Periodograms. — Plate 11, which has been arranged to illustrate the work of the periodograph, shows several of the early periodograms which are comparatively free from obvious instrumental defects. In each the range of periods is marked on the left margin. Periods are indicated by the vertical band or ribbon breaking up into a series of horizontal dots or beads. For example, plate 11, a, is a periodogram of the 5-year standard period made for the purpose of calibrating the work of the periodograph. The 5-year period is very prominent near the top of the diagram in the plate. At 10 years its first harmonic appears with double crest, showing still that it is a 5-year period. At 15 years the second harmonic shows with a triple crest, and at 7.5 years the 3/2 overtone is evident with 3/2 crests. These overtones are always readily distinguished from the fundamental on the differential pattern. The differential pattern of this 5-year standard is shown in plate 12, q. The instrument is set for analysis at 5.0 years. In this position the integrating lens sums up the rows of light crests as a series of dots on the periodogram.
Plate 11, b, is the analysis of a mixed standard used for calibrating the instrument. The curve contains sharp triangular crests at intervals representing periods of 7, 9, 11, 13, and 17 years, all mixed together and no two starting intentionally from the same point. These are all separated in the periodogram and the overtones of some may be seen. Such overtones can be distinguished from the fundamental on the differential pattern.
Plate 11, c, gives a periodogram of the sunspot numbers from 1610 to 1910, using before 1750 the probable times of maxima suggested by Wolfer. The best period is at 11.1 as usually quoted. If the variation from 1750 only is taken, the best period comes at 11.4. This periodogram shows a period at about 8.6. The degree of accuracy with which one can pick out the periodic point is a real criterion of the accuracy of the result selected. The differential pattern of this same series of sunspot numbers will be found in plate 12, a, in which the vertical rows of crests are readily distinguished. The sudden change in direction of the lines a little below the center of this and the two following periodograms is an instrumental defect due to slight unevenness in the track and therefore is without significance.
Plate 11, d and e, give an analysis of the Arizona 500-year record. The chief points of interest are the well-defined double-crested 11.6-year period and the 19-year and 22-year periods. Other weaker periods may be seen from place to place.
Resolving power of the periodograph. — The accuracy with which a period can be determined by the periodograph may be readily observed in the differential pattern and the periodogram. The pattern indicates a period by showing a row of light spots or crests in line. The accuracy