24 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 94 



In this sample the table contains five lines. Of 11 such tables il- 

 lustrated in figure 11 by plots depicting the ii -month periodicity from 

 low sun-spot temperature departures, there are four tables of four 

 lines, four tables of five lines, one of six lines, and two of seven lines. 

 It is clear enough that the mean values from columns as short as 

 these are subject to a large fractional error. As remarked above, 

 the presence in the data of other periodicities than that sought, and 

 of accidental departures, cannot but distort mean curves depending on 

 so few values per point. 



If, now, the general mean value is taken at all times of low sun- 

 spot numbers through more than a century, it results as follows. The 

 unit is still the tenth of i degree Centigrade. An arbitrary zero is 

 chosen to give positive and negative values about equally. 



0.4 1.2 0.8 I.I 1.3 — 0.4 — 0.6 — 0.5 — 0.3 — 0.4 0.7 



But if it is assumed that the true period is 11 months minus 3 days, 

 then the corresponding general mean is as follows : 



—1.5 —0.5 —0.1 0.7 1.7 2.0 0.9 —0.3 0.0 —0.6 —0.3 

 The latter periodicity has an amplitude of o.°35 C, about twice the 

 amplitude of the former. It results from 56 lines of smoothed values 

 of temperature departures covering all periods of low sun-spot num- 

 bers from 181 1 to 1925. The method of allowing for the 3-day de- 

 crease of period is partially indicated by the broken inclined line of 

 figure II. In detail the method is as follows: In the computation of 

 the general mean, the 1 1 means which represent individual periods of 

 few sun-spots were arranged in a table in such a manner that the 

 values connected by the broken inclined line in figure 11 composed 

 together one vertical column. The mean form, with phase chosen 

 to agree with that expected of the top curve, ai of the figure, is 

 given in curve li at the bottom of figure ii."*" It is obvious that 

 curve ai, just singled out for numerical illustration is not in the 

 expected phase, but is 3 months out of phase with the best periodicity. 

 This selection for illustration was, indeed, made to draw attention 

 to occasional irregularities of phase, to which we shall recur. Had 

 I permitted myself to alter arbitrarily the phases of two or three of 

 the mean curves by 2 months each, on the plea of accidental displace- 

 ment by terrestrial influences, then the general mean would have had 

 an amplitude of a full half degree Centigrade. 



It seems difficult to avoid the conclusion that a periodicity lacking 

 3 days of II months in length, and with an average amplitude of 

 o.°35 C, persists in the temperature of Berlin during times of low 

 sun-spot activity for the interval of 1 14 years covered. 





The mean for 1 1 m. d. is given by curve li . 



