VARIATIONS OF THE MAGNETIC NEEDLE. 277 



The means corresponding to each epoch are given in the 

 lowest lines of the preceding Tables. On examining them, it 

 will be seen that the law of the diurnal changes in the force and 

 direction of the currents is very systematic. In both lines the 

 current flows southwards from ll b 30 m A.M. to 7 h 30 m P.M. inclusive; 

 and northwards at the remaining epochs. The maximum of the 

 southerly current occurs at l h 30 m P.M., and that of the northerly 

 current at 7 h 30 m A.M. 



6. Let us now compare these results with those deducible from 

 the diurnal changes of the magnetic declination and horizontal 

 force, on the assumption that the forces which produce the latter 

 are due to electric currents traversing the upper strata of the 

 earth in a horizontal direction. 



Let rj denote the disturbing force by which the north pole of 

 the magnet is urged to the eastward of its mean position ; , that 

 by which it is impelled northward. Then, on the assumption 

 above* referred to, the force of the current in the magnetic 

 meridian, flowing northward, = aij, a being an unknown constant ; 

 and that of the current perpendicular to the magnetic meridian, 

 flowing eastward, = - . Hence, the force of the current in any 

 direction, making the angle e with the magnetic meridian measured 

 to the east of north, is 



/ = a (n cose -K sins). 



The quantities r? and % are given, in terms of the horizontal 

 component of the earth's magnetic force, by the readings of the 

 two horizontal magnetometers. For it is evident that 



X being the horizontal component of the earth's magnetic force, 

 uiid \ft the magnetic declination ; and 



= X - X = $X. 



7. Now, to reduce the preceding formula into numbers, we 

 have e = a - 1//, in which a is the azimuth of the line connecting 

 the two stations, measured from the true meridian eastward. The 

 observations of Sir James Boss, at Derby, give 



= - 22 25' ; 



