ANNUAL VARIATION. 1'29 



CHAPTER V. 



ANNUAL VARIATION. FOURIER COEFFICIENTS. 



36. To throw more light on the nature of the annual variation in the amplitude of the diurnal 

 inequalities, the ranges, the sum of the 24 hourly differences from the mean, and the amplitude Cj of tha 

 24-hour wave were analysed in the Fourier series 



M + PI sin (t + 0j) + P 2 sin (2t + S ) + .... 



where t represents time counted from January 1st, a month in t answering to 30. M represents, of 

 course, the mean value for the year, while P 1( P 3 are the amplitudes, d v # s the phase angles of the 12-month 

 and 6-month waves. Differences in the lengths of the calendar months were neglected. The values of 

 PD P 2 , 0j, # 2 , Pj/M, P 2 /M and P^P! for the several elements dealt with are recorded in Table XLIV. 



Means of the quantities in the last 5 columns, derived from D (all days), H, V and I are compared with 

 corresponding means derived from the D, H, V and I results (on quiet days during 1890 to 1900) at 

 Kew. As the Antarctic results are based on only two years' observations, they are presumably not so 

 close an approximation to what exactly represents average conditions as are the Kew results. Still, they 

 present features which can hardly be regarded as the result of accident, and which seem of much interest. 



We know already that the Antarctic diurnal inequality varies little in type throughout the year, and that 

 the 24-hour Fourier wave is largely dominant. Thus we might have anticipated that no very large 

 differences would exist between the values of 6 l or the values of P : /M derived from the ranges, the sum of 

 the 24 differences and Cj in any one element. But we could not have foreseen that the differences would 

 be so small as appears from Table XLIV. 



There is also remarkably little difference between the values of 6 l or between the values of Pj/M which 

 are derived from the Horizontal Force, the Vertical Force and the Inclination. There is a somewhat con- 

 spicuous difference between the values of 0j and between the values of Pj/M derived, in the case of the 

 Declination, from all and from quieter days. Also, somewhat curiously, whilst the all-days' value of Pj/M 

 accords closely with the corresponding values for H, V and I, it is the quieter-days' value of O l that accords 

 most closely with the corresponding angles for the other elements. 



The fact that the quieter-days' Declination value of Pj/M is enhanced indicates that, relatively considered, 

 the seasonal variation in the amplitude of the diurnal inequality is greater for quieter days than for 

 all days. 



In all cases the 6-month wave is smaller than the 12-month wave, but on the average of the elements its 

 relative importance appears greater in the Antarctic than at Kew. 



The large difference between the values of 0i at Kew and in the Antarctic arises almost entirely from 

 the six-month difference in the season. If we add 180, i.e. six months, to the Antarctic value of O l we 

 get to within 3 or roughly three days of the Kew value. In the case of the 6-month term the 

 difference between the mean values of 6* for the Antarctic and Kew is 188, or about three months and 

 four days. This means that this wave also is at Winter Quarters very nearly opposite in phase to what 

 it is at Kew, 



