carbon and chlorine gave those of the other clements in the same table. Columns fourth, fifth, and sixth, in Table VII., have the same signification as the corresponding columns of Tables V. and VI.

The results tabulated in V., VI., and VII., are sufficient to show that the interferential equivalents of compounds may, in many cases, be computed with a tolerably close approximation from those of the constituent atoms. The approximation is, however, much less close than in the cases of mixtures. On the other hand, the rule fails entirely with certain compounds. Thus, the six liquids of the aromatic series forming group fifth of Table IV., present very marked exceptions. In these cases, no values of the interferential equivalents of carbon, hydrogen, and oxygen, can be found which will enable us to compute the molecular equivalents. Mr. Gladstone has met with similar exceptions in the refractive equivalents of the benzol series, and suggests,

*

* Journal of the Chemical Society [2] Vol. 8, p. 101.

in substance, that these are probably due to the fact that, optically, each molecule may be regarded as composed of groups of atoms, each group possessing a specific optical character. So far as the interferential equivalents are concerned, further data are necessary to enable us to test this explanation.

Landolt has given the densities and indices of refraction of a number of mixtures. I have not discussed these results from my own point of view, because since the publication of his work the progress of organic chemistry has shown that many of the substances with which Landolt dealt could not have been absolutely pure, though prepared with great care for the special purpose of his investigation.* I think I have shown that the so-called interferential constants possess a real value as numerical characteristics easily determined by measurements of two indices of refraction and a single observation of density at the same temperature. But the value of the new constants in quantitative analyses can only be fairly estimated when we possess determinations of indices and densities for a series of mixtures for which the proportions, densities, and indices of the constituents are accurately known. The time has also arrived when a much greater degree of accuracy in the determination of indices of refraction is necessary. Even five decimal places do not answer the present requirements of science. Six are attainable with spectrometers reading to two seconds of arc.

It is easy to see that the numerical value of an interferential constant depends in part upon the angular distance of the spectral lines between which the bands are counted. The lines C and G are particularly well adapted for standard limits, as they are hydrogen lines always obtainable by a small Ruhmkorff coil and hydrogen tube. The interferential constant may be taken as a measure of the dispersive power of a body; and it is readily shown that with this measure, also, the total dispersive power from A to H is the sum of the partial dispersions from A to B, B to C... G to H. The theory and construction of achromatic lenses might also be based upon this measure of dispersive power, but it would probably possess no practical advantages over the ordinary method.

*I refer to the improvements in separating liquids of different boiling-points introduced by Linnemann, - improvements which have shown that up to the period of his work we had no really accurate knowledge of the boiling-points of a number of liquids long known to science, but never before obtained in a state of perfect purity.

II. ON A METHOD OF MEASURING REFRACTIVE INDICES WITHOUT THE USE OF DIVIDED INSTRUMENTS.

The importance of an accurate determination of all the physical constants which characterize any substance having a definite chemical constitution becomes daily more and more evident. The researches of Gladstone, Landolt, and others have shown that indices of refraction possess a peculiar value and interest. As the instruments necessary for their determination are expensive, and often beyond the reach of working chemists, a simple and sufficiently accurate method of measuring them by means of the spectroscope alone will doubtless be welcomed.

The method which I propose is one of comparison, and applies with convenience only to the case of liquids. A hollow prism is to be filled with the liquid to be examined, placed upon the stage of the spectroscope, and turned until a given ray the line D, for instance is seen by the observing telescope to be in the position of minimum deviation. The eye-piece of the telescope should have two parallel spider-lines placed very near each other in the plane of the diaphragm. When the dispersion is sufficiently great to separate the line D into its two components, either component may be made to bisect the interval between the two spider-lines, or the two components may be made to occupy such positions that their middle line shall bisect the interval. The observing telescope is then to be firmly clamped. The prism is now to be removed, the liquid poured out, and the prism cleaned and dried carefully. It is then to be filled with any liquid the indices of refrac tion of which are known, and which the observer judges to have a mean index not greatly differing from that of the liquid to be measured. The prism is to placed upon the stage of the spectroscope, and turned until the observer ascertains that the two spectra would be in the field of view if both could be seen at the same time; or, what is the same thing, that they would be more or less completely superposed. Should this not be the case, another comparison-liquid must be chosen; and so on until one is found which fulfils the requisite conditions. Supposing that this is successfully accomplished, the prism is to be turned until, for the position of minimum deviation, a known line in the spectrum exactly bisects the interval between the two spiderlines. The index of refraction of the given liquid for the line D is VOL. X. (N. S. 11.)

27

then the same as that of the known line in the spectrum of the liquid used for comparison; for we have for each case

and, since P is constant, and D' = D, it follows that n' = n.

16

By this method, the index of refraction of a given liquid may be determined for a single line; as, for instance, for D. This is sufficient for the optical analysis in the form in which it has been developed by Landolt. Two objections to this method present themselves at once. The first is the necessity of finding by tentative processes a comparisonliquid which shall have about the same mean index of refraction as the liquid an index of which is to be determined. I admit the force of the objection, but it must not be estimated too highly. Whole classes of liquids agree pretty nearly in their optical characters; as, for instance, the oils of the C1o Hic series, the ethers of the fatty acids, hydrocarbons and saline solutions. The second objection is that, with liquids of low dispersive powers, it is not easy to distinguish the spectral lines with absolute certainty. This difficulty is easily avoided by using a second prism, with a high dispersive power, placed next to the collimator so as to form a long spectrum, which shall fall upon the trial-prism. The final dispersion is then the sum of the dispersions of the two prisms, and no difficulty will be found in distinguishing the spectral lines. It is, of course, necessary that the subsidiary prism shall have the same position in both cases. Two or more subsidiary prisms either of flint-glass or of carbonic disulphide may be used with great advantage, but one will usually be found sufficient. The indices of refraction of the comparison-liquids being known for at least three lines, the values of the constants a, b, and c in Cauchy's formula

may be determined. It then only remains to compute the index of refraction of the line which has been found to have the same index as the line D, for instance, of the liquid examined. This is easily done when the line in question has been identified by means of Kirchhoff's chart so that its wave-length is known. It will, of course, often happen that no line in the comparison-liquid exactly corresponds with the line D selected for the liquid examined. In this case the index of the nearest line may be employed instead, when great accuracy is not required and when subsidiary prisms are used, or we may use a filar

micrometer, and interpolate so as to obtain the index of a coincident line by measuring the distance of the relative line D from one or more visible lines in the comparison-spectrum. The eye-piece micrometer suggested by Professor Rood* would also give all necessary precision, and would have the advantage of being very much cheaper than a filar micrometer.

The method above given enables us to determine the index of refraction of a single line only, unless the prism is emptied, cleaned, dried, and the operation then repeated with a second selected line. To obviate this difficulty, I have employed the following modification of the prism with entire success. The prism is divided into two by a septum perpendicular to its refracting edge. Each prism thus formed has an opening in its base by which liquid may be introduced or removed, and which can be closed with a cork. When the two glass plates are carefully cemented to the brass frame, the two prisms will have the same refracting angle. One of them is then to be filled with the comparison-liquid, the other with the liquid the indices of which are to be determined. The double prism being now placed upon the stage of the spectroscope, one face of the prism containing the comparison-liquid is to be covered with a slip of metal. The spectrum of the liquid to be examined will then be seen by means of the observing telescope. Any line-as, for instance, C-may then be selected, brought into the position of minimum deviation, and the telescope adjusted until this line bisects the space between the parallel wires in the plane of the diaphragm of the eye-piece. The telescope is then to be clamped as before without disturbing the adjustment. If now one face of the prism containing the liquid examined be covered with the slip of metal removed from the face of the other prism, the spectrum of the comparison-liquid will be seen, and it will be easy to determine what line in this spectrum most nearly corresponds in position to the line C of the other spectrum. By alternately covering the faces of the two prisms with the metal slip, coincidences or near coincidences may be observed for D, E, F, &c.; and in this manner the data obtained for the constants in Cauchy's dispersion-formula for the liquid examined, in a short time and with great facility. It must be borne in mind that the two spectra in this process cannot be seen simultaneously, their images being combined by the observing telescope into one.†

* Am. Journal, 3d series, vol. vi. p. 44.

† Mr. S. P. Sharples has suggested to me that if a cylindrical lens were employed as the object-glass of the observing telescope, the two spectra could be seen in the field at the same time.