98 ELECTRICITY [ELECTROMOTIVE FOKCE. metal we are considering, then, from what has been shown (10), Tait s conjecture leads to the result that this curve is a straight line; and if the standard inetal be lead, for which, according to Le Roux s results, the Thomson effect is zero, then the coefficient k of the Thomson effect is the tangent of the inclination of the representative line to the axis of abscissae. And not only so, but it follows from formula (9) and (7) that, if A AN, B BN (fig. 54) be the Fig. 54. lines corresponding to two metals, say Cu and Fe (of which the former is above the latter in the thermoelectric series at ordinary temperatures), and if AB, A B be the ordinates corresponding to and & , then the electromotive force in a circuit of the two metals whose junctions are at the tempera tures 6 and , tending to send a current from Cu to Fe across the hotter junction, is represented by the area ABB A . The Peltier effects at the two junctions are represented by the rectangles AB&a and A B 6 a , and the Thomson effects, in the Cu and Fe respectively, by AA DC and BB GF, or by AA a a and BB7/6, which are equal to these. At N, where the lines intersect, the Peltier effect vanishes. N therefore is the neutral point ; and, if the higher tempera ture lie beyond it, the electromotive force must be found by taking the difference of the areas NA B and NAB, and so on. All the phenomena of inversion may be studied by means of this diagram, and the reader will find it by far the best means for fixing the facts in his memory. Expcri- For several years back Tait 1 and his pupils have merits of been engaged in verifying the consequences of this con- ait, &c. j ec t ur e ; and it has been shown, first, for temperatures within the range of mercury thermometers, and latterly for temperatures considerably beyond this range, that the hypothesis accords with experience. The methods em ployed by Tait in his experiments at high temperatures are of great interest and importance. One of these was to con struct a curve whose ordinate and abscissa are the simul taneous readings of two thermoelectric circuits whose hot and whose cold junctions are kept at common tempera tures. It is a consequence of the foregoing assumption that the curve thus obtained ought to be a parabola. Very good parabolas were in many cases obtained. In some cases, however, the curves, so far from being parabolas, were actually curves having points of contrary flexure. This anomaly led Tait to the discovery of the astonishing fact that the Thomson effect in iron changes its sign cer tainly once at a temperature near low red heat, if not a second time near the melting point. It was found that the inflected curves could be represented by piecing to gether different parabolas. Hence the line for iron in the Trans. R. S. E., 1873. thermoelectric diagram is a broken line made up of two if not three straight pieces. This peculiarity of the iron line was very strikingly shown by forming circuits of iron with the alloys Ptlr or PtCu. Such circuits exhibit two or even three neutral points (see fig. 55), Another very elegant ^^At ^pa- pica method of verification consisted in using along with an iron wire a multiple wire of Au and Pd, the resistances of whose branches could be modified at will. It is easy enough to show that the line for the Au-Pd wire is a straight line, passing through the neutral point of Au and Pd, and such that it divides the part of an ordinate lying between the Au and Pd lines in the ratio of the respective conductivities of the Au and Pd branches. Thus, by in creasing ratios of the conductivities of the Pd and Au branches from up to co , we can make the Au-Pd line sweep through the whole of the space between Au and Pd (fig. 55), and thus explore the part of the Fe line lying in the space. We get in this way first one neutral point, then two, then one, and then none in our Fe, Au-Pd circuit. Tait has pointed out that, by using Ptlr and Fe, and Cu keeping the hot and cold junctions at the two neutral fro temperatures, we get a current maintained solely by the excess of the heat absorbed in the hotter iron over that a i c developed in the colder. The electromotive force is repre sented by the area inclosed by the part of the zigzag on the Fe line cut off by the Ptlr line (fig. 55). A similar case of thermoelectromotive force without Peltier effects may be obtained with three metals, such as Fe, Cd, Cu, whose neutral points lie within reasonable limits. The electromotive force in this case is represented by the triangle between the three lines. We subjoin a table, calculated by Professor Everett from Tail s Ta diagram. The thermoelectric power is given in electromagnetic res (C.G.S.) units, in terms of the temperature (t) in centigrade degrees, by means of the formula a + 0t, where a and ft have the tabulated values : a
a
Fe -1734 -1139 - 839 - 662 - 593 - 709 - 577 + 61 - 260 - 544 - 224 + 1207 + 4-87 + 3-28 + 0-00 + 0-55 + 1-34 + 0-63 + 0-00 + 1-10 + 075 + 1-10 + 0-95 + 5-12 Cd - 266 234 - 4-29 - 2-40 - 1-50 - 1-02 - 0-95 + o-oo - 0-55 - 0-39 + 3-59 + 5-12 24 10 Steel Zn Ft Ir? Ac - 214 - 283 - 136 + + 43 + 77 + 625 + 2204 + 8449 + 307 Ptlr(5p.c. Ir) Do. (10 do. ) Do. (15 do. ) Do. (15 do. ) Pt soft Au .... Cu Pb Sn Al Pt hard Pd Pt Ni Ni to 175 C Do. 250 to 31 0"C. Do. from 340 C. M".. .. German silver + 512 We need scarcely warn the reader that the results in this table must not be rashly applied to any specimens of the rnetals taken at random. The temperature limits lie between 18 C. and 420 C.
It would be extremelv interesting to compare the results