Page:The New International Encyclopædia 1st ed. v. 06.djvu/874

ELECTRICITY. plates: and, further, wherever they strike any solid obstacles. disturbances in the ether are produced, which in turn cause other radiation. These were discovered by Röntgen and are called "Röntgen rays" or "X-rays" (q.v.). The best discussion of cathode rays is given in Les rayons cathodiques, by Villard (Paris, 1900),

Laws or Steady Electric Currents. Advantage is taken of the action of an electric current on a magnet to define a 'unit current.' A unit pole in magnetism is defined as such a pole that, if two of then are at the distance of one centimeter apart in a vacuum, the force between them will be one dyne. A unit current is defined as being one of such intensity that, if it is passing through a wire bent into the form of a circle of radius one centimeter, the force due to it on a unit pole at the centre of the circle is 2π. where π = 3.14159. This unit is called the 'C. G. S. electromagnetic unit' and it has been shown by experiment that its ratio to the 'C. G. S. electrostatic unit' is 3 × 10°. A current of intensity 2 around the same circular circuit would produce the force 4π on a unit pole at the centre: and experiments show that if a current of intensity i is passed around a circular circuit of radius r centimeters, the force on a unit pole at the centre is

$$\frac{2 \pi i}{r}$$

If there are n turns of wire making up a flat coil of radius r, the force on a unit magnetic pole placed at the centre is

$$\frac{2 \pi n i}{r}$$

The ‘dimensions’ of a magnetic pole are $$\mathrm{M}^{\frac{1}{2}} \mathrm{L}^{\frac{1}{2}} \mathrm{T}^{-1} \mu^{\frac{1}{2}}$$ (see Magnestism); and since the force on a pole of strength m due to an elec- tric current as just described is $$\frac{m2\pi i}{r}$$

dimensions of this fraction must he those of a force, ie. $$\mathrm{MLT}^{-2}$$, Since the dimensions of m are given and r is a length, i, the current-strength has the dimensions $$M^{\frac{1}{2}} L^{\frac{1}{2}} T^{-1} \mu^{\frac{1}{2}}$$, Therefore, on the C. G. S. electromagnetic system, an electric quantity has the dimensions $$M^{\frac{1}{2}} L^{\frac{3}{2}} T^{-1} \mu^{\frac{1}{2}}$$ $$\mu$$ in these expressions represents the dimensions of magnetic permeability. or inductivity, as it is called.

If a small magnetic needle is pivoted at the centre of a coil with its axis in the plane of the coil, there will be a couple (q.v.) acting on the needle tending to make it turn at right angles to the coil. This couple may be balanced against a couple due to the earth's field of magnetic force; and in this manner the current-strength i can be measured in terms of the earth's field of force. Such an instrument is called a ‘galvanometer.’ because it measures a steady electric current. By means of it Faraday’s laws of electrolysis may be verified. The number of grams of any substance liberated each second when a unit current passes through an electrolyte is called the ‘electro-chemical equivalent’ of that substance. The values of this quantity for some elements is given in the following table:

Hydrogen 0.000104 Oxygen... 0.000829 Copper. 0.003290 Zine. . 0.003385 Silver... 0.011180

The number of tubes of magnetic induction (see Magnetism) which pass through any coil of wire when it carries a unit electric current is called its ‘coefficient of self-induction’; and the number of tubes which pass through a second coil of wire owing to this unit current in the first coil is called the ‘coeficient of mutual induction’ of the two coils, It may be proved that this same number would pass through the first coil if there were a unit current in the second. These coefficients of self and mutual induction—sometimes called simply ‘the induction’ —are mathematical functions of the size and shape of the coils, of their relative positions, and of the surrounding medium, but are independent of the currents. If L, is the coefficient of self-induction of one coil, and M that of mutual induction between it and a second coil, and if currents of intensities $$i_1$$, and $$i_2$$, respectively, are flowing in the two coils, the number of tubes of induction through the first coil is $$\mathrm{L}i_1 + \mathrm{M}i_2.$$

If the electro-motive force applied to the terminals of a metal wire are varied, and the corresponding current measured. it is observed that one hears a constant relation to the other. If i is the current strength and E the electro-motive force, E=Ri, where R is a constant for the given wire, and is found to vary directly as the length of the wire and inversely as its cross section, and to be different for different metals or for the same metal at different temperatures. Ri is called the ‘electrical resistance’ of the given wire at whose terminals the E. M. F. E. is applied. This law connecting E. R. and i is called 'Ohm's law.’

The heating effect in the conductor has been shown to he Eit; and so this may be written Rt, showing that the effect is the same for a plus as for a minus current. i.e. it is independent of the direction of the current.

Measurement of Electrical Quantities. As already explained, the intensity of an electrical current may be measured in terms of the earth's magnetic force by a galvanometer. and the value of this force may be determined by suitable measurements, (See Magnetisim.) Thus the numerical value of any current on the C. G. S. electromagnetic system may be obtained. (There are other and better methods, depending upon the attraction of two parallel coils of wire carrying currents.) The intensities of two currents may be compared by making them pass through a voltameter (q.v.), and then applying Faraday’s first law of electrolysis. To measure the electrical resistance of a conductor the simplest method—at least theoretically—is to measure by means of a calorimetric experiment the heating effect in it produced by passing through it a current whose intensity is measured. The heating effect is $$i^2\mathrm{R}t$$; and, as both i and t are easily obtained, R can be calculated. This will be its numerical value on the ‘C. G. S. electro-magnetic system.’ To compare the electrical resistances of different conductors. the simplest and most accurate method is the use of ‘Wheatstone’s bridge’ (q.v.). If the resistance of a given conductor is known. and if the current produced through it by any E. M. F. can be measured, the numerical value of this E. M. F. is given by Ohm's law. Methods for the comparison of different electromotive forxes are desxribed in all text-books on physics and electrieity. Owing to the inconvenient magnitnde of the units of resistance and of electro-motive force on the C. G. S. electro-