phere a statical force of mutual repulsion is, at the same time, in operation, by virtue of which its two constituent ethers are media capable of opposing an elastic resistance to compression, and of transmitting impulses by wave propagation.

The first fact to be noted with regard to the dynamical action exerted upon a molecular envelope, by the nucleus and ether immediately surrounding it, is that it originates inward acting, or attractive waves, which are thence propagated indefinitely outward. The intensity of the wave force thus developed, at any point of the envelope, depends on the inequality of action exerted on its constituent atoms lying at slightly different distances from the nucleus; and thus upon the rate of variation of u regarded as a function of R. It may thus be regarded as proportional to For this, as we have already seen, we have the equation

du

dR

This has its maximum positive value at the distance, R, at which u=0; and decreases as R increases until the maximum value of u is reached, where it becomes zero. It may be seen, then, that the system of attractive waves under consideration will have a resultant centre lying in the vicinity of the lower or inner surface of the envelope. The entire action of this wave system should be nearly proportional to the value of at the zero point of u, which we will call v'. In former papers I have denoted the coëfficient of this attractive action of one molecule on another, by n.3 We have then n const. X v'.

=

du

d R

But the dynamical repulsive action exerted between the constituent atoms of the envelope should also originate a system of repulsive waves. The resultant centre for these should lie toward the outer surface of the effective envelope. The coefficient of this wave system I have denoted by m. Regarding this, for the present, as constant for all molecules at the same temperature, we have ท const. X v'.

m

Another system of repulsive waves should be developed, in the luminiferous ether below the envelope, by the dynamic collapses of the envelope. These will be propagated by the luminiferous ether. The expression given in former papers for the force of effective molecular action,3 represents the result of the joint action of the three systems of waves, on a contiguous molecule. It will be

Sce Journal of Science, May 1879, p. 346.

n

m

seen, then, that we have a mathematical relation established between a definite mechanical feature of the molecular envelope, indicated by v', and the ratio upon which the force, or representative curve of effective molecular action, depends. We shall see hereafter that definite relations may also be derived between the mechanical condition of the molecule and the physical and chemical properties which it exhibits.

Let us now take up the question of the determination of the comparative dimensions of the ultimate molecules of different substances. If the nuclei (i. e., the single central atoms) of molecules are all of the same density, the radius, r', of any nucleus, and approximately in our formulæ, should be proportional to the 3/m, orat. weight. But the marked differences of property, exhibited by certain elements of nearly the same atomic weight, show that their constituent atoms must differ in some other particular than mass, or weight. The simplest and most probable supposition that can be made is that they differ in size for the same mass, or in other words in density. This theoretical conclusion accords with the speculative hypothesis I ventured to suggest several years since, from other considerations, that the atoms of bodies might be masses of condensed ether, but does not necessitate this supposition. A similar conception of the probable constitution of the atom has been propounded by Sir William Thomson, and other eminent physicists.

Adopting the idea that the nuclei of molecules may vary in density, the value of C' may vary from one element to another by reason of the varying density of the molecular nucleus, and also by reason of the varying distance between the nucleus and the envelope; since the mass of ether acting repulsively on the envelope will vary with this distance. If the comparative densities of the atoms of elements were known, in addition to their comparative weights, or masses, we could by means of our formulæ deduce their dimensions, and also the diverse capabilities of action of the elements considered; and could test our theory in a direct and decisive manner. In the absence of this à priori knowledge the only possible mode of proceeding is to deduce from certain recognized properties of any element under consideration, as experimentally determined, the values of r, r', C', R, R', and v', and all the mechanical features of the molecule; and from these derive, if possible, expressions for the other comparative properties of the

element, and then compare the numerical results obtained with the results of actual experiment. The process of calculation actually pursued is this. The experimental data assumed are the molecular volume of the substance, and its tenacity, or instead, its coëfficient of elasticity (E). If the substance be considered in the liquid state, and at the boiling point, the molecular volume alone suffices. The tenacity, or coëfficient of elasticity, makes known the comparative ratio and the molecular curve, and thus the comparative value of v' by means of the relation already given. From the molecular volume we derive the radius of the molecular volume, and thence the radius, R', of the effective molecule, by means of the neutral distance derivable from the value of We then have, to find and C', the equations

n

m'

n

m

and v1 =

2 X at. weight

(b)

(c)

The numerical results obtained for a variety of substances are given in Table I. For the designations of the captions of the columns, v', c', R', R, r, r', and u', see ante. The values of x are the exponents of the power to which the atomic weight is to be raised to produce r, and the values of are the corresponding exponents answering to the values of r. The comparative values of r', R', and v', for the elements, are graphically represented in Figs. 1 and 2. The comparative densities of the atoms, or nuclei of the molecules, are also shown in Fig. 2.

Upon the present theory the heat pertaining to a molecule consists in the vibratory movement of its envelope, or the correlative pulsation of the ether at the surface of the nucleus; for the two are related as action and reaction. This conception gives for the specific heat of a molecule the expression,

Specific heat=

v (R-2

× (R' - R) × u'

(4) where' denotes the radius of the actual nucleus, under the supposition that the ethereal heat-pulses are reflected from the surface of the nucleus. I find that this expression gives the value of the molecular heat obtained by experiment, if a value of r' be taken somewhat less than that of r. We may assume, then, that the radius of the actual nucleus is equal to the value of determined, or is somewhat less than this. The results of the calculations of the molecular heat are given in Table II. The assumed values of rare given in Table I.

Before proceeding farther with the calculations proposed I will consider briefly two or three topics which have a bearing on the deductions that remain to be made.

(1). Indefinite extension of a single isolated molecule. That no theoretical limit would exist, to the extension of the envelope of a single isolated molecule, appears from the value of u (Eq. 2). This increases from zero to a maximum, and then decreases indefinitely.

(2). Condition of the electric ether between molecules, as to tension and density. On examining Fig. 3, it will be seen that

FIG. 3.

OHO

the effective attraction exerted by two molecules, on the electric ether lying to one side of the line of their centres, will give rise to an effective force directed toward this line and condensing the ether upon it. At the surface of a body all the pairs of contiguous molecules will exert a similar compressing action, directed inward and thus determining a certain density and tension of the electric ether occupying the interstitial spaces in the interior of the body.

(3). The relation between the tension of the interstitial electric ether and that of the luminiferous ether between the molecular envelopes and the nuclei. Between these tensions an equilibrium should subsist, or tend to subsist. If this equilibrium should be in any way disturbed, the immediate consequence would be either a contraction or expansion of the molecular envelopes, with attendant electric or ethereal wave movements. The tendency of such wave movements, emanating from the disturbed molecules, should be to urge the envelopes of neighboring molecules either toward or from

their nuclei, according as they occur in the interstitial electric ether or in the luminiferous ether. Such disturbances of equilibrium of tension, with these attendant results, may result from a change of either of the two individual tensions, ethereal or electric. The ethereal tension may be increased by the access of heat pulses. The interstitial electric tension may be altered, by a surface contact with a substance of greater or less electric tension, or by the mixture of liquids or gases, in which the electric tension, u, of the molecules is unequal.

We are now in a position to make definite determinations of the electric and chemical relations of substances. From what has been stated it may be seen that if the ethereal tension below a molecular envelope be increased, or the interstitial electric tension be diminished, an instantaneous effective force will come into operation that will tend to urge the envelope outward, and initiate wave impulses in the interstitial electric ether. The force of electric tension thus developed I will designate by f. The energy of the electric movement originated by this force I denote by f" and call the electro-motive force. For f I obtain the following expression.

Let f = then ƒ"=ƒ'× molecular volume.

(5)

(6)

The values of f, f', and f", computed for the elements included in Table I, are given in Table II. The comparative values of f, as well as of f", for these elements, are also represented in Fig. 4. It is to be observed that the substances marked with an * are taken in the molecular condition in which they exist in certain liquid compounds at the boiling point. Thus the quantities given in the Table for oxygen answer to oxygen molecules in water at its boiling point. The same is true of Table I. By the neutral distance, in Eq. (5), is meant the distance between two contiguous molecules of a body, in its ordinary undisturbed state. It is the value of x, in the expression for the force, F, of effective molecular action, at which F0. (See Journal of Science, May, 1879, pp. 346 and 347. The neutral distance is represented by Oa in the molecular curve on p. 347.)

When the molecules of two substances brought into contiguity act on each other chemically, the process consists in an expansion