50 Generating Economic Cycles 



the second, one-half of the range, one would certainly 

 not be justified in holding that they represent real 

 recurrent cycles. Figures 11 and 12 depict these two 

 Fourier constituents of the price curve. Figure 11 

 also shows the curve that is obtained by combining 

 the mean of the Sauerbeck index numbers with the 

 96-year Fourier constituent. Likewise Figure 12 gives 

 the compound curve made up of the mean of the Sauer- 

 beck index numbers and the 96-year and 48-year 

 Fourier constituents. 



With two of the four important values of J. ^ in 

 Table II accounted for, the possibility of real cycles in 

 the 96-years record is limited to the remaining two 

 epochs between 24 and 16 years and between 8.7 and 

 7.4 years. The mean of the limiting values of the latter 



8 7+74 

 period is — =8.0 years, and the limits of the 



other period are respectively twice and three times this 

 mean value. The value of ^ ^ in Table II corresponding 

 to a period of exactly 8 years is small, but if the com- 

 putation had been confined to the interval 1857-1913 its 

 value would have been 7.95. 



Thus far the argument as to the existence of real 

 periods has been based upon the size of A - which is the 

 criterion used by Professor Schuster. An additional 

 criterion has been offered by Professor Turner. In his 

 fundamental memoir ^ he has pointed out that when a 

 striking periodicity is present, there is a tendency for 

 the signs of a and h to change between consecutive 



1 H. H. Turner, "On the Expression of Sun-spot Periodicity as a 

 Fourier Sequence," Monthly Notices of the Royal Astronomical Society, 

 1913, p. 716. Cf. also, pp. 722, 723. 



