280 Effects produced by Fog and Vapour on the Intensity of Sound. the waves passed from the rarer to the denser portion, or from the denser to the rarer. In an irregular, or flocculent, admixture of air and vapour of water such an abrupt change of density would not be possible; but there might be changes of density more or less rapid from point to point without change of elasticity; and, so far as these changes tend to be abrupt, partial reflection of the waves might ensue. It is also to be considered that the reflections would always take place in the directions of most rapid change of density, whether the density be increasing or decreasing; so that in a flocculent admixture there might be reflections in various directions, and the sound might be dispersed or absorbed in a manner analogous to the absorption of light on its entrance into an opaque or partially transparent medium. Thus air charged with vapour in an invisible state, although optically transparent, might be in various degrees impervious to sound. That this is actually the case was clearly demonstrated by the experiments. This view is confirmed by the fact, observed on October 8, that the intensity of the sound was increased by a heavy fall of rain, the effect of which would be, as is remarked by Dr. Tyndall, to remove to a certain amount by condensation and precipitation the invisible vapour to which the diminution of the intensity of sound is mainly attributable.

Thus theoretical reasons can be given for the experimental results that fog and haze do not diminish, and may even increase, the audibility of sounds, and that loss of sound is chiefly due to certain conditions of the invisible vapour mixed with the air. Theory also indicates that neither by fog and haze, nor by that condition of invisible vapour which diminishes or absorbs sound, is the rate of propagation sensibly altered. But I know of no à priori means of determining whether the amount of vapour in regular admixture with the air may not have some influence on the velocity of sound; and this, I think, is a point which is open to further inquiry by experimental means.

The greater distance to which sounds are audible to leeward than to windward of the place of excitation, is very little owing to the transmission being accelerated by the wind in the former case and retarded by it in the other. It is chiefly due to the circumstance that in those vibratory movements of the air to which the loudness of the sound is principally due there is an excess of condensation above rarefaction, and the consequent excess of the velocity corresponding to the condensation is in the same direction as the current of the wind on the leeward side and opposed to it on the windward side. As the action on the ear is in each case proportional to the square of the compound velocity, the result will be an excess of intensity on the leeward side.

In concluding these remarks, I take occasion to advert to the solution I have given, on hydrodynamical principles, of the problem of lines of magnetic force, this problem being in its conditions analogous to that of determining the effect of the small globules of water in a foggy atmosphere on the intensity of sound. (See the "Note on the Hydrodynamical Theory of Magnetism" in the Philosophical Magazine for July 1869, pp. 42-45, and arts. 4-8 of a new discussion of the same theory in the Number for June 1872). In that solution I have argued that a stream, or a vibration, of the æther receives an impulse on entering into a magnet by reason of the contraction of channel resulting from the occupation of space by the atoms of the magnet, and that this impulse is proportional to the number of atoms in a given space. On the hypothesis, therefore, that the density of the magnet increases by slow degrees from one end to the other, a given element of the æther will receive successive impulses as it moves towards the denser end, and in this way a permanent stream will be maintained in opposition to the inertia of the fluid. In the case of the transmission of sound in a foggy atmosphere, there is not an analogous increment of the globule-density in the horizontal direction of the propagation; but so far as experiment indicates that an impulse is given to the sound-vibrations by the presence of the globules and the intensity of the sound is thereby increased, the two kinds of phenomena are alike, and the proposed theoretical explanations of them are mutually confirmatory.

Cambridge, March 18, 1874.

XXXIV. Connexion between Capillary and Electrical Phenomena. By GABRIEL LIPPMANN*. [With a Plate.]

THE present investigation was made in the laboratory of Professor Kirchhoff, to whom I am greatly indebted for his counsel and for his kind assistance. It might well have been difficult to seek à priori for relations between electrical variables and the so-called constants of capillarity; and in fact I only gradually arrived at such relations, starting from an experiment for which I am indebted to Professor Kühne of Heidelberg, and which is essentially as follows.

A drop of mercury is introduced into dilute sulphuric acid in which is dissolved a trace of bichromate of potash; a polished * Translated from Poggendorff's Annalen, vol. exlix. p. 546.

[Note. In a paper by Mr. C. F. Varley, read before the Royal Society, January 12, 1871, and published in this Journal, vol. xli. p. 310, some of the results contained in this paper have been anticipated.-ED. PHIL. MAG.]

iron wire is fixed near it so as to dip in the acid and just touch the edge of the drop of mercury. As soon as contact has taken place, the drop performs regular vibrations which may last for hours. The resemblance between this phenomenon and the movements of mercury electrodes (see Wiedemann, Galvanismus, 1872, § 368) is striking, and the explanation is manifestly the same. From the view hitherto received it would be as follows. The solution containing chromic acid would oxidize the surface of the drop and thus flatten it. In contact with iron an iron-mercury couple is formed. The current would reduce the surface by electrolysis; the drop would contract, and the contact with the iron would be broken; the same succession of phenomena would ensue as before, and so forth. By using a sufficiently concentrated chromic acid solution these processes are actually seen to take place; but with a dilute solution the surface always remains bright. Measurements have shown in fact that the polarization of mercury by hydrogen effects a contraction, and that we need only remember the depolarizing action of chromic acid to explain the above phenomenon.

Experiments which I will now detail more completely have shown that the capillary constant (superficial tension, coefficient of Laplace's formula) at the contact-surface of mercury and dilute sulphuric acid is an invariable function of the electromotive force of the polarization at the same surface.

I. Variation of the Capillary Constant with the Electromotive Force of the Polarization.

Measurements.-The apparatus consisted of a vertical calibrated glass tube, G G', which was connected at the bottom by means of an india-rubber tube with a reservoir of mercury, A (Plate II. fig. 1). The mercury rose thus in the tube G G', but underwent there a capillary depression which was measured with the cathetometer, and from which the capillary constant could be determined in the ordinary manner. The upper part of the glass tube was filled with dilute sulphuric acid (one eleventh of the volume of acid), which wetted the meniscus of the mercury M, and was continued by the glass siphon, H, into the glass vessel, B, which also contained dilute sulphuric acid. At the bottom of the vessel was a layer of mercury, B, to serve as a. second electrode. The capillary depression of the mercury in the tube GG' was, of course, corrected for the pressure of the dilute acid. In order to evoke in M a known E. F. P. (Electromotive Force of Polarization), the two masses of mercury (namely, that in B and the mass A M) were respectively connected with two points, P and Q, of the circuit of a Daniell's element by means of the platinum wires a, B, which may be called the poles of the appa

ratus.

A branch current then traversed the apparatus, which now acted as a decomposing cell, until the E. F. P. produced was equal to the difference of potentials between P and Q. The E. F. P. bears the same relation to the electromotive force of a Daniell as the resistance P Q bears to the resistance of the entire circuit. This relation may be deduced from the deflection of a tangent-compass contained in this circuit. The ratio of the surfaces of mercury in M and in B was intentionally taken very small, in order that the electromotive force of polarization in M need alone be taken into account; for it is clear that a quantity of electricity which is sufficient to produce in M any given hydrogen polarization would give on the surface B, which is many thousand times as large, no appreciable oxygen polarization. Thus was obtained from the indications of the compass the E.F.P. in M, and from the indications of the cathetometer the simultaneous capillary constant. In order to reduce the E. F. P. in M to zero, all that was necessary was to interpose a simple metallic circuit between a and B. The magnitudes to be measured are not small. Thus the depression in a tube having a radius =0.32 millim. is 14 millims. for an electromotive force of polarization = 0; for an electromotive force equal to one Daniell it is 18.90 millims. ; the alteration in level is therefore equal to 4.90 millims. =0·35 of the original depression. The constant of capillarity, therefore, is equal to 30-4 for an electromotive force equal to 0; and is equal to 40.6 for an electromotive force of polarization equal to one Daniell.

In order to measure the alterations in the constant of capillarity with still greater accuracy, instead of the tube G G' an extremely hollow open point yy (fig. 2) was used, which was prepared by drawing out one end of a glass tube. Mercury was poured into this tube to such a height that it penetrated into the fine point and partially filled it (fig. 2). The point dipped in dilute sulphuric acid; the bubble of air which at first occupied the end was removed by pressing out some mercury. There was thus in the point a wetted hemispherical* meniscus M of about Too millim. radius, whose capillary pressure counterbalanced the pressure of the mercury contained in the tube (750 millims. in height). The dilute acid was also in contact with a second mass of mercury, B, which, as before, was to serve as positive electrode ; by means of platinum wires both masses could be connected with the external poles a, B. These poles were first placed in metallic connexion with each other, whereby the E. F. P. in M was equal to zero, and a microscope so placed in front of the point that with a 220-fold magnification one of the cross-threads was in

* The angle which mercury forms with glass under dilute sulphuric acid is always zero.

the tangent plane of the meniscus (fig. 3). To make a measurement, a Daniell's element, for instance, was interposed between a and 8: the column of mercury disappeared from the field of view; and in order to adjust the mercury to the thread a new pressure, which might be called the compensating pressure, had to be exerted upon the column of mercury which supported the meniscus. This compensating pressure bears to the former pres sure the same ratio that the increase of the constant of capillarity at the meniscus does to the former value of this magnitude. This is clear from Laplace's formula, in which the curvature must be assumed to be constant when the adjustment of the meniscus is constant, and thus the pressure is proportional to the constant of capillarity. In the example given the compensating pressure amounts to 260 millims. of mercury (more than one third of an atmosphere) when a Daniell's element is interposed that is, 0.35 of the former pressure (750). The constant of capillarity has increased by 0.35 of its former value.

The compensating pressure was exerted by means of compressed air, produced and measured by means of an air-pump and of a mercury manometer. Electromotive forces of polarization which were equal to known fractions of a Daniell were produced by the above-described method of branch currents. It was thus found that to every value of the E. F. P. a perfectly definite value of the constant of capillarity corresponds; so that from the one magnitude may be inferred the value of the other.

In all of these experiments in which the circuit was closed (that is, where between a and ẞ either a mere wire or a constant electromotive force was interposed), it was surprising to observe how constant were the results-that is, the constant of capillarity and the invariability of the position of equilibrium of the meniscus. We have been accustomed to certain "disturbances" which occur in capillary experiments arranged in the ordinary manner (that is, without completion of the electrical circuit), and which, of course, occurred here also when a and B were insulated from each other. These disturbances are as follows: (1) the position of equilibrium is different according to the direction of the previous motion of the mercury; (2) it may suddenly change on agitation, as, for instance, by tapping; (3) the position of equilibrium may slowly change with time and only cease to become displaced hours after. But when the circuit was closed by interposing, for instance, a wire between a and B, all irregularities at once disappeared and they could not be reproduced; that is, the position of equilibrium became so constant that the meniscus was at once adjusted to the cross-wire with a precision which, in spite of the 220-fold magnification, left nothing to be desired. Moreover the cause of these disturbances was discovered (p. 290).