Page:Proceedings of the Royal Society of London Vol 69.djvu/71

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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-

sponding to the position of the earth in its orbit.
 * The word " planetary " is used in this paper to characterise a variation corre-

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.