Periods in the strict sense of the term have not been discovered either in solar or meteorological data. However, the variation in spottedness of the sun over an irregular period of roughly 11 years represents a type of period which may vary in length systematically, and such periods are found in both classes of data.
The periodogram analysis has given very uncertain indications of the existence of periods of constant length, and it is pointed out that the results of such methods of analysis are entirely consistent with the hypothesis of variability in periods and can be properly interpreted only by the aid of other methods of analysis.
By means of statistical methods results are obtained which, interpreted by certain criteria, indicate the existence and probable length of a more or less regular recurrence. The period is isolated either by employing suitable smoothing formulae or by a free-hand smoothing of graphs or a combination of both methods. Epochs of maxima and minima are then selected from the graphs and their reality determined by non-mathematical criteria which are peculiar to the methods employed.
A summary is given of the various kinds of solar data made use of, and it is pointed out that since only one-half of the solar surface is visible at any time there must necessarily result more or less irregularity in the variations of periods, especially the shorter ones.
The mean heliographic latitude of the entire spotted area has a well-marked 11-year variation in which there is a maximum excess of spots in the northern hemisphere three to four years before the epoch of sunspot maximum and a maximum excess in the southern hemisphere about a year before the sunspot minimum. When the average latitude of spots is high, there is an excess of spots in the northern hemisphere; when low, there is an excess of spots in the southern hemisphere.
When the 11-year variation is eliminated from the latitude data in half-yearly means, there are disclosed short period variations of irregular length, the mode or most frequent length being about 2.4 years. If these variations were of a purely accidental nature, the most frequent length would average about 1.6 years. Self-correlation of the data likewise indicates a well-marked recurrent feature of about 2¼ years in length. These two results should be regarded, in view of the strictly impersonal character of the results and the wide divergence from random data, as adequate evidence for the existence of a periodicity in the latitude data. Definitive epochs of maxima and minima from 1855 to 1925 are given and the average length of the period is found to be 2.55 years with the most frequent interval 2.50 years.
After the 11-year variation is eliminated, this short period appears in the relative numbers as well as in their scatter, as measured by the interdiurnal variability. It is less regularly shown, however, than in the latitude data.
The epochs of maxima and minima derived from the relative numbers indicate that the length of the period is around two years at sunspot maxima and three years at sunspot minima. This result is consistent with the fact that a relatively short interval occurs between a minimum and a maximum phase when the latter is exceptionally intense.
There are given new determinations of the epochs of maxima and minima of the elemental 11-year variation in the relative numbers.
New determinations of the 11-year epochs of maximum and minimum magnetic declination range are given and there are derived epochs of the 28-month variation in the range. These epochs average about .07 year later than the corresponding epochs for the relative numbers.
An 11-year variation occurs in the length of the 28-month period in terrestrial temperatures with long and short intervals about four years after the Wolfer epochs of minima and maxima respectively.
The short period variations in temperature have a closer causal relation to the solar latitude than to the relative number variations. It is found from data extending over a period of 75 years that the epochs of maximum and minimum temperature occur about one year later than the epochs of maximum southern and northern heliographic latitude respectively, and about four months before the epochs of minimum and maximum spottedness.
A discussion of the significance and evidential value of the results of the investigation follows and certain criticisms are answered.