Relations between Electrical Measurements. 457 



we can measure the current and electromotive force, or even the 

 ratio of these magnitudes, we should, ipso facto, have measured 

 the resistance of the circuit. The methods by which this ratio 

 has been measured, founded on the laws of electromagnetic in- 

 duction, are fully described in Appendix D (Brit. Assoc. Re- 

 ports, p. 163). Other methods may be founded on the measure- 

 ment of currents and electromotive forces described in 18, 19, 

 20, 27, and 28. Lastly, a method founded on the gradual 

 loss of charge through very great resistances will be found in 

 Part IV. (45). The equation (25) there given for electrostatic 

 measure is applicable to electromagnetic measure when the 

 capacity and difference of potentials are expressed in electro- 

 magnetic units. 



30. Electric Resistance in Electromagnetic Units is measured 

 by an Absolute Velocity. — The dimensions of R are found, by 



comparing those of E and C, to be ^, or those of a simple velo- 

 city. This velocity, as was pointed out by Weber, is an absolute 

 velocity in nature, quite independent of the magnitude of the 

 fundamental units in which it is expressed. The following illus- 

 tration, due to Professor Thomson, will show how a velocity may 

 express a resistance, and also how that expression may be inde- 

 pendent of the magnitude of the units of time and space. 



Let a wire of any material be bent into an arc of 57^° with 

 any radius, k. Let this arc be placed in the magnetic meridian 

 of any magnetic field, with a magnet of any strength freely sus- 

 pended in the centre of the arc. Let two vertical wires or rails, 

 separated by a distance equal to h, be attached to the ends of 

 the arc ; and let a cross piece slide along these rails, inducing 

 a current in the arc. Then it may be shown that the speed 

 required to produce a deflection of 45° on the magnet will mea- 

 sure the resistance of the circuit, which is assumed to be con- 

 stant. This speed will be the same whatever be the value of £, 

 or the intensity of the magnetic field, or the moment of the 

 magnet. In this form the experiment could not be easily car- 

 ried out ; but if a length, I, of wire be taken and rolled into a 

 circular coil at the radius k> and the distance between the ver- 



k 2 

 tical rails be taken equal to -j) then, if the resistance of the cir- 

 cuit be the same as in the previous case, the deflection of 45° will 

 be produced by the same velocity in the cross piece, measuring 

 that resistance ; or, generally, if the distance between the rails 



be p y, then p times the velocity required to produce the unit 



deflection (45°) will measure the resistance. The truth of this 

 Phil Mag. S. 4. Vol 29. No. 198. June 1865. 2 H 



