400 DR. C. CHEEE : ANALYSTS OF RESULTS FROM THE FALMOUTH MAGNETO- 



differences is somewhat under +1 minute, which answers to about 0'25 millim. on the 

 magnetograms. As the sign of individual differences, owing to their exceeding 

 smallness, must be largely fortuitous, the only safe conclusion is that whilst there is a 

 preponderance of + signs (i.e., of cases when the event is later at Falmouth than at 

 Kew), the differences may be accidental and are certainly exceedingly small. The 

 above results refer to the average year, and no inference can safely be drawn as to 

 the differences between Kew and Falmouth in different individual years. 



Variation throughout the Year (Fourier Series). 



15. The ranges of the diurnal inequalities, the sums of the 24 differences from 

 the mean, and the amplitudes of the 24-, 12-, 8-, and 6-hour terms have had their 

 annual variations expressed in Fourier series, the constants being calculated from the 

 monthly values. Table XVIII. gives the results for the 12-year period. The time t 

 is counted from midnight of December 31 to January 1, and a month is equivalent 

 to 30. The amplitudes of the annual and semi-annual terms which suffice to 

 express the variation very completely are denoted respectively by P! and P 2 . The 

 table gives the ratio of P 2 to P l5 and also of P l and P 2 to M, the mean of the 12 monthly 

 values of the element concerned. The reservations necessary are discussed in 

 (A), 37. 



The excess of the values of Pi/M, &c., at Falmouth, over those at Kew are given as 

 usual in small type ; in the case of c s and c 4 these differences are omitted for P 2 /Pi as 

 too uncertain. Except in the annual term in c 4 the phase angles differ compara- 

 tively little amongst themselves ; the same phenomenon appeared at Kew ( (A), 

 Table XXX.). 



Considering the smallness of c 4 , one would be disposed to suspect that the large 

 difference between the phase angles of the annual term in that element and the 

 other angles, though appearing in both D and H, was due to defects in the obser- 

 vations or reductions. Exactly the same phenomenon appeared, however, in the 

 corresponding case at Kew (see (A), Table XXX.). 



The ratios borne by the amplitudes of the annual and semi-annual terms to the 

 mean value of the element at Kew and Falmouth differ comparatively little. But if 

 we exclude c 4 , where the element and its variable part are both very small, we see 

 that on the whole the annual term at Falmouth is somewhat less important as 

 compared either to the semi-annual term or to the absolute mean than it is at Kew. 

 This is what Tables IX. and XIII. would lead us to expect. 



16. The dates of occurrence of the maximum in the annual terms, and of the 

 earliest maximum in the semi-annual terms, are given in Table XIX. As explained 

 in (A), 38, these dates may be uncertain to the extent of a whole day, for they are 

 based on a treatment which disregarded differences between the lengths of the several 

 months. 



