64 Messrs. W. N. Shaw arid R. W. Cohen. On the Seasonal 



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. 



