The following paper is mainly concerned with the analysis of the seasonal variation of temperature of the British Islands into a series of simple harmonic curves. The variation of temperature is so irregular that the use of this method of analysis for the investigation of the subject may seem to be arbitrary and inappropriate, and a few words of introduction are accordingly necessary to indicate the circumstances under which this mode of dealing with the subject showed itself to be specially adapted for the purpose.
Observations have been made for the Meteorological Office since 1871 with self-recording instruments at the four observatories, Kew, Aber- deen, Falmouth, and Valencia, and the daily means of pressure and temperature from the twenty-four hourly readings of the curves of the barometer and dry-bulb thermometer have been worked out for twenty- five years, but have not yet been published. The means for temperature are represented in Diagram 1 (p. 62), by curves whose co-ordinates are respectively proportional to the number of days since the beginning of the year, and the corresponding twenty-five-year mean of the day's temperature at the several observatories.
The following points may be noticed upon an inspection of the curves :
(1.) The summer portions of the curves have a larger amplitude and a shorter duration than the winter portions.
(2.) The curves do not exhibit a smooth run, but show a number of irregularities which are, in some instances, particularly in May and December, of considerable magnitude.
Under these circumstances it is difficult to assign any specific number as the normal mean temperature for the particular day to which any actual observed temperature can be referred. To put the same point in other words, it is difficult to say whether a depression between two elevations is to be regarded as a period of abnormally low temperature- between two normal periods, or as a period of normal temperature between two abnormally high periods.
It will be noticed that on the diagram smoothed curves have been drawn, which represent with remarkable fidelity the general sweep of the curve, cleared of the irregularities of small period. The smoothed
