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which the galvanometer is connected being no longer at the same potential, a current is indicated by the galvanometer.^[1]

Fig. 29.

The tranverse electromotive force is equal to KCH/D, where C is the current, H the strength of the field, D the thickness of the metal, and K a constant which has been termed the rotatory power or rotational coefficient. (See Hopkinson, Phil. Mag., 1880, 10, 430). The following values of K for different metals are given by E. H. Hall, the positive sign indicating that the electromotive force is in the same direction as the mechanical force acting upon the conductor. A. von Ettinghausen and W. Nernst (Wien. Ber., 1886, 94, 560) have found that the rotational coefficient of tellurium is more than fifty times greater than that of bismuth, its sign being positive. Several experimenters have endeavoured to find a Hall effect in liquids, but such results as have been hitherto obtained are by no means free from doubt. E. A. Marx (Ann. d. Phys., 1900, 2, 798) observed a well-defined Hall effect in incandescent gases. A large effect, proportional to the field, has been found by H. A. Wilson (Cam. Phil. Soc. Proc., 1902, 11, pp. 249, 391) in oxygen, hydrogen and air at low pressures, and by C. D. Child (Phys. Rev., 1904, 18, 370) in the electric arc.

Metal.	K × 1015	Metal.	K × 1015
Antimony	+114000	Copper	−520
Steel	+12060	Gold	−660
Iron	+7850	Nickel	−14740
Cobalt	+2460	Bismuth[2]	−8580000
Zinc	+820

Electro-Thermal Relations.—The Hall electromotive force is only one of several so-called “galvano-magnetic effects” which are observed when a magnetic field acts normally upon a thin plate of metal traversed by an electric current. It is remarkable that if a flow of heat be substituted for a current of electricity a closely allied group of “thermo-magnetic effects” is presented. The two classes of phenomena have been collated by M. G. Lloyd (Am. Journ. Sci., 1901, 12, 57), as follows:—

Galvano-Magnetic Effects.	Thermo-Magnetic Effects.
1. A transverse difference of electric potential (Hall effect).	i. A transverse difference of electric potential (Nernst effect).
2. A transverse difference of temperature (Ettinghausen effect).	ii. A transverse difference of temperature (Leduc effect).
3. Longitudinal change of electric conductivity.	iii. Longitudinal change of thermal conductivity.
4. Longitudinal difference of temperature.	iv. Longitudinal difference of electric potential.[3]

If in the annexed diagram ABCD represents the metallic plate through which the current of electricity or heat flows in the direction AB, then effects (1), (2), (i.) and (ii.) are exhibited at C and D, effects (4) and (iv.) at A and B, and effects (3) and (iii.) along AB. The transverse effects are reversed in direction when either the magnetic field or the primary current (electric or thermal) is reversed, but the longitudinal effects are independent of the direction of the field. It has been shown by G. Moreau (C. R., 1900, 130, pp. 122, 412, 562) that if K is the coefficient of the Hall effect (1) and K′ the analogous coefficient of the Nernst effect (i.) (which is constant for small values of H), then K′ = Kσ/ρ, σ being the coefficient of the Thomson effect for the metal and ρ its specific resistance. He considers that Hall’s is the fundamental phenomenon, and that the Nernst effect is essentially identical with it, the primary electromotive force in the case of the latter being that of the Thomson effect in the unequally heated metal, while in the Hall experiment it is derived from an external source.

Attempts have been made to explain these various effects by the electron theory.^[4]

Thermo-electric Quality.—The earliest observations of the effect of magnetization upon thermo-electric power were those of W. Thomson (Lord Kelvin), who in 1856 announced that magnetization rendered iron and steel positive to the unmagnetized metals.^[5] It has been found by Chassagny,^[6] L. Houllevigue^[7] and others that when the magnetizing force is increased, this effect passes a maximum, while J. A. Ewing^[8] has shown that it is diminished and may even be reversed by tensile stress. Nickel was believed by Thomson to behave oppositely to iron, becoming negative when magnetized; but though his conclusion was accepted for nearly fifty years, it has recently been shown to be an erroneous one, based, no doubt, upon the result of an experiment with an impure specimen. Nickel when magnetized is always positive to the unmagnetized metal. So also is cobalt, as was found by H. Tomlinson.^[9] The curves given by Houllevigue for the relation of thermo-electric force to magnetic field are of the same general form as those showing the relation of change of length to field. E. Rhoads^[10] obtained a cyclic curve for iron which indicated thermo-electric hysteresis of the kind exhibited by Nagaoka’s curves for magnetic strain. He also experimented with nickel and again found a resemblance to the strain curve. The subject was further investigated by S. Bidwell,^[11] who, adopting special precautions against sources of error by which former work was probably affected, measured the changes of thermo-electric force for iron, steel, nickel and cobalt produced by magnetic fields up to 1500 units. In the case of iron and nickel it was found that, when correction was made for mechanical stress due to magnetization, magnetic change of thermo-electric force was, within the limits of experimental error, proportional to magnetic change of length. Further, it was shown that the thermo-electric curves were modified both by tensile stress and by annealing in the same manner as were the change-of-length curves, the modification being sometimes of a complex nature. Thus a close connexion between the two sets of phenomena seems to be established. In the case of cobalt no such relation could be traced; it appeared that the thermo-electric power of the unmagnetized with respect to the magnetized cobalt was proportional to the square of the magnetic induction or of the magnetization. Of nickel six

1. E. H. Hall, Phil. Mag., 1880, 9, 225; 1880, 10, 301; 1881, 12, 157; 1883, 15, 341; 1885, 19, 419.
2. The large Hall effect in bismuth was discovered by Righi, Journ. de Phys., 1884, 3, 127.
3. References.—(2) A. von Ettinghausen, Wied. Ann., 1887, 31, 737.—(4) H. W. Nernst, ibid., 784.—(i.) and (iv.); A. von Ettinghausen and H. W. Nernst, Wied. Ann., 1886, 29, 343.—(ii.) and (iii.); A. Righi, Rend. Acc. Linc., 1887, 3 II, 6 and I, 481; and A. Leduc, Journ. de Phys., 1887, 6, 78. Additional authorities are quoted by Lloyd, loc. cit.
4. P. Drude, Ann. d. Phys., 1900, 1, 566; 1900, 3, 369; 1902, 7, 687. See also E. van Everdingen, Arch. Néerlandaises, 1901, 4, 371; G. Barlow, Ann. d. Phys., 1903, 12, 897; H. Zahn, ibid. 1904, 14, 886; 1905, 16, 148.
5. Phil. Trans., 1856, p. 722. According to the nomenclature adopted by the best modern authorities, a metal A is said to be thermo-electrically positive to another metal B when the thermo-current passes from A to B through the cold junction, and from B to A through the hot (see Thermo-Electricity).
6. C.R., 1893, 116, 997.
7. Journ. de Phys., 1896, 5, 53.
8. Phil. Trans., 1887, 177, 373.
9. Proc. Roy. Soc., 1885, 39, 513.
10. Phys. Rev., 1902, 15, 321. The sign of the thermo-electric effect for nickel, as given by Rhoads, is incorrect.
11. Proc. Roy. Soc., 1904, 73, 413.