greater than the internal one. It is therefore advantageous to multiply the number of couples. Generally not fewer than 25 couples are used in order to form a thermo-pile. 406, Let us now, instead of increasing the number of cells, adhere to one cell, but increase the size of the plates. In this case the electro-motive force will be unaltered, remaining equal to E, but the internal resistance will be diminished, since the cross section of the conductor is increased. If the area of each plate be increased 10 times, we shall have, i Now if the ex = E R = +r IO E R+ Ior ternal resistance be small compared to the internal, we see that the intensity will vary nearly as the area of the = IO E 10, we shall have for the I, while for the small plates, i = E ΙΟΙ large plates, i the former of these being nearly ten times as great as the latter. Hence when the external resistance is small we gain most by increasing the size of the plates. This is the case when the battery is used to produce thermal effects. Thus if we wish to melt an iron wire, it is more advantageous to have a few cells of large size than a great number of small cells. 407. We thus perceive how the intensity of the current due to any arrangement of cells may be determined. Ohm likewise showed that the intensity is the same in all parts of the circuit; that is to say, the same quantity of electricity passes through all cross sections of a battery in the same time, whether the cross section be that of the cell or of the conducting wire. This has also been verified by experiment. 408. Suppose now that we have a galvanometer inserted in a voltaic circuit, and that the intensity of the current, as determined by its influence upon the needle, is i. Suppose also that 12.36 metres of tin wire of the cross section of one square millimetre form part of this circuit, and that we take away the tin wire and replace it with silver wire on the same E thickness, but of 100 metres in length. It will be found that the intensity of the current is unaltered by this substitution; but since i == it follows that the resistance of the whole R current is the same in both cases, and hence (since the other parts of the circuit were common to both) that the resistance of the silver wire is equal to that of the tin wire. Now if the resistance of 100 metres of silver wire is equal to that of 12.36 metres of such tin wire, it follows (Art. 403) that the resistance of equal lengths of such silver and tin wire may be represented by and and hence the con100 12.36 I I ductivities of the two metals, which are reciprocal to these resistances (Art. 402), will be represented by 100 and 12.36. 409. Electric Conductivity.—By this, or by some other similar method, we may obtain the electric conductivity of the various metals. The following results are those of Dr. A. Matthiessen and M. von Bose : Name of Metal. Silver (hard-drawn) Zinc. Cadmium Tin Lead. Arsenic. Antimony Bismuth Electric conductivity at 100° C. (Silver at o° C. = 100) 71956 23172 16.77 It has been remarked by Principal Forbes that metals follow one another in the same order, whether as conductors of heat or of electricity, and this is borne out by comparing the above table with that of Art. 219. Tait has furthermore lately shown that if two specimens of the same metal vary in their electrical conductivity, they vary in the same manner as regards their thermal conductivity. Finally, it would appear that both the electric and the thermal conductivity of metals are diminished by increasing their temperature, in such a manner that the conductivity varies inversely as the absolute temperature (Art. 247). LESSON XLVI.-EFFECTS OF THE ELECTRIC CURRENT. 410. Physiological Effects.-The discharge of a Leyden jar battery (Art. 351) may perhaps be likened to that of a cannon-ball from a field-piece, while a voltaic battery may be likened to a machine which keeps perpetually discharging enormous quantities of excessively small shot. The one effect is sudden and awe-inspiring, the other is continuous and of a comparatively quiet nature. There is great tension, i.e. electro-motive force, in the Leyden jar battery, but the quantity of electricity which passes is not great. On the other hand, the tension of voltaic electricity is so small that it is only a very powerful battery that can send its spark across an appreciable thickness of air. But the quantity of electricity which passes in a voltaic battery is very great; and a battery of this kind which has been in silent action for a few minutes may probably have accomplished as much work as could be done by a flash of lightning, in which phenomenon the greatest possible effect is produced with the smallest possible means as regards quantity of electricity. The destructive effect of the voltaic current upon animal life is not therefore so great as that of a Leyden jar battery. With a single cell the shock produced is hardly perceptible, but with 100 or 150 cells it is very great, and would be dangerous if continued for any length of time. current is 411. Thermal Effects. When the electric made to pass through a circuit it heats this circuit, and the heating effect is proportional to the resistance (Art. 402) which the circuit interposes to the passage of the current. By means of this resistance, that species of energy which we term electricity in motion is converted into that other species of energy which we term heat, and the heat so produced is proportional to the resistance offered to the current. Now if we diminish in any proportion the cross section of a wire we increase its resistance in the same proportion (Art. 403), and it therefore follows that by reducing to onehalf the cross section of a wire, we double the amount of heat generated in it by the passage of the same quantity of electricity. Again, since this double amount of heat has only half the amount of metal to influence, it follows that the initial rise of temperature will be increased fourfold; that is to say, the initial increase of temperature produced in one second by the passage of the same quantity of electricity will vary inversely as the square of the cross section. 412. In the next place, the heat generated in a given time is proportional to the square of the intensity of the current. We may deduce this from the previous law by supposing that we have two wires of single thickness close together, while single currents are made to pass through each simultaneously, so that we may imagine one current to go through the one wire and one through the other. Therefore by means of this double current going through a double wire, twice as much heat will be generated in a given time as by a single current going through a single wire; but we have just seen that when a double current goes through a single wire, twice as much heat is generated as when it goes through a double wire; that is to say, four times as much as when a single current goes through a single wire. 413. We have previously seen (Art. 407) that the quantity of electricity which passes in unit of time through every cross section of a closed circuit is the same ; and we have also seen (Art. 402) that the resistance is inversely proportional to the conductivity; we can therefore, if we know the electric conductivity of the various materials of which the circuit is composed, find the distribution of heat in the various parts of the circuit. Thus let one part be composed of a metre of silver wire two square millimetres in cross section, and another of five metres of zinc wire four square milli meters of cross section, what will be the relative heating effects of the current on these two wires? If we call the heat produced in the first wire unity, that produced in the second will be =8·62, in which expression the second ΙΧ × 5 × 2/ 4 29 factor is on account of conductivity (see table, Art. 409), the third on account of length (Art. 403), and the last on account of cross section. 414. We can thus tell the relative distribution of heat in the various parts of a battery; but in order to tell the whole heating effect produced from first to last, we must bear in mind the origin of the heat. This is, in fact, the burning of the fuel zinc, the potential energy of which is converted in the first instance into electricity in motion, and ultimately (let us suppose) into heat. Now a certain quantity of zinc consumed will give us a certain definite quantity of heat, neither more or less; and it has been shown by Joule that if the same quantity of zinc be combined with acid in an ordinary vessel, it will give out the same amount of heat as if it were consumed by means of the voltaic arrangement. Thus the difference between dissolving zinc by acid in an ordinary vessel, and doing so by the voltaic arrangement, is not in the quantity of heat which it gives out, but in the distribution of this heat. For in the voltaic arrangement heat may be developed many miles from the cells in which the combustion takes place, but in the ordinary case the heat is produced in the vessel in which the zinc is dissolved. 415. Electric Light.-When a voltaic battery is very powerful, it is not always necessary to bring the poles into actual contact with each other, for the current will pass through a small interval of air. This current will give out a continuous light, the nature of which will depend upon the nature of the substances which form the terminals; the light in fact consists of small particles of the terminals and of the intervening air, intensely luminous, and often in a state of vapour. When the poles are formed of carbon, this light is the most intense which we can produce by any means, and almost rivals in lustre the light of the sun; it is called, by way of distinction, the electric light. |