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 stars. 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.

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

calculation, but the principles involved would be the same.

When the distances and positions of the two components of a binary star have been carefully observed by astronomers for a certain number of years, it has been found possible in many instances to determine the elements of their orbit, its ellipticity, the inclination of its plane to the ecliptic, the time of one complete revolution, the apparent maximum elongation, &c. &c. But the distance of the double star from the earth has hitherto remained unknown, because that is dependent upon the real size of the orbit, and observation (without the spectroscope) gives only the apparent size of it. Knowing the elements of the orbit we can, indeed, calculate the velocity of either of the stars in the direction of the earth at any moment, relatively to that which it has at any other moment. But the determination of the absolute velocity requires the distance of the stars from the earth to be known. Now a few observations (if perfectly correct) of the deviation of the ray X supply this wanting element, viz. the actual velocity at the time of observation, and likewise enable us, as I have already explained, to eliminate the proper motion of the double star. This might be sometimes difficult, but geometrical considerations, quite in harmony with those now employed by astronomers to determine the other elements of the binary system, would undoubtedly effect this also.

In what I have written above, I have supposed great precision in the observations-greater, no doubt, than would be practicable with the optical means now in use; but this makes no difference in the theory of the subject, which for a certain time may be allowed to pass ahead of its practical realization. It will doubtless be remembered that the method of determining the sun's distance by means of a transit of Venus was proposed by James Gregory in his 'Optica Promota,' and by Halley in his 'Catalogus Stellarum Australium,' nearly 100 years before an opportunity offered of testing it by an actual observation.

On the Nutoscope, an Apparatus for showing Graphically the Curve of Precession and Nutation. By Professor CHARLes V. Zenger.

In the case of a rapidly revolving solid body two different cases may occur, the mass of the solid body being quite uniformly distributed around the axis of rotation, or, on the contrary, the uniformity being destroyed by the accumulation of matter on one side of the axis.

In the first instance the centrifugal force will act symmetrically on opposite sides of the solid body in rotation, and be in equilibrium. It then gives rise to the phenomenon of a free axis; that is to say, the axis of rotation steadily holds its position during the rotation, because the particles of the body will also have the tendency to retain their position while the motion is going on with sufficient speed.

These facts may best be shown by Fessel's apparatus, called the gyroscope, in which a circular disk is put in rapid rotation round an axis freely movable in every direction,

If there is a force acting only on one side, for instance a weight pressing on the axis, or an impulse given to it, the axis will show a lateral motion, and describes a cone, or at its extremity a circle.

But if there is on the disk itself an unequal distribution of the mass, which is produced by fastening a small circular disk or sheet of paper with an excentric hole upon the axis, the motion becomes more complicated; and if the velocity be considered uniform for the short time required for the axis to describe a circle, there will be an additional lateral motion produced by the adhering paper sheet disturbing the motion, and a small ellipse will be described by the end of the axis revolving upon the circle, as is shown in the diagram traced on blackened paper by the top of such an apparatus.

The greater the mass of the disturbing paper sheet, and the more the speed of the motion diminishes, the larger becomes the diameter of the ellipse described by the top, and the more disturbed are its revolutions on the periphery of the circle, both axis of the ellipses becoming much larger. Diminution of the speed originates, instead of the circular motion of the top, a spiral motion, and the effect is

that the velocity of the disk's motion decreasing, the top no longer describes a circle, but a continuous spiral line, on which the small ellipse revolves.

These motions, however complicated they may be, may be graphically shown by holding a blackened paper to the top of the axis of the apparatus, and causing it to approach steadily, when the axis becomes more inclined by the diminution of the velocity.

To do this more easily and with more precision, near the rotating disk is placed a support, with a brass frame for holding a sheet of blackened paper, exactly at a right angle to the support. The top of the inclined axis may be brought into slight contact with the blackened surface of the paper by lowering the brass frame on the stand by means of a micrometer-screw, so as to maintain the contact for some time. The specimens of curves described by the apparatus show that without any disturbing force the top describes a circle.

If we put a circular disk excentrically on the axis of the apparatus, it still describes a circle, but also an ellipse revolving on its periphery, whose length of axis depends on the weight of the circular disk fastened to the axis. If the top marks for a longer time, instead of a circle a spiral line is described, with ellipses revolving on it.

Diagrams were exhibited, showing the same curves, but with heavier circular disks on the axis.

These experiments may be made also by putting on the top of the axis a globule of silvered glass, reflecting the light of the sun, or of a lamp, showing at a considerable distance the pretty designs of the nutation curves. It is very instructive to exhibit and explain the complicated phenomena of the luni-solar precession and nutation of the earth's axis by the same apparatus.

The combined action of the sun and moon's masses on the earth are represented by the small paper sheets put excentrically on the axis of the rotating brass disk of the apparatus.

The sun and moon's distances from the centre of the earth continually changing, produce the same effect as those circular disks put excentrically upon the axis of the apparatus, and produce an entirely similar motion of the axis of the earth, describing likewise a cone, or a circle on the top of the earth's axis; and by the changing action of the sun and moon at different distances from the earth, there is produced an additional small elliptical motion, quite similar to those represented in the diagrams exhibited. Similar but still larger elliptical motions are produced in the same manner by the combined and varying action of the sun and earth's masses on the moon, known in astronomy as the precession of the nodes of the moon, and as the nutation and evection of its axis.

LIGHT.

Description of a Set of Lenses for the Accurate Correction of Visual Defect. By PHILIP BRAHAM.

The lenses shown were plano-spherical and cylindrical. By using plano- instead of double spherical lenses, we are enabled to add or diminish the power of any given plano-lens to the greatest nicety; so that without multiplying the tools used by the lens-grinders, any graduation of focus can be obtained.

In correcting astigmatic defect, the cylindrical lenses being plano-, and the edges ground to the same exact diameter as the spherical, they fit together and act as one lens.

Description of a Paraboloidal Reflector for Lighthouses, consisting of silvered facets of ground-glass; and of a Differential Holophote. By THOMAS STEVENSON, F.R.S.E., M.I.C.E.

The superior advantages of the Dioptric as compared with the Catoptric systems

of illumination for lighthouses are generally admitted. There are, however, many cases, such as harbour-lights and ship-lights, where the expense of construction becomes a barrier to the employment of refracting apparatus.

In order to reduce the expense, it occurred to the author that it would be desirable to revive the old form of mirror, consisting of facets of ordinary silvered glass. Instead of making them small and with plane surfaces, the size may be much increased; and they may be bent or ground and polished on both faces to curves osculating the parabola, ellipse, or whatever form may be required. If the edges of these facets were fixed together by Canada balsam (a substance which has nearly the same index of refraction as plate-glass), the large loss of light which takes place at the edges of each facet in the old reflectors will be in great measure saved. There will not, as formerly, be any refraction of the rays in passing through the edges, and thus the whole will become practically monodioptric; or, in other words, will be optically nearly the same as if the paraboloid had been made of one whole sheet of glass, while the advantage due to accurately curved surfaces, instead of plane surfaces, will be secured. It would be a further improvement to select different points in the flame for the foci of the different facets, so as to secure the useful destination of more of the rays. Besides, by grinding each facet to different vertical and horizontal curves, the light may be condensed or diverged by means of a single agent; and the same result may be effected with different totally reflecting plates of flint or other glass cemented to lighthouse prisms with Canada balsam, so as to form composite prisms. When coloured lights are wanted, the facets would consist of glass tinted to the required hue, so as to render stained muffles or chimneys unnecessary. The economy of the proposed method of construction will render it peculiarly applicable to harbour-lights and ship-lights.

The author exhibited a paraboloidal reflector constructed on the method to which he referred. The facets were successfully constructed by Messrs. Chance, of Birmingham. The pieces of glass having been first bent upon a mould, were afterwards ground by rubbing-surfaces worked by machinery of the same kind as is employed for dioptric apparatus. The facets were afterwards silvered by the patent process of Messrs. Pratt and Co., of St. Helens, Lancashire, who inform the author that so long as the paint is not removed from the back of the silvering its reflecting power will remain unaltered.

Differential metallic Mirror and Holophote.-The same construction may also be adopted, as the author has already hinted, for producing a differential holophote which will, by means of single optical agents, collect, with uniform density in azimuth, the whole sphere of diverging rays into any given cylindric sector. For such a purpose each facet must, in the vertical plane where no divergence is wanted, be ground to a parabolic profile, while in the horizontal it must be of such hyperbolic, elliptic, or other curve as will give the required horizontal divergence without interference with the apparatus for the central cone of rays, which will be dealt with according to the requirements of the case, by means either of Fresnel's beehive fixed apparatus or of a differential lens-an instrument which the author has elsewhere described. In order to test the practicability of such an arrangement, a mirror was constructed of small glass facets, which were arranged optically on a surface of putty, and which answered the purpose as far as was possible with plain pieces of glass. The author sees therefore no great difficulty in making this new kind of mirror of separate facets of silvered glass of small size; but he found such difficulties in constructing one with a continuous surface that he consulted his friend Professor Tait, who kindly gave him his assistance in the solution of this difficult problem by supplying the general formula; and he has no doubt, now that the simpler form of facet has been so successfully constructed, a differential holophote will soon be made.

Notice of the Researches of the late Rev. William Vernon Harcourt, on the Conditions of Transparency in Glass, and the Connexion between the Chemical Constitution and Optical Properties of different Glasses. By Professor G. G. STOKES, F.R.S.

The preparation and optical properties of glasses of various compositions formed