short, but probably shorter when the complementary part is more massive, as in the case of a nitrate, than it is in the case of a chloride. But between complete freedom and complete incorporation in a chemical compound there is a considerable gradation, and the capacity of the part to vibrate at particular rates will have a corresponding gradation, and the part may moreover be frequently under the influence of molecules, or parts of molecules, with which it does not combine. This influence will probably be greater as the molecule exerting the influence is greater whether more massive, or, as in the case of such colloids as alcohol, more voluminous. These considerations reconcile all the facts as to the spectra I have observed with the hypothesis I have made.

There are, however, other facts to be reconciled with that hypothesis. I mean the facts of ionization, of osmotic pressure and the correlative facts of the rise of boiling point, and fall of crystallizing point, of solutions. In regard to all these effects the freedom of the parts is the primary postulate, far more definitely so than in the case of vibrations such as my observations relate to. The laws I have tried to investigate appear to hold good up to the point of saturation of the solutions, which is not the case with the laws of osmotic pressure and of change of boiling and freezing points, which have been established for dilute solutions. Further, ionization implies a certain distribution of energy in the field, the ions are charged with electricity. That is not necessary for the absorption of light, which will depend, primarily at least, on the form of the internal energy of the vibrating mass, that is on its structure. That a redistribution of energy occurs at every rupture of a molecule seems certain, solution is attended with thermal effects and so is dilution, and it is only when equilibrium is reached, and as much change takes place in one direction as in the opposite, that the manifestation of such redistribution ceases. How much of the intrinsic energy of the molecules takes the form of heat and how much is retained in the field at the rupture of the molecules we do not know. It is however quite conceivable that the circumstances under which the rupture takes place may determine whether any, or how much, energy is retained by the field, that is whether any, or how many, of the ruptured parts become ions.

The plates, which are all reproductions of photographs, will be found at the end of the volume.

XV.

The Echelon Spectroscope. By Professor A. A. MICHELSON, Sc. D.

[Received 19 October 1899.]

THE important discovery of Zeeman of the influence of a magnetic field upon the radiations of an approximately homogeneous source shows more clearly than any other fact the great advantage of the highest attainable dispersion and resolving power in the spectroscopes employed in such observations.

If we consider that in the great majority of cases the separation of the component lines produced by the magnetic field is of the order of a twentieth to a fiftieth of the distance between the sodium lines, it will be readily admitted that if the structure of the components themselves is more or less complex, such structure would not be revealed by the most powerful spectroscopes of the ordinary type.

In the case of the grating spectroscope, besides the difficulty of obtaining sufficient resolving power, the intensity is so feeble that only the brighter spectral lines can be observed, and even these must be augmented by using powerful discharges-which usually have the effect of masking the structure to be investigated.

Some years ago I published a paper describing a method of analysis of approximately homogeneous radiations which depends upon the observation of the clearness of interference fringes produced by these radiations. A curve was drawn showing the change in clearness with increase in the difference of path of the two interfering pencils of light,—and it was shown that there is a fixed relation between such a "visibility curve" and the distribution of light in the corresponding spectrum-at least in the case of symmetrical lines*.

It is precisely in the examination of such minute variations as are observed in the Zeeman effect, that the advantages of this method appear, for the observations are entirely free from instrumental errors; there is practically no limit to the resolving power; and there is plenty of light.

There is however the rather serious inconvenience that the examination of a single line requires a considerable time, often several minutes, and during this time the character of the radiations themselves may be changing.

Besides this, nothing can be determined regarding the nature of these radiations until

* In the case of asymmetrical lines another relation is necessary, and such is furnished by what may be called the "phase curve.”

the "visibility curve" is complete, and analyzed either by calculation or by an equivalent mechanical operation.

Notwithstanding these difficulties, it was possible to obtain a number of rather interesting results, such as the doubling or the tripling of the central line of Zeeman's triplet, and the resolution of the lateral lines into multiple lines; also the resolution of the majority of the spectral lines examined, into more or less complex groups; the observation of the effects of temperature and pressure on the width of the lines, etc.

so serious

It is none the less evident that the inconveniences of this process are that a return to the spectroscopic methods would be desirable if it were possible (1) to increase the resolving power of our gratings; (2) to concentrate all the light in one spectrum.

It is well known that the resolving power of a grating is measured by the product nm of the number of lines by the order of the spectrum. Attention has hitherto been confined almost exclusively to the first of these factors, and in the large six-inch grating of Prof. Rowland there are about one hundred thousand lines. It is possible that the limit in this direction has already been reached; for it appears that gratings ruled on the same engine, with but half as many lines, have almost the same resolving power as the larger ones. This must be due to the errors in spacing of the lines; and if this error could be overcome the resolving power could be augmented indefinitely.

In the hope of accomplishing something in this direction, together with Mr S. W. Stratton, I constructed a ruling engine in which I make use of the principle of the interferometer in order to correct the screw by means of light-waves from a homogeneous source. This instrument (only a small model of a larger one now under construction) has already furnished rather good gratings of two inches ruled surface, and it seems not unreasonable to hope for a twelve-inch grating with almost theoretically accurate rulings.

As regards the second factor-the order of the spectrum observed, but little use is made of orders higher than the fourth, chiefly on account of the faintness of the light. It is true that occasionally a grating is ruled which gives exceptionally bright spectra of the second or third order, and such gratings are as valuable as they are rare, for it it appears that this quality of throwing an excess of light in a particular spectrum is due to the character of the ruling diamond which cannot be determined except by the unsatisfactory process of trial and error.

If it were desirable to proceed otherwise-to attempt to produce rulings which

FIG. 1.

should throw the greater part of the incident light in a given spectrum, we should try to give the rulings the form shown in section in Fig. 1.

I am aware of the difficulties to be encountered in the attempt to put this idea into practical shape, and it may well be that they are in fact insurmountable-but in any case it seems to be well worth the attempt.

Meanwhile the idea suggested itself of avoiding the difficulty in the following way:

FIG. 2.

Plates of glass (Fig. 2), accurately plane-paralleled and of the same thickness, were placed in contact, as shown in Fig. 2. If the thicknesses were exactly the same, and were it not for variations in the thickness of the air-films between the plates, the retardations of the pencils reflected by the successive surfaces would be exactly the same, and the reflected waves would be in the same conditions as in the case of a reflecting grating-except that the retardation is enormously greater.

The first condition is not very difficult to fulfil; but in consequence of dust particles which invariably deposit on the glass surfaces, in spite of the greatest possible precautions, it is practically impossible to insure a perfect contact, or even constancy in the distances between surfaces*.

If now instead of the retardation by reflection we make use of the retardation by transmission through the glass, the difficulty disappears almost completely. In particular the air-films are compensated by equivalent thicknesses of air outside, so that it is no longer necessary that their thickness should be constant. Besides, the accuracy of parallelism and of thickness of the glass plates necessary to insure good results is now only one-fourth of that required in the reflection arrangement.

In Fig. 3 let ab=s, the breadth of each pencil of rays; bd=t, the thickness of each element of the echelon; 0, the angle of diffraction; a, the angle adb; m, the number of waves of length corresponding to the common difference of path of the successive elements. The difference of path is mλ = μt — ac.

To find the angle corresponding to a given value dλ, differentiate for λ and we find

For the majority of optical glasses b varies between 0.5 and 1.0.

The expression (II) measures the dispersion of the echelon. To obtain the resolving power, put €= dλ/λ for the limit. For this limiting value the angle will be λ/ns,

where n is the number of elements; whence ns = the effective diameter of the observing telescope. Substituting these values we find

To obtain the angular distance between the spectra, differentiate (I) for m; we find