6. On the Period of Vibration of Electrical Disturbances upon the Earth. By Professor G. F. FITZGERALD, Sc.D., M.A., F.R.S., F.T.C.D.

Professor J. J. Thomson and Mr. O. Heaviside have calculated the period of vibration on a sphere alone in space and found it about 059 second. The fact that the upper regions of the atmosphere conduct makes it possible that there is a period of vibration due to the vibrations similar to those on a sphere surrounded by a concentric spherical shell. In calculating this case it is not necessary to consider propagation in time for an approximate result, and it was pointed out that a roughly approximate result could be obtained by equating the electric force at the centre of the earth to a simply harmonic distribution of electricity on its surface and on that of a concentric shell, to the electric force due to the rate of variation of the Vector potential of the electric currents calculated on the assumption of a simply periodic variation of the electric distribution. It appears that the displacement currents between the outer and inner shells are the only contributors to the Vector potential. The value of the time of vibration obtained by this very simple approximation is

Applying this to the case of the earth with a conducting layer at a height of 100 kilometres (much higher than is probable) it appears that a period of vibration of about one second would be possible. A variation in the height of the conducting layer produces only a small effect upon this if the height be small compared with the diameter of the earth. In the case of the sun the period of vibration would be about a hundred times as great. An approximate estimate was made as to the electric density at the pole required to produce a horizontal force at the equator equal to about the hundredth part of the earth's horizontal force, and it was found to be eight electrostatic units per square centimetre. Anything very much greater than this should produce a measurable reduction of barometric pressure. Attention was called to the desirability of having a sufficient number of magnetic stations in a ring round the magnetic pole to be able to determine whether there were simultaneous, easterly or westerly, waves of disturbance of horizontal force. Such a simultaneous disturbance, of which there was some evidence from the present sparsely distributed observatories, would mean that there was an earth current which was running through the earth in such a way that it must be continued by auroral discharges in the upper regions of the air.

7. The Moon's Atmosphere and the Kinetic Theory of Gases.
By G. H. BRYAN, M.A.

[The possibility of applying the kinetic theory of gases to explain the absence of any perceptible atmosphere round the Moon seems to have been contemplated ever since the earliest days of the kinetic theory itself. Mr. S. Tolver Preston claims to have been the first to suggest this explanation ('Nature,' Nov. 7, 1878); but the idea was thought of long before then, for Waterston, in his now wellknown paper on 'The Physics of Media' (Phil. Trans. R.S.,' 1892 [A]), specially considers the problem of the Moon's atmosphere. His investigation would, however, require all the molecules of a gas to have the same velocity, which we now know to be incorrect, and it leads to the conclusion that the existence of a lunar atmosphere would be possible at ordinary temperatures.]

Now, according to the well-known 'error' law of distribution of velocity among the molecules of a gas, there must always be some molecules moving with sufficiently great speeds to overcome the attraction of any body, however powerful, and some whose speed is too small to enable them to escape from the attraction of

any body, however feeble. On this assumption no planet would theoretically have an absolutely permanent atmosphere. If, however, the proportion of molecules which escape is relatively exceedingly small, the atmosphere of the planet may be regarded as practically permanent. In order, therefore, to test the relative

degree of permanence of the atmospheres of different celestial bodies, the author has calculated what proportion of the molecules of oxygen and hydrogen at different temperatures have a sufficiently great speed to fly off from the surfaces of, and never return to, the Moon, Mars, and the Earth. The corresponding results for the Sun are also given, not, however, at its surface, but at the Earth's distance from the Sun's centre, where the critical speed is, of course, 2 x the speed of the Earth's orbital motion.

The numbers, which are given in Table I., p. 684, represent, in each case, the average number of molecules, among which there is one molecule whose speed exceeds the critical amount. Thus, for oxygen at temperature 0° C. rather over one molecule in every three billion is moving fast enough to fly off permanently from the Moon, and only one in every 2.3 x 10329 is moving fast enough to escape from the Earth's atmosphere, while the Sun's attraction, even at the distance of the Earth, prevents more than one in every 2 × 101940 from escaping.

Now it is generally stated that at the Earth's surface there are somewhere about 18 x 1018 molecules in a cubic centimetre of air. If we suppose the Moon's surface were invested with an atmosphere, say of oxygen, of this density, every cubic centimetre would contain, roughly, about six million molecules moving with sufficient speed to carry them away from the Moon. But the velocity requisite to overcome the Earth's attraction would only be attained by one molecule in a volume of 1.3 × 10310 cubic centimetres, that is, in a globe of radius about 2 × 1098 kilometres. In our Earth's atmosphere the acquisition of the requisite speed by a single molecule would only occur once at rare intervals, and would probably be far too rare to affect the permanency of the Earth's atmosphere, even during the long periods of time through which we are wont to trace the history of the solar system.

In the case of Mars the corresponding figure shows that an atmosphere containing oxygen is practically permanent at all ordinary temperatures, but that such an atmosphere could not remain on the planet if its temperature were as high as 819° C.

If the Earth possessed an atmosphere of hydrogen at temperature 0° C., containing 1018 molecules per cubic centimetre, there would be one molecule in every 60 cubic centimetres whose velocity would be sufficient to carry it away permanently. Remembering that the Earth at one time was much hotter than at present, we see that the absence of hydrogen from the Earth's atmosphere (except in the form of water) is easily accounted for. In the case of the Sun, a hydrogen atmosphere would be permanent at 0° C., even as far off as the Earth, as is shown by the number 2.7 × 10307. At one-tenth of the Earth's distance from the Sun we should obtain the same number with an absolute temperature ten times as high, i.e., 2730° absolute, or 2457° C., and so on. A considerably higher temperature would, however, be consistent with permanency. Thus the kinetic theory quite explains the existence of hydrogen in the Sun's atmosphere at high temperatures.

The present theory seems to preclude the possibility of the Moon ever having had an atmosphere. If the Moon were formerly much hotter than at present the proportion of gaseous molecules tending to fly off would be greater, and such a loss would be exactly the reverse of the process which the nebular hypothesis assumes to be taking place in the solar system.

But it would seem probable that this flying off of gaseous molecules is not an essential condition in explaining the Moon's absence of atmosphere by means of the kinetic theory. It is only necessary to assume the existence of a distribution of matter of excessive tenuity pervading interplanetary space in order to account for a gradual increase taking place in the atmospheres of all the planets, and such an assumption, taken in conjunction with the kinetic theory, is quite compatible with the absence of any perceptible atmosphere surrounding the Moon, and of any perceptible resistance to the motions of the Moon and planets.

The kinetic theory enables us to compare the densities at different points of a mass of gas in equilibrium under such fixed central forces as the attractions of the celestial bodies. If we apply the theory to the system consisting of the Sun, Moon, and Earth, we shall find the relative densities given in Table II., the density

Position relative to
attracting body

TABLE I.—Average Number of Molecules of Gas to every one whose Speed is sufficiently great to overcome the Attraction of the Corresponding Body.

Position relative to
attracting body

TABLE II.—Relative Densities of Oxygen and Hydrogen in a Permanent Distribution, taking their Densities at the Earth's Surface as

Unity.

Position relative to
attracting body

Interstellar space

TABLE III.—Relative Densities in a Permanent Distribution, taking the Average Densities of Distribution in Interstellar Space as Unity.

of the corresponding gas in the atmosphere at the Earth's surface being taken as unity. If we take the density at an infinite distance from the Sun to be unity, the corresponding results will be given by Table III.

The assumption on which these results are calculated may be called an 'equilibrium theory,' since it takes no account of the motions of the bodies in question, and it assumes a permanent distribution to have been attained, so that the whole of the gas is at a uniform temperature.

When every allowance is made for the artificial character of the assumptions it is still highly unreasonable to suppose that the Moon could have an atmosphere so far in excess of that required by the equilibrium theory that its presence could be detected even by the most careful observations; and a very few molecules of oxygen and nitrogen flying about in interstellar or interplanetary space would represent a number far in excess of that required by the equilibrium theory, and would therefore tend to augment the total mass of the Earth's atmosphere.

If we try to compare the atmospheres of different planets, such as the Earth and Mars, the 'equilibrium theory' breaks down completely, as is only natural when we remember how rarely a single molecule leaves the atmosphere of either planet.

It is different in the case of two bodies so near each other as the Earth and Moon. Among the molecules of gas which at any time might find themselves in the neighbourhood of the Moon and Earth the greater number would be drawn in by the more attractive body, and the Moon would not, therefore, be likely to obtain an atmosphere like that surrounding the Earth.

At no period has it possessed an atmosphere of oxygen and nitrogen comparable in density with that of the Earth. A decrease of density in a planet's atmosphere could only take place by the condensation in liquid form of vapours present in it, not by matter leaving the planet.

Thus the kinetic theory of gases is capable of accounting for absence of air from the Moon without making any assumptions contradictory to the nebular hypothesis.

8. On Grinding and Polishing. By Lord RAYLEIGH, Sec.R.S.

9. Simple Apparatus for Observing and Photographing Interference
and Diffraction Phenomena. By W. B. CROFT, M.A.

A wooden screen 16 inches high and 9 inches broad has an opening at a height of 10 inches which will take a spectroscope slit or a thin metal plate with a pinhole: a convex lens focusses sunlight or limelight on the small aperture; a lamp, however, gives sufficient light for the main effects without the finer detail. At about 2 feet distance an A or B Huygens' microscope eyepiece is adjusted so that its field is evenly covered with the light; about 6 inches in front of this is the holder for the diffraction-objects-a stiff-jointed arm about 3 inches long is a convenient adjustment for height. Various things are fixed on 3-inch squares of wood which have a central hole inch square; a slot in the middle of one side of the wood goes over a screw at the end of the jointed arm; a nut clamps it, but allows movement in a vertical plane. The chief simple objects are: Single edge, square corner, double edge, bi-prism, inclined mirrors, needle-eyes, needle-points, needles of various thicknesses, needle with opaque slip on one side, needle with mica slip on one side, perforated zinc, wire gauze, shot cemented on glass for Arago's bright spot at the centre of the shadow of a circular screen, holes of graduated sizes in a metal plate.

If the eyepiece is passed through a collar which will fix on the front of a camera in the place of the ordinary lens, an image is made on the ground glass which can be photographed. The rays emerge parallel and the image varies in size, but remains in focus for all positions of the eyepiece and ground glass.

In illustration of the two modes of observing these phenomena the author drew attention to an old set of diffraction objects, consisting of fifty-nine small geo

metrical figures on glass. They were intended to be placed in front of a telescope focussed to a distant point of light, according to the plan of Fraunhofer and Schwerd. The result is a system of radiating lines, which consist of spectral images of the point of light; but if the same are viewed as above with the eyepiece alone, the extending spectra mostly disappear, and more elaborate and finely defined central figures are formed.

10. On Wilson's Theory respecting the asserted foreshortening of the inner side of the Penumbra of the Solar Spots when near the Sun's Limb, and of the probable thickness of the Photospheric and the Penumbral Strata of the Solar Envelopes. By Rev. FREDERICK HOWLETT.

For a considerable portion of the period of upwards of thirty years, during which the author of this paper has maintained a more or less continuous record of the solar spots during, be it noted, three full successive periods of the maximum, minimum, and intermediate conditions of solar-spot activity, and including some thousands of careful and roughly micrometric observations-one point has not a little excited his surprise, viz., to have scarcely in any one undoubted instance been able to verify the observation first made by Dr. Wilson, Professor of Practical Astronomy in the University of Glasgow, as long ago as the months of November and December 1769, as well as on, he affirms, many subsequent occasions.

The phenomena in question which Wilson claims to have frequently seen is, in brief, this, that if a spot, when well on the disk, has its penumbra equally distributed on all sides of the umbra, the effects of foreshortening on the sphere, in consequence of the funnel-shaped nature of a spot, will be that whenever a spot is near the limb the side of the penumbra nearest to the sun's centre will be extremely foreshortened, and that when very near the limb, not only the whole of the inner side of the penumbra, but the whole of the umbra itself, will become invisible, the outermost side of the penumbra alone remaining in sight.

Wilson tells us (as recorded in the Philosophical Transactions' for 1774) that he effected his observations by direct vision, using a small, and he says an excellent, Gregorian reflecting telescope of 26 inches focal length, with a magnifying power of 112 linear.

The author's observations were made by projecting the sun's image on a large screen nearly 5 feet by 4 feet, using a small but excellent refractor by the elder Dollond of 3 inches aperture with 46 inches focal length, with magnifying powers

of from 80 to 200 times linear.

When using power 80, with the screen placed 4 feet 3 inches from the eyepiece, the projected image of the sun has a diameter of 32 inches, so that, consequently, each inch of the image is equivalent to just about 60" of celestial arc, and which is the scale on which the author's drawings are usually made. A sort of micrometer, moreover, consisting of a small disk of glass ruled off into the two-hundredths of an inch, is placed in the focus of the eyepiece, so that the divisions on the glass disk are distinctly seen projected also on the screen, each exactly half an inch apart.

When a power of 200 linear is used the sun's image is seen 6 feet 4 inches in diameter on the screen when placed at the same distance from the eyepiece as before mentioned, and when each minute of arc thereon measures 2 inches, so that, in fact, in such enlarged images seconds of arc can be readily measured by a pair of common dividers.

Now as regards Wilson's observations-with which the author professes himself to be most strongly at issue, especially when spots of any considerable magnitude are concerned-nothing could be stated in a more exact, cautious, and circumstantial manner. And it is, in all probability, in consequence of this that the phenomena Wilson claims to have seen have been handed down as facts (without their having been adequately verified or disproved) in almost all works on physical astronomy to the present day.

The author, however, had the honour of calling the special attention of astro