282 F. H. Bigelow — Studies on the General Circulation 



success in the present state of the development of this branch 

 of science. We mean to include under the former method of 

 rigid analysis, (1) the usual application of the theory of least 

 squares for the detection of an unknown period, by the 

 criterion of the sum of the squares of the departures being a 

 minimum ; (2) Professor Schuster's Harmonic Analysis and 

 Periodogram for the detection of hidden periodicities, Terr. 

 Mag. 1898 ; (3) the Fourier series in various forms of the 

 harmonic analysis ; (4) Professor JNTewcomb's criterion for 

 fluctuations without any discernible period, Am. Phil. Soc, 

 vol. xxi, part v, 1908. 



Periodic and aperiodic synchronism. 



There is one general principle underlying each of these 

 methods of analysis, namely, that they seek a definite period, 

 and assume as the premise of argument that synchronism 

 between solar and terrestrial variations depends upon the 

 existence and proof of such a period. It has, how T ever, not 

 been established that the cycle of the solar thermodynamic 

 processes is periodic, in anything like the same sense that the 

 annual orbital motion of the earth about the sun produces one 

 true period in the processes within the earth's atmosphere, 

 while the rotation of the earth on its axis produces another 

 true periodic cycle of variations. On the contrary, the 

 observed solar processes are so irregular as to be distinctly 

 aperiodic. The so-called 11-year period varies between 8 years 

 and 14 years in length in an irregular succession ; the synodic 

 rotation of the sun on its axis varies in latitude and altitude 

 above the photosphere, from 26' 7 days at the equator to 31*0 

 days near the poles for the level of the photosphere, but from 

 26*0 days at the equator to something like 29 days for the 

 upper levels of the chromosphere. There are numerous 

 irregularities noted in the irruption of the prominences in dif- 

 ferent longitudes so that they appear earlier in the middle 

 latitudes of the sun than in the equatorial and the polar zones. 

 Furthermore, it is found that in the analysis of the sun spot 

 numbers, the prominence frequencies, and the magnetic field 

 intensities, there is usually superposed upon the long period, 

 ranging from 8 to 14 years, four minor crests, though only 

 three of them are fully developed in some periods. If, for 

 example, we assume a long period of variable length, hav- 

 ing three or four minor variations within each of them, and 

 attempt to sum them together on any assumed definite period, 

 the result will be similar to that displayed in fig. 3. If the 

 11-year period with four crests be summed with an 8-year 



