INSTRUMENTS AND TECHNIQUE 45 



THE CYCLOGRAPH (PERIODOGRAPH) 

 COMPARISON OF ANALYZING METHODS 



This study of tree-rings has become a study of the history of 

 climatic cycles. The technique so far described covers the production 

 of tree-record curves ready for analysis by a special instrument 

 designed for the purpose and called a cyclograph. The number of 

 curves to be analyzed is so great and the data sought so complex that 

 this work would hardly have been done by a mathematical process. 

 Harmonic analysis in its mathematical form has been so successful in 

 numberless studies that many investigators have come to regard it as 

 essential. A very clever illustration of its power is Miller's reduction 

 of a facial contour to a mathematical formula which when plotted 

 reproduces the contour. Of course, this was done by combining a 

 long descending scale of period lengths with the distribution of empha- 

 sis (amplitudes) on just the right ones. But after this beautiful illus- 

 tration we must not forget that this form of contour analysis has 

 nothing to do with the physical causes of the contour, nor does it help 

 us in predicting other contours. It is like a photographic plate: it 

 merely places that one on record. 



So in the case of the sunspot cycle, we can reproduce the known 

 historic sunspot curve by 20 harmonics with different amplitudes, but 

 when done we can not insist that the sunspot variation is really built 

 of those harmonics. So also with climatic cycles, we do not know yet 

 how far their physical causes are harmonic, and therefore the expression 

 of climatic variations in a Fourier series begs the question. Evidence 

 in a later chapter suggests distinctly that climatic cycles are simple 

 fractions rather than harmonics of a fundamental. So the photo- 

 metric process described below is permissible. Add to this its rapidity,, 

 which is of the order of 50 times as great as the mathematical process, 

 while its flexibility belongs to a different class altogether. The mathe- 

 matical process is not flexible at all in the sense this is. The process 

 here used bears somewhat the relation to the mathematical process 

 that calculus does to algebra; it is differential. In applying a cycle 

 to a long sequence of values, one sees at once at every point how far 

 the values depart from the cycle. A varying cycle enters simply as a 

 curved line, while a fixed period appears as a straight one. Two 

 interfering cycles, forming a false third, enter as two straight lines or 

 bands intersecting and their intersections form the third. In this 

 process the operator not merely gets an analysis of the whole sequence 

 of values, but of every possible fraction of them, an accomplishment of 

 the highest difficulty in any mathematical solution. For example, 

 Schuster analyzed the sunspot variations since 1750, dividing the 

 whole series into two parts, and missed the points of discontinuity 

 near 1788, 1830, and so forth. These discontinuous points are the 

 most conspicuous features of the cyclograph analysis here used. 



