Relations between Electrical Measurements. 449 



pended in the centre of the circle will turn with the end which 

 points to the north away from the observer. This may be taken 

 as the simplest case, as every part of the circuit is at the same 

 distance from the magnet, and tends to turn it the same way. 

 The force is proportional to the moment of the magnet, to the 

 strength of the current as defined by § 15, to its length, and 

 inversely to the square of its distance from the magnet. 



Let the moment of the magnet be ml, the strength of the cur- 

 rent C, the radius of the circle k, the number of times the cur- 

 rent passes round the circle n, the angle between the axis of the 

 magnet and the plane of the circle 6, and the moment tending to 

 turn the magnet Gr, then 



G =mlC.27rnJc^ cos d, (8) 



which will be unity if ml, C, k, and the length of the circuit be 

 unity, and if 0=0°, 



The unit of current founded on this relation, and called the 

 electromagnetic 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 mag- 

 netism, and Gthe moment of this on the magnet, G = mlK sin 6, 

 whence the strength of the current 



C = ^-Htan0, (9) 



where k 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 6 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 galvano- 

 meter. The instrument called a sine galvanometer may also be 

 used, provided the coil is circular. The equation is similar to 

 that just given, substituting sin 6 for tan 6. 



To find the dimensions of C, we must consider that what we 

 observe is the force acting between a magnetic pole, m, and a cur- 

 rent of given length, L, at a given distance, L p and that this 



force = T a . Hence the dimensions of C, an electric current 



1 , L*M* 

 thus measured, are —7^ — • 



19. Measurement of Electric Currents by their mutual action 



