34 
deflected from its position of equilibrium and then allowed 
to vibrate round a vertical axis, it will be seen through 
the small hole to pass and re-pass the nearer scratch, 
and an observer keeping his eye in the same plane as 
the scratches can easily tell without sensible error the 
instant, when the magnet passes through the position of 
equilittium. Or, a line may be drawn across the bottom 
of the box so as to join the two scratches, and the ob- 
server keeping his eye above the magnet and in the piane 
of the scratches notes the instant when the magnet going 
in the proper direction is just parallel to the horizontal 
line. The operator should deflect the magnet by bring- 
ing a small magnet near to it, taking care to keep the small 
deflecting magnet always as nearly as may be with its length 
in an east and west line passing through the centre of 
the suspended magnet. If this precaution be neglected 
the magnet may acquire a pendulum motion about the 
point of suspension, which will interfere with the vibra- 
tory motion in the horizontal plane. When the magnet 
has been properly deflected and left to itself, its range 
of motion should be allowed to diminish to about 
3° on either side of the position of equilibrium be- 
fore observation of its period is begun. When the 
amplitude has become sufficiently small, the person ob- 
serving the magnet says sharply the word “Now,” when 
Fic. 2. 
the nearer pole of the magnet is seen to pass the plane 
of the scratches in either direction, and another ob- 
server notes the time on a watch having a seconds 
hand. With a good watch having a centre seconds 
hand moving round a dial divided into quarter-seconds, 
the instant of time can be determined with greater accu- 
racy in this way than by means of any of the usual 
appliances for starting and stopping watches, or for regis- 
tering on a dial the position of a seconds hand when a 
spring is pressed by the observer. The person observing 
the magnet again calls out “ Now” when the magnet has 
just made ten complete to and fro vibrations, again after 
twenty complete vibrations, and, if the amplitude of vibra- 
tion has not become two small, again after thirty ; and the 
other observer at each instant notes the time by the watch. 
By a complete vibration is here meant the motion of the 
magnet from the instant when it passes through the position 
of equilibrium in either direction, until it next passes through 
the position of equilibrium going in the same direction. 
The observers then change places and repeat the same 
operations. In this way a very near approach to the true 
period is obtained by taking the mean of the results of a 
sufficient number of observations, and from this the value 
of the product of # and H can be calculated. 
NATURE 
[Wov. 9, 1882 
For a small angular deflection @ of the vibrating 
magnet from the position of the equilibrium the equation 
of motion is 
MER GS, 
2 x 
where » is the moment of sits of the vibrating magnet 
round an axis through its centre at right angles to its 
length. The solution of this equation is 
6=Asin$ af 2H — Bh 
fod 
and therefore for the period of oscillation 7 we havé 
iS ay yn 
m LH 
Hence we have 
Ele le 
T? 
Now, since the thickness of the magnet is small compared 
2 
with its length, if WV” be the mass of the magnet p is W, 
and therefore 
an PW 
mH = re (3) 
combining this with the equation (1) already found we 
get for the arrangement shown in Fig. 1. 
2 n*(° — 1°)? Wtan 6 
3 
Mm = : 
LP 
(4) 
and 
8 mlrW 
3° T?(72= Fy tan 0 - G) 
If either of the other two arrangements be chosen we 
have from equations Sloss and (3) 
P+ ?)i Wtand. . 
H2= 
aC 6) 
and : 
cages wl Ww (7) 
3 (7? +/)i T* tan 6 
Various Een which are not here made ure of 
course necessary in a very exact determination of H/. 
The virtual length of the magnet, that is, the distance 
between its poles or ‘‘centres of gravity” of magnetic 
polarity, should be determined by experiment: and allow- 
ances should be made for the magnitude of the arc of 
vibration ; the torsional rigidity of the suspension fibre 
of cocoon silk of the magnetometer in the deflection ex- 
periments, and of the suspension fibre of the magnet in 
the osciJlation experiments ; the frictional resistance of 
the air to the motion of the magnet ; the virtual increase 
of inertia of the magnet due to motion of the air in the 
chamber ; and the effect of induction in altering the mo- 
ment of the magnet. The correction for an arc of oscil- 
lation of 6° is a diminution of the observed value of 7 of 
only gy per cent., and for an arc of 10° of 3}, per cent. 
Of the other corrections the last is no doubt the most 
important; but even its amount for a magnet of glass- 
hard steel, nearly saturated with magnetism, and in a 
field so feeble as that of the earth, must be very small. 
The deflection-experiments are, as stated above, to be 
performed with several magnets, and when the period of 
oscillation of each of these has been determined, the magne- 
tometer should be replaced on its stand, and the deflection 
experiments repeated, to make sure that the magnets have 
not changed in strengthin the mean time. The length of 
each magnet is then to be accurately determined in centi- 
metres, and its weight in grammes; and from these data 
and the results of the experiments, the values of #7 and of 
#1 can be found for each magnet by the formulas investi- 
gated above. Equation (5) is to be used in the calcula- 
tion of 7 when the arrangements of magnetometer and 
deflecting magnet, shown in Fig. 1, is adopted, equation 
(7), when that shown in Fig. 2 is adopted. 
H? 
