30 Generating Economic Cycles 



the one employed in the treatment of the yield and 

 prices of farm products. In the latter case a parabola 

 of the type 



y = a -{■ bx -{- cx^ -\- dx^ 



was found to give a satisfactory fit. But in the descrip- 

 tion of the secular trends in the production of coal and 

 iron an additional term was added to the above equa- 

 tion, and a parabola of the fourth order 



y = a+hx-\- ex- + dx^ + ex^ 



was fitted to the data. The graphs in Figure 9 show the 

 secular trend of both coal and iron, and the correspond- 

 ing equations are given in the legend descriptive of 

 Figure 9. 



After the secular trend of coal and the secular trend of 

 iron were ascertained, the percentage deviations of the 

 production of each commodity in the years from 1882- 

 1913 were computed. These percentage deviations 

 were then combined into an index number of the devia- 

 tions in the production of coal and iron by summing 

 the percentage deviations for each year. The data 

 are given in Table V of the Appendix. Because of the 

 abnormal demand for coal and iron during the war the 

 figures were not extended beyond 1913. 



If now the index numbers of the deviations in the 

 production of coal and iron from 1882 to 1913 are 

 scrutinized with a view to discovering periodicities, 

 we find that the periodogram takes the shape that is 

 pictured in the second curve in Figure 7. The data are 

 given in Table III of the Appendix. 



It is obvious from the periodogram that if there are 

 real cycles in the production of coal and iron, the most 



