where is the fraction of the total volume which is occupied by atoms.

It is clear that this is of the right order of magnitude. For oxygen, hydrogen, nitrogen at the density of the air the refractive index is roughly 1.00025 *, giving

k=1.0005.

Substituting this value in the formula just found for k (and neglecting the difference between atoms and molecules, since this will not affect the order of magnitude of the quantities concerned), we get 0='0007.

Now the density of liquid oxygen, nitrogen, &c., is roughly 1000 times that of air, so that the value of 0 just found will be at any rate comparable with the true value."

Dielectrics, Conductors, and Electrolytes.

§ 41. It will be seen that the foregoing theory of the specific inductive capacity of a dielectric is virtually that of Mossotti†. The atoms or molecules must not be regarded as perfect conductors, but they arrange themselves so that their external surfaces are equipotentials, and therefore behave like conductors to all external points.

In a solid body each ion will be in equilibrium under the forces arising from all the ions in the solid. In the case of some substances, the solid may be regarded as a collection of atoms, or molecules, each individual atom retaining its identity; whereas for other substances the body must simply be regarded as a confused mixture of ions which have placed themselves in equilibrium.

The difference is that between a dielectric and a conductor. If the former body is placed in an electric field, the molecules will arrange themselves so that their surfaces are equipotentials, and we have a dielectric of which the theory of Mossotti gives a good account.

When a body of the second sort is placed in an electric field, the ions (possibly all ions, or possibly only the ions of the outermost layer) will be free to move from one molecule to another, and will therefore arrange themselves so that the whole surface of the body is an equipotential. In one half of the body there would be an excess of negative ions, in the other half an excess of positive ions: the former is the socalled "induced charge" of negative electricity, the latter of *Preston, 'Theory of Light,' p. 137.

+ Maxwell, Elect. and Mag. § 62. Phil. Mag. S. 6. Vol. 2. No. 11. Nov. 1901.

2 H

positive. Before the ions have taken up their equilibrium positions there will be a flow of ions through the body, and this is a "current of electricity.

A third class of body can be imagined in which the ions are closely bound into atoms, but the bond between the various atoms of a molecule is very slight: this is the class of electrolytes. A current in this case involves an actual transfer of atoms through the electrolyte.

Consider, for instance, the electrolysis of hydrochloric acid. The hydrogen atom has a convergence of force equal and opposite to that of a negative ion. Every pair of hydrogen atoms as they arrive at the cathode will combine with two of the negative ions which have been conveying the current through the metal cathode, and will together form a neutral hydrogen molecule. So also at the anode, the pairs of chlorine atoms combine into molecules, and in doing so liberate the ions which are to carry the current away from the anode. Faraday's Laws of electricity follow at once.

Conclusion.

§ 42. This concludes the comparison between the phenomena which are to be expected from our hypothetical matter and those which are observed to occur in nature. It must be left for individual judgments to decide whether the test afforded in this way is sufficiently strict to be worth anything; and if so, to decide what is the measure of probability that our hypothetical matter gives a clue to the structure of actual matter.

§ 43. In conclusion, reference may be made to a question which demands an answer in the case of this, as in the case of every other hypothesis which attempts to place the structure of matter on a purely electrical or æthereal basis. The only difference which the æther-equations of electricity can recognize between a negative and a positive charge of electricity is a mere difference of sign; so that if we regard a negative ion as an æther-structure, we are inevitably led to regard the possibility of positive ions differing from negative ions only by a difference of sign. On the other hand, the predominance of the negative ion in most material phenomena, and in the emission of light (as evidenced by the Zeeman Effect) seems to suggest the view that positive and negative ions differ in something more than mere sign. Any attempt to explain matter in terms of æther must therefore face the problem of reducing what appears to be a difference in quality to a difference in sign only.

We can explain these facts, in terms of our present theory, by supposing (§ 26) that the outermost shell of ions in any

atom consists exclusively of negative ions, but there still remains the question as to why it is that the positive ions rather than the negative are excluded from the outermost shells of the atom; we have not yet removed the essential difference in quality between positive and negative ions.

We cannot suppose that all atoms with positive ions at the surface are unstable; for corresponding to any stable arrangement with negative ions at the surface, there must be a stable arrangement which is exactly the same except that the sign of every ion is changed. If an ordinary atom is referred to as a positive atom, this other kind of atom may be referred to as a negative atom.

Let us refer to the atoms of the various chemical elements as A, B, C,...., and let the imaginary corresponding negative atoms be referred to as A', B', C',.... In order that a system of chemical elements A, B, C..... may have a permanent existence it is not only necessary that the individual atoms A, B, C,.... shall each be statically stable, but also that when any atom A meets another atom B, the atoms A and B shall not lose their identity. Now the forces exerted between A and B when in proximity will arise mainly from that part of the potential-function which represents the divergence of the forces exerted by the ions near the point of closest approach from those calculated on the ordinary electrostatic law, and will possibly depend largely upon the signs of the ions in these outermost shells. Thus if A and B do not unite so closely as to lose their separate identity, it is not difficult to imagine that A' and B would be drawn together until a complete rearrangement of ions had been effected and a new atom or atoms formed. If this supposition be accepted it will be clear that a condition that a system of elements should have a permanent existence is that the outermost layers of all the atoms shall be of the same sign. We can imagine a number of positive and negative ions initially scattered at random in space to condense into matter of both kinds, but whenever a collision takes place between two atoms of different kinds, the result is a rearrangement of parts, until finally only one class of matter is left in the field.

This last suggestion is of a very speculative kind; but it may be noticed that if matter is an æther-structure, and if the difference between positive and negative electricity only enters in the æther-equations through a mere difference of sign, then the observed difference between the relations of the two kinds of electricity to material phenomena can only arise from a difference in the initial conditions, such as that just described.

XLIV. A Contribution to the Theory of Magnetic Induction in Iron and other Metals.-Part II. By JOHN BUCHANAN, D.Sc.(Lond.)*.

IN

N the Phil. Mag. for March of this year there appeared a paper of mine with the above title. It will be referred to below as Part I. We are now in a position to discuss in more detail the application of the general theory there given to some of Dr. Ewing's experimental results.

As in all such cases, the question resolves itself into the operation of determining constants-in other words, of finding the form of the graph which represents the initial conditions, such conditions being expressed by x=0 in (11) Part I. Work of this kind requires the expenditure of a good deal of time, so that I am able to give here a first approximation only.

My objects in presenting these approximate results are to indicate the nature of the problem involved in the application of the general theory to the experimental facts, to suggest the form of the solution, and to compare the values of found here with those obtained in Part I. by an entirely different method.

The methods used and the results obtained will be found, I trust, of sufficient interest to justify their publication.

Curve for Annealed Iron (cf. B. fig. 1, Part I.).

In the footnote, p. 336, Part I., I have given = 1.2 for this curve, whilst the saturation intensity of magnetization (c) is given as 0.84, that is 0.84 x 1700=1428 c.G s. units.

These results were obtained by the determination of the constants in the case where the specimen of iron was subjected to a continuous increase of magnetizing force.

I propose now to consider that curve of fig. 14, plate 59 of Dr. Ewing's paper in the Phil. Trans. pt. ii. 1885, which refers to the behaviour of the same specimen when the magnetizing force was varied cyclically.

This curve was subjected by me to harmonic analysis. The period was taken as 180; 90 readings of I were taken off the curve at equal intervals of H. By help of 4-figure mathematical tables I get as the harmonic constituents of the curve

The amplitudes of the octave and the third harmonic are inappreciable, as indeed the shape of the curve itself would suggest.

The presence of the epochs in the harmonic constituents is of course the indication of hysteresis and of residual magnetism in the material.

Equation (11) Part I. may be written in the form

I= 1⁄2" D,e ̈2√x* sin(277 H

Σ

r=1

sin(-x+6), (15)

R

R

where D,, x, and 0, are constants whose values are to be determined.

For the curve in question it appears that r assumes odd values only.

This last condition suggests a modification of fig. 5, Part I., as a possible form of the graph for Izzo which would apply to such an experimental curve as we have under examination. A somewhat prolonged arithmetical study of the matter leads me to a general form of graph for Izzo like that shown here in fig. 6.

By the application of Fourier's methods, we find as the