of Edinhuryh, Session 1888-84. 
551 
the displacement of the image when the current is made. There is 
no difficulty in detecting an error of V in the position of the coil 
hy the motion of the reflected image. Evidently this magnification 
must not be carried so far as to make the initial torsion of the fibre 
seriously comparable with the magnetic couple. The plan described 
above of depriving the fibre of initial torsion was introduced for 
this reason. 
If the displacement of the mirror he observed with a sufficient 
degree of optical magnification, the process of giving sensibility hy 
reversing F may be dispensed with. When F = H, 8 becomes 
and the angular displacement of the reflected ray is equal to the 
error in position of the fame. 
The form of frame (with two parallel coils) shown in fig. 2 has 
been chosen in order to minimise the error produced by excen tricity 
on the part of the magnetometer. The proportions of the frame 
have been calculated as follows : — 
Let a length of the frame. 
„ & = J height 
„ Cj = distance of the nearer face of each coil from the centre. 
,, ^2 = distance of the further face of each coil from the centre. 
Suppose the coil he set with the plane of ah perpendicular to the 
magnetic meridian. Take the centre of the frame as origin of co- 
ordinates. 
As we are only concerned with the direction in azimuth, we shall 
consider excentricity in the horizontal plane only. From the sym- 
metry of figure there will be no error, so far as direction is con- 
cerned, when the centre of the magnet is on either axis NS or EW 
(see next figure). 
Let the centre of the magnet he at a point (fa, Sc) from the 
origin. The angle which the lines of force at {8a, 8c) make with 
the axis of NS will be the error due to excentricity. Call this angle 
€, then, 
_ force in direction WE 
^ force in direction NS ’ 
IL 
F, 
say . 
