METHODS OF PERIODIC ANALYSIS. 97 



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. 



