46 Generating Economic Cycles 



was ground for believing that there were real periodic- 

 ities in the sunspot data, and if so, to ascertain their 

 approximate lengths. The same problem had been 

 considered by Professor Schuster wdth the aid of the 

 method of the periodogram, but, according to Professor 

 Turner, the Schuster method was needlessly complex, 

 involving an unnecessary amount of computation. 

 An adequate solution was thought to be obtained if a 

 Fourier series were computed for the whole series of 

 data, and the several terms of the series were investi- 

 gated more in detail according as the magnitudes 

 and signs of the coefficients of the several terms indi- 

 cated the possible presence of a real cycle. In order 

 to carry out this idea, Professor Turner computed 

 for the 156 years of sunspot data the harmonics for 

 the periods of the following number of years: 156, 

 156/2, 156/3 . . . 156/54. The principal advantage 

 claimed by Professor Turner for the method of Fourier 

 Sequence is this: The development of the Fourier 

 Sequence is 



(1) Necessary. — "Since each term of the Fourier 

 Sequence is independent of every other, it can- 

 not be inferred from any other. Hence we 

 must at least calculate all these terms." ^ 



(2) Sufficient. — "If we desire to know to what ex- 

 tent any periodicity intermediate between two 

 of those directly tabulated is represented in the 

 observations . . . we are able to deduce this 

 information from the sequence." - 



1 "On the Expression of Sun-spot Periodicity as a Fourier Sequence," 

 Monthly Notices of the Royal Astronomical Society, 1913, p. 715. 

 ^Ibid., p. 715. 



