The refractive index of an ionized medium

There has recently been some discussion as to the appropriate formula connecting the refractive index μ of a medium with its atomic characters, in particular of whether it is the Sellmeyer formula S = μ2 — 1 (1) or the Lorentz formula L = 3 (μ2 — 1)/u2 + 2 (2) that is related to them. It has long been accepted that for many substances, in particular for transparent liquids, the L formula is correct, but there are other substances which as certainly demand a formula in S. The distinction is by no means trivial, and it proves a surprisingly subtle matter to find the proper discrimination on theoretical grounds. It will probably come as a surprise to most who have not studied the subject in detail (as it did at first to the present writer) that a question of principle of this kind should still be unsettled, when the main work on it was done more than fifty years ago, for it is not as though it were an obscure point outside the general field or interest of physicists, and, moreover, there has never been any doubt as to the soundness of the basic principles from which one must start. The present paper really falls into two parts. From 7 onwards there is presented what appears a satisfactory method of discussing the subjects. It is free from the central difficulty, the consideration of the internal electric fields in matter, and supplies sufficient (though perhaps not necessary) conditions for discriminating between substances requiring the two types of formula, and it gives the rule for a mixture of the two kinds of substances, a result I believe to be new. But it was not possible to be content with these developments without a discussion of the older methods, for the subjects has been incorporated in the text-books, and there will be many who have regarded it as a settled question. Therefore it seemed proper to devote some space to the much more formidable task of criticizing these older methods. The chief difficulty of the subject has been that it is only too easy to find arguments, quite as convincing as many of those always accepted in theoretical physics, which lead to either of the two contradictory formulæ. It is quite easy to see weaknesses in these arguments, but it is as easy to see them in the right ones as in the wrong. Now it is probable that for many purposes we shall have to continue to use such rather inadequate arguments, and so it seemed worth while to see whether the discrepancies could be cleared up without a radical change in the method of approach. This is the subject of 3—6, and though the great difficulty in getting clear-cut arguments suggests most of all the need for a wholly different approach to the question, yet such arguments, in a general way and without any precise criteria, do show that a medium with free electrons should obey the S formula and one with isolated atoms the L. It has proved extraordinary difficult to avoid fallacies in this part of the work, and it is possible that it still contains some; if so, the fact is to be taken chiefly as confirmation of the necessity of having methods free from such troublesome subtlety.