62 Generating Economic Cycles 



from 1884 to 1914. The continuity of the 

 cycles is shown in Figure 16. 



(3) The cycles in the yield per acre of the crops 

 from 1760 to 1913 generated derived cycles in 

 the prices of organic raw materials of produc- 

 tion which, in consequence of the law of com- 

 petitive price, must have tended to induce 

 eight-year cycles in the general prices of com- 

 modities ; 



(4) The analysis of the Sauerbeck index numbers 

 shows that, as a matter of fact, during the 

 century for which the Sauerbeck numbers are 

 given, 1818-1913, general prices did pass through 

 cycles of approximately eight years. 



In Figure 16 an eight-year cycle is fitted to the resid- 

 uals of the Sauerbeck index numbers. We found in 

 our analysis of the Sauerbeck residuals that the equa- 

 tion to the indicated cycle of 8.73 years was 



y = 3.8sinf— i+9°Y 

 ^ \8.73 /' 



and that the equation to the indicated cycle of 7.38 



— — t + 92° J. The eight-year 



cycle which is representative of the Sauerbeck residuals 

 in Figure 16 was constructed from these two equations 

 in the following way : Its period of eight years is the mean 



of the periods of these two cycles — '■ — = 8.05; 



the ampHtude of the eight-year cycle is the mean of 



Q Q I Q 1 



the amplitudes of these two cycles, — ^ = 3.45; 



