24 



ANNUAL VARIATION 



Returning to the last vertical column in the table, headed " mean," we have 

 there the monthly values of the declinometer readings (in scale divisions), and in 

 their differences when compared month for month, the joint effect of the secular 

 change, and of the annual inequality. To eliminate the effect of the secular 

 change, we determine its annual amount as follows : Subtracting the mean annual 

 reading 559.64, corresponding to July 1, from each monthly mean, and putting 

 x = monthly effect of the secular change (considered as uniform), each monthly 

 mean reading furnishes an equation for the determination of K, thus : for 



January 

 February 

 March 

 April . 



4.56 = 5.5 x 

 3.34 = 4.5 * 

 5.22 = 3.5 x 

 4.39 = 2.5 *, etc., 



which, when combined by least squares, give x = l d -.227, hence the annual change 

 14 d .7 or 6'.7 of increasing westerly declination. 1 



Deducting the effect of the secular change, and comparing the monthly remainders 

 with their mean values, we obtain the annual inequality of the declination as 

 follows : 



in the annual inequality indicates an f easterly deflection. 



The sign f 



I + ' I westerly 



According to these results the magnet (north end) is deflected to the east of its 

 mean annual position in summer, and to the west in winter. It is, however, 

 desirable to test the result by submitting the first and the second 21 years of 

 observations separately to the same process of investigation. The first 31 months 

 in the years 1840, '41, and '42, give a result almost identical with that just deduced; 



of the diurnal, both on account of the much smaller frequency of the period, and the difficulty of 

 preserving the instrument in the same unchanged condition during the much longer time, or of determining 

 and allowing for its changes when they do occur. Accordingly, although the annual period may be 

 traced in the observations of Gilpin and is decidedly displayed in those of Bowditch, it has evaded the 

 researches of recent observers. There is but a faint indication of its existence in the Gottingen observa- 

 tions, which were made at the hours of 8 A. M. and 1 P. M., and Professor Gauss and Dr. Goldschmidt 

 find, in their analysis of these observations, no important fluctuation dependent on season. A similar 

 negative result is deduced by Dr. Lament from the Munich observations, which were made twelve times 

 in the day." 



1 This value (+6'. 7), as resulting from a different combination of observed and partly interpolated 

 values, may not be preferable to that ( + 4'.5) deduced in Part I. of this discussion, but must necessarily 

 be employed in the present investigation. The most reliable value, +5'.0, was deduced from independent 

 observations, as already remarked, and lies between the two. 



