DIURNAL INEQUALITIES. FOURIER COEFFICIENTS. 



127 



When discussing the Kew results, I hazarded the remark that the diflbruncc observed there between the 

 phenomena in the 24-hour and 1 2-hour waves might be associated with the further difference that the 

 12-hour phase angle is largest in Summer, while the 24-hour phase angle is largest in Winter. Referring 

 to Tables XXXIV and XXXVI, it will be seen that in the Antarctic, the 24-hour phase angle agrees with 

 the 12-hour phase angle there and at Kew in being larger at Midsummer than at Midwinter. This is, of 

 course, in accordance with the suggestion which I threw out, but much weight ought not to bo attached 

 to what not unlikely may be a mere coincidence, especially as the seasonal variation of a\ in the Antarctic 

 is not large. 



The difference of phase is not the only difference between all- and quieter-days' Declination results. The 

 amplitudes, at least in the case of the 24-hour wave, are markedly less for the quieter days, but this we 

 could have foreseen from simple comparison of the diurnal inequalities in Tables XIII and XV. 



TABLE XLI. Declination. Quieter-days' Phase Angle - All-days' Angle. 



TABLE XLII. Declination. Quieter-days' Phase Angle - All-days' Angle. 



35. The most consistent and striking phenomenon in Tables XXXIII to XL is the relatively small 

 amplitude of the Fourier waves of shorter period as compared to the 24-hour wave. To bring this out 

 more clearly, Table XLIII records the ratios of the amplitudes of the 12-, 8- and 6-hour waves to the 

 corresponding amplitude of the 24-hour wave in the diurnal inequalities for the several elements and 

 seasons. D' relates to the quieter-days', D to the all-days' Declination results. The ratios of the arithmetic 

 means of the 12 monthly values of C 2 , c 3 , and c to the corresponding mean for Ci are also given. The 

 figures in the sixth row are means derived from the four elements D, H, V and I. For contrast, the 

 seventh row gives corresponding results from the Kew Declination on ordinary days. 



Comparing the results under the heading " Year," we see that relative to the 24-hour wave the 

 importance of the 12-hour and 6-hour waves is, in the Antarctic, only about a third of what it is at Kew, 

 while the relative importance of the 8-hour wave in the Antarctic is only about a sixth of that at Kew. 



