8 Economic Cycles: Their Law and Cause 



harmonic analysis. The perfection of the method 

 whereby the findings may be subjected to the test of 

 probability is the work of Professor Arthur Schuster 1 

 of Manchester. 



We may begin the presentation of the method with a 

 definition of a series of terms that constantly recur in 

 the treatment of periodic phe- 

 nomena. Figure 1 will facili- 

 tate the exposition by affording 

 a graphic description of the 

 terms dealt with. 



Suppose that the point Q 

 moves uniformly in the circle 

 of Figure 1, that is to say, sup- 

 pose that the point Q describes 



equal arcs in equal times and, therefore, proportional 

 arcs in different times. Then, if the measurements of 

 the arcs of the circle are made from the point A and 

 the reckoning of time is begun when Q is at E, the 

 angle A E is called the angle at epoch, or simply 



Fourier's own work: Theorie analytique de la chcdeur. In Freeman's 

 English translation the treatment is found on pp. 137-212. 



1 The fundamental memoirs of Professor Schuster are 



"On the Investigation of Hidden Periodicities with Application 

 to a Supposed 26 Day Period of Meteorological Phenomena." 

 Terrestrial Magnetism for March, 1898. 



"The Periodogram of Magnetic Declination as obtained from the 

 records of the Greenwich Observatory during the years 1871-1895." 

 Cambridge Philosophical Society Transactions, Vol. 18, 1899. 



"On the Periodicity of Sunspots." Philosophical Transactions of 

 the Royal Society of London, A, Vol. 206, 1906. 



"The Periodogram and its Optical Analogy." Proceedings of 

 the Royal Society of London, A, Vol. 77, 1906. 



