year temperature curve of each of the British stations, a perfectly
regular and recognisable periodic effect, which has positive maxima
at the end of January and the end of July, and negative maxima
about the end of April and the end of October. It will be seen later
on (pp. 65, 66, and 77) that this curious and well-marked effect with a
period of six months, having maxima about the end of January and
July, is characteristic only of the British Isles, among the places whose
temperature statistics have been investigated from that point of view.
It is equally conspicuous in the variation of sea temperatures, and is
particularly marked in the variation of barometric difference between
London and Aberdeen (see Table III, p. 66).
This paper is devoted to a further discussion of this effect, and an attempt to trace its cause. As the process of harmonic analysis gave results for the twenty-five years which corresponded with the synthetic examination of the curves, it seemed better to deal with the observa- tions in the better recognised and more rigorous way.
Harmonic Analysis of Twenty-five-year Mean Values of Daily Temperatures
at Kew.
The mean temperature of any day may be represented by the equation
6 = a + P! cos (x - ju^) + P 2 cos 2 (x - /x 2 ) + ,
where o is the mean value of the curve for the year, and PI, P> . . . represent the amplitudes of the first, second, and higher order curves, while /AI, Hz - - represent the period of the year, expressed in degrees since the beginning of the year, at which the first maximum of each curve occurs. From this equation, by means of a formula which has been worked out by Sir R. Strachey,* the values of these harmonic co-efficients P 1} P 2 , &c., and p\, /x.,, &c., have been determined in the Meteorological Office from the twenty-five-year means of the five-day mean temperatures at Kew, Aberdeen, Valencia, and Falmouth. The results of this analysis are shown in Table I. It will be seen that in each case there is a second-order curve whose amplitude is about one* eighth of that of the first-order curve, and that the amplitudes of the curves of a higher order are generally so small as to be negligible, and moreover are very much more variable than the values of the co- efficients of the second-order curve.
Thus it appears that the twenty-five-year mean curve of daily tem- perature indicates the existence of two effects, represented respectively by a first-order and a second-order curve. The first-order curve re- presents a primary solar effect, with which we are not here concerned. The purpose of this investigation has been to ascertain the nature arid physical cause of the second-order effect.
- ' Roy. Soc. Proc.,' vol. 42, pp. 61-79.
