Secondly, that the constants of the bivalent, trivalent, quadrivalent, and apparently quinquivalent groups are practically the same, ranging about 101.
Thirdly, that when a metal combines in a proportion that indicates a lower valency than that ordinarily assigned to it, its constant is somewhat elevated.
I refrain at present from pointing out minor analogies between closely-allied metals, and from attempting to explain the difference between the univalent and the other groups; why sodium should fall away from the value proper to the alkaline group, and closely approximate to that of all the other groups; or why beryllium, bivalent tin, and tri valent iron should be represented by such exceptionally high figures.
It is to be understood that the values given are all deduced from compounds in which the metal plays the part of an electro-positive radicle. Where they combine with oxygen to form the electronegative radicle, the values are completely altered, just as we find in the case of several non-metallic elements.
If we calculate these constants for the square root of the atomic weight instead of that of the combining proportion, we shall obtain Refraction of the Elements and their Chemical Equivalents. 145 for the means—
Univalents .............. 1‘30 Bivalents................. 1'40 Trivalents............... T75 Quadrivalent^.......... 2T2 Quinquivalent......... 2T9
This arrangement does not, as in the former case, give a practically identical constant for the bivalent, trivalent, quadrivalent, and quinquivalent metals. The fact that these numbers increase nearly in the proportion of the square roots of 2, 3, 4, and 5, indicates that the relation involved is not between the specific refraction and the atom, but rather between it and the combining proportion or chemical equivalent of the metal. This brings the optical property into analogy with Faraday’s law of electro-chemical equivalents.
I propose to give this product the descriptive name, “ Refractive constant of equivalent weights.” It may be represented by—
SE* = constant, where S is the specific refraction, and E the chemical equivalent of the metal. Some physicists may prefer to make use of the square of the above formula, namely, S2E = constant.
