Ill —WNote on the Bifilar Magnetometer. By J. A. Brown, F.R.S. 
(Read 7th May 1877). 
In a paper on “The Bifilar Magnetometer, its Errors and Corrections,” 
&c., which appeared in the Transactions of the Royal Society of Edinburgh, 
vol. xxii. p. 467, it was shown that, in turning the apparatus which carries the 
upper extremities of the two wires through an angle exceeding by v that 
through which the lower extremities and the magnet are moved, the upper 
end of each wire is also turned through an angle greater by v than the lower 
end. The whole force acting on the magnet, to turn it from the meridian, is 
compounded of the bifilar and the unifilar torsion—only the former of which 
had been considered in the method issued by the Committee on Physics of the 
Royal Society of London for the instruction of directors of observatories. 
It was sought in the paper cited to show the change that the neglected 
forces would introduce into the expression for the unit coefficient, which was 
found to be 
k = cot (v + B) Ax, 
instead of 
k= cot oA, 
where Av is the arc value of one scale division of the instrument, and 6 is 
the variation of v due to the unifilar torsion. There were errors of copying, 
including omissions in the investigation given. I also remarked, after the 
paper was printed, that the value of & found was /ess than when the unifilar 
torsions were neglected (since cot (v + 8) < cot v); whereas all the deter- 
minations by other methods, in which the unifilar torsions were included, had 
shown a greater coefficient. 
Having had some time ago to re-examine questions connected with this 
instrument, I found that there was an error in the investigation, which I now 
desire to correct. It was assumed that the right hand side of equation (3) of 
the paper (equation (1) of this note) might be represented by G sin ov (where 
v > v), which cannot be allowed if v varies, especially as v is not small.* 
Let us suppose as before, that, in turning the torsion circle carrying the upper 
ends of the two wires, the horizontal line in which they lie is carried through 
an angle of 90° + v, by which means the suspended magnet and the horizontal 
line passing through the lower ends of the wires are carried through an angle 
of 90° (that is, the magnet is then at right angles to the magnetic meridian) ; 
* The applications of the formula found (Edinburgh Royal Society Transactions, xxii. p. 468, arts. 
5, 6, and 7) are not affected by this error. 
VOL. XXVIII. PART I. L 
