Dmrnal Meteorological Conditions at Kimherley. 153 



£gments of the mathematical imagination ? Some of the most ac- 

 comphshed physicists claim the former — others object ! Eliot seems 

 — if I am not mistaken — to regard the first and second as certainly, 

 and the third and fourth as probably, belonging to the former. Thus, 

 evidently, the problem is in the unusual position for a mathematical 

 subject of depending upon experiment, and not theory, for its solu- 

 tion. And, perhaps equally evidently, the harmonic analysis may 

 not be expected to separate out every contributory to the composite 

 curve. Bessel seems to have favoured, on the whole, the latter and 

 perhaps the safer alternative. He observes, for instance, in his 

 paper on the determination of the law of a periodical phenomenon, 

 *' that, by the determination of the development which belongs to 

 a phenomenon, we meet its theory half-way. Thus, e.g., the observed 

 solar longitudes, if developed in this way, according to the yearly 

 period, would give a formula from which, if Kepler's discovery were 

 yet to be made, we could discover the elliptic motion much more 

 easily than from the observations themselves. . . ." " Prof. Cleve- 

 land Abbe, dealing with the complex formulae representing the rela- 

 tions between the pressures and motions of the atmosphere on a 

 rotating globe remarks that "it is to be expected that long before we 

 have attained to what may be called a complete solution of all these 

 equations of condition, we shall, by means of general theorems, have 

 at least obtained some approximately correct ideas concerning the 

 general mechanics of the atmosphere. Already many have proposed 

 to skip this long process of reasoning, and substitute for each locality, 

 and for the prospective rigorous solutions, some approximate sine 

 and cosine formula, as though it were certain that the Bessel-Fourier 

 series, or some other combination of periodicities, would satisfactorily 

 represent the motions and other phenomena of the atmosphere. But 

 the problem is undoubtedly too complex for plane harmonics, &c." t 

 At any rate, whether the separate constituents are actual physical 

 entities, or merely portions of terms in the algebraic equation to a 

 curve, it seems not unlikely that a study of their respective changes, 

 when any of the elements either of climate or locality are made to 

 vary, may eventually suggest the explanation of the double diurnal 



* Quarterly Weather Eeport for 1870, Appendix. 



t Monthly Weather Review, 1901, p. 558. The student may also, with advantage, 

 •consult "A theorem on Fourier Series, and its application in Geophysics," by 

 A. Nippoldt, Jr., in Terrestrial Magnetism for June, 1902; also "The Diurnal 

 Variation of Barometric Pressure," by F. N. Cole in Weather Bulletin No. 6. 

 Lord Kelvin, in a paper read before the British Association at Plymouth, in 1877, 

 recommended that in order to avoid the enormous bulk of accumulated statistics, 

 all meteorological results should be published in the shape determined by harmonic 

 analysis. But I have only seen a short abstract of his paper. 



