Variation of Temperature in the British Isles, &c. 63 



curves are not drawn by eye merely to smooth out the irregularities, but 

 they have been arrived at by a process of synthesis of simple harmonic 

 curves of the first arid second orders. 



The irregular lines were first compared with a simple harmonic curve 

 of an annual period, drawn so as to give the same area as the irregular 

 line above and below the line of mean annual temperature, and a 

 general lag of about a month of all the seasons behind the planetary* 

 seasons. The comparison at once disclosed that apart from the irregu- 

 larities of short period, there was a lag of spring and an acceleration 

 of autumn, and a corresponding exaggeration of the summer maximum 

 and moderation of the winter minimum. This result, which is essen- 

 tially characteristic of the combination of a second-order sine curve 

 with one of the first order having a maximum at the same epoch, 

 suggested the idea that a normal curve of reference could be formed 

 by combining two such curves. 



The first-order sine curve for Kew was accordingly placed so as to 

 make the lag of spring and the acceleration of autumn, as roughly 

 estimated, equal; under these circumstances, the maximum fell on 

 July 23, which coincides satisfactorily with the maximum of the 

 original curve. The second-order sine curve was compounded with 

 this the period of the second-order curve being six months and its 

 amplitude! was so arranged as to produce the observed lag of spring 

 and acceleration of autumn ; as these had been taken to be equal to 

 each other, the maximum of the second-order curve, and therefore of the 

 compounded curve, corresponded with that of the first-order curve and 

 of the original smoothed curve. A similar process was followed for 

 the other three stations. It is apparent that these new compounded 

 curves give very satisfactory smoothed curves for the whole year for 

 each of the stations. Thus it would appear that the regular periodic 

 variations of mean atmospheric temperature at Kew may be practically 

 represented by the summation of two effects, one of which corresponds 

 with a sine curve having an amplitude of 12 0- 04F., and a period of 

 one year, and the other with a sine curve having half the period and 

 an amplitude of 1'4F. Similar statements with suitable numerical 

 magnitudes are true of the other stations. These results, which had 

 been reached synthetically, were confirmed analytically within narrow 

 limits, \ and gave rise to the conclusion that there is in the twenty-five- 



* The word " planetary " is used in this paper to characterise a variation corre- 

 sponding to the position of the earth in its orbit. 



t The relation between lag and amplitude is as follows : The double amplitude 

 of the second-order curve = annual range x sine of angular lag. 



J The dotted lines in Diagram 1 show the combination of the synthetic curves 

 of the first and second order ; the crosses mark points on the curve of the first 

 order. A comparison with Table I shows that a sensible error was introduced by 

 assuming the maxima of the first- and second-order components to be synchronous 

 in the case of Kew and of Aberdeen. 



