Au F We find from calculation, = 7·54 and the corresponding experimental ratios, 5.70 and 3-95, give thus a relative value for gold which is somewhat too small, but show very good agreement for the relative values of silver and aluminium. Retaining for F its significance as "effective" negative. charge, so as to account for the spacial distribution of the electrons, this would indicate a contribution from each atom proportional to its charge. Here two remarks present themselves: one that when applying an expression for Q to the scattering from a volume, in which extinction and absorption are nil, it would be very satisfactory to find the contribution of the individual atom to the total intensity of one reflexion. proportional to F and not to F2. In fact, F in such a case only determines the scattering from the individual unit of the pattern, so that a variation of F does not affect the range through which reflexion occurs, different from N in expression (3); the other that it is questionable whether an equation of this type can actually be applied to express the scattering when extinction is absent. The two points are not so widely different as they appear, since, in considering the scattering from crystals, the scattering from one atom by itself has no physical meaning. On the other hand, in making these remarks we must bear in mind that the general evidence from structure analysis and from absolute determinations on lighter elements is in agreement with (3) also in cases where this expression has been applied to measurements from microcrystalline mosaics and fine powders. It seems, therefore, of interest to discuss the present measurements in terms of this expression, when they indicate that the relations verified for lighter elements seem not to be satisfied in a general way. The writer is indebted to Prof. W. L. Bragg, F.R.S., for various facilities, among which is the use of a transformer obtained by means of a grant of the Royal Society, and to the Leembruggen Trust for a special grant. He wishes in particular to express his thanks to Mr. W. E. Dawson, M.Sc., for his help in the earlier stages of this work, and to Mr. J. Adamson, M.Sc., for assistance received in the more recent experiments. Manchester, XII. The Magnetic Energy of Permanent Magnets and of Linear Currents. By H. V. LOWRY". UPPOSE the field has an applied electric force E' and permanent magnetism I, then using Maxwell's equations f(E';)de — S(E)de = −√(E—E', curl H – -D) dv at (curl E-E', H)dv + + √(E - E. 3D) dv + [[EH],dS δε = √( 3, (B− Io),H )dv+ √(1 -I),H)dv+ (E-E', dv, the integrals being taken over all space, so that S[EH]ds=0. (1) In an isotropic medium of constant permeability and capacity the right-hand side of 1 becomes S(E)de is the rate at which work is done on the field by the applied forces; S(Ej) do is the rate of dissipation of energy; and hence the right-hand side of (1) represents the rate of increase of the electrical energy of the field. This energy is in two parts, the first of which definitely depends on the magnetic properties of the field. If the field contains permanent magnets and no currents, this part becomes W = = √(IH) dv because (BH) dr becomes zero in a magnetostatic field. If the field contains no permanent magnets and the currents are steady and flow in circuits, N being the total induction through a circuit carrying a current i. If we regard the permanent magnets as made up of *Communicated by the Author. molecular currents, we can look on W and T as two different ways of uniting √μH3dv, just as W=Σprere. and W,=129,V,V s are different ways of writing the electrostatic energy ΣeV. From the magnetostatic point of view the force corre sponding to the coordinate x is (-3W), ), and, as this is obtained by keeping Io constant, it is better to write it But when the magnets are replaced by currents, the currents must be kept constant during the displacement Sa in order that the equivalent magnetization shall remain constant. For two circuits T={{ L1122+2Mi1i2+ Ni22}, so that keeping L1 and L, and the shapes of the two circuits Hence the increase of energy of the circuit E1i+ Egi—R1122 — R2¿‚2 —X 8x=21128M-X 8x These different expressions arise solely from the two Phil. Mag. S. 7. Vol. 6. No. 34. July 1928. different ways of writing fμH'dv, and are analogous to the electrostatic equations дх V=const = (+ WY) дх e=const. If absolutely permanent magnets were possible the energy 28T would have to be supplied from molecular sources. We obtain the same result if we assume that the magnets have induced magnetization only, and that during a displacement this is kept constant by the application of an external magnetic force. For such magnets the energy is W'-(IH)dv. In a displacement in which I is kept constant, SW' = −√(ISH) dv. To keep I constant in such a displacement an external magnetic force SH must be applied, and this will do work It is only the gradients of the energy that occur in the equations of motion and in the expressions for the generalized forces. The potential energy of a system of magnets is not necessarily (μH'de, because its kinetic energy is + SuH2dv; both T and W are equal to sμH2, and the equations The confusion arises because the quantities kept constant in the partial differentiation are often omitted. XIII. Chemical Interactions corresponding to the Constant of Mass Action, being a Function of the Volume and Masses of the Constituents, as well as of the Temperature and Catalytic Action.-I. By R. D. KLEEMAN, B.A., D.Sc. § 1. Introductory Remarks. THE writer has shown † that, in general, the constant of mass action of a gaseous interacting mixture is a function of its volume and masses of the constituents as well as of the temperature. In a subsequent paper the differential equations were developed which determine the functional nature of the constant of mass action in any given case. They were applied to investigate some well-known reactions by the help of the gas equation where p denotes the pressure of M mols of a pure gas at the volume and absolute temperature T. In the particular cases considered, it was found that the constants of mass action are independent of the volumes of the reacting mixtures, as shown by experiment. The effect of the masses of the constituents on the constant of mass action was not investigated. It was shown in a subsequent paper § that, strictly according to thermodynamics, the equation of a perfect gas is where is a function of T, v, and M, which is practically equal to unity except for temperatures close to the absolute zero, and for very large volumes. It would follow, then, that strictly in all cases the constant of mass action of a mixture in the perfectly gaseous state is a function of the volume, notably when it is very large, and the masses of the constituents, as well as of the temperature, though it may practically independent of these quantities except of the temperature over a large range of values. In this paper it will be shown that the constant of mass action may be appreciably a function of the foregoing three quantities for reactions * Communicated by the Author. § Phil. Mag. v. p. 1191 (1928). be |