Fluidity Experiments. A Spindle Oil. Olney Bros. Sample 16. Seconds required 276. Temperature. 159. 210.5 Aiken & Seconds required to empty pipette. 09 345. Temperature. Seconds required to empty pipette. 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 clasticity, and possibly also of chemical changes. 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. 2. The Electric Envelope, consisting of a less subtle ether, the 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 = (1) in which m = mass of nucleus atomic weight of substance; Ccoefficient 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 R2 ' (R − r)2 (2) Let C1, and C2=√; then for the zero value of u, R=C; and for max. value of u (or u'), R' = r}—c2 For the rate of variation of u with R, we have 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 |