108 Economic Cycles: Their Law and Cause 



the deviation of the yield per acre of the crops from its 

 general cyclical movement associated with the devia- 

 tion, in the following year, of the production of pig- 

 iron from the general cyclical movement of pig-iron? 

 The answer is found by correlating the differences, 

 always remembering that the difference for the yield 

 per acre in any given year is to be taken with the dif- 

 ference of the production of pig-iron in the following 

 year. The coefficient of correlation is r = .254. 



We come now to the association between the cyclical 

 movement of the yield per acre of the crops and the 

 cyclical movement of the production of pig-iron. Each 

 of these movements is superposed upon a rising secular 

 trend, and before we can test the degree in which the 

 cycles are related the secular trends must be eliminated. 

 If, as a first approximation, the secular trend in each 

 case is assumed to be linear, then by fitting a straight 

 line 1 to the data, it is possible to calculate the fluctua- 

 tions of the cycles of crop yield and of production of 

 pig-iron about their respective trends, and these fluctua- 

 tions may be correlated. In Table IV of the Appendix 

 to this chapter, the data for the calculation of the con- 

 nection between the cycles are given. In columns 2 

 and 5 are tabulated the general cyclical movements of 



1 The equations to the linear secular trends are, respectively, 

 y = .1844s +98.57, for the yield per acre of crops; and y = 582.71z+ 

 9525, for the production of pig-iron. The origin in the first case is 

 at 1871 and in the latter case, at 1890. The first equation was com- 

 puted from the data for the years 1871-1906, and the second equa- 

 tion, from the data for 1871 to 1910. 



