but as regards the fundamental principles themselves there has been no alteration.

It is, of course, to be understood that I do not, in making the preceding statement, contradict any allegation of Mr. Heath's as to matters of fact; for doubtless his information as to the history and state of thermodynamics must have been derived from writings with which I am unacquainted.

I have only to add the following remark as to Mr. Heath's explanation of how he conceives that the capacity of a vessel containing moving particles not exerting sensible attractions or repulsions might be diminished without accelerating the motion of the particles. He supposes the piston to be moved inwards during the intervals between the impulses of the moving particles upon it, and to be at rest at the instant of each of those impulses. According to this supposition there would, of course, be no addition to the energy of the particles; but at the same time there would be no work done in moving the piston, for it would meet with no resistance to its inward motion, and all the energy expended by the external force in setting the mass of the piston in motion after each impulse of a particle would be obtained back again in the act of stopping it before the impulse of the next particle.

As to the proposition that when work is done in moving the piston inwards against the reactions due to the motions of the particles alone, the additional energy due to the acceleration of the particles is exactly equivalent to that work, it might be treated simply as a particular case of the general principle of the conservation of energy. For elementary purposes, however, it may be desirable to use a special demonstration, such as the following. Let the piston be moving inwards with the uniform velocity +u. At a given instant let -v be the normal component of the velocity, relatively to the vessel, with which a set of particles are moving towards the piston. The normal velocity of those particles relatively to the piston is (v+u). They strike the piston and rebound with the velocity ++u relatively to it, so that after the collision their velocity relatively to the vessel has become v+2u instead of v, which it was before.

Let m be the aggregate mass of the particles which act on the piston in one second. Their total change of velocity is 2(v+u); therefore the outward pressure exerted by them on the piston, and the inward pressure exerted by the external force which pushes the piston inwards, are each equal to 2m(v+u). The piston moves through the distance u in a second; therefore the work done in driving the piston inwards in each second is

The aggregate energy of the mass m of particles before the

collision is

mv2

and after the collision

2

m(v + 2u)2
2

; therefore the increase of the energy of the moving particles in one second is

being exactly equal to the work done in pushing the piston inwards.

For the sake of simplicity, the preceding demonstration has been applied to elastic particles striking a piston and rebounding; but the same principle can be proved for any mode of internal motion of matter in a confined space; and when the particles exert attractions and repulsions, it can be proved for the work done by that term in the value of the external pressure which is equal and opposite to the outward pressure due to the motions of the particles—a term which, according to the second law of d thermodynamics, is found by performing the operation T upon the external pressure, 7 being the absolute temperature. For example, when a mass of saturated vapour occupying the space S, at the pressure p, and absolute temperature 7, is compressed into the liquid state, occupying then the volume s, the temperature and pressure during the compression being maintained constant by abstracting the heat produced, the principle just mentioned gives for the amount of that heat in dynamical units

a result which is known to be exactly confirmed by experiments on various fluids.

For detailed information, however, on this and other points I must again refer to Professor Tait's treatise on Thermodynamics, and to the original papers referred to in that treatise.

I am, Gentlemen,

Your most obedient Servant,

Glasgow, September 10, 1870.

W. J. MACQUORN RANKINE.

XXXV. On an Object-glass Spectral apparatus.
By SIGMUND MERZ*.

N Gilbert's Annalen

IN

[With a Plate.]

der Physik for 1823, Fraunhofer gives a description of his observations upon the spectra of the light of the fixed stars. He therein says, "I have recently constructed a large instrument arranged solely for this purpose; it is provided with an object-glass the aperture of which is 4 inches. French measure (=4.26 English). The flint-glass prism of this instrument has an angle of 37° 40′, and is of the same diameter as the object-glass."

These are, without doubt, the earliest experiments on stellar spectra. More than twenty years elapsed before further investigations on this subject were entered upon, first by Lamont, then by Donati, Secchi, Jannsen, Huggins, Lockyer, and Zöllner, all of whom, however, had abandoned the method employed by Fraunhofer, and commeuced their observations by means of an arrangement adapted to the eyepiece.

Father Respighi in Rome has recently endeavoured to reintroduce the method of observation employed by Fraunhofer. His first experiments gave such brilliant results that Father Secchi wrote to me thereupon as follows:-" Professor Respighi relates wonders to me about the prism you sent to him," and gave me the commission to construct an object-glass spectral apparatus for the refractor of the observatory of the Collegium Romanum.

Now, as the apparatus in question has been for some time for warded to its destination, and as Father Secchi has given an ac count thereof in the Comptes Rendus of November 22, 1869, it may not be considered out of place to make mention of it in this periodical as well.

Fig. 1, Plate III. represents the arrangement as mounted for fitting on to the cell of the object-glass. Fig. 2 represents the apparatus with the prism removed. Fig. 3 shows the prism itselft. The refracting angle of this prism is 12°. It is worked out of the purest and most colourless flint-glass, so that the loss of light in traversing it may be taken to be 0. Its aperture is 6 inches French measure (=6·39 English). The setting is provided with the requisite arrangements for adjustment.

Now, in spite of this prism reducing the effective aperture of the 9-inch refractor at Rome (=9.59 English) by more than half, the illumination far exceeds that of the refractor with

* From Carl's Repertorium für Experimental-Physik, vol. vi. p. 164. Communicated by W. G. Lettsom, Esq.

Fig. 3 is of the size of the figure in the original plate. Figs. 1 and 2 are considerably reduced.

Action of Low Temperatures on Supersaturated Saline Solutions. 295

the full aperture of 9 inches when an eyepiece-spectroscope with direct vision is employed. (Secchi says, "the aperture of the refractor becomes thus reduced by more than half its surface, yet notwithstanding the light is so intense that it greatly exceeds that which one obtains with interposed direct-vision prisms near the eyepiece. The dispersion is so considerable that it is at least six times that which I have obtained with the most pow→ erful spectroscopic eyepiece, and even that of the spectroscope without slit, with cylindrical lens, which I originally employed.") The price of this object-glass spectral apparatus amounted to 525 Bavarian florins, equal to £45.

With a certain loss of light there could, however, be given to this object-glass spectral apparatus for analyzing stellar light a disposition for observing by direct vision. Within these few days an object-glass spectral prism with direct vision has been completed, composed of crown- and flint-glass, which has completely borne out what was anticipated from it. This arrangement has an aperture of 34 French lines (=3.02 English inches); and its dispersive power is equivalent to that of a flint-glass prism the refracting angle of which is 26°.

XXXVI. On the Action of Low Temperatures on Supersaturated Saline Solutions. By CHARLES TOMLINSON, F.R.S.* TWO years ago I had the honour of bringing before the

Chemical Section of the British Association an account of an experiment in which it was shown that crystals of magnesic sulphate, sodic sulphate, and one or two other salts do not necessarily act as nuclei to their supersaturated solutions. My object was to show, by an extreme case, that if a body which is usually a most powerful nucleus be made chemically clean, the solution adheres to it as a whole, and there is no separation of salt.

I propose to-day to bring before the Section another case, which seems to me as extreme as the former one. It is intended to illustrate this position, namely that, in the absence of a nucleus, highly supersaturated solutions reduced to the zero of Fahrenheit's scale, or from that to -10°, solidify into unstable hydrates rather than crystallize; and on exposing such solidified solutions to a temperature of about 32°, they rapidly liquefy into clear, bright, supersaturated solutions without any separation of salt. This effect may be produced any number of times, provided the solution be preserved from the action of nuclei or carriers of nuclei, such as the air. The only precaution to this

* Communicated by the Author, having been read before the Chemical Section of the British Association at Liverpool, September 20, 1870.

end is to use clean filtered solutions in clean tubes, kept plugged with cotton-wool.

For example, the sulphates of zinc and magnesia in atomic proportions, with a small quantity of water, are heated in a flask, boiled and filtered into test-tubes in which they are again heated nearly to boiling, and then plugged and set aside to cool. When cold, one of the tubes is put into a freezing-mixture at about -10°; and in about ten minutes or so large tetrahedral crystals beautifully formed begin to grow, as it were, from the side of the tube, and they go on increasing until the whole of the solution is transformed into a solid mass. If the tube be now transferred to snow and water at 32°, the solid melts rapidly and the solution becomes clear as before. If, however, the cotton-wool be removed for a moment, either when the solution is solid or liquid, it crystallizes, in the one case during the melting, and in the other immediately.

The solidification of the solution must not be regarded as case of freezing, since no ice is formed; it is rather a case of abnormal crystallization of the saline molecules in combination with the water, and capable of existing only at this low temperature under the defined conditions. I call it a case of abnormal crystallization, because most of the solutions that were tried behaved in the same manner; that is, they formed tetrahedral crystals at about 0° and melted rapidly at 32°.

Take another example. A supersaturated solution of the double sulphate of copper and magnesia was reduced to about -4° F., when tetrahedral crystals formed on the surface, the solid angles growing downwards until the whole of the solution became solid. The deep blue colour had disappeared, and the solid presented different shades of very light blue. When the tube was put into snow and water at 32°, the solid retreated from the sides of the tube, and the clear solution appeared intensely blue in contrast with the nearly white solid.

Sulphate of zinc and potash-alum in atomic proportions formed tetrahedral crystals at 4°. The triple salt was afterwards crystallized in an open dish, and 200 grains of it, boiled with five drachms of water, formed a clear solution, which was filtered into a clean tube, plugged, and left to repose during six days. It was then placed in a freezing-mixture at 0°, when a white powder, probably of a basic sulphate of alumina and anhydrous sulphate of zinc, was thrown down, and on this grew a brilliant white foliage resembling ivy, having an exquisite effect. This ivy-leaf pattern seems to me to result from deformations of the tetrahedral crystals, as I believe was also the case with a supersaturated solution of the double sulphate of copper and nickel, which at 0° formed beautiful feather-shaped crystals. A supersaturated