558 REPORT — 1901. 



this convergency factor is not present. The paper called attention to two matters 

 connected with this solution : — 



(1) The series which are used — when the string starts from a position of rest 

 with sharp corners — is not capable of differentiation twice with regard to .r and i. 



(2) The equation ^'- = «- •{, being obtained on the assumption that the 



string forms a curve without sharp corners, cannot without discussion be applied 

 to these cases. 



Department II. — Physics. 

 The following' lleports and Papers were read : — 



1. Report on Underground TemjKrature. — See Reports, p. G-1. 



2. Report on Seismological Investigation. — See Reports, p. 40. 



3. On the Seasonal Variation of the Atmospheric Temperature of the 

 British Isles and its Relation to Wind-direction. By W. N. Shaw, 

 M.A., F.R.S., and R, Waley Cohen, B.A.^ 



If the tweoty-five-year means of temperature for each day of the year at the 

 four principal stations of the British Meteorological Office be plotted the curves 

 do not exhibit a smooth run, but show a number of irregularities — often of con- 

 siderable magnitude. It is thus difficult to assign any specific number as the 

 normal mean temperature for a particular day, and the immediate object of the 

 work described below was to obtain a smooth curve to which the actual observed 

 temperature of any day might be referred and to study its characteristics. The 

 curves of actual daily means were first compared with simple harmonic curves 

 having an annual period, a maximum about July 21, and the same area as the 

 irregular curves. The comparison at once disclosed a lag of spring and an 

 acceleration of autumn, and a con-esponding exaggeration of the summer 

 maximum and moderation of the winter minimum. These features, being 

 essentially characteristic of the combination of a first and second order sine 

 curve with a maximum at the same epoch, suggested the idea of combining 

 two such curves to obtain a normal curve of reference. These combined curves 

 give very satisfactory smoothed curves for the whole year for each station, and 

 show that the periodic variations of atmospheric temperature at Kew may be 

 very approximately represented by the summation of two eli'ects, one of which 

 corresponds to a sine curve with an annual period and an amplitude of 12°'04 F. 

 and the other to a sine curve with a semi-annual period and an amplitude of 

 1°'4 F. Similar statements with similar numerical magnitudes are true of the 

 other stations. This result has been confirmed analytically. 



The curves of daily mean atmospheric temperature have been harmonically 

 analysed for each of the stations, and the values of the harmonic coefficients 

 have been determined in the Meteorological Office by means of Sir II. Strachey's 

 formula.'- In each case there is a second order curve whose amplitude is about 

 one-eighth of that of the first order, and the amplitudes of the curves of higlier 

 order are so small as to be negligible. The first order curve has a maximum at a 

 date which varies at the four stations from July 23 to August 1, and the second 

 order curve has maxima which vary from January 28 to February 3, and July 30 



' See Proc. Royal Soc. 



■ Proc. Royal Soc, vol. slii. pp. 61-79. 



