Fluidity Experiments. Champion Oil. Downer Oil Co. Sample 28. Seconds required 531.5 681. 840. Neatsfoot Oil. Temperature. Fluidity Experiments. Seal Oil. Sample 21. Seconds required 578.5 Alexander Boyd & Sons. Seconds required to empty pipette. 315.5 Temperature. DETERMINATION OF THE COMPARATIVE DIMENSIONS OF ULTIMATE MOLECULES; AND DEDUCTION OF THE SPECIFIC PROPERTIES OF SUBSTANCES. BY WILLIAM A. NORTON, of New Haven, Conn. In papers on topics pertaining to Molecular Physics, read before the National Academy of Sciences, and subsequently published in the American Journal of Science, I have presented an alternative conception of the constitution of an ultimate molecule to that commonly entertained, viz.: that, instead of being a group of similar atoms endued with inherent forces, of repulsion at the more minute distances and attraction at all greater distances, it consists of a single atom surrounded by an envelope of electric ether, immersed in and permeated by the luminiferous ether condensed upon the atom; and that this investiture with an ethereoelectric atmosphere gives to the atom its panoply of power. I have shown that this conception leads to that of the operation of forces of attraction and repulsion, emanating from different centres, and varying according to the law of inverse squares; and given a mathematical expression for the result of the joint action of these forces, which I term the Force of Effective Molecular Action. I have also shown that the general mechanical laws and properties of bodies may be deduced from the force thus precisely expressed; that numerical determinations of tenacities, etc., may be obtained, in close correspondence with experimental results,-that every substance has its own precise formula and corresponding curve of effective molecular action, capable of determination, which represents all its mechanical properties, general and specific,- and that to the liquid and gaseous states of a substance answer particular curves which sustain numerical tests no less successfully than that which represents the solid state.1 It has also been made evident that upon the conception adopted, the ultimate molecule should have the property of variability, in its dimensions and forces, which seems to furnish a key to the satisfactory explanation of a variety of phenomena; as the set of materials after a force of stress has been applied to them, viscosity, and numerous other consequences of imperfect elasticity, and possibly also of chemical changes.2 In the present paper I propose to consider the conditions of 1 In Journal of Science, May and June, 1879. 2 In Journal of Science, March, 1879. equilibrium of individual molecules, and undertake the theoretical determination of the comparative dimensions and mechanical features of the molecules of different substances, as well as the mathematical deduction of the comparative properties and relations of substances, from the mechanical, physical, and chemical points of view. In giving a detailed exposition of the mechanical constitution of a molecule, we have to consider : 1. The Nucleus, or atom, surrounded by an ethereal atmosphere condensed upon it by the attraction, or virtual attraction, of the nucleus. the 2. The Electric Envelope, consisting of a less subtle ether, atoms of which are at the same time attracted by the nucleus and repelled by the condensed ether resting on the nucleus. Each atom is solicited by an effective force equal to the difference of these individual forces. This is represented by the expression C'm R* r2 (R− r)2 (1) in which m= mass of nucleus atomic weight of substance; C=coefficient of attraction of nucleus; C'=coeff. of repulsion of ethereal atmosphere; R distance from centre of nucleus to any point of = envelope; r distance from centre of nucleus to centre of ethereal repulsion; ueffective force soliciting atom of envelope. The equilibrium obtains, at all points of the envelope between the entire compressing action due to this effective force and the elastic resistance of the compressed ether. If C' be expressed in fractional parts of C regarded as unity, the expression for the effective force becomes C' u = m r* (R − r)2 3 Let C1=√, and C2 =3√7; (2) then for the zero value of u, R; and for max. value of u (or u'), R' = For the rate of variation of u with R, we have (3) The equilibrium here considered is a dynamical one. It is a fundamental hypothesis of the theory, that the attractive and repulsive forces exerted on the envelope of a molecule consist of incessantly recurring impulses (or may be so represented). Between the contiguous atoms of the entire ethereo-electric atmos 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 dR 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 n 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 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 3m, 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 |