Origin of Eight-Year Generating Cycle 



79 



of rings for 500 3Tars. Referring to these Flagstaff 

 pines, Professor Douglass makes these statements as to 

 the cyclical variations in their growth: ''The interval 

 from 1830 to the present time divides . . . fairly well 

 in (a period) of 7.3 years" (p. 108). As to the whole 

 record of 500 years, he says, "a 7-year period is also 

 frequently observed" (p. 101). In Table 8 (p. 108) 

 Professor Douglass indicates that this cycle of approxi- 



RESIOUALJ OF5AUER&eCK'5 INDEX NUMBERS. WOKEN UHI 



Cycles or Prices, smooth curve. 



Cycles OF Qrowth. dmhidcurvc. -... 



Figure 29. Cycles in the residuals of Sauerbeck's index numbers of general wholesale 



prices in England and in the growth of pines near Flagstaff, Arizona. 

 Equation to the cycle of prices, : j/ = 3.1 sin (|-^**3- t + 92°), origin at 1818; 



Equation to the cycle of growth, : y = .05 sin (2- ^'^ <+ 137° 57'), origin at 1818. 



raately 7.3 years has been continuous since 1817. By 

 an odd coincidence Sauerbeck's index numbers of gen- 

 eral prices in England begin just one year later, in 1818. 

 In the analysis of the Sauerbeck numbers we found 

 that the eight-year cycle was the mean of two cycles, 

 one of about 8.7 and the other of about 7.38 years. In 

 Figure 22 the smooth graph records the 7.38-year cycle 

 in Sauerbeck's index numbers, and the dashed graph,' 



^ The data to which the cycle was fitted covered the 88 years from 

 1818 to 1905 and were taken from Professor Douglass' work, p 113. 



