542 The Rev. Dr. Lloyd on the Deter-ndnation of 



tion Z7, and the consequent difficulty and uncertainty of the elimination: more- 

 over, the position which has been adopted for the deflecting needle will not 

 admit of the required alteration of distance. 



Now here I premise, that it is not necessary that the usual deflection dis- 

 tance should be one of the series employed in deducing the coefficients of the 

 inverse powers of the distance in the value of U: it is not even requisite that the 

 relative positions of the two magnets should be the same in the two cases. For 

 if the value of the corresponding function be found, for any other position, and at 

 any distance, that of U will be known by a comparison of the deflections pro- 

 duced. Accordingly, I propose 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 be- 

 comes 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 de- 

 flecting 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 = MV ; 

 in which V is of the form 



F--i-il + ^+l- + &c' 

 where 



Let Fi, Fs, Fa, &c., denote the values of F corresponding to the distances Z)„ 



