water, and introduced into the compartment destined to receive and absorb the gas evolved by the action of tartaric acid upon bicarbonate of soda placed in the other compartment; the apparatus is then closed.

After several days of digestion, the liquid, saturated with carbonic acid and retaining in solution a certain quantity of the oxide with which it had been in contact, is decanted, and left to spontaneous evaporation, either in the open air or in loosely stopped bottles. The hydrated carbonates are then deposited very slowly, either in the form of pulverulent flakes, or in more or less distinct crystals, sometimes several millimetres in diameter. In this way the author has produced a hydrated carbonate of magnesia in large and perfectly transparent crystals, by digesting in water charged with carbonic acid, a mixture of carbonates of lime and magnesia obtained by precipitating a neutral liquid containing dolomite dissolved in nitric acid by carbonate of ammonia. The water dissolved carbonate of lime and a still larger quantity of carbonate of magnesia. When exposed to the air it deposited from the very first day small acicular crystals of carbonate of lime; then the liquid being reduced to about a sixth of its original volume by spontaneous evaporation in the open air for about two months, it gave crystals of hydrated carbonate of magnesia. These crystals of several millimetres in diameter are derived from an oblique rhomboidal prism, presenting the same angles observed in the hydrated carbonate of magnesia, MgO, CO+4Ag., described by Marignac. Exposed to a slight heat these crystals lose a part of their water, and become opake. They contain no lime.

Water charged with carbonic acid dissolves considerable quantities of protoxide of iron, and peroxides of zinc, lead, silver, and copper; the latter gives the liquid a fine sky-blue colour. These solutions were left for several months to spontaneous evaporation; some of them deposited carbonates in pellicles or amorphous flakes, others exhibited some microscopic crystals.-Comptes Rendus, March 16, 1857, p. 561.

NOTE ON A NEW CYANOMETER. BY FELIX BERNARD.

If it be true that the proportion of polarized light contained in a ray emanating from a determinate point in the sky varies with the transparency of the atmosphere, and consequently with the brilliancy of its tint, it is however not evident, that, as has generally been admitted hitherto, these two quantities vary in the same proportion; the measuring instruments founded upon the proportionality of these two elements can, therefore, only lead to results of doubtful exactitude, and this doubt must remain as long as this question is unsolved by experiment. On the other hand, if this agreement were completely established, the employment of one of these means exclusively would be insufficient for the study of the laws of atmospheric polarization, as these must be deduced from observations made in perfectly definite circumstances. These considerations have led me to intro. duce some very simple modifications into the polarimeter, which I have already submitted to the Academy of Sciences*, and these

• Comptes Rendus, October 23, 1854.

allow me to apply this instrument to direct and precise cyanometric observations.

To convert this apparatus into a cyanometer, the plate with double rotation is removed; a Nicol's prism is substituted for the doubly refracting prism; a jointed screen, consisting of a frame upon which a sheet of white paper is stretched, is fitted to the objective extremity of the tube; between the two Nicol's prisms a plate of quartz of 1 millim. in thickness is placed perpendicularly to the axis and a thin plate parallel to the axis, giving a violet tint, and its complementary colour in polarized light. The first of these may be taken out of the apparatus by a lateral aperture into which the piece supporting it slides; the second, fixed at one extremity of an alidade, is placed at the centre of the circle of polarization in a grooved piece; the rotation of this plate, independent of that of the analyser, is nevertheless measured upon the same circle by means of a vernier supported upon the other extremity of the alidade. This arrangement also allows the plate to be removed to regulate the instrument.

The white light reflected by the screen, after undergoing the action of the crystalline plates, acquires a tint which depends upon the inclination of the axis of the thin plate to the plane of the principal section of the polarizer, and upon the azimuth of the principal section of the analyser.

This system, as we shall see hereafter, allows the tint of any part of the sky to be reproduced with facility; but to operate with certainty, it is necessary that the intensity of the latter should be brought to the intensity of that with which it is compared; for this purpose a second tube, furnished with two Nicol's prisms, is fitted by grinding into a collar screwed to the first portion of the instrument parallel to the first; the rays which have traversed these two systems are completely reflected at a right angle upon the hypothenuses of two isosceles right-angled prisms, by means of which the images, being brought together until they almost touch, may be examined at a single glance. The instrument being directed to the part of the sky to be observed, we try which is the azimuth of the analyser of the system for reproducing the tint, for which this tint approaches that of the other image most closely; the latter is then brought to an intensity exactly equal to the former by a suitable rotation of the corresponding analyser; the difference of tint, if it exists, is thus more apparent, and may be corrected either by varying the azimuth of the analyser of the other system, or by slightly changing the inclination of the thin plate, so as to compensate the excess of green or violet light which occurs in the primitive tint. This comparison is very easily made with a little practice.

By means of these two angles furnished by observation and the known thickness of the two plates of quartz, we may determine what I shall call the cyanometric state of a point of the sky, that is to say, the relation of the quantity of blue light to that of white light, the mixture of which would produce the tint observed by the eye. From the thickness of the plate of quartz, we deduce, as has been shown by M. Biot, the rotation of the planes of polarization

relative to the rays of the principal tints of the spectrum; we know consequently the inclinations of the axis of the thin plate to each of these planes; we calculate the corresponding intensities of the emerging light by means of one of Fresnel's formulæ for thin crystalline plates. Lastly, we apply to these values Newton's rule, reduced to formulæ by M. Biot, which allows us to determine the nature of the tint and its comparative intensity.

To avoid calculating each observation, it will be convenient to construct double entry Tables, containing the cyanometric states corresponding with the azimuth observed.

The mode of determining the origin of the angles is very simple. Before operating, the screen is removed, to allow a direct passage to the light; the plates of quartz are removed, and the azimuth corresponding with the extinction of the polarized ray of the system reproducing the tint is noted, pointing it towards a brightly luminous part of the sky; this is easily obtained in a minute or two. The thin plate is then replaced and turned by means of the alidade until the extinction of the light again takes place; in this position the axis of the plate is parallel to the principal section of the polarizer.

In order that the tint of the sky may not be altered, care must be taken to direct the principal section of the polarizer of the other system in the plane of polarization of the incident light; for this purpose, the polariscope with double rotation is employed, as I have already indicated in describing the polarimeter.-Comptes Rendus, November 17, 1856, p. 982.

COMPARATIVE EXAMINATION AND ANALYSIS OF EUDIALITE AND EUKOLITE. BY A. DAMOUR.

Eudialite, a mineral which receives its name from the facility with which it may be dissolved by acids, has only been observed hitherto in a single locality, Kangerdluarsuk, on the western coast of Greenland, where it was discovered fourteen years ago by Dr. Giesecke. The numerous specimens which have been since collected in the same locality, exhibit this substance associated with sodalite and Arfvedsonite.

More recently a mineral has been found in the zirconian syenite of Brevig, in Norway, the physical and chemical characters of which have much analogy with those of eudialite. This new mineral was first of all classed as a distinct species under the name of eukolite. Subsequently Scheerer analysed and thought that it might be referred to Wöhlerite. The resemblance between eudialite and eukolite leading to a presumption that they might have the same composition, the author has submitted them to a comparative examination.

Eudialite forms crystals derived from a rhombohedron of 73° 30'; it occurs also in crystalline masses, sometimes exhibiting a tolerably distinct double cleavage which leads to the hexagonal prism of 120°. Planes of cleavage parallel to the faces of the primitive rhombohedron and to those of a more obtuse rhombohedron, have also been mentioned. Its colour is rose or violet-red, presenting tints identical with those of different varieties of almandine garnet. Eudialite is

sometimes transparent, but is usually cracked in every direction, and only translucent at the margins of its thin fragments. It scratches apatite, and is scratched by felspar. Its density is 2.906. With the blowpipe, it fuses into a transparent glass of a dull green colour; it is readily attacked by acids and reduced to a thick jelly. Eukolite forms small glassy fragments of a brownish-red colour, sometimes presenting two pretty distinct cleavages, which, as in eudialite, lead to a regular hexagonal prism. Some specimens exhibit a certain amount of transparency, but it is usually fissured in different directions. Its hardness is the same as that of eudialite; its density=3.007. When examined with polarized light, it exhibits a single optical axis, like eudialite; with this slight difference, that the axis is positive in eudialite and negative in eukolite. The chemical characters of both are identical. The following are the average results of several analyses :

The only difference is the presence of a few parts per cent. of oxides of cerium and lanthanium in eukolite which do not occur in eudialite. By adding the oxygen of the tantalic acid and silica, and that of the oxide of cerium to that of the zirconia, we get the same proportions for eukolite that Rammelsberg assigned to eudialite. These bodies may thus be represented under the same general formula,6RO+R2O+6SiO3.

-Comptes Rendus, December 29, 1856, p. 1197.

LONDON, EDINBURGH AND DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

[FOURTH SERIES.]

I

JUNE 1857.

LIV. On the Motion of Electricity in Wires.
By G. KIRCHHOFF*.

HAVE attempted to establish a general theory of the motion of electricity in an infinitely thin wire, by assuming certain facts which are observed in constant currents, and in currents whose intensity alters but slowly, to be universally valid. I will here develope this theory, and show its application to some cases of a simple nature.

I picture to myself a homogeneous wire possessing the same thickness throughout and of circular cross section. In the axis of this wire I take a fixed point and a variable one; the portion of the axis between both points I call s. Through the changeable point I permit a transverse section to pass, and call the polar coordinates of a point of this section, with reference to a system of ordinates whose origin is the centre, p and y. I will calculate the electromotive force which tends to separate, in the direction of the length of the wire, the two electricities in the vicinity of the point determined by s, p and y. This force is partly derived from free electricity, partly from the induction which takes place in consequence of the alteration of the strength of the current in all parts of the wire. With regard to the first portion, we may make use of the electrostatic law of Coulomb. Let V be the potential of the free electricity with reference to the point under consideration; that is to say, the sum of all the single quantities of free electricity, each divided by its distance from the point. The quantities of electricity are here to be referred to a mechanical unit; the unit of electricity shall be that which, acting * Translated from Poggendorff's Annalen, 1857, No. 2. Phil. Mag. S. 4. Vol. 13. No. 88. June 1857.

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