too far in one direction, making the tested period very small, would require a great number of duplications of the curve, while too great an angle the other way, making the tested period very large, catches the curve in the nonsymmetrical form and introduces errors. In the periodograms actually made of the sunspot curve the minimum period tested was 7 years and the maximum 24. One notes especially that this is a continuous process and that all periods from the minimum to the maximum are tested.
Application to length of sunspot period. — The interest in the sunspot period makes a special consideration of plate 9, c, worth while. This figure is a photograph of plate 9, b, taken out of focus for the purpose of calling attention to certain general features. In b the eye naturally turns to the sharp outlines and notes its minute details. In c the crests of b are changed into large blotches connecting somewhat with their nearest neighbors and varying in intensity. The alinement which they form in a nearly vertical direction is a graphic representation of the period. If the line were exactly vertical the period would be 10 years. The slant to the right shows more than 11. If the line were straight the period would be constant. It is evident that there are several irregularities in it. Having a number of exactly similar lines side by side, the irregularities are repeated in each and thus strike the consciousness with the effect of repeated blows. These irregularities are the discontinuities referred to by Turner in connection with his hypothesis. It is evident at a glance that the sunspot sequence divides itself into three parts, namely, a 9.3-year period, 1750-1790; then an interval of readjustment, 1800-1830, with a 13-year period; and lastly an 11.4-year period lasting to the present time (values approximate). But the latter is not perfectly constant, for after 1870 there is a change in intensity. The breaks thus shown and Turner's dates of discontinuity are compared in table 6.
- In discussing the periodicities of sunspots (19062, pp. 75-78) Schuster divided his 150 years, from 1750 to 1900, into two nearly equal parts. He found in the first part two periods of 9.25 and 13.75 years acting successively, and in the second part, a period of 11.1 years.