INTENSITY OF THE EARTH'S MAGNETIC FORCE. 267 



to determine, in the first place, the value of the corresponding 

 function in a different relative position of the two magnets, and 

 by means of deflections at the usual distances; and thence to 

 conclude that of U in the position of the magnets here employed. 



In using the dip-circle for this purpose, it will be found most 

 convenient to adopt the third of the methods above described, in 

 which the equilibrium is produced by turning the instrument in 

 azimuth until the deflected magnet becomes vertical ; for in this 

 case the deflecting magnet is always horizontal, and can be placed 

 in the usual position with respect to the deflected magnet without 

 difficulty. For this purpose the apparatus is provided with a gun- 

 metal bar, the middle of which is broad, and has a rectangular 

 aperture which enables it to pass over the box containing the 

 deflected magnet : this bar rests horizontally on two supports 

 fixed outside the box, on the level of the agate planes. The 

 deflecting magnet is to be placed on this support at different 

 known distances, and on each side of the deflected magnet, its 

 axis being in the plane in which the latter moves ; and the 

 apparatus is to be turned in azimuth until the deflected needle is 

 vertical. In this case equation (2) becomes 



- X cos a = m V ; 

 in which V is of the form 



where 



n = --- - - , q = -- ----- / - 6 --- 



,,i m m m m 8 m 



/., -HI r, ,. flaw's 45 ;;/.-, 



- 3- , q = 3 -- 15 ----- / + - 6 --- 7> 



Let F,, F-, F 3 , &c., denote the values of V corresponding to the 

 distances D,, A, -D 3 , &o. ; and a,, a 2 , a ;i , &c., the corresponding 



azimuths observed ; then it is obvious that 



V-. cos ! - Fi cos a, = 0, F 3 cos ai - F, cos a a = 0, & 



from which equations the values of the coefficients j>, J . 

 obtained by elimination in the usual manner. IIen- / is com- 

 pletely determined. 



Now let the deflecting magnet be removed from the horizontal 

 bar, and placed in its ordinary position between the microscopes ; 

 and let the observation be it-peat ed, tin- tnrfniment being turned 



