38 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 94 



The little double table (table 8) extracted from table 7 emphasizes 

 this behavior. The 11 -month periodicity as computed from January 

 1819 to December 1829, and from January 1830 to November 1841, 

 shows high maxima at the fifth month. From December 1841 to 

 November 1852 and from December 1852 to October 1864, on the 

 contrary, deep minima are found at the sixth month. The transition 

 from the first of these types to the second is abrupt. To show its 

 abruptness the last 22 months ending with November 1841 may be 

 contrasted with the first 22 months beginning with December 1841. 



Table 8. — Abrupt Phase-change. Berlin 11 -month Temperature Periodicity 



— 2 — 2 — 2 — 2 o — 4 — s — 10 — 9 — 19 

 — 13 — 16 o — I 6 2 I — I 4 13 9: Nov. 1841 



Mean —7-5 —8.0 — i.o —1.5 3.0 — i.o —2.0 —0.5 —3.0 2.0 —5.0 



Dec. 1841 : 870 — 4 o — 3 — 4 ^i — 5 — 11 — 4 



— I —5 —4 3 —7 —14 —10 —6 —10 —5 2 



Mean 3.5 1.0 —2.0 —0.5 —3.5 —8.5 —7.0 —3.5 —2.5 —8.0 —1.0 



Obscured as they are by the influences of other periodicities and 

 accidental effects, yet in the mean of the first two lines of table 8 

 the maximum occurs on the fifth month, and in the mean of the last 

 two lines the minimum occurs on the sixth month, just as happens with 

 the general means found in table 7. Even in details the two mean 

 curves representing 22 months each are opposite, as shown by figure 17. 



B. The 21-month Periodicity 



Take as an example of another type the 21 -month periodicity shown 

 in figure 16. In this instance the transition from left to right in type 

 usually occurs at each ii| years, though not invariably. One type 

 holds for instance through the two periods of ii| years each from 

 October 1841 to June 1864. But then, note the abrupt transition 

 between the 42 months preceding and the 42 months following July 

 1864. The mean of the first pair of lines is almost precisely opposite 

 to the mean of the last pair, as is shown in figure 17 and table 9. 



Of the 10 curves illustrating the 21 -month periodicity, numbers i, 

 3, 4, 6, 8, and 9, beginning 1819, 1841, 1852, 1875, 1897, and 1910, 

 respectively, are generally similar in phase, and not greatly different 

 in amplitude. Opposed in phase are curves 2, 5, 7, and 10, but they are 

 not quite so similar each to each. From this we see that during about 

 70 years out of no, the 21-month periodicity, whether we regard it 

 as true or spurious, would have produced nearly identical effects upon 

 the temperature of Berlin. The general mean effect over 70 years, as 



