467 
XX.— The Bijilar Magnetometer, its Errors and Corrections, including the Deter- 
mination of the Temperature Coefficient for the Bifilar employed in the Colonial 
Observatories. By JoHn ALLAN Broun, F-.R.S., Director of the Trevandrum 
Observatory. 
(Read 4th February 1861.) 
In 1845, a paper by me on the balance magnetometer was read to the Royal 
Society of Edinburgh (see Trans. vol. xvi. p. 67), which contained an examination 
of some of the difficulties to be considered and overcome in relation to that in- 
strument. No similar examination has yet appeared, as far as [am aware, of 
the bifilar magnetometer. When it is considered that the value of the results 
obtained from this instrument in so many observatories is dependent on an exact 
knowledge and elimination or correction of its errors ; and, as will appear here- 
after, that the temperature coefficients employed in the discussion of the Colonial 
observations are in some cases so erroneous that the uncorrected observations 
would have been nearer the truth than after correction, the following communi- 
cation may not appear unnecessary. 
2. The bifilar magnetometer, as devised by Dr Luoyp, was employed in all the 
British and Colonial observatories with one exception; a description of the in- 
strument will be found in the introductions to the “ Makerstoun Observations,” 
forming part of the Society’s Transactions. 
3. It is well known that if W represent the weight of the magnet and its appen- 
dages, 7 the magnetic moment, X the horizontal force of the earth’s magnetism, 
ithe length of the wires, a and 0 their intervals above and below, 7 the angle 
which they make with the vertical, v the angle of twist, and w the angle which 
the magnet makes with the magnetic meridian ; then, 
mxX sin u = 

Wad. 
Tos; 2% : ‘ ‘ie (ls) 
This, however, is on the supposition that the wires are lines without elasticity ; 
for if AC, BD, represent the vertical projections of the wires on the horizontal 
plane, then (to consider one wire only) it is evident that the 
upper end of the wire BD has turned through the angle v 
more than the lower end. Let us suppose that the wire BD 
is suspended alone with a weight equal _ , whose magnetic ‘ 
moment = m (or whose ratio to m is known); let the upper 
extremity of the wire be turned through the angle v, and 
the magnet be moved from the meridian through the angle 0, then, if the torsion 
force for unity of arc be p, we have 
p (v— 6) = mX sin 8, 
or, py=mX sind, . : i , . SAE 
VOL. XXII. PART III. OE 

