meter deflection is the same whether the key be depressed or not. When this condition of things is attained the battery resistance is balanced by those of the other three arms. (Not a reliable method.)

362. Measurement of Capacity of a Condenser. The capacity of a condenser may be measured by comparing it with the capacity of a standard condenser-such as the microfarad condenser shown in Fig. 106,-in one of the following ways:

(a) Charge the condenser of unknown capacity to a certain potential; then make it share its charge with the condenser of known capacity, and measure the potential to which the charge sinks; then calculate the original capacity, which will bear the same ratio to the joint capacity of the two as the final potential bears to the original potential.

(b) Charge each condenser to equal differences of potential, and then discharge each successively through a ballistic galvanometer (Art. 204), when the sine of half the angle of the first swing of the needle will be proportional in each case to the charge, and therefore to the capacity.

(c) Charge the two condensers simultaneously from one pole of the same battery, interposing high resistances in each branch, and adjusted so that the potential rises at an equal rate in both; then the capacities are inversely proportional to the resistances through which they are respectively being charged.

(d) Another method, requiring no standard condenser, is as follows:-Allow the condenser, whose capacity is to be measured, to discharge itself slowly through a wire of very high resistance. The time taken by the potential to fall to any given fraction of its original value is proportional to the resistance, to the capacity, and to the logarithm of the given rraction.

363. Resistance Expressed as a Velocity.—It will be seen, on reference to the table of "Dimensions" of electromagnetic units (Art. 324), that the dimensions of resistance are

given as LT-1, which are the same dimensions (see Art. 258) as those of a velocity. Every resistance is capable of being expressed as a velocity. The following considerations may assist the student in forming a physical conception of this:Suppose we have a circuit composed of two horizontal rails

(Fig. 134), CS and DT, I centim. apart, joined at CD, and completed by means of a sliding piece AB. Let this variable circuit be placed in a uniform magnetic field of unit intensity, the lines of force being directed vertically downwards through the circuit. If, now, the slider be moved along towards ST with a velocity of n centimetres per second, the number of additional lines of force embraced by the circuit will increase at the raten per second; or, in other words, there will be an induced electromotive force (Art. 394) impressed upon the circuit, which will cause a current to flow through the slider from A to B. Let the rails have no resistance, then the strength of the current will depend on the resistance of AB. Now let AB move at such a rate that the current shall be of unit strength. If its resistance be one "absolute" (electromagnetic) unit it need only move at the rate of 1 centim. per second. If its resistance be greater it must move with a proportionately greater velocity; the velocity at which it must move to keep up a current of unit strength being numerically equal to its resistance. The resistance known as 66 one ohm " intended to be 109 absolute electromagnetic units, and therefore is represented by a velocity of 109 centimetres, or ten million metres (one earth-quadrant) per second.

is

364. Evaluation of the Ohm.-The value of the ohm in absolute measure was determined by a Committee of the British Association in London in 1863. It being impracticable to give to a horizontal sliding-piece so high a velocity as was necessitated, the velocity which corresponded to the resistance of a wire was measured in the following way :-A ring of wire (of many turns), pivoted about a vertical axis, as in Fig. 135, was made to rotate very rapidly and uniformly. Such a ring in rotating cuts the lines of force of the earth's magnetism. The northern half of the ring, in moving from west toward east.

will have (see Rule Art. 395) an upward current induced in it, while the southern half, in crossing from east toward west, will have a downward

S

W

Fig. 135.

E

current induced in it. Hence the rotating ring will, as it spins, act as its own galvanometer if a small magnet be hung at its middle; the magnetic effect due to the rotating coil being proportional directly to -N the horizontal component of the earth's magnetism, to the velocity of rotation, and to the number of turns of wire in the coil, and inversely proportional to the resistance of the wire of the coils. Hence, all the other data being known, the resistance can be calculated and measured as a velocity. The

existing ohms or B.A. units were constructed by comparison with this rotating coil; but there being some doubt as to whether the B.A. unit really represented 109 centims. per second, a redetermination of the ohm was suggested in 1880 by the British Association Committee.

"

364 (bis). The Legal Ohm-At the International Congress of Electricians in Paris 1881 the project for a redetermination of the ohm was endorsed, and it was also agreed that the practical standards should no longer be constructed in German silver wire, but that they should be made upon the plan originally suggested by Siemens, by defining the practical ohm as the resistance of a column of pure mercury of a certain length, and of one millimetre of cross-section. The original "Siemens' unit was a column of mercury one metre in length, and one square millimetre in section, and was rather less than an ohm (0°9415 B.A. unit). Acting on measurements made by the best physicists of Europe, the Paris Congress of 1884 decided that the mercury column representing the legal ohm shall be 106 centimetres in length. [Lord Rayleigh's determination gave 106'21 centimetres of mercury, as representing the true theoretical ohm (= 109 absolute units).] Our old B. A. ohm is only o'9887 of the new legal ohm; and our old volt is o'9887 of the legal volt.

NOTE ON THE RATIO OF THE ELECTROSTATIC TO THE ELECTROMAGNETIC UNITS.

365. If the student will compare the Table of Dimensions of Electrostatic Units of Art. 258 with that of the Dimensions of Electromagnetic Units of Art. 324, he will observe that the dimensions assigned to similar units are different in the two systems. Thus, the dimensions of "Quantity" in electrostatic measure are M L T-1, and in electromagnetic measure are Mt Lt. Dividing the former by the latter we get LT-1, a quantity which we at once see is of the nature of a velocity. This velocity occurs in every case in the ratio of the electrostatic to the electromagnetic measure of every unit. It is a definite concrete velocity, and represents that velocity at which two electrified particles must travel along side by side in order that their mutual electromagnetic attraction (considered as equivalent in moving to two parallel currents) shall just equal their mutual electrostatic repulsion, see Art. 337. This velocity, "v," which is of enormous importance in the electromagnetic theory of light (Art. 390), has been measured in several ways.

(a) Weber and Kohlrausch measured the electrostatic unit of quantity and compared it with the electromagnetic unit of quantity, and found the ratio v to be 3'1074 X 1010 centims. per second. (b) Sir W. Thomson compared the two units of potential and found

=

(c) Professor Clerk Maxwell balanced a force of electrostatic attraction against one of electromagnetic repulsion, and found

(d) Professors Ayrton and Perry measured the capacity of a condenser electromagnetically by discharging it into a ballistic galvanometer, and electrostatically by calculations from its size, and found

(e) Professor Joseph J. Thomson compared the capacity of a condenser as measured electrostatically by calculation and as measured electromagnetically on a Wheatstone's bridge, and deduced

ข

= 2'963 X 1010. The velocity of light is believed to be = 2'9992 X 1010; or, according to G. Forbes's latest determination,

the velocity of red light is

29826 X 1010.

CHAPTER VII.

HEAT, LIGHT, AND WORK, FROM ELECTRIC CURRENTS.

LESSON XXXI.—Heating Effects of Currents.

366. Heat and Resistance.-A current may do work of various kinds, chemical, magnetic, mechanical, and thermal. In every case where a current does work that work is done by the expenditure of part of the energy of the current. We have seen that, by the law of Ohm, the current produced by a given battery is diminished in strength by anything that increases the external resistance. But the strength of the current may be diminished, in certain cases, by another cause, namely, the setting up of an opposing electromotive force at some point of the circuit. Thus, in passing a current through a voltameter (Art. 214) there is a diminution due to the resistance of the voltameter itself, and a further diminution due to the opposing electromotive-force (commonly referred to as "polarisation") which is generated while the chemical work is being done. So, again, when a current is used to drive an electromagnetic motor (Art. 375), the rotation of the motor will itself generate a back-current, which will diminish the strength of the current. Whatever current is, however, not expended in this way in external work, is frittered down into heat, either in the battery or in some part of the circuit, or in both. Suppose a quantity of electricity to be set flowing round a closed circuit. If there were no resistance to stop it it would