468 MR JOHN ALLAN BROUN ON THE BIFILAR MAGNETOMETER, 
4, If we now consider the wire BD in the bifilar arrangement, and suppose it 
moveable round an axis at 0, so that mn which, when the wires were vertical. 
was parallel to OD, still remains parallel to OD, and we then turn B round the 
axis 0, so that mn shall be in the same line as AB; the moment of this twist 
through the angle v, for both wires, in turning the magnet round O, must be 
added to equation (1), and we have, if w = 90°, 
Wab . 
mX = Teos 7 BY + 2pu : , : (3). 
= Gsinv + 2mX sin 0, , , : (4). 
Wab 
where G =~ 
1 cos 7 
If we assume 
mX = G sin v’, : ' : (5). 
neglecting the variation of 7, we have 
vty 


QmX =GoosT~sin(v—v), . . (6). 
Whence, approximately, 
gin (oat) SO oad wild 51898 CGY 
If sin (v—v’)=tan B, then, 
mX = G (sin v — cos v tan 8) = fone since (v' =v) (8). 
and, ce ee | VC mmua na e paRS  ( 
whereas by equation aes SHENe PAO Me et ke ee ee 
If we know the torsion force of the wires, @ may always be computed from 
equation (7). The following experiments have been made to determine the pro- 
bable value of (. 
5. Torsion Force of Wires.—Silver wire used in Grubb’s bifilar, 0-007 inch dia- 
meter ; magnet suspended whose moment = m (= 9-0 English units approxi- 
mately), and weight = idl when it was found that 1° of torsion gave ©’ = 1-56. 
If v = 60°, then by equation (7), 
v—y = 5° 22’ 
6. This implies an error in the unit coefficient so much greater than is shown 
by the different methods of determining it, that I made the following experiments 
for its verification. The same magnet suspended with the same wire as bifilar, 
» = 47° 47’ (weight = W), magnet at right angles to the magnetic meridian; one 
wire was turned through angles of 10° right and left ; the corresponding changes 
of scale reading were found, for 1° of torsion = 1-65; therefore, for two wires and 
for 47° 47’ of torsion, 7 — v = 2° 376 nearly. By equation (7) we find, 
ev = 2° 216, 

