Generating Cycles in a Century of Prices 43 



is a summary description of economic history during a 

 century of unparalleled development between two 

 world-wide catastrophes, supplies unique material for 

 an inductive quest of economic regularities. 



The method used in the inquiry is Fourier's Theorem 

 as it has been developed for statistical purposes by 

 Professor Schuster and Professor Turner. 



The Savilian Professor of Astronomy at Oxford, 

 Professor Turner, has said that "apart from the plane- 

 tary motions periodicities in nature are seldom clear- 

 cut." ^ As we shall attempt to estabhsh certain 

 economic cycles and to trace their cause to periodicities 

 in nature, the part of wisdom would seem to be to 

 profit by the experience of natural scientists who have 

 dealt with the problem of isolating natural periodicities. 



It is well known that Fourier's celebrated theorem 



y = Ao-{- aiCOfikt-\- a2Cos2kt-\- . . . 

 + bi sin kt + 62 sin 2kt + . . . 



if carried out to a sufficient number of terms will repro- 

 duce almost any type of graph. Tliis equation may be 

 expressed also in the form 



y = Ao + Ai sin {kt -f eO + A2 sin i2kt + 62) + . . . 



When the parameters of this equation are determined 

 from statistical data the question arises as to the signifi- 

 cance of the several terms in the Fourier series. Do 

 the successive terms in the sine series correspond to 

 real periodicities in nature, or are they merely formal 

 terms the summation of which will give the observed 



1 H. H. Turner, Tables for Facilitating the Use of Harmonic Analysis, 

 p. 44. 



