CYCLOGRAM ANALYSIS 41 



measure and check all cycles within a length range of 5 to 40 terms in a curve 

 showing 175 terms. 



The efficiency of this form of analysis has resulted largely from the 

 automatic production of the pattern called the cyclogram. The cyclogram 

 may be described as an adjustable 3-dimensional plot 1 containing — 



1. A general horizontal time scale. 



2. An enlarged vertical time scale giving residuals from some convenient 

 exact period such as 10 years. This procedure separates different periods 

 into different straight lines pointing in different directions. In the mechani- 

 cal plotting of the cyclogram this "convenient exact period" may be made to 

 take successively changing values over a long range. 



3. The original ordinates are changed into a third dimension and repre- 

 sented in half-tones by light intensities. 



DEVELOPMENT OF CYCLOGRAPH 



It was Schuster's work on the periodogram (fig. 21, page 42) that started 

 our cyclogram type of analysis. The first step was a question: How can 

 we perform quantitative integration in any desired direction other than the 

 vertical? and the answer came at once, "By light intensities." So the 

 "multiple plot" was tried in 1913 (see vol. I, Climatic Cycles and Tree Growth, 

 Carnegie Inst. Wash. Pub. No. 289, 1919, Plate 9b) and its integration at 

 continuously changing angle (in A of the same plate) by a cylindrical lens 

 and a photographic plate moving across a slit. 



The multiple plot was simply a pictorial reproduction of the integration 

 table given a few pages back. The series of data was plotted many times in 

 solid white on a black background. These plots were mounted one below 

 the other at equal vertical intervals and between each repetition there was 

 a constant horizontal off-set amounting to a convenient average cycle length, 

 just as in the table. An integration of the light values in the vertical by a 

 positive cylindrical lens with vertical axis summated any cycle that existed 

 in vertical direction across the multiple plot. The integration was recorded 

 on a photographic plate and measured for quantity of light. The whole 

 multiple plot was rotated into a different angle and a new integration made 

 in the vertical and another period tested. The movements of plot and plate 

 were made continuous by clockwork. 



A periodogram was thus produced (see Plate 12A), which indicates the 

 presence of a period by breaking up into corrugations, since it is merely the 

 merging of periodic maxima in the multiple plot. Volume I, referred to 

 above, gives several periodograms in Plate 11. They are very crude but are 

 part of the history. Except for these photographs and some tests on vari- 

 able stars (in 1918; see appendix) the use of the periodogram was dropped 

 after about 1916. 



1 It may also be described as an optical, photometric mechanical plot produced 

 automatically in a complete form from a prepared curve of data; in it the time displace- 

 ment of any maximum from its periodic position is plotted at its observed time. 



