96 CLIMATIC CYCLES AND TREE-GROWTH. 
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 differ- 
ential 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, 8, isthe 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 varia- 
tion 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 uneven- 
ness in the track and therefore is without significance. 
Plate 11, p and 8, 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 
