GRAPHS ON "QUIET" DAYS DURING THE TWELVE YEARS 1891 TO 1902. 393 



Perhaps the most comprehensive way of describing the conspicuous seasonal 

 variation in the part of the curve which answers to the night hours is by reference to 

 the two peaks that tend to form, one about 6 A.M., the other about 7 P.M. From 

 November to February the former is dominant. In March the evening peak begins 

 to assert itself, and its predominance remains undisputed during the summer months, 

 whilst the morning prak tends to disappear. In October the morning peak )>ecome8 

 again apparent. In most months there is at least an indication of a subsidiary peak 

 near midnight. 



The curves are simplest and most symmetrical in June and July. In August the 

 afternoon peak is remarkably sharp both at Falmouth and Kew. In October a very 

 small loop appears, a retrograde movement setting in about midnight. The loop 

 enlarges in November and becomes most prominent in December, contracting in 

 January and February. In March there is a very tiny loop in the Kew curve 

 shortly after midnight, and a curious indentation. The Falmouth curve shows only 

 the indentation. On the other hand, the April curve shows a tiny loop about 7 P.M. 

 at Falmouth, whilst at Kew there is only a peak. 



The Kew curves for three months, December, March and June, appeared in (A). 



Vector diagrams for Greenwich were given by Sir G. B. AIRY for each month of 

 the year, for the periods 1841 to 1847 and 1848 to 1857, treated separately,* and 

 laterf for the four months January, April, July and October in each of three 

 successive years. In making any comparison it should be noticed that AIRY counted 

 time from Gottingen nooii in the earlier curves, and from Greenwich noon in the 

 later. The different Greenwich curves for the same month of the year differ some- 

 what widely amongst themselves, and none of them resemble very closely the corre- 

 sponding Kew or Falmouth curves. There is, on the other hand,* a pretty close 

 resemblance between individual Kew and Falmouth vector diagrams and the corre- 

 sponding ones for Pare St. Maur, from the period 1883 to 1897, given on p. 261 of 

 Professor MASC ART'S ' Magne*tisme Terrestre.' 



Analysis of the Diurnal Inequality in Fourier Series. 



12. As in (A), 31, the analysis is supposed to be effected in the two alternative 



forms 



a, cost + bi sin J + a, cos 2t + b t sin 21+..., 



GI sin (t + a,) + c t sin (2t + a,) + . . ., 



where t represents Greenwich mean time counted from midnight, and an hour is 

 equivalent to 15. If local time were used, the corrections required to the phase 

 angles a, would be obtained by adding 4 45''6 to those given in (A), Table XIX. ; 

 for a, the addition would be 9 U 31', and so on. 



' Phil. Trans.' for 1863, Plates 18 and 19. 

 t ' Phil. Trans.' for 1885, Plate 74. 

 VOL. OCJV. A. 3 E 



