of the one set of molecular envelopes and an attendant contraction of the other set. That it may be initiated it is essential that the values of ƒ should be unequal for the two substances. The molecular envelopes of the substance which has the larger value of ƒ will expand, and those of the other contract. The former may be termed electro-positive with regard to the latter; and the latter electro-negative with regard to the former. In the chemical process the electric movement is from the former to the latter. Thus when zinc combines with the oxygen of water in the voltaic cell, the envelopes of the zinc molecules expand, and those of the oxygen molecules contract, and the electric movement is from the former to the latter. The final result is that the ratio is increased in value for the oxygen molecules, and diminished for the zinc molecules, and thus brought approximately to the same value for the two sets of molecules (see Journal of Science, May, 1879, p. 346). The process of "chemical combination" consists in a modification of the condition of molecular envelopes (by expansion and attendant contraction) by which the two sets of molecules are brought into correspondent conditions (whether answering to the solid, liquid, or gaseous state). The initiating cause is an inequality in the values of the force f, for the two substances, and the effective force in operation is the excess in the intensity of ƒ for the electropositive substance over that for the electro-negative. The energy of the process of change depends on the excess in the value of ƒ for the former substance over that for the latter.

It is important to observe that f and f" have not certain fixed values for each particular substance. The value of each, for any substance, varies with the temperature and with the state of aggregation. The chemical relations of substances may thus vary materially with the temperature at which they are brought together. These are definitely shown by the comparative values of f, at the temperature considered. They are, however, liable to material modification by the proximity of other substances whose forces, f, come into simultaneous operation. The case of contact along a definite extent of surface (as in the contact of a zinc plate with the water in a voltaic cell) is to be distinguished from that of the mixture of two liquids. In the former case the distance between

the molecules of each substance becomes a modifying factor; and it is conceived that a nearer approximation to the chemical relations will be obtained by dividing ƒ and f" by neut. dist. (See columns 9 and 10, Table II).

As to the effect of heat to promote chemical combination it may be readily seen that its general tendency is to raise the value of f. It may thus promote oxidation and combustion by raising the value of ƒ for the combustible above that which obtains for oxygen. Heat, it is to be observed, in such cases, brings the molecules into the condition in which an effective force, f, comes into operation. The heat subsequently developed,— the "heat of combination,”— is the result of the electro-motive energy that comes into play. It is also in part due to the diminution of the neutral distance between the molecules whenever a lower state of aggregation is reached.

The chemical relations of substances to oxygen are shown by the comparative values of f. On consulting Table II it will be seen that the values of ƒ for the metals, lithium, sodium, and potassium, are greater than for oxygen in the condition in which it exists in water at the boiling point, and accordingly these metals should be electro-positive to the oxygen, and have a strong tendency to combine with it when brought in contact with water. For the other metals mentioned in the table the value of ƒ is less than for oxygen, and the electro-positive state, indicated by the value of f, requires to be exalted by heat before such combination can take place; or else the combination must be promoted by favorable conditions afforded by the presence of other substances. The value of ƒ is the lowest for platinum. The large values of f" for the alkaline metals give intimation of great energy in the process of combination with oxygen. The general chemical relations of the elements to oxygen may be seen at a glance by examining Fig. 4. The theoretical chemical relations of the elements to hydrogen, or any other individual element, may be obtained in a similar manner from Table II, or by examining Fig. 4.

In the direct union of two gases, heat, or the electric spark, is the inciting cause of the transformation of the molecules.

The proportions in which two substances may combine should depend on their comparative values of f, and the range of variation which these may experience under the influence of heat and other external relations. It is to be observed here that of two substances, A and B, A may be electro-positive to B under certain conditions of temperature, etc., and under other conditions electronegative to it; since A may have a larger value of ƒ than B in the one case, and a smaller value in the other case. By examining the ascertained values of ƒ for the elements in our Table we may

get an insight into the physical peculiarities correspondent to the terms univalence, bivalence, etc., used by chemists; but this topic cannot now be enlarged upon. We will only state a general principle that here becomes applicable, viz., that in the process of a chemical combination that molecule which expands has its value of ƒ reduced thereby, and that which contracts has the value correspondingly augmented.

Mendelejeff's Law of the Periodicity of the Elements is clearly indicated in the results of our calculations. Compare the values of f, as well as those of v', given in Tables I and II, and represented in Figs. 2 and 4. The values of ƒ give intimation of chemical relations; and those of v' of mechanical relations-but these are not wholly dependent on v'. The law would be more completely indicated if we were to insert the approximate values of ƒ and for certain substances, as fluorine, silicon, etc., for which the data necessary for accurate calculations have not yet been obtained. The theoretical explanation of this law is, that it results from periodic fluctuations in the densities of the nuclei of the ultimate molecules (i. e., of the atoms of the elements). On comparing Figs. 2 and 4, the general correspondence between these fluctuations of density and those of the values of v and ƒ, may be seen-it being observed that an increase in the density of the atom should tend to increase v and diminish f.

Another important theoretical deduction that may be made is that of an expression for the comparative hardness of substances. This should depend on the greater or less susceptibility of the molecular envelopes to compression in the direction of the compressing force and to expansion in the lateral direction. From this point of view we have for the theoretical expression for the comparative hardness of substances, 9 J'Xmolec. vol.' molec. vol. Now we are informed (Phil. Mag., Oct., 1879), that Bettone has determined the hardness of substances by finding the time required for a steel drill to penetrate to a certain depth, and has by this means shown that in fact the hardness of an element is almost precisely inversely proportional to its molecular volume.

or

or

1

I can only briefly allude to another theoretical determination by means of which an additional test can be applied to the general theory. It is that of the points of fusion of the elements whose molecular status has been determined. The essential criterion of the point of fusion of an element is that condition of expansion and vibration of the molecular envelopes at which the ratio

the diagonal forces of the elementary cube, becomes 4.92, or the molecular curve for these forces becomes tangent to the axis of distances. The temperature of the point of fusion above the absolute zero is accordingly assumed to be proportional to the amount of heat energy required to raise the molecules to this condition. From this point of view it may be seen that if we designate by T the rise of temperature, from the absolute zero to the point of fusion, we shall have T.; ;d representing the neutral distance between the molecules, v the molecular volume, and f" the electro-motive force. In a few instances, for reasons that cannot be adequately given, the calculations have been made by the formula T= ; 7 being the molecular volume of iron

v

const.

=

const.

d.

f.d. (7) and f' Now, let T1 = value of T for wrought iron, as given by the formula, T, temperature, in Fahrenheit degrees, above absolute zero, at the point of fusion of wrought iron, and T' the corresponding temperature for the substance considered; and we have T' ToT, and for the point of fusion, Po, Po — T'— 459°. In the calculations made I have taken T。 4400° F., which is a little less (141° F.) than the value for pure iron, given by Wedding (a standard German authority), and about the same amount, greater than the value assigned by Carnelly (Phil. Mag., Oct., 1879).

T

=

The results of the calculations are given in Table II. It is not claimed that the above formulæ are exact, nor can it reasonably be supposed that all the molecular data employed have been accurately determined in this first attempt in an entirely new field of investigation. It would seem, however, that the calculated results are sufficient approximations to the experimental determinations to lend an additional support to the general theory, and justify the assumptions made in the process of calculation; as well as furnish a desirable verification of previous molecular computations.

In bringing this paper to a conclusion, I would ask attention to the fact that in this and my former papers, to which reference has been made, definite numerical results have been obtained in several departments of Molecular Physics in which no exact investigations have been found possible from the ordinary molecular point of view, and precise experimental tests have been applied. If these results do not suffice to induce the reader to abandon his own molecular standpoint for that which is here taken, he may still be

See Journal of Science, May, 1879, pp. 346-7-8, and June, 1879, p. 447.

not unwilling to receive the molecular theory that has been discussed as a scheme of representation, and as a definite working hypothesis furnishing a basis for numerical computations in mechanical, physical and chemical fields of research. Let it here be understood that the point of view we have assumed does not call upon us to discard any of the established principles of the mechanical theory of heat, nor to abandon the doctrine of energy. For the basis of the present molecular theory is as truly dynamical as is that of the alternative theory commonly held. It is the dynamical system alone that is different.

But little assured progress has hitherto been made toward a physical theory of chemical phenomena. It is true, diligent use has been made of the cumbrous hypothesis of compound molecules, capable of breaking up into a host of independent atoms, at a summons issuing from the depths of the unknown, and then marshalling themselves anew into other complex groups; but no definite conception has yet been reached of this great complexity of change as a mechanical process. It is at best but a hypothetical representative scheme. In place of such vague and complex conceptions we now offer the hypothesis of simple ultimate molecules, consisting of single atoms of each substance, surrounded by ethereal atmospheres which expand and contract as a consequence of inequalities in their mechanical state, and thus bring the dissimilar molecules into corresponding mechanical conditions and capabilities. We trust that what has now been offered in its support may secure for it serious consideration.

Let me, in conclusion, epitomize the whole discussion undertaken in this and previous papers, in two general statements.

(1). It has been shown that the mechanical laws and specific relations of bodies, in the three different states of aggregation, may be deduced from one general molecular formula; and that from their atomic weights and certain comparative dimensions assigned to their atoms, may be derived definite expressions representative of the various properties of special substances.

(2). We see that the diverse phenomena of inanimate nature are but different consequences of variations of ethereal tension, produced by propagated ethereal waves of varying tension; and that, contemplated from the highest point of view, they may be conceived to result from the operation of one primary form of force on one primordial form of matter.