that a deflection of 25° indicated an amount of heat represented by 26°5; for the heat which produced the deflection of 25° was the sum of the two amounts represented separately by 20° and 6°.5. By a succession of steps of this kind, the calibration (as this process is called1) can be extended nearly to 90°.

This mode of investigation covers any want of proportionality which may exist in the production of thermo-electric currents, as well as in the proportionality of these currents to the deflections.

721. General Law for Magnetic Force due to a Current.-In every case, the magnetic force at a given point due to a current, can be computed by dividing the current into elementary portions, each sensibly straight, and compounding by the parallelogram of forces the effects due to these separate elements. The force due to each element is normal to the plane drawn through the element and the given point, and is proportional to C, sin 0, where C denotes the strength of the current, I the length of the element, r the distance between the element and the given point, and 6 the angle between the joining line and the element. The force at the centre of a single circular current of radius a is therefore C2 C2, and the force

a2

a

at the centre of a circular galvanometer-coil of n convolutions, if all can be regarded as in one plane and of the same radius a, is C2rn.

a

When a galvanometer needle is deflected, it is no longer in the plane of the coil, and this circumstance complicates the relation between current and deflection. Helmholtz has overcome this difficulty by placing the needle midway between two equal and parallel coils, whose distance apart is equal to the radius of either, the two being connected in series so that the same current flows through both. The lines of magnetic force in the intervening region can be shown to be very nearly straight.2

722. Effect of Instantaneous Current.-When the duration of a current is small in comparison with the time of vibration of the needle, and the total deflection small, the velocity which the current gives the needle is jointly proportional to the duration of the current and its average strength. It is, therefore, simply proportional to the

1 From its analogy to the calibration of a thermometer.

"A drawing of the lines will be found in Maxwell's Ele tricity and Magnetism, vol. ii. fig. xix,

EFFECT OF INSTANTANEOUS CURRENT.

707 quantity of electricity which passes. This velocity is equal to that acquired in the return movement to zero; and this latter obviously follows the same law as the motion of a simple pendulum, for in both cases the effective force is proportional to the sine of the displacement. In the case of the pendulum, the square of the velocity acquired in the whole descent is proportional to the vertical height descended, and this vertical height multiplied by the diameter of the circle in which the pendulum moves, is equal to the square of the chord; hence, the velocity acquired is proportional rigorously to the chord, and approximately to the arc of descent if small. The same rule must hold for the needle; that is to say, the velocity acquired must be proportional to the extreme displacement. The quantity of electricity transmitted through the galvanometer coil by an instantaneous discharge is therefore proportional to the distance to which the needle swings.

723. The Galvanometer a True Measurer of Current.-This reasoning assumes the principle that the force exerted by a current on a needle is a true measure of the strength of the current (defined as the quantity of electricity conveyed per unit of time); and conversely, the observed fact that, when known quantities of electricity are discharged through a galvanometer, the swings produced are proportional to these quantities, establishes the principle. The experiment has frequently been made by discharging a condenser (§ 628) which has been charged by a galvanic battery; and Faraday obtained a similar result with Leyden-jars which had been charged by a powerful frictional machine, the jars being discharged through a wet thread or string leading to the galvanometer. He found that the swing was independent of the length and thickness of the thread or string, as well as of the number of jars employed, and was proportional to the number of turns that had been given to the electrical machine in charging the jars.

The proportionality of force to current might have been inferred à priori from the consideration that, if we have two parallel wires close together, conveying equal currents, the resultant force on a pole will be the sum of the forces due to each, and will therefore be double of the force due to one alone. The force will not be altered by allowing the wires to touch each other all along their length; and in this position they form a single conductor conveying a double

current.

724. Needle Deflected by Motion of a Charged Body.-The question

has been raised whether the carrying of electricity by the motion of a charged body produces effects similar to those of a current flowing through a conductor, and in particular, whether it is capable of deflecting a magnetized needle. The matter has been put to the test by Professor Rowland of Baltimore, in an experiment performed at the laboratory of the Berlin University.1

The carrier of the electricity was a rapidly revolving horizontal disc of ebonite, gilt on both sides, and maintained in a high state of electrification by means of a fixed discharging point connected with one of the coatings of a battery of Leyden-jars. The needle to be deflected was suspended over it near its circumference, the length of the needle being perpendicular to the radius of the disc, so that the motion of the electricity beneath the needle was parallel to its length. Between the needle and the revolving disc, a larger fixed disc of glass, gilt on one side and connected with the earth, was interposed; and there was a similar disc on the lower side. The needle was one of an astatic pair, the other needle being at a much greater height; and both were inclosed in a brass case, to protect them from electrostatic influences. The deflection was observed by means of a mirror attached to the stem of the needles, and a telescope for viewing in the mirror the reflected image of a scale. The disc, which was 8 inches in diameter, revolved at the rate of about 60 turns per second, and the deflections observed amounted to from 5 to 71⁄2 divisions of the scale, the deflection being to the one side or the other, according as the charge of the disc was positive or negative. The observations extended over several weeks, and conclusively proved, subject to small errors of observation and reduction, that the magnetic effect of carrying a charge of electricity is the same as that of the flow of the same quantity of electricity in the same time through a conductor.

1 See Phil. Mag. September, 1876, pp. 211-216.

CHAPTER LV.

ELECTRO-CHEMISTRY.

725. Electrolysis.-When a current is passed through a compound liquid, decomposition is frequently observed, two of the component substances being separated, one at the place where the current enters and the other at the place where it leaves the liquid. This decomposition is called electrolysis, and the substance decomposed or electrolysed is called the electrolyte. The action only occurs in the case of liquids, and these must be conductors.

The process may be illustrated by the decomposition of water as represented in Fig. 472. The apparatus consists of a vessel con

taining water to which a little sulphuric acid has been added, and in which two strips of platinum are immersed, connected respectively with the two poles of a battery. When the connections are completed, bubbles make their appearance at the surfaces of the two

strips and rapidly rise to the surface. If two tubes filled with the liquid are inverted over the two strips, the gases will bubble up through the liquid into the upper part of these tubes and the level of the liquid will gradually fall as shown in the figure. It will be found that the volume of the hydrogen is about double that of the

oxygen.

The two strips of platinum are called the poles or electrodes of the decomposing cell; the one in connection with the positive pole of the battery is called the anode (literally the way up) and the one in connection with the negative pole the cathode or kathode (way down). The direction of the current through the liquid is from the anode to the kathode. The gas which is given off at the anode (in the present case oxygen) is called the anion (that which goes up) and that which is given off at the kathode the kathion or cation (that which goes down). The anion is often called the electronegative element, because it moves as if attracted by the positive and repelled by the negative pole. For a similar reason the kathion is called the electro-positive element.

In many cases, the separation effected by the direct action of the current is followed by secondary actions due to chemical affinities. Thus, in the decomposition of acidulated water above described, the first effect, according to modern theory, is a breaking up of the sulphuric acid (SO, H2O) into hydrogen and sulphion (2 H and SO), the latter being a substance which has never been obtained by itself. The hydrogen travels to the negative pole and there escapes. The sulphion goes to the positive pole, but instead of escaping enters into combination with the hydrogen of the liquid, forming again the primitive compound (S O., H, O) and leaving the oxygen of the liquid to escape.

3

726. Transport of Elements.-It is a remarkable fact that the separated elements

make their

never

hibited, at intermediate points. The appearance is as if the gases could vanish from one extremity and appear at the other without passing through the intermediate space. The only possible explanation of this phenomenon seems to be what is known as Grotthus'