Nov. 9, 1882 | 
NATURE 
22 
Pere) 
point at right angles to the direction in which a long thin 
magnet hung by a single silk fibre there places itself. 
One of these magnets is placed, as shown in Fig. 1, with 
its length in that line, and at such a distance that a 
convenient deflection of the needle is produced. This 
deflection is noted and the deflecting magnet turned end 
for end, and the deflection again noted. Make in the 
same way a pair of observations with the magnet at the 
same distance on the opposite side of the magnetometer, 
and take the mean of all the observations. These de- 
flections from zero ought to be as nearly as may be the 
same, and if the magnet is properly placed, they will 
exactly agree ; but the effect of a slight error in placing 
the magnet will be nearly eliminated by taking the mean 
of all the deflections as the deflection of the magnet for 
that position. The exact distance in cms. of the centre 
of the deflecting magnet from the mirror is also noted. 
The same operation is gone through for each of the 
magnets, which are carefully kept apart from one another 
during the experiments. The results of each of these 
experiments give an equation involving the ratio of the 
magnetic moment of the magnet to the value of H. Thus 
if #z denote the magnetic moment of the magnet, 7’ the 
magnetic moment of the needle, 27 the distance of the 
centre of the magnet from the centre of the needle, 27 the 
distance between the poles of the magnet which, for a 
uniformly magnetised magnet of the dimensions stated 
Fic. 1. 
above is nearly enough equal to its length, and 2/7’ the 
distance between the poles of the needle, 7, /, and /’ 
being all measured in cms., we have for the repulsive force 
(denoted by F in Fig. 1) exerted on the blue’ pole of the 
needle by the blue pole of the magnet, supposed nearest to 
the needle, as in Fig. 1, the value of = te ! 
21° 21 (r—ly* 
since the value of 7’ is small compared with 2 Similarly 
for the attraction exerted on the same pole of the needle 
by the red pole of the magnet, we have the expression 
m m' I 
2l° 20° (r+ly 
by the magnet on the blue pole of the needle is 
Hence the total repulsive force exerted 
, 
= els 2 8= A) Us ete De 
all ((r—22 +225 i CTD 
Proceeding in a precisely similar manner, we find 
that the magnet 7 exerts an attractive force equal to 
ip ee The needle 
i CD 
is therefore acted on by a couple which tends to turn it 
round the suspending fibre as an axis, and the amount of 
this couple, when the angle of deflection is 9, is plainly 
or 72 
m on the red pole of the magnet. 
equal to 22m’ cos 6. But for equilibrium this 
q q 
2a 
Cay 
couple must be balanced by mH sin 8; hence we have 
the equation :— 
m _ (7 — ~)? 
ese () 
HT 27 
The angle 6 is to be measured thus :—The number of 
divisions of the scale which measures the deflection 
divided by the number of such divisions in the distance 
of the scale from the mirror, is, if the scale is placed 
. tan 6 
© The convention according to which magnetic polarity of the same kind 
as that of the earth’s northern regions is called blue, and magnetic polarity 
of the same kind as that of the earth’s southern regions is called red, is here 
dopted. ‘he letters B, R, 4, vin the diagrams denote blue and red. 
as described above in the magnetic north and south line, 
equal to tan 26. 
Instead of in the east and west horizontal line through 
the centre of the needle, the magnet may be placed, as 
represented in Fig. 2, with its length east and west, and its 
centre in the horizontal north and south line through the 
centre of the needle. If we take 7, 7’, /,/, and r to have 
the same meaning as before, we have for the distance of 
either pole of the magnet from the needle, the expression 
72 +2. Let us consider the force acting on one pole, 
say the red pole of the needle. The red pole of the 
magnet exerts on it a repulsive force, and the blue pole an 
attractive force. Each of these forces has the value 
m nm I 
22 2l PAP 
equivalent toa single force, F, ina line parallel to the mag- 
net, tending to pull the red pole of the needle towards the 
left. The magnitude of this resultant force is plainly 
5 i dice mm d 
a2) Pt ers ey 
it can be shown that the action of the magnet on the 
red pole of the needle is a force of the same amount 
tending to pull the blue pole of the needle towards the right. 
The needle is, therefore, subject to no force tending to 
produce motion of translation, but simply to a “couple” 
tending to produce rotation. The magnitude of this 
couple when the needle has been turned through an angle 
ee 2iscosd a If there be 
meee cae 
equilibrium for the deflection @, this couple must be 
balanced by that due to the earth’s horizontal force, 
But the diagram shows that they are 
In the same way 
cos 6. 
which, as before, has the value #’H sin 6. Hence 
equating these two couples we have— 
m F 
— = (r?2-+ /*)? tan 0. 2 
Mm (2+ 2) @) 
Still another position of the deflecting magnet relatively 
to the needle may be found a convenient one to adopt. 
The magnet may be placed still in the east and west line, 
but with its centre vertically above the centre of the needle. 
The couple in this case also is given by the formula just 
found, in which the symbols have the same meaning as 
before. 
The greatest care should be taken in all these experi- 
ments, as well as in those which rollow, to make sure that 
there is no movable iron in the vicinity, and the instru- 
ments and magnets should bekept at a distance from any 
iron nails or bolts there may be in the tables on which 
they are placed. 
We come now to the second operation, the determina- 
tion of the period of oscillation of the deflecting magnet 
when under the influence of the earth’s horizontal force 
alone. The magnet is hung in a horizontal position in a 
double loop formed at the lower end of a single fibre of 
unspun silk, attached by its upper end to the roof of a 
closed chamber. A box about 30 cms. high and 15 cms. 
wide, having one pair of opposite sides, the bottom and the 
roof made of wood, and the remaining two sides made of 
plates of glass, one of which can be slided out to give access 
to the inside of the chamber, answers very well. The fibre 
may be attached at the top to a horizontal wire which can 
be turned round from the outside so as to wind up or let 
down the fibre when necessary. The suspension-fibre 
is so placed that two vertical scratches, made along the 
glass sides of the box, are in the same plane with the 
magnet when the magnet is placed in its sling, and the 
box is turned round until the magnet is at right angles to 
the glass sides. A paper screen with a small hole in it is 
then set up at a little distance in such a position that the 
hole is in line with the magnet, and therefore in the 
same plane as the scratches. The magnetometer 
should be removed from its stand and this box and sus- 
pended needle put in its place. If the magnet be now 
