44 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 94 



3. Each of the subfigures is the result obtained from 23 years of 

 observation, including four repetitions of the periodicity. Although 

 not a century, 23 years is, after all, a long time. 



4. The ranges of the smoothed 68-month curves are substantial. 

 For curves I, II, III, IV, and V, the ranges are o.°4, i.°i, i.°i, o.°5, 

 and i.°o Centigrade, respectively. The extreme range of the original 

 data before any periodicities at all were removed, but smoothed by 

 5-month traveling means, seldom exceeds 5.°o Centigrade. This in- 

 cludes, as we have seen, several short interval periodicities of a range 

 of o.°5 Centigrade or more, which when combined in common phase 

 may produce a range of at least 2.°o Centigrade. Hence much of the 

 original range disappears with their removal. This makes it apparent 

 that the 68-month curves contain a very considerable part of the 

 residual range remaining available to disclose long periods. 



5. Each 68-month curve is the mean of four mutually supporting 

 constituents. As an example, comparing the constituents of curves 

 II and III, each of the four individual constituents in group II shows 

 positive departures at the two ends and negative departures at the 

 middle. Each of the four individual constituents in group III, on the 

 contrary, shows negative departures at the two ends and positive de- 

 partures in the middle. This behavior of reversal in phase, exactly 

 at 46 years after January 181 9, is precisely similar to that which we 

 have many times refen-ed to, relating to the short periodicities, whose 

 validity seems unquestionable because of the great numbers of repeti- 

 tions on which they depend. Thus the behavior of the 68-month curves 

 is exactly in line with reasonable expectation. 



6. Corroboratively, the curves I, III, and V, covering (with two 

 intermissions of 23 years each) no years, are so nearly similar in 

 phase as to yield the mean form VI, figure 18. It has a range of o.°6 

 Centigrade. 



But why, the reader may ask, have so many periodicities additional 

 to those heretofore recognized in the variability of the sun been added 

 in the list of terrestrial periodicities, and why are they chosen as 

 integral submultiples of 23 years? The answer is that they are forced 

 upon our attention by the progress of the computations. One illustra- 

 tion has been given. As stated above, the periodicity of 9f months 

 was discovered because the curves for 68 months showed seven waves. 

 Similarly the periodicity of 34 months was discovered because pre- 

 liminary computations of the periodicity of 68 months (not here re- 

 produced) showed the half-period curves of 34 months too plainly to 



