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, 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 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, 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 



