ON COMPARISON AND REDUCTION OF MAGNETIC OBSERVATIONS. 223 



activity falls later in the year now than in the epochs dealt with by 

 Dr. Stewart and Mr. Ellis. The different character of the materials 

 employed in the several cases must be borne in mind. Dr. Stewart took 

 into account all observations except the comparatively small percentage 

 falling under General Sabine's definition of disturbed, and Mr. Ellis took 

 all but days of considerable magnetic disturbance ; thus the material 

 dealt with by both possessed presumably much greater heterogeneousness 

 than that dealt with in Table VIII. Again, the mode in which the 

 results were treated was difl'erent. Dr. Stewart, it is true, apparently 

 took the means from groups of four successive years, but Mr. Ellis took 

 the mean of the ranges deduced from each single year's records. The 

 taking a group of years probably depresses the mean range most in those 

 months in which the progress of the diurnal inequality is least regular. 



Harmonic Analysis of Monthly Ranges. 



§ 15. I have analysed into harmonic tei'ms the quantities measuring 



,, , , . -^ c ,1 >• .- mean range for month ^ , ,, 



the departures from unity oi the tractions ^ — ^ tor both 



mean range tor year 



declination and H.F. Putting for brevity 



x = 2ntl\2 (8) 



where t is time in months from the middle of January, I find for the 



declination 



mean range for month , ,,-, , i^ • n o 



*?- —1= —•-10 cos a; +"14 sin x — 'll cos 2x 



mean range for year 



+ •08 sin 2a;+'01 cos 3a; — ^04 sinSi^^ + ^Ol cos 4a; + *00 sin 4a; 



+ •04 cos 5a; — '03 sin 5a;+^03 cos 6a; . . . . . (9) 



for the Horizontal Force 



mean range for month , , ., , ao • at o 

 ° —1:= — •4.J cos x+-(jo sin a; — '07 cos 2a; 



mean range for year 



+ •03 sin 2a; + ^00 cos 3.r— •OO sin 3a; + ^03 cos 4a; + -03 sin 4a; 



+ •03 cos 5a; + ^01 sin .'5a;+-01 cos 6x- (10) 



In both cases the terms whose period is the full year are greatly pre- 

 dominant. There appears also in both cases an appreciable semi-annual 

 variation ; but the terms with shorter periods are very small, and little 

 weight can be attached to their numerical measure. 



Annual Variation. 



§lfi. The variation of a magnetic element throughout the year, like 

 its variation throughout a qidet day, is most simply regarded as composed 

 of two parts, a uniform drift or secular variatio7i, and a cyclic portion, 

 which may be called the anyiual inequality. This is a somewhat arbi- 

 trary separation. The increase of the horizontal force, for instance, from 

 year to year, got out from the observations of most observatories, is far 

 from uniform ; and if this be a true phenomenon the hypothesis that the 

 secular drift is uniform throughout the whole of one year can hardly 

 claim a physical basis. It is, however, at any rate a convenient mathe- 

 matical fiction whose adoption can do no harm when its true character 

 is explicitly recognised. 



