change either way is perfectly reversible. When we thus have two different states present together in contact with one another, we have a perfectly obvious distinction, and we can properly continue to call one of them a liquid state and the other a gaseous state of the same matter. The same two names may also reasonably be applied to regions or parts of the fluid state extending away on both sides of the sharp or definite boundary, wherever the merging of the one into the other is little or not at all apparent. If we denote geometrically all possible points of temperature and pressure jointly, by points spread continuously in a plane surface, each point in the plane being referred to two axes of rectangular coordinates, so that one of its ordinates shall represent the pressure and the other the temperature denoted by that point, and if we mark all the successive boiling- or condensingpoints of pressure and temperature as a continuous line on this plane, this line, which may be called the boiling-line, will be a separating boundary between the regions of the plane corresponding to the ordinary liquid state and those corresponding to the ordinary gaseous state. But by consideration of Dr. Andrews's experimental results (Phil. Trans. 1869), we may see that this separating boundary comes to an end at a point of temperature and pressure which, in conformity with his language, may be called the critical point of pressure and temperature jointly; and we may see that from any ordinary liquid state to any ordinary gaseous state the transition may be gradually effected by an infinite variety of courses passing round the extreme end of the boiling-line.

Fig. 1 is a diagram to illustrate these considerations and some allied considerations to which they lead in reference to transitions between the three states, the

gaseous, the liquid, and the solid. This figure is intended only as a sketch to illustrate principles, and is not drawn according to measurements for any particular substance, though the main features of the curves shown in it are meant to relate in a general way to the substance of water, steam, and ice. AX and AY are the axes of coordinates for pressures and temperatures respectively; A, the origin, being taken as the zero for pressures and as the zero for temperatures on the Centigrade scale. The curve L represents the boiling-line. This terminates towards one direction in the critical point E; it passes in the other direction to T, the point of pressure

and temperature where solidification sets in. This point T is to be noticed as a remarkable point of pressure and temperature, as being the point at which alone the substance, pure from admixture with other substances, can exist in three states, solid, liquid, and gaseous, together in contact with one another. In making this statement, however, the author wishes to submit it subject to some reserve in respect to conditions not as yet known with perfect certainty. He observes that we might not be quite safe in assuming that the melting-point of ice solidified from the gaseous state is the same as the melting-point of ice frozen from the liquid state, and in making other suppositions, such as that the same quantity of heat would become latent in the melting of equal quantities of ice formed in these two ways. Such considerations as these into which we are forced if we attempt to sketch out the course of the boiling-line, and to examine along with it the corresponding boundary-lines between liquid and solid and between gas and solid, may be useful in suggesting questions for experimental and theoretical investigation which may have been generally overlooked before. Proceeding, however, upon assumptions such as usually are tacitly made, of identity in the thermal and dynamic conditions of pure ice solidified in different ways, the anthor points out that we must suppose the three curves (namely, the line between gas and liquid, the line between liquid and solid, and the line between gas and solid) to meet in one point, shown at T in the figure. This point of pressure and temperature for any substance may then be called the triple point for that substance. In the figure the line TM represents the line between liquid and solid. It is drawn showing in an exaggerated degree the lowering of the freezing temperature of water by pressure, the exaggeration being necessary in order to allow small changes of temperature to be perceptible in the diagram. The line TN represents the line between the gaseous and the solid states of water substance. The two curves T L and TN, one between gas and liquid and the other between gas and solid, have been constructed for water substance through a great range of temperatures and pressures by Regnault, from his experiments on the pressure of saturated aqueous gas at various temperatures above and below 0° Centigrade. He has represented and discussed his results above and below the temperature at which the water freezes (which in strictness is not 0° C., but is the freezing temperature of water in contact with no atmosphere except its own gas), as if one continuous curve could extend for both. As brought out experimentally, indeed, they present so little appearance of any discontinuity that the distinctness of the two curves from one another might readily escape notice in the consideration of the experimental results. Prof. Thomson points out, however, that the range from temperatures below to temperatures above freezing comprises what ought to be regarded as two essentially distinct curves meeting one another in the point T; and he further suggests that continuations of these curves, sketched in as dotted lines T P and TQ, may have some theoretical or practical significance not yet fully discovered. He thinks it likely that out of the three curves at least the one, MT, between liquid and solid may have a practically attainable extension past T, as shown by the dotted continuation T R. Various known experiments seem to render this supposition tenable, whether the condition supposed may have been actually realized in experiments hitherto or not. He thinks, too, that there is much reason to suppose that the curve LT between gas and liquid has a practically attainable extension past T, as shown by the dotted continuation TP.

In reference to the continuity of the liquid and gaseous states, Prof. Thomson showed a model in which Dr. Andrews's curves for carbonic acid are combined in a curved surface, obtained from them, which is referred to three axes of rectangular coordinates, and is formed so that the three coordinates of each point in the curved surface shall represent, for any given mass of carbonic acid, a pressure, a temperature, and a volume, which can coexist in that mass. This curved surface shows in a clear light the abrupt change or breach of continuity at boiling or condensing, and the gradual transition round the extreme end of the boiling-line. Using this model and a diagram of curves represented here in fig. 2, the author explained a view which had occurred to him, according to which it appears probable that although there be a practical breach of continuity in crossing the line of boilingpoints from liquid to gas, or from gas to liquid, there may exist, in the nature of * Mémoires de l'Académie des Sciences, 1847, pl. viii.

things, a theoretical continuity across this breach, having some real and true significance. The general character of this view may readily be seen by a glance at fig. 2, in which Dr. Andrews's curves are shown by continuous lines (not dotted),. and curved reflex junctions are shown by dotted lines connecting those of Dr. An

Fig. 2.

n

drews's curves which are abruptly interrupted at their boiling- or condensing-points of pressure. It is to be understood that each curve relates to one constant temperature, and that pressures are represented by the horizontal ordinates, and corresponding volumes of one mass of carbonic acid constant throughout all the curves are represented by the vertical ordinates. The author points out that,,by experiments of Donny, Dufour, and others, we have already proof that a continuation of the curve for the liquid state past the boiling stage for some distance, as shown, dotted in fig. 2, from a to some point b towards f, would correspond to states already, attained. He thinks we need not despair of practically realizing the physical conditions corresponding to some extension of the gaseous curve such as from e to d in the figure. The overhanging part of the curve from e to f he thinks may represent a state in which there would be some kind of unstable equilibrium; and so, although the curve there appears to have some important theoretical significance, yet the states represented by its various points would be unattainable throughou. any ordinary mass of the fluid. It seems to represent conditions of coexistent tem-perature, pressure, and volume, in which, if all parts of a mass of fluid were placed, it would be in equilibrium, but out of which it would be led to rush, partly into the rarer state of gas, and partly into the denser state of liquid, by the slightest inequality of temperature or of density in any part relatively to other parts.

*Donny, Ann. de Chimie, 1846, 3rd series, vol. xvi. p. 167; Dufour, Bibliothèque Universelle, Archives, 1861, vol. xii,

1871.

3

Observations on Water in Frost Rising against Gravity rather than Freezing in the Pores of Moist Earth. By Professor JAMES THOMSON, LL.D. In this paper Prof. Thomson, in continuation of a subject which he had brought before the British Association at the Cambridge Meeting in 1862*, on the Disintegration of Stones exposed to Atmospheric Influences, adduced some remarkable instances which he had since carefully observed. In one of these, observed by him in February 1864, he showed that water from a pond in a garden had in time of frost raised itself to heights of from four to six inches above the water surfacelevel of the pond by permeating the earth-bank, formed of decomposed granite, which it kept thoroughly wet, and out of the upper surface of which it was made to ascend by the frost, so as to freeze as columns of transparent ice, rather than that it would freeze in the earth-pores. The columns were arranged in several tiers one tier below another, the lower ones having been later formed than those above them, and having pushed the older ones up. From day to day during the frost the earth remained unfrozen, while a thick slab of columnar ice, made up of successive tiers of columns, formed itself by water coming up from the pond and insinuating itself forcibly under the bases of the ice-columns so as to freeze there, pushing them up, not by hydraulic pressure, but on principles which, while seeming not to have been noticed previously to their having been suggested by the author at the Cambridge Meeting, appear to involve considerations of scientific interest, and to afford scope for further experimental and theoretical researches. In the case referred to, the remarkable phenomenon showed itself very clearly, of water passing from a region of less than atmospheric pressure in the wet pores of the earth, into a place in the base of the columns where it was subject to more than atmospheric pressure, and subject also to stresses unequal in different directions, from its being loaded with the mass of ice and also with some gravel or earthy substances above it; and this action went on rather than that the water would freeze in the pores of the moist earthy bottom on which the columns stood, and which was above the water surface-level of the pond.

ASTRONOMY.

Note on the Secular Cooling and the Figure of the Earth. By Prof. CLIFFORD.

Observations on the Parallax of a Planetary Nebula.

By Dr. GILL.

On the Coming Solar Eclipse. By M. JANSSEN.

On the Recent and Coming Solar Eclipses. By J. NORMAN LOCKYER, F.R.S.

On the Construction of the Heavens. By R. A. PROCtor, B.A.

On Artificial Coronas. By Professor OSBORNE REYNOLDS.

On a Method of Estimating the Distances of some of the Fixed Stars.
By H. Fox TALBOT, LL.D., F.R.S.

The method proposed in this paper for ascertaining the distances of the stars applies only to binary systems, which are not too faint or too close to be well observed. It has this peculiarity, that it can be applied to remote stars with as much accuracy as to nearer ones, always supposing that such remote stars are still bright

* Brit. Assoc. Rep. 1862, Trans. of Sect. p. 35.

enough to allow of accurate observation; whereas the method of determining the distance of a star by its parallax becomes more difficult as the distance of the star increases, notwithstanding any brightness which it may have.

The method now proposed is founded on that of spectral analysis. I suppose a certain ray, which I will call X, to be chosen as the standard ray, and to be carefully observed at various times in each of the stars of a binary system during an interval of some years. The orbit described by the stars around their common centre of gravity must not lie in a plane perpendicular to the visual ray joining those stars and the earth, nor must it approach that position too nearly, otherwise the true result would be masked by the errors of observation. The simplest case is that of two stars, equal in mass and brightness, and revolving in circles about their common centre of gravity. Supposing such a system of two stars to exist, the most favourable case is when the plane of their motion passes through the earth. If it does so, the stars will appear to move in straight lines. Supposing them to be, when first observed, at their greatest elongation, they will approach each other with an increasing apparent velocity, varying as the sine of the time (or circular arc described) until they come into apparent conjunction, when one star will be hidden by the other for a certain time, after which they will recede from each other in like manner as they had approached. But the observer would not be able to say with certainty which of the two stars was nearest to him, since the same phenomena would be presented if the distances of the two stars were interchanged, and at the same time the direction of their motions reversed. Now suppose the method to be applied which I have proposed. At the time of their conjunction, or near it, neither star would be approaching the earth, consequently the observed deviation of the ray X (if any) from its normal position would be due to the proper motion of the system of the two stars relatively to the earth, which is a constant quantity to be allowed for in all other observations. Now suppose another set of observations to be made at the time of the greatest elongation of the two At that time each of the stars is apparently stationary, but in fact one of them is approaching and the other receding from the earth with a maximum velocity. The observed deviation of the ray X will therefore be different in the spectra of the two stars, and (allowance having been made for the proper motion of the system) it will appear at once which of the two stars is approaching the earth, and the question of its direct or retrograde orbit will be resolved. At the same time the distance of the two stars from the earth will result from the calculation. It will be well, perhaps, to take a hypothetical example, which will show how this element results from observation.

stars.

I suppose, then, that observation has shown:

(1) The period of one complete revolution of the binary star round its centre of gravity to be fifty years.

(2) The greatest elongation of the stars to be ten seconds.

(3) And at the time of this greatest elongation the deviation of the ray X to be such as to prove that one of the stars is then approaching the earth at the rate of ten miles per second, and the other star receding from the earth at the same rate. And this will evidently be their true velocity in their orbit.

Now 50 years 1,577,880,000 seconds, and therefore since each star moves in its orbit at the rate of ten miles per second, it describes in the course of one whole revolution of 50 years a circle of 15,778,800,000 miles in circumference. The radius of this circle is the distance of the star from the common centre of gravity, and therefore the diameter of the circle is the distance of the two stars from each other (which in the hypothetical example I have selected is constant). This diameter will be found to be about equal to 54 radii of the earth's orbit. Now, when the stars were at their greatest elongation, observation showed their angular distance to be ten seconds. Consequently we have only to calculate at what distance from the earth a length of 54 radii would subtend an angle of 10", and we find that this would occur at a distance of 1,113,500 radii. Such, then, is the distance of the binary star from the earth, namely, 1,113,500 times the distance which separates the earth from the sun.

So simple a case as the hypothetical one which I have here calculated is, indeed, not likely to occur in practice; most cases would require a greater complexity of