ELECTROMOTIVE FORCE.] E L E T R I C I T Y D7 ing only on tlie nature of the metals. In accordance with this, the thermoelectromotive force in the circuit would be C(0 - &} that is, it would be proportional to the difference between the temperatures of the junctions. Now this conclusion is wholly inconsistent with the existence of thermoelectric inversions. We must therefore either deny the applicability of the second law, or else seek for rever sible heat effects other than those of Peltier. This line of reasoning, taken in connection with another somewhat more difficult, satisfied Sir "Win. Thomson that reversible heating effects do exist in the circuit elsewhere than at the junctions. These can only exist where the current passes from hotter to colder parts of the same wire or the reverse. Thomson was thus led to one of the most astonishing of all his brilliant discoveries; for he found, after a series of researches distinguished alike for patience and experi mental skill, that an electric current absorbs heat in a copper conductor when it passes from cold to hot, and evolves heat in iron under similar circumstances. This phenomenon was called by its discoverer the electric con vection of heat. He expressed the facts above stated by saying that positive electricity carries heat with it in an unequally heated copper conductor, and negative electricity carries heat with it in an unequally heated iron conductor. The first statement is perhaps clearer ; the value of the one given by Thomson consists in the suggestion which it con veys of a valuable physical analogy with the transport of heat by a current of water in an unequally heated pipe. 1 If two points AB of a uniform linear conductor, in which a current I is flowing from A to B, and evolving heat, be kept at the same constant temperature, but for the electric transport of heat the temperature distribution would be symmetrical about a point of maximum tem perature half way between A and B Owing to the electric transport of heat, the maximum will be shifted towards A in iron, towards B in copper. 2 This remark contains the principle of the experiments made by Thomson to detect the new effect. The first experiment in which the effect was satisfactorily estab lished was made with a conductor ABCDEFG, formed of a num ber of strips of iron bound together at A, C, E, and G, but opened out widely at B, D, and F, to allow these parts to be thoroughly beated or cooled. At C and E small cylindrical openings allowed the bulbs of two delicate mercurial thermometers to be inserted in the heart of the bundle of strips. The part D of the conductor was kept at 100" C. by means of boiling water, and the parts B and F were kept cool by a constant stream of cold water. The current from a few cells of large surface was sent for a certain time from A to G, then for the same length of time from G to A, and so on. In this way the effects of want of symmetry were eliminated, and the result was that the excess of the temperature at E over that at C was always greatest when the current passed from G to A ; whence it follows, as stated above, that a current of positive electricity evolves heat in an iron conductor when it passes from cold to hot. . Le Koux 3 has made a series of interesting experiments on the Thomson effect in different metals. He found that the effect varies as the strength of the current, and gives the following numbers representing its relative magnitudes in different metals. In lead the effect is insensible. Suppose fcr simplicity we have a circuit of two metals only. Let Equa- the current go from A to B over the hot junction, and let the heat tions of absorbed in passing from a point at temperature to a neighbour- Thorn- ing point at temperature e + de in A be a-^de per unit of current sou. per unit of time ; let ir.jlO be the corresponding expression for B. Then it is obvious, from the result of Magnus (see above, p. 95), that <T I and <r^ can be functions of the temperature merely ; they depend, of course, on the nature of the metal, but are independent of the form or magnitude of the section of the conductor. The first and second laws now give respectively E = n - n> + 1 , /e n n "0 <T I - de (4), (5), where E is the whole thermoelectromotive force, and n and n are the same functions of 6 and tf respectively. By differentiation we get from (5) whence we easily get E = , (7). or 5=5 de This last equation enables us to determine E in terms of n, and conversely. When the difference between the temperatures of the junctions is very small, equal to d6 say, the thermoelectro motive force is n , fdo (8). The coefficient -i by which we must multiply the small temperature difference to get the electromotive force is called by Thomson the thermoelectric power of the circuit. If we have a circuit of three metals, A, B, C, all at the same temperature 0, then we know that + - Sb 64 Fe 31 Cd 31 Bi 31 Zn 11 Arg 25 Ag 6 Pt 18 Cu 2 Al o-i Sn o-i We may now apply the mathematical reasoning given above, taking into account Thomson s effect. 1 Trans. R.S.E., 1851. s See Verdet, Thtorie Mecaniqne de la Chaleur, t. ii. 260. 8 Ann. de Ckim. et de Phi/s., 1867 whence n A c Ur.c or, in other words, the thermoelectric power of B with respect to A is equal to the difference between the thermo electric powers of a third metal C with respect to A and B respectively. Thus far we have been following Thomson. But as yet Tait s we have no indication how o-, the coefficient of the Thomson conjee- effect, depends on the temperature. Thomson himself ture- seems (see his Bakerian Lecture, 1. c., p. 706) to have ex pected that a- would turn out to be constant. Certain considerations concerning the dissipation of energy led Tait, however, to conjecture that a- is proportional to the absolute temperature. If we adopt this conjecture, Thomson s equations give us at once the values of the Peltier effect and the electromotive force in the circuit. If <r l kfl, <r. 2 = k.fi, we get from (6) and (7) successively 4 (10), . . (11), where 12 is the neutral temperature. Also, since in a circuit of uniform temperature there are no Thomson effects, and the sum of the Peltier effects is zero, we get for any three metals (* t -i^u+(* a -* 1 )4 1 +(* 1 -* a )4 l -0. (12). Taking up the idea of a thermoelectric diagram origi nally suggested by Thomson, Tait has shown how to repre sent the above results in a very elegant and simple manner. Suppose we construct a curve whose abscissa is the abso lute temperature 6, and whose ordinate is the thermo electric power of some standard metal with respect to the 4 Tait, Proc. R. S. E., 1870-1-2. VIII. 13 Thermo- electric diagram "ii velop- e.lby
Tait.