100 



DIURNAL INEQUALITIES. 



25. In forming the diurnal inequalities, use was made of the readings for the first and last midnights 

 of the local day. The non-cyclic increment N i.e. the algebraic excess of the mean value for the second 

 over that for the first midnight was eliminated by applying to the mean value for hour, n, the correction 

 + N (12 -n)/24, where n is counted from to 24. Particulars of the mean diurnal non-cyclic change for 

 the days actually employed in calculating the diurnal inequalities are given in Table XXIII. 



TABLE XXIII. Non-cyclic Changes. 



In the case of the Declination, results are given both for all days and for quieter days, i.e. for the days on 

 which depend the inequalities in Tables XII and XIV respectively. Omitting March, 1902, for which no 

 quieter-days' results existed, we find that the mean daily non-cyclic change of Declination from the 18 months 

 April, 1902, to September, 1903, was + 0''37 for all days, as against - 0'-56 for quieter days. So substantial 

 a difference suggests that the difference between the quieter days and the others is not wholly accidental. 

 The great preponderance of individual months in which the all-days' non-cyclic change is algebraically 

 larger than the quieter-days' change points to the same conclusion. Accepting the difference as real, we 

 should infer that on the representative quieter day the progressive increment of the easterly Declination 

 is algebraically less than on the representative all-day by the amount 0''56 + 0''37, or /- 93. We have 

 already seen in Table IV that the mean value of the easterly Declination for the representative quieter 

 day was less than that for the representative all-day to the extent l' - 46. An analogous phenomenon has 

 been observed elsewhere in the case of the Horizontal Force. Thus according to ELLIS the average non-cyclic 

 increment of Horizontal Force at Greenwich on quiet days from 1890 to 1895 was +4'3y, while the 

 absolute value of the force on the representative quiet day of the epoch 1889 to 1896 exceeded that from 

 the average day by 3 - 3y. The apparent parallelism may be pure accident, but it merits recognition as a 

 possibly important key to the study of the relationship between non-cyclic changes and disturbances. 



Taking the all-days' Declination results, the mean non-cyclic change from the 18 months April, 1902, to 

 September, 1903, as already stated, is + 0''37. If we include March, 1902, the mean falls to + 0'-20 ; while 

 if we take a mean from a year, combining common months in 1902 and 1903, it falls to +0' - 083. Even at 

 the last figure we should deduce an annual change of + 30' - 0, which is much in excess of the secular change 

 obtained in Table VII. Both the non-cyclic and the Table VII secular-change data can claim to be 

 regarded as natural magnetic changes only if the base-line value of the Declination curves was invariable. 

 But if this be granted, it would appear at first sight that they ought to give identical values for the 

 secular change. It should, however, be remembered that the non-cyclic data in Table XXIII are based 

 only on days on which the record was complete, so that all highly disturbed days are excluded, whereas 

 all days, however disturbed, contribute to the secular change. There is thus no necessary inconsistency 

 between the results of Tables XXIII and VII. If, however, 'we are to avoid an inconsistency, we must 

 suppose that on the average day for which no complete Declination record existed or we may say for the 



