Here the observations contained in a horizontal series all refer to the same metallic layer. Accordingly theory would require that the values of the constant e should be identical in both cases (reflection in air and reflection in glass), and that the quo

tient of should be equal to the exponent of refraction μ of 03 glass, given in the last column. These requirements of theory are evidently only very imperfectly fulfilled-which necessitates the assumption that, in consequence of a different molecular constitution of the metallic surfaces adjacent to air and to glass, the constants of reflection assume somewhat different values. Similar are the results of the series of observations given in § 43, for the reflection-constants of the same silver surfaces in air, water, and oil of turpentine :

€1 =87° 24',

101=0·5178,

=1·234, μ=1·336, | 0=1·440, μ=1·474.

With regard to transparent metallic layers the first question is, whether the degree of transparency required by theory agrees with that found by experiment. As the factor D2 is contained in the expression for the intensity of the ray after transmission, that factor must first be determined. With the aid of the above given optical constants of silver for Fraunhofer's lines D and H, 1 the values contained in the following Table, of for various D2

thicknesses of silver, are easily calculated on the supposition of perpendicular incidence :

When, further, we set up the actual intensity-expression for the ray which has passed through the system of silver and flint. glass, in which the loss of intensity in the passage through the uncoated surface of the glass also comes into consideration, we

find that the value of D2 with perpendicular incidence is to be multiplied by a numerical factor which, as the thickness increases, approaches the limiting value 1.747 for Fraunhofer's line D, and 2-2556 for the line H; so that the greater transparency for rays of higher refrangibility is thereby rendered more apparent.

Quincke found (Opt. Unters. § 52) that silver of 0.09 millim. thickness, gold of 0.16, and platinum of 0.40 still appeared transparent. The succession of degrees of transparency is, with regard to the optical constants of these metals, that which, from the theory, was to be expected; and the value 009 for silver may be regarded as a limiting value satisfactorily in accordance with the theory, since the extinction at this thickness has proceeded to about 6 of the original intensity.

π

4

Although the phenomena hitherto discussed have revealed deviations from the theory which could only be explained by the assumption of certain molecular differences in the metallic surfaces, occasioning a variation in the optical constants, yet the general character of the phenomena was in accordance with the theory. On the contrary, a fundamental difference between theory and experiment occurs in the Newton's colour-rings observed by Quincke on thin metallic lamellæ (Opt. Unters. §§ 49-64). Silver, gold, and platinum undoubtedly belong to the group of metals for which the condition e+u>· u> is fulfilled, for which therefore, as was above shown, in the transmitted light generally no maxima and minima can occur. As regards the maxima and minima of the reflected light, there are of course an infinite number of them, which yet, as may easily be shown, escape observation through their small intensity. Considering that, for 0.1 millim. thickness of silver, only variations of intensity of the order of about 4 of the total can be expected, only the number of maxima and minima which as far as this thickness are, according to the theory, to be expected need be counted. 4πс0, cos (e+u) For A=0.1 millim., 2L=

λι

.0.1 millim. In

the simplest case of perpendicular incidence, c=1, u=0; further, for Fraunhofer's line D, λ=0.5888 millim., so that we obtain

2L=0.1825.2π=65° 42'.

As far as this thickness, therefore, the periodic terms of the function have not yet run through one fifth part of their period, and, independently of the bright or dark centre, in the favourable case perhaps only one maximum or one minimum will have been observed.

More remarkably, the breadth of the bright and dark streaks

observed by Quicke was not essentially influenced either by the colour or the angle of incidence. If, however, they are to be regarded as Newton's interference-lines, it will thence follow that Cauchy's theory of reflection cannot, without essential modification, be applied to such thin metallic lamella; considerably different values must be assigned to the optical constants; particularly the constant e must have a considerably smaller value than for opaque metals, in order to be in accord with experiment. But thence will necessarily result the further consequence that, even in opaque metals, the arrangement of the æther in a superficial layer of measurable thickness is essentially different from that in the interior of the metal, so that the quantities 1 and e lose their character as constants, and that, as Quincke has assumed, the reflection takes place not in a geometrical bounding surface, but within an intermediate layer of finite thickness.

The middle of the system of fringes observed by Quincke, corresponding to A=0, appeared dark in silver lamella when the reflection took place in air, bright when in glass-which agrees with the above-developed result of the theory. The action of gold and platinum was somewhat anomalous."

I refrain for the present from a closer discussion of the expressions for the phases, and merely refer to an easily controllable result of experiment which likewise stands in contradiction to the theory. M. Quincke found (Gött. Nachr. Dec. 1870) that the difference between the directions of the rays transmitted through air and through metal amounted to nearly for different thicknesses of metal <0·04 millim. For minute thicknesses of metal, the condition of a constant direction-difference between metal and air cannot generally be fulfilled by the theory. For greater thicknesses, the phase d approximates, as before mentioned, to the limiting form L-, and the quantity L, increasing with the thickness, would be equal to the corresponding quantity for air, if the direction-difference were to assume the constant value . The condition thence following is

This cannot be fulfilled for any angle of incidence. Let it hold good for perpendicular incidence, and approximately for small angles of incidence, it will be reduced to 0, cos e=1, whereas for silver 0, cos e=0.5373 was found above. But even in the case of its being fulfilled the constant direction-difference would not be found equal to +7, because the angle lies in the first quadrant.

Leignitz, January 1871.

always

LXII. Intelligence and Miscellaneous Articles.

ON HARMONIC RATIOS IN SPECTRA. BY J. L. SORET,

THE HE idea of seeking harmonic relations between the different lines of the spectrum of one and the same body is doubtless not new, several savants having already occupied themselves with this question*; but the article which has just been analyzed†, as well as Mr. Stoney's previous note, appears to us to present a special interest:-1st, by the extreme precision with which the calculated wave-lengths coincide with those deduced from experimental determinations which are capable of inspiring great confidence; 2ndly, by the high order of the harmonics which are indicated—such that the ratios of the numbers of vibrations are by no means very simple. The complication of these ratios, particularly for chlorochromic acid, as well as the absence of the greater number of the harmonics in the case of hydrogen, is even of a nature to excite doubts of the correctness of the hypothesis which is to be controlled.

Nevertheless the coincidence of the calculated with the observed values is too exact for it to be possible to attribute it to chance: if not due to the existence of harmonics, it must proceed from some other determinate cause. It seems, then, to us that here are motives for urging the study of this interesting subject. By taking into account the ultra-violet lines, of which a great number have already been determined photographically by M. Mascart, we should have a much more extensive field than if we confined ourselves to the visible spectrum, which does not comprise even an entire octave.

As an example, I will notice some relations at which I arrived with facility in a very superficial and incomplete examination of the question.

It is known that the spectrum of magnesium presents, among other bright lines, a group of three green lines (coinciding with the solar lines 6). M. Mascart, in studying the ultra-violet portion of this spectrum, has found two other groups of three lines perfectly resembling the preceding in their appearance; and to his record of this fact he adds:"The reproduction of such a phenomenon can hardly result from chance; is it not natural to admit that these groups of similar lines are harmonics, depending on the molecular constitution of the luminous gas?"

The wave-length of the least-refrangible of the three lines in each

Among others, M. Lecocq de Boisbaudran (Comptes Rendus de l'Acad. des Sciences, 1869 and 1870) has noticed a great number of approximately simple ratios between the wave-lengths of the various lines belonging to one and the same body, as well as certain relations between the positions of the lines of different bodies

† Messrs. Johnstone Stoney and Reynolds's article, in the Philosophical Magazine for July 1871, “On the Absorption-spectrum of Chlorochromic Anhydride."

Comptes Rendus de l'Acad. des Sciences, 1869, vol. Ixix. p. 337.

of these groups is given by the following numbers :

millim.

1st group, A=0·0005183 (Ångström's determination),

nearly identical with the ratio between the wave-lengths of the hydrogen-lines C and F, lines which Mr. Stoney regards as the 20th and 27th harmonics of one and the same fundamental vibration. The first two groups of magnesium also might therefore be regarded as the 20th and 27th harmonics of a fundamental group of vibrations, of which the wave-length, for the least-refrangible line, would be 00103660 millim. As to the third group, it would not represent the 32nd harmonic (as this is done by the hydrogen-line h), but, very nearly, the 31st.

27

20

Facts of the same kind are found also for the lines of cadmium which have been determined by M. Mascart*. Thus the ratio of the wave-length of the 1st line (λ=0·00064370) to that of the 18th (X=0·00025742) is exactly as 5 to 2. Further, between the 2nd line of cadmium (A=0·0005377) and the 8th (X=0.00039856) the ratio is found, with an approach to accuracy very near the limit of the errors of observation. These two lines might, then, be regarded as the 20th and 27th harmonics of one and the same fun damental vibration. The 32nd harmonic is not found; but, as in the case of magnesium, the 31st harmonic nearly coincides with the 10th line (λ=000034645). The 6th line (X=0.00046765) represents very exactly the 23rd harmonic of the same fundamental. Finally, the 6th and 10th lines are also connected by the same ratio of 20'

27

It seems difficult to admit these coincidences to be fortuitous; and probably others still would be discovered on a closer examination of the question.-Bibliothèque Universelle, Archives des Sciences Physiques et Naturelles, September 15, 1871.

ON THE ELECTROMOTIVE FORCE OF INDUCTION IN LIQUID CONDUCTORS. BY DR. L. HERMANN.

On the occasion of experiments on the excitation of the nerve by induction in itself, which I shall elsewhere communicate, the question suggested itself whether the electromotive force of the induction demonstrated by Faraday in liquid conductors was the same as that in metallic ones, other conditions being the same.

Since under

* Annales de l'Ecole normale, 1867, vol. iv. p. 28. Phil. Mag. S. 4. Vol. 42. No. 282. Dec. 1871.

2 H