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 l 

 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 O E is called the angle at epoch, or simply 



Fourier's own work: Theorie analytique de la chaleur. 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 Analog}'." Proceedings of 

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



