7 
The quantity denoted by JU, in this position, is a function of the 
distance of the centres of the two needles, and of the ratios of certain 
integrals which depend upon their magnetic distribution. It may be 
shown that the variations of these ratios, arismg from the gradual 
changes of magnetism of the needles, may be disregarded; so that, if 
the distance be invariable, the function U will be constant. This is a 
point of considerable importance ; for it follows from it that, even if 
the value of U be unknown, £ will be relatively determined by a 
process which is independent of the changes in the magnetic moments of 
the two needles. Hence, if the value of the force be found at any one 
place, by any independent means, it will be absolutely known at all. 
But the value of the constant U may be found by deflection, by the 
instrument itself, and the method therefore rendered rigorously abso- 
lute. In using the dip-circle for this purpose, it will be convenient to 
produce the equilibrium by turning the instrument in azimuth until 
the deflected needle is vertical; for, in this case, the deflecting magnet 
is always horizontal, and can be placed in the usual position with re- 
spect to the deflected magnet, without difficulty. For this purpose the 
apparatus is provided with a gun-metal bar, having a rectangular aper- 
ture, by means of which it passes over the box containing the deflected 
magnet, and rests on two supports fixed outside 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 
- Xcos a= UV; 
in which FP is of the form 
2 ike, a2 
Va a(t + &e. ) 
The quantities p and q¢ are to be found in the usual manner, by repeat- 
ing the observation at several known distances, and eliminating among 
the resulting equations. This being done, the deflecting magnet is to 
be removed from the bar, and placed in its ordinary position between 
the microscopes ; and the observation is to be repeated. If a denote 
the corresponding azimuth, ; 
- X cosa,= HU; 
whence 
COS a, 
U=V = 
COs a 
The method here proposed appears to offer the following advantages 
to the travelling observer :— 
1. It is applicable, with equal accuracy, at all parts of the globe. 
2. It dispenses with the employment of a separate instrument for 
