for resistance is the same as that for velocity; that in fact a resistance in electromagnetic measure is expressible as a velocity; and hence we may with propriety speak of a resistance of one ohm as a velocity of 109 centimetres per second.

The first experiments for the realization of the ohm were made by the British Association Committee, and later determinations have been made with varying results by experimenters in different parts of the world. The method used by the committee was one suggested by Sir W. Thomson, in which the current induced in a coil of wire revolving round a vertical diameter in a magnetic field was measured by the deflection of a magnetic needle hung at the centre of the coil. The principle of the method is exactly the same as that of the ideal method, with slider and bars, sketched above. According to the results of the committee the ohm is represented approximately by the resistance of a column of pure mercury 1048 centimetres long, one square millimetre in section, at the temperature o° C. Coils of an alloy of two parts of silver to one of platinum, which had a resistance of one ohm at a certain temperature, were issued by the committee as standards to experi

menters.

Concordant experiments by Prof. Rowland in America, by Lord Rayleigh and by Mr. Glazebrook at Cambridge, and by Messrs. Mascart, de Nerville, and Benoit in Paris, have shown that the B.A. unit is probably about 1.3 per cent. too small. A very careful determination by Lord Rayleigh and Mrs. H. Sidgwick gives '98677 earth-quadrant per second as its value.* Lord Rayleigh and Mrs. Sidgwick also measured the specific resistance of mercury

*Phil. Trans. R. S. 1883.

in terms of the B.A. unit.* Their result, together with their value of the B.A. unit gave 106°21 cms. as the length of a column of pure mercury of section I sq. mm. and temp. o°C. which has a resistance of 1 ohm.

A determination of the ohm in terms of the B.A. unit has recently been made by Messrs. L. Duncan, G. Wilkes, and C. T. Hutchinson at the Johns Hopkins University, Baltimore, with apparatus designed by Prof. H. A. Rowland. Their result is 9863 earth-quadrant per second = 1 B.A. unit, and this taken with a redetermination of the specific resistance of mercury made by the last-named two gentlemen,t gives 106 34 cms. as the length of the mercury column specified as above.

It has been agreed by the Congress of Electricians held at Paris in 1884, to adopt temporarily as the Legal Chm, a resistance equal to that of a column of pure mercury 106 cms. in length and one square millimetre in section, at the temperature of o°C. When a sufficient number of exact determinations of the ohm have been obtained the legal value will no doubt be brought into as close as possible accord with the true value.

It is obvious from equation (1) that if V and R, each initially one unit, be increased in the same ratio, C will remain one unit of current; but that if V be, for example, 108 C.G.S. units of potential, or one volt, and R be a resistance of 109 cms. per second, or one ohm, C will be one-tenth of one C.G.S. unit of current. A current of this strength-that is, the current flowing in a wire of resistance one ohm, between the two ends of which a difference of potential of one volt is maintained, has been adopted as the practical unit of current, and called * Phil. Trans. R. S. 1883. See also below, p. 242. Phil. Mag. Aug. 1889. See also below, p. 242. Ibid. July, 1889.

one ampere. Hence it is to be remembered one ampere is one-tenth of one C.G.S. unit of current.

The amount of electricity conveyed in one second by a current of one ampere is called one coulomb. This unit, although not quite so frequently required as the others, is very useful, as, for instance, for expressing the quantities of electricity which a secondary cell is capable of yielding in various circumstances. For example, in comparing different cells with one another their capacities, or the total quantities of electricity they are capable of yielding when fully charged, are very conveniently reckoned in coulombs per square centimetre of the area across which the electrolytic action in each takes place.

The magneto-electric machine we have imagined gives us a very simple proof of the relation between the work done in maintaining a current, the strength of the current, and the electromotive force producing it. In dynamics work is said to be done by a force when its place of application has a component motion in the direction in which the force acts, and the work done by it is equal to the product of the force and the distance through which the place of application of the force has moved in that direction. The rate at which work is done by a force at any instant is therefore equal to the product of the force and the component of velocity in the direction of the force at that instant. The work done in overcoming a resistance through a certain distance is equal by this definition to the product of the resistance and the distance through which it is overcome. Among engineers in this country the unit of work generally used, is one foot-pound, that is, the work done in lifting a pound vertically against gravity through a distance of one foot, and the unit rate of working is one horse-power, that is 33,000 foot-pounds per minute. The

weight of a pound of matter being generally different at different places, this unit of work is a variable one, and is not used in theoretical dynamics. In the absolute C.G.S. system of units, the unit of work is the work done in overcoming a force of one dyne through a distance of one centimetre, and is called one centimetre-dyne or one erg. The single word Activity has been used by Sir Wm. Thomson as equivalent in meaning to "rate of doing work," or the rate per unit of time at which energy is given out by a working system; and to avoid circumlocutions in what follows we shall frequently use the term in that sense.

We have seen above (p. 46) that every element of a conductor, carrying a current in a magnetic field, is acted on by a force tending to move it in a direction at right angles to the plane through the element, and the direction of the resultant magnetic force at the element, and have derived from the expression for the magnitude of the force a definition ( (2) p. 46) of unit current in the electromagnetic system. From these considerations it follows that a conductor in a uniform magnetic field, and carrying a unit current which flows at right angles to the lines of force, is acted on at every point by a force tending to move it in a direction at right angles to its length, and the magnitude of this force for unit length of conductor, and unit field, is by the definition of unit current equal to unity.

Applying this to our slider in which we may suppose a current of strength C to be kept flowing, say, from a battery in the circuit, let Z be the length of the slider, v its velocity, and I the intensity of the field; we have for the force on the moving conductor the value ILC. Hence the rate at which work is done by the electromagnetic action between the current and the field is IL Cdx/dt or IL Cv, and this must be equal to the rate at

which work would be done in generating by motion of the slider a current of strength C. But as we have seen above, ILv is the electromotive force produced by the motion of the slider. Calling this now E, the symbol usually employed to denote electromotive force, we have E C as the electrical activity, that is, the total rate at which electrical energy is given out in all forms in the circuit.

By Ohm's law this value for the electrical activity may, when the work done is wholly spent in producing heat, be put into either of the two other forms, namely, E2/R, or CR. In the latter of these forms the law was discovered by Joule, who measured the amount of heat generated in wires of different resistances by currents flowing through them. This law holds for every electric circuit whether of dynamo, battery, or thermoelectric arrangement.

We have, in what has gone before, supposed the slider to have no resistance comparable with the whole resistance in the circuit. If it have a resistance r, and R be the remainder of the resistance in circuit, the actual difference of potential between its two ends will not be I Lv or E, but E.R/(R+ r) (p. 83). The rate per unit of time at which work is given out in the circuit is however still E C, of which the part E C. r/(R+r) is given out in the slider, and the remainder, E C. R/(R + r), in the remainder of the circuit. In short, if V be the actual difference of potential, as measured by an electrometer, between two points in a wire connecting the terminals of a battery or dynamɔ, and C be the current flowing in the wire, the rate at which energy is given out is VC, or if R be the resistance of the wire between the two points, C2R.

The activity in the part of the circuit considered is