494 



SCIENCE. 



[N.S. Vol. XVIII. No. 459. 



rely upon it for telling us what the nature 

 of the general circulation of the atmos- 

 phere really is, it would be desirable to 

 find out by observation or experiment what 

 dynamical and elastic properties must be 

 attributed to an extremely thin sheet of 

 compi-fissible fluid rotating about an axis 

 with a velocity reaching 1,000 miles an 

 hour, and subject to periodic heating and 

 cooling of a very complicated character. 

 It would be more in consonance with the 

 practice of other sciences to find out by 

 observation what the general circulation is 

 before using mathematics to explain it. 

 What strikes one most about the mathe- 

 matical treatises on the general circulation 

 of the atmosphere is that what is true about 

 the conclusions is what was previously 

 known from observation. It is, I think, 

 clear that that method has not given us 

 the working ideal upon which to base our 

 theory. 



Consider next the attempts to regard at- 

 mospheric phenomena as periodic. Let me 

 include with this the correlation of groups? 

 of atmospheric phenomena with each other 

 or with those of the sun, when the peri- 

 odicity is not necessarily regular, and the 

 scientific process consists in identifying 

 corresponding changes. This method has 

 given some remarkable results by the com- 

 parison of the sequence of changes in the 

 meteorological elements in the hands of 

 Pettersen and Meinardus, and by the com- 

 parison of the variation of pressure in dif- 

 ferent parts of the globe by Sir Norman 

 Lockyer and Dr. W. J. S. Lockyer; as 

 regards the earth and the sun the subject 

 has reached the stage of productive discus- 

 sion. As a matter of fact, by continuing 

 this address I am preventing Sir Norman 

 Lockyer from telling you all about it. 



For the purpose of dealing with perio- 

 dicity in any form we substitute for nature 

 an ideal system obtained by using mean 



values instead of individual values, and 

 leaving out what, from this point of view, 

 are called accidental elements. The sim- 

 plification is perfectly legitimate. Passing 

 on to the consideration of periodicity in the 

 stricter sense, the process which has been 

 so effective in dealing with tides, the mo- 

 tions of the liquid layer, is very attractive 

 as a means of attacking the problems of 

 the atmosphere, becatlse, in accordance with 

 a principle in dynamics, to every periodic 

 cause there must correspond an eiiect of 

 the same period, although the relation of 

 the magnitude of the effect to the cause is 

 governed by the approximation of the 

 natural period of the body to that of the 

 cause. 



There are two forms of the strict peri- 

 odic method. One is to examine the general- 

 ized observations for periodicities of known 

 length, whether it be that of the lunar 

 rotations or that of simspot frequency, or 

 of some longer or shoi'ter period. In this 

 connection let me acknowledge a further 

 obligation to Professor Schuster for tack- 

 ing on to his address of last year a devel- 

 opment of his work on the detection of 

 hidden periodicities, by giving us a means 

 of estimating numerically what I may call 

 the reality of the periodicity. The other 

 method is by harmonic analysis of a series 

 of observations, with the view of finding 

 causes for the several harmonic com- 

 ponents. I may say that the Meteorological 

 Office, supported by the strong opinion of 

 Lord Kelvin, has favored that plan, and on 

 that account has for many years issued the 

 hourly results for its observatories in the 

 form of five-day means as representing the 

 smallest interval for which the harmonic 

 analysis could be satisfactorily employed. 

 Sir Richard Strachey has given some ex- 

 amples of its application, and the capabili- 

 ties of the method are by no means ex- 

 haiisted, but as regards the general problem 



