Page:Climatic Cycles and Tree-Growth - 1919.djvu/123

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METHODS OF PERIODIC ANALYSIS.

of the period is the accuracy with which the direction of this line can be ascertained. This depends on the length of the row of crests, on the shortness of each crest, and on their individual regularity or alinement. These characteristics may be noted in the plates and especially in plate 12, q. Expressed in other terms, these resolving features are respectively as follows: (1) Number of cycles covered by the given curve. (2) Shortness of maxima in relation to length of cycle; if the maximum is sudden and sharp, as in rainfall, the accuracy may be very great; if the maximum is long, as in a sine curve, the accuracy is less. (3) Regularity in the maxima and freedom from interference. These features all appear in the differential pattern and hence the accuracy of any period is its most evident feature and all observers can judge it equally well. It is exactly analogous to the accuracy of a straight line passed through a series of plotted points which theoretically ought to form a straight line but which do not do so exactly.

The most important part of the constructed instrument which may alter the accuracy of analysis is the analyzing plate. The accurate spacing and parallelism of the lines is a mechanical feature and can be produced with care and attention to details, but the relation of width of transparent line to center-to-center spacing of the lines is a matter of judgment and the necessities of photography. As this relative width increases, the length of each crest in the pattern becomes longer and the row of crests becomes wider and less definite in direction. If the maxima in the curve under test are of the sine-curve type this relation is less important, for the light crests in the pattern will be long in any case, but for sharp, isolated maxima resolution is lost if the width of the transparent line is too great. In the instrument now constructed the ratio of transparent line to center-to-center spacing is 3:10, but a smaller ratio such as 1:10 could advantageously be used in certain cases if there is sufficient light to make photography easy.

The accuracy in reading a periodogram is at once apparent on its face. When the number of cycles is great as in plate 11, a, the rhythmic or beaded effect is short and very limited in extent, as in the 5-year period there indicated, and the period is accurately told. But if the number of cycles is reduced (as in plate 11, b or c) the periodic effect in the photograph extends over a greater range and its center can not be told with the same precision. The accuracy of estimation in the periodogram is therefore the actual accuracy of the result.