42 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 94 



also the Qf-month mean curves for Berlin and Copenhagen as com- 

 puted from the original data and again from the residuals after re- 

 moval of many other periodicities. I hope that this may be a step 

 toward promoting greater confidence in the procedure. But the curves 

 about to be referred to, representing other periodicities, will furnish 

 other grounds for confidence in these methods. 



It has already been pointed out in the analysis of the original data 

 that the expiration of an integral multiple of 23 years from January 

 1819 is often the signal which warns us of a reversal of phase im- 

 pending in the temperature periodicities. As this also occurs fre- 

 quently in periodicities which are computed from the residuals which 

 remain after removal of many determined periodicities by ii|-year 

 and 23-year steps, it would seem to indicate that the data were not 

 harmed by such removal. For it is to be recalled that the eflfect of such 

 removal, applying as it does the actual mean values over each ii|- 

 or 23-year period to correct all monthly values within that very period, 

 must tend in the strongest zvay to smooth the residual curve which 

 remains after such removal. If then such a smoothed residual curve 

 shows plainly the newly sought periodicity, and not only shows it in 

 approximately the same phase at many intervals during a century, 

 but also shows the reversal of its phase at the critical dates, after the 

 manner often noted in earlier analyses — the combination of these 

 regularities of behavior seems to strongly support the hypothesis that 

 the computed periods are veridical, and cumulatively defends the 

 method used in their removal. 



But still another type of confirmation of veridity is available. It 

 will be noted that in the list of 10 periodicities which were said to 

 have been removed before seeking the 12-month periodicity, one of 

 9f months was mentioned last. This periodicity was not noticed in 

 the original data, nor was it suspected until after the 68-month curve 

 was determined. Then seven waves appeared so definitely in the mean 

 curves for 68 months, as shown in figure 18, that no question of the 

 reality of the 9|-month periodicity could be entertained. Yet the 68- 

 month curves themselves were not computed until after the entire 

 previous list of eight periodicities had been removed in ii|- or 23- 

 year parcels. That the 9|-month curve should have survived so much 

 modification of the data seems to indicate that real and not spurious 

 periodicities had been found and removed. In order further to demon- 

 strate this argument more conclusively, I show in figure 15 the 95- 

 month curves for Berlin and Copenhagen, both as computed from the 

 original data and as computed after nine periodicities had been re- 

 moved therefrom. 



