98 ANNUAL REPORT SMITHSONIAN INSTITUTION, 193 5 



The analysis of these records was very laborious, involving thou- 

 sands of pages of tabular matter. As a result, however, every 

 periodicity found in the solar variation, except one of 39^2 months, 

 was also found in the departures from normal temperature and pre- 

 cipitation at all these stations. In addition, periodicities of 12, 13.6, 

 55, and 138 months were discovered. These, like the solar periodici- 

 ties, are also approximately aliquot parts of 23 years, being closely 

 represented, respectively, by 23 years divided by 23, 20, 5, and 2. 

 These relationships hold within the limits of accuracy to which the 

 periods are determinable. 



The magnitudes of the periodicities in temperature ranged from 

 0°.2 to 1°.5 C. (0°.4 to 2°.7 F.), and in precipitation from 20 to 

 300 percent of normal. But though so large as to be obvious, the 

 periodicities in weather in no case continued in the same phase 

 throughout the entire intervals of from 60 to 110 years over which 

 the several investigations extended. On the contrary they often 

 abruptly reversed in phase, so that the part of a period which had 

 consistently been a maximum for many years suddenly changed into 

 a minimum and so continued for many years to follow. 



By a very lucky observation it was discovered that there is a 

 saving regularity about these abrupt changes of phase. For if we 

 take January 1819 as a time of departure, we find that the changes 

 of phase tend to occur at integral multiples of lli/^ years measured 

 from that date. This is the case at all stations employed, and both 

 for temperature and precipitation. 



Figure 4 gives for Berlin the 11-month and the 21-month periodic- 

 ities in temperature departures. For each of these two periodic- 

 ities there are shown curves which express the results arising from 

 successive intervals of about lli^ years from 1819 to 1930. In the 

 case of the 11-month periodicity the forms of the curves evidently 

 occur in pairs, so that for each 23 years at a time the temperature 

 follows a single law in its 11-month periodicity. However, in the 

 case of the 21-month curves, changes of form generally occur each 

 liy2 years, though with some exceptions, as from 1841 to 1864, when 

 for 23 years there is no marked change. 



Figure 5 shows how very abrupt is the change from one form to 

 its inverse. In the upper part of the figure are given two curves 

 relating to the 11-month period at Berlin, representing respectively 

 the last 22 months prior to December 1841 and the first 22 months 

 following that date. Even in details the two curves are opposite. 

 The first gives its maximum at the fifth month, just like the first 

 two curves in figure 4, while the second curve of figure 5 gives its 

 minimum at the sixth month, just like the second pair of curves in 



