On the Relationship Between Hardness and the Physical Constants of Elements.

P. Lazarev. (Proceedings of the Academy of Sciences, 1918).

In three papers the author examines the relation between hardness and other physical constants. First of all, a relation is established between atomic concentration and hardness, the latter being defined as the force which must be applied to a molecule in order to be able to balance the forces of molecular attractions and thus move the particle to a neighboring place. The above relation shows that the hardness \(H\) is proportional to the concentration of the atoms of the element \(N\). It is assumed here that the law of action of molecular forces is the same for all elements. The force holding atoms at the surface must be proportional to the force which holds the atom inside the body, and under the influence of which the atom acquires its own oscillations of a definite period. Calling \(N\) the number of oscillations and \(A\) the atomic weight, it can be shown that \(N = \sqrt{\frac{H}{A}}\), and this relation, as is seen from the tables given in the paper, is excellently confirmed by experiment, with \(N\) borrowed from Nernst’s data.

Further, it is quite simply derived that \(H\) must be proportional to \(E\), the modulus of elasticity in tension. This relation is confirmed by experimental data.

Finally, the proportionality of \(H\) to the latent heat of fusion \(Q\) has been established theoretically, and this relation holds for many elements. The exceptions are \(Fe\), \(Ni\), and \(Pt\), \(Pd\).

In the third paper the author gives an empirical relation between the number of atoms in a unit volume \(N\) and the limit of elasticity \(G\); here, in a series of elements, it is clearly seen that with an increase of \(N\), \(G\) also increases. Some of these relations were empirically indicated by Benedicks.

As an epigraph to this work one may take the words of Faraday, who possessed the gift of profound physical intuition: “I believe with many other lovers of natural knowledge, that the various forms under which the forces of matter are made manifest have one common origin; or, in other words, are so directly related and mutually dependent that they are convertible, as it were, one into another, and possess equivalents of power in their action” (Life and Letters of Faraday by Dr Bence Jones 1870 p. 199).

B. V. Ilyin.