September 17, 1903] 



NATURE 



471 



Kepler. Let me make this clear. Kepler's contribution to 

 physical astronomy was to formulate laws which no 

 heavenly body actually obeys, but which enabled Newton 

 to deduce the law of gravitation. The first great step in 

 the development of any physical science is to substitute for 

 the indescribably complex reality of nature an ideal system 

 that is an effective equivalent for the purposes of theoretical 

 computation. I cannot refrain from quoting again from 

 Plato's " Republic " a passage which I have quoted else- 

 where before. It expresses paradoxically but still clearly 

 th" relation of natural philosophy to natural science. In 

 the discussion of the proper means of studying sciences 

 Socrates is made to say " We shall pursue astronomy with 

 the help of problems just as we pursue geometry : but we 

 shall let the heavenly bodies alone if it is our design to 

 become really acquainted with astronomy." What I take 

 to be the same idea is expressed in other words by Rayleigh 

 in the introduction to his " Sound." He there points out 

 as an example that the natural problem of a sounding 

 tuning-fork really comprises the motion of the fork, the 

 air, and the vibrating parts of the ear ; and the first step 

 in sound is to simplify the complex system of nature by 

 assuming that the vibrations of the fork, the air, 

 and the ear can be treated independently. Frequently 

 this step is a most difficult one to take. What student of 

 nature, contemplating the infinity of heavenly bodies and 

 unfamiliar with this method of idealism, would imagine 

 that the most remarkable and universal generalisation in 

 physical science was arrived at by reducing the dynamics 

 of the universe to the problem of three bodies? When we 

 look round the sciences each has its own peculiar ideals 

 and its own physical quantities : astronomy has its orbits 

 and its momentum, sound its longitudinal vibration, light 

 its transverse vibration, heat its energy and entropy, elec- 

 tricity its " quantity " and its wave, but meteorology has 

 not yet found a satisfactory ideal problem to substitute for 

 the complexity of nature. I wish to consider the aspect 

 of the science from this point of view and to recall some 

 of the attempts made to arrive at a satisfactory modification 

 of reality. I do not wish to refer to such special appli- 

 cations of physical reasoning as may be involved in the 

 formation of cloud, the thermodynamics of a mixture of air 

 and water vapour, the explanation of optical or electrical 

 phenomena, nor even Helmholtz's application of the theory 

 of gravitational waves to superposed layers of air of different 

 density. These require only conventions which belong 

 already to physics, and though they may furnish suggestions 

 they do not themselves constitute a general meteorological 

 theory. 



The most direct efforts to create a general theory of 

 atmospheric circulation are those which attempt to apply 

 Newtonian dynamics, with its more recent developments 

 on the lines of hydrodynamics and thermodynamics. 

 Attempts have been made, mathematical or otherwise, to 

 determine the general circulation of the atmosphere by the 

 application of some form of calculation, assuming only the 

 sun and a rotating earth, with an atmosphere, as the data 

 of the problem. I confess that these attempts, interesting 

 and ingenious as they are, seem to me to be somewhat 

 premature. The " problem " is not sufficiently formulated. 

 When Newton set to work to connect the motions of the 

 heavenly bodies with their causes, he knew what the 

 motions of the heavenly bodies were. Mathematics is an 

 excellent engine for explaining and confirming what you 

 know. It is very rarely a substitute for observation, and 

 before we rely upon it for telling us what the nature of the 

 general circulation of the atmosphere 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 compressible fluid rotating about 

 an axis with a velocity reaching looo miles an hour, and 

 subject to periodic heating and cooling of a very com- 

 plicated 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 explam it. What strikes one most about the mathe- 

 matical treatises on the general circulation of the atmo- 

 sphere 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. 



NO. 1768, VOL 6^'\ 



Consider next the attempts to regard atmospheric pheno- 

 mena 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 periodicity, is not necessarily 

 regular, and the scientific process consists in identifying 

 corresponding changes. This method has given some re- 

 markable results by the comparison of the sequence of 

 changes in the meteorological elements in the hands of 

 Pettersen and Meinardus, and by the comparison of the 

 variation of pressure in different 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 discussion. As a matter of fact, by con- 

 tinuing this Address I am preventing Sir Norman Lockyer 

 from telling you all about it. 



For the purpose of dealing with periodicity in any form 

 we substitute for feature 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 simplification is perfectly legitimate. Pass- 

 ing on to the consideration of periodicity in the stricter 

 sense the process which has been so effective in dealing 

 with tides, the motions of the liquid layer, is very attractive 

 as a means of attacking the problems of the atmosphere, 

 because, in accordance with a principle in dynamics, to every 

 periodic cause there must correspond an effect 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 periodic method. One 

 is to examine the generalised observations for periodicities 

 of known length, whether it be that of the lunar rotations 

 or of sunspot frequency, or of some longer or shorter period. 

 In this connection let me acknowledge a further obligation 

 to Prof. Schuster for tacking on to his Address of last year 

 a development of his work on the detection of hidden perio- 

 dicities 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 

 components. I may' say that the Meteorological Office, 

 supported by the strong opinion of Lord Kelvin, has 

 favoured that plan, and on that account has for many years 

 issued the hourly res.ults for its observatories in the form 

 of five-day means as representing the smallest interval for 

 which the harmonic analysis could be satisfactorily em- 

 ployed. Sir Richard Strachey has given some examples of 

 its application, and the capabilities of the method are by 

 no means exhausted, but as regards the general problem 

 of dynamic meteorology harmonic analysis has not as yet 

 led to the disclosure of the required generalisation. 



I ought to mention here that Prof. Karl Pearson, with 

 the assistance of Miss Cave, has been making a most 

 vigorous attempt to estimate the numerical value of the 

 relationship, direct or inverse, between the barometric read- 

 ings at different places on the earth's surface. The attempt 

 is a most interesting one as an entirely new departure in 

 the direction of reducing the complexity of atmospheric 

 phenomena. If it were possible to find coordinates which 

 showed a satisfactory correlation it might be possible to 

 reduce the number of independent variables and refer the 

 atmospheric changes to the variations of definite centres 

 of action in a way that has already been approached by 

 Hildebrandsson from the meteorological side. 



Years ago, when Buys Ballot laid down as a first law of 

 atmospheric motion that the direction of the wind was 

 transverse to the barometric gradient and the force largely 

 dependent upon the gradient, and when the examination of 

 synchronous charts showed that the motion of air could be 

 classified into cyclonic and anticyclonic rotation, it appeared 

 that the meteorological Kepler was at hand, and the first 

 step towards the identification of a working meteorological 

 unit had been taken — the phenomena of weather might be 

 accounted for by the motion and action of the cyclonic de- 

 pression, the position of the ascending current, the baro- 

 metric minimum. The individual readings over the area of 

 the depression could be represented by a single symbol. 

 By attributing certain weather conditions to certain parts 

 of the cyclonic area and supposing that the depression 

 travelled with more or less unchanged characteristics the 

 vagaries of weather changes can be accounted for. For 



