126 



DIURNAL INEQUALITIES. FOURIER COEFFICIENTS. 

 TABLE XL. Inclination. Amplitudes (Unit 1') and Phase Angles. 



34. Before making some general remarks on Tables XXXIII to XL, it is convenient to deal with an 

 interesting result deducible from the Declination Tables. If we compare Tables XXXIII and XXXV, or 

 XXXIV and XXXVI, it will be observed that the differences between the phase angles derived from all 

 days and from the quieter days are to some extent systematic, at least in the case of the 24-hour and 

 12-hour waves. 



This will be more easily recognised on consulting Tables XLI and XLII, which show the algebraic 

 excess of the phase angle from the quieter-days' inequality over that from all days. Thus, taking 

 Table XLI, we find the quieter-days' value of ai the larger in 13 months out of 18, the average excess for 

 the 18 months being no less than 4 29'. This signifies that on the average quieter day the maximum 

 and minimum of the 24-hour wave occurred about 18 minutes earlier than on the average day for which 

 records existed. The quieter-days' phase angle a* is also the larger in a substantial majority of the months ; 

 the average excess is, however, only 2 42', representing about 5-4 minutes of time. The excess would, 

 however, have been very substantially larger but for the results from the later months of 1903, which are 

 based on a rather smaller number of days than usual. The results from the seasonal and mean annual 

 diurnal inequalities in Table XLII point in the same direction. The yearly results in this table for a 3 

 and 0.4 have the same sign as those for 0.1 and a 2 , but the phenomena in individual months, and even in 

 individual seasons of the year, appear too irregular to justify our regarding the difference between all and 

 quieter days as established for the 8-hour and 6-hour waves. 



In the case of the 24-hour and 12-hour waves the difference does seem fairly established. As to its 

 most probable size, if we take a mean from the yearly results in Table XLII and the final means in 

 Table XLI, we find for the advance in quieter days in the time of maximum or minimum 15-2 minutes 

 for the 24-hour wave and 20'2 minutes for the 12-hour wave. 



This is not the first occasion on which a difference has been noted between the phase angles on ordinary 

 and on quiet days. Recently* it was pointed out that a substantial difference existed at Kew between the 

 24-hour and 12-hour phase angles derived from the Astronomer Royal's quiet days and those derived 

 from all days of the month. There is, however, a certain remarkable difference between the Antarctic 

 phenomena and those at Kew. In the Antarctic we have found the quieter-days' angles to be the larger, 

 both for the 24-hour and the 12-hour waves; but at Kew, while the quieter-days' phase angle was 

 the larger in the case of the 12-hour wave, it was the smaller in the case of the 24-hour wave. 



* ' Phil. Trans.,' A, vol. 208, 1908, pp. 223, &( 



