[JACKSON] STUDY OF MAGNETIC DECLINATION 101 



each day an average of one hour and twenty-six minutes more at 

 Mcanook than Agincourt. 



As these Diurnal curves are cycHcal they may be expressed in 

 Fourier Series of the form 



F = ai sin («i + t) + a^ sin {a^ + 2t) + as sin («3 + 31) + 



where ai ao , «i «2 are constants and t is the time 



counted from hours and expressed in degrees at the rate of one hour 

 to fifteen degrees. 



If sufficient terms are taken the error between the computed and 

 observed curves may be reduced to less than any assigned quantity 

 however small. The curves under consideration for the year 1917 have 

 been grouped according to season for this analysis, winter comprising 

 the four months November, December, January and February, 

 equinox the four months, March, April, September and October and 

 summer the remaining four months. May, June, July and August. 

 The probable error on any individual hour between the computed and 

 observed curve for the different seasons at Agincourt is less than 0-2' 

 and for Meanook is less than 0-3' whilst the error for the mean of the 

 day is less than 0-03' for Agincourt and less than 0-07' for Meanook. 



The .constants ai, a^, etc. are called the amplitudes and the 

 constants ai, a<>, etc. the phase angles. The values of these quan- 

 tities are given in table V. The time of occurrence of maximum in each 

 wave is obtained by making (ai + nt) = 90° or 450° since the sine 

 has its maximum at 90° -|- 2n tt and this time for the first maximum 

 in each wave is also given. 



In the 24-hour wave the phase at Meanook is 2h 33m later than at 

 Agincourt in summer and 2h 8m later in winter, the winter times at 

 both places being earlier than in summer. In the 12-hour and 8-hour 

 waves the earlier phase is in the summer at both places, but in the 12- 

 hour wave although Agincourt is 32 minutes ahead in summer it is 

 14 minutes behind in winter, whilst in the 8-hour wave Agincourt is 

 only 9 minutes ahead in summer but 1 hour 7 minutes in winter. The 

 6-hour wave is more erratic in phase, particularly in summer, when its 

 amplitude is very small, but at both places the phase is later in winter. 



The amplitudes of the first two waves are the important ones at 

 both places. If the amplitudes are expressed in percentages it is 

 seen that the 24-hour and 8-hour waves are most effective at the 

 equinoxes and that the 12-hour wave is most effective in summer and 

 the 6-hour wave in winter. At Agincourt the 24-hour and 12-hour 

 waves are of about equal value and account for about 80% of the 

 amplitude, whilst in Meanook the 24-hour wave is about double the 

 12-hour wave and yet together they account for about 86% of the 

 total ampitude. The Meanook diurnal curve approaches nearer a 



