TRANSACTIONS OF THE SECTIONS. 9 
the ordinates from the June observations, to show the agreement of both series in 
the conclusion, that the maximum westerly declination occurs nearest noon at the 
Ἢ higher station. 
Observations. were made both in June and in August at the foot of the hill, but 
no greater difference from the simultaneous Makerstoun observations appeared than 
could be explained by errors of observation. 
On the Mechanical Compensation of the Bifilar and Balance Magnets for 
Variations of the Magnetic Moment with Temperature. | By J. A. Broun, 
FPLR.SE. 
The bifilar magnetometer consists of a magnet suspended by two wires or threads, 
by twisting which, the magnet is forced to a position at right angles to that which 
it would naturally occupy, namely, at right angles to the magnetic meridian. The 
equation of equilibrium between X, the earth’s horizontal magnetic force acting on 
m, the magnetic moment of the bar, and W, the weight of the magnet seeking the 
lower position, from which it has been raised by the twisting of the wires, is as 
follows : 
mX=W* sin v, 
where a is the interval of the wires, and / is their length, and v is the angle of twist. 
If we suppose X, W, and v to be constant, then the magnet may change its posi- 
tion from variations of m, a, and /, all of which vary with temperature. It is the 
elimination of changes of position due to the variations of these three quantities 
that is so essential to obtain from this instrument the variations of the horizontal 
magnetic force. I shall not enter upon the troublesome, not to say inexact pro- 
cesses which have been adopted in order to determine the variation of m with tem- 
perature: the changes due to variations of a and J are computed from the known 
coefficients of expansion of the metal which separates the wires, and of the metal of 
the wires. 
Differentiating the previous equation, and reducing, we find the coefficient, q, for 
the temperature correction to be 
qa + Qe—e’, 
m 
where 6 is the coefficient of expansion for the metal which separates the wires, brass ; 
and e’ is the coefficient of expansion for the wires, generally silver: since when brass 
and silver are the two metals, 6 is nearly equal to e’, we shall have 
Am 
erent 
where e may be supposed to represent the expansion of the interval of the wires at 
the top, the expansion of the length of the wires being compensated by the expan- 
sion of their interval below. We shall now make 
q=0 when pt ei 
m 
that is to say, when the interval of the wires at the top has a contraction coefficient 
equal to the value of Am for 1° Fahr. The physical explanation of this destruction 
Ὁ ἢ 
of ῳ is evident :—the contraction of the interval of the wires diminishes the force 
with which the north end of the magnet is kept from the north, while the reduction 
of the magnetism of the bar by the same increase of temperature diminishes the 
force with which it is pulled ¢o the north by the earth’s magnetism. 
The following is the process by which I obtain the required contraction :—Let the 
upper extremities of the wires be attached to the ends of two brass rods, which ap-— 
proach each other within an interval equal to the diameter of the lower wheel 
which separates'the wires, and let the other ends of the brass rods be fixed to a beam 
of wood, so that an increase of temperature will cause the free ends of the rods to 
approuch each other, by an amount equal to the difference of their expansion and 
that of the wooden beam to which they are fixed; the contraction required is ob- 
