ON STANDARDS OF ELECTRICAL RESISTANCE. 119 
axis, the couple exerted on a magnetic needle of the moment ml, when deflected 
2 
to the angle d, will be “ys 
The equal and opposite couple caused by the earth’s magnetism will be 
Hmlsind. Hence 
ml cos d. 
1’? V 
4k? R 
LV 
THiAdidGt “oi | kok te Rw tinea (10) 
an equation from which the earth’s magnetic force and the moment of the sus- 
pended magnet have been eliminated, and by which the absolute resistance 
(R) can be calculated in terms of the length, L, the velocity, V, the radius, &, 
and the deflection, d. The resistance thus calculated is expressed in electro- 
magnetic absolute units, because equation (10) is a simple consequence of equa- 
tions (1), (3), and (5)—fundamental equations in the electromagnetic system. 
The essence of Professor Thomson’s method consists in substituting, by aid 
of the laws of electromagnetic induction, the measurements of a velocity and 
a deflection for the more complex and therefore less accurate measurements 
of work and force required in the simple fundamental equations. But, how- 
ever simple in theory the method may be, the practical determination of the 
absolute resistance of a conductor by its means required great care and very 
numerous precautions,—some of an obvious character, while the need of others 
only became apparent during the course of the experiments. 
The apparatus consisted of two circular coils of copper wire, about one foot 
in diameter, placed side by side, and connected in series ; these coils revolved 
round a vertical axis, and were driven by a belt from a hand-winch, fitted 
with Huyghens’ gear to produce a sensibly constant driving-power. A small 
magnet, with a mirror attached, was hung in the centre of the two coils, and the 
deflections of this magnet were read by a telescope from the reflection of a scale 
in the mirror. A frictional governor controlled the speed of the revolving 
coil. The details and a drawing of the apparatus are given in Appendix 
D. and Plate VI.; but a short account may fitly be given here of the points 
of chief practical importance, the difficulties encountered, and the improve- 
ments still desirable. 
It is essential that the dimensions of the coil be very accurately known, 
that the axis round which it revolves should be truly vertical, and that, except 
in the coil itself, no currents affecting the position of the magnet be induced in 
any part of the apparatus. To measure the angular deflection the distance 
of the scale from the mirror is required, and the scale must be truly parallel 
to the mirror when the magnet is undeflected, or, in other words, when the 
coil is at rest. All these conditions were fulfilled without difficulty; but 
the scale by the reflection of which the deflections were measured was, 
towards the end of the experiments, found not to be very accurately divided ; 
and although a correction for this inaccuracy has been applied in the caleu- 
lations, an improvement can in future experiments be effected by the use of 
a more perfect scale. The magnet was suspended by a single silk fibre, eight 
feet long, inside a wooden case, and by suitable adjustments was brought very 
carefully to the centre of the coils. The whole suspended system was so 
screened from currents of air, and so well protected from vibration, that when 
the coil revolved at its full speed of 350 revolutions per minute, the reflection 
in the mirror was as clear and undisturbed as when the coil was at rest. 
The torsion of the long fibre was determined by experiment, and the slight 
tan d= 
or 
