68 CLIMATIC CYCLES AND TREE GROWTH 



can not be assigned with exactness but they give roughly the intervals 11, 

 12, 11, 13, 11, 11, 11, and 11 years. 



In 1906 Schuster performed his celebrated analysis and found several 

 different cycles or periods as shown in his periodogram, our figure 21, page 

 42. He divided the interval from 1750 to 1906 into two parts and thus se- 

 cured an improved idea of the variations in the cycle and the localizing of 

 special cycle lengths. Turner in 1913 using similar analysis expressed the 

 "discontinuities" in the cycle, as he called them. A discontinuity is an 

 interruption or abrupt change in length, phase, or amplitude in any cycle 

 sequence. Schuster and Turner, while noticing changes in length, have 

 been strongly influenced by the changes in amplitude, and Clayton by changes 

 in phase. In a cyclogram, however, the story of change in period is laid out 

 clearly for all who can read it. The fundamental form of the cyclogram of 

 the sunspot numbers since 1750 is shown in figure 20, page 39, which gives suc- 

 cessive cycle values at about 9.5 years, 14 years, 7 years, and 11.4 years in 

 length. 1 These changes were evident in the first cyclogram photographed in 

 December 1914 (I; Plate 9), and called differential pattern in the Astro- 

 physical Journal, April 1915. We can describe the solar changes as a per- 

 sistent cycle clinging near a general average of 11.3 years, whose variations 

 between 7 and 16 years are not scattered at random but are gathered into 

 several short intervals at fairly definite periods. Out of 16 cycle lengths be- 

 tween maxima, 9 followed lengths closely similar. In the last hundred years 

 the length has been nearly constant. From these facts we have a good prob- 

 ability that the next maximum will be separated from the last one by the same 

 interval that fell between the last and the one before. This is different from 

 random picking of values between 7 and 16 years as implied in some descrip- 

 tions of the sunspot variations. Studies have long been in operation to see 

 if we can not find what the sunspot cycle was doing in the last thousand years 

 or more. 



Analysis of Annual Numbers Since 1610 — Before 1750 the telescopic ob- 

 servations of sunspots were far from systematic. After Galileo's first view 

 in 1610, many views of them were placed on record but there evidently was 

 a great dearth of spots from 1645 to 1715 (Maunder and Spoerer's results). 

 A maximum had probably occurred near 1615, very weak; one near 1626, 

 stronger, and one near 1639, very weak. The full records during the dearth 

 with comments by contemporary observers can be repeated here, after 

 Maunder : 



1648-60 often called spot-free. 

 1649 exceedingly few spots. 



1660 spots seen April and May. 



1661-70 none seen. 



1671 spots seen August and September. Memorandum: "Now 



20 years since many spots." 



1 The sequence takes a form depending on the slant of the analyzing lines: the 

 pattern is inverted but otherwise identical, when the slant is changed from right to left 

 or vice versa. Note form also in Plate 15B. 



