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, asin 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 rhythnfiec 
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. 
