140 nerort—1863. 
The unit of current founded on this relation, and called the electromag- 
netic unit, is therefore that current of which the unit of length placed along 
the circumference of a circle of unit radius produces a unit of magnetic force 
at the centre. 
The usual way of measuring C, the strength of a current, is by making it 
describe a circle about a magnet, the plane of the circle being vertical and 
magnetic north and south. Thus, if H be the intensity of the horizontal 
component of terrestrial magnetism, and G the moment of this on the mag- 
net, G=mlH sin 6, whence the strength of the current— 
ke? 
Qrn 
C= 
tan. 0,50 ah (surisleneat ae, en 
where & is the radius of the circle, n the number of turns, H the intensity 
of the horizontal part of the earth’s magnetic force as determined by the 
usual method, and @ the angle of deviation of the magnet suspended in the 
centre of the circle. As the strength of the current is proportional to the 
tangent of the angle 6, an instrument constructed on this plan is called a 
tangent galvanometer. The instrument called a sine galyanometer may 
also be used, provided the coil is circular. The equation is similar to that 
just given, substituting sin 6 for tan @. 
To find the dimensions of C, we must consider that what we observe is 
the force acting between a magnetic pole, m, and a current of given length, L, 
mCL 
3 
TMi 
aE 
19. Measurement of Electric Currents by their mutual action on one another. 
—Hitherto we have spoken of the measurement of currents as dependent on 
their action upon magnets; but this measurement in the same units can as 
simply be founded on their mutual action upon one another. Ampére has in- 
vestigated the laws of mechanical action between conductors carrying currents. 
He has shown that the action of a small closed circuit at a distance is the 
same as that of a small magnet, provided the axis of the magnet be placed 
normal to the plane of the circuit, and the moment of the magnet be equal 
to the product of the current into the area of the circuit which it traverses. 
Thus, let two small circuits having areas Aand A, be placed at a great distance 
D from each other in such a way that their planes are at right angles to each 
other, and that the line D is in the intersection of the planes. Now let cur- 
rents C and C, circulate in these conductors; a force will act between them 
tending to make their planes parallel, and the direction of the currents op- 
posite. The moment of this couple will be 
pe aa 8d) ch, y 
Dp? 
Hence the unit electric current conducted round two circuits of unit area 
in vertical planes at right angles to each other, one circuit being at a great 
distance, D, vertically above the other, will cause a couple to act between the 
at a given distance, L,, and that this force= Hence the dimensions of C, 
an electric current thus measured, are 
5s eee see 
1 ic A f: ity 
circuits of a magnitude Dp" The definition of the unit current (identical with 
the unit founded on the relations given in § 18) might be founded on this 
action quite independently of the idea of magnetism. 
