Central Standard. Telescope used was a four-inch BRASHEAR equatorial, with Herschelian eye-piece, power 78. NOTES ON THE TOTAL ECLIPSE OF THE SUN, JANUARY 21-22, 1898, IN INDIA. BY COLONEL A. Burton-BROWN, R. A., F. R. A. S. The central line of totality on the west coast of India passes between Ratnagiri and Rajapur, the latitude of which place is 16° 40′ N., and longitude 73° 35′ E. of Greenwich. Totality commences 22d-o" 47" 42; has a duration of nearly 2m 23, and the Sun's altitude is 53°, about. The line of shadow strikes across India, cutting the river Ganges a few miles south of Balia and passing on to Jubang in Nepaul, where the duration of totality would be reduced by about 23 and Sun's altitude by about one-third. There are many circumstances which will influence observers in selecting stations beyond that of the Sun's altitude and length of totality. The most important one will probably be the weather conditions between oh 30m and 2" 15". Now, if India were a great plain, we might consider that in the third week in January that the conditions of weather will be equally favorable from the west coast to the Ganges, but as the country is a series of undulations, including some hills, local circumstances must be taken into account, and from my own observations and those of others, I am inclined to consider the height of the station which is from 500 to 1500 feet above the sea would be the most satisfactory if not in close proximity to higher ground, and if not within twenty miles either of the seacoast or the Ganges river. Places from 73° 30' to 75° 45′ east longitude I find are slightly freer from cloud than places east and west of that longitude. Although the daily mean cloud in other places may not be greater, it is often more variable. I am inclined to advise, from atmospheric conditions as well as the position of the Sun and length of totality, that a fairly elevated position on or near the central line between those limits be taken up. No doubt stations north of Rajapur and Nagpur will be selected by some observers, but while the climatic conditions should be good there, they will probably not come up to a carefully selected spot near Indapur, Aundh, or Parainda, none of which are difficult to get to with the requisite instruments. I would here take the opportunity of saying, if a fairly large party is formed, they should be divided as much as possible. This I strongly urged for the British-Norwegian expedition in 1896, but instead of selecting places near Bodo on the west coast and places on the Tana Fjord and Russian frontier, as well as Vardoe and Vadsoe, they all huddled together at the latter two most accessible places, where, unfortunately meeting with unfavorable atmospheric conditions, no good results were obtained. It must not be forgotten that two or three exceptional circumstances are now occurring in India — famine and plague—and more recently, earthquakes, so that it may be impossible much before the close of the year to give an exact locality suitable for a scientific expedition. We all hope that in the cooler season these unfortunate conditions will be materially improved and that there may be no obstacle to progress in any part of the country. An elevated post near Indapur would give about 1 58 totality at Sun's altitude of about fifty degrees. THE CAUSE OF GRAVITATION.* BY V. WELLMAN. According to NEWTON'S law of gravitation, the attractive force of matter is proportional to the mass and inversely proportional to the square of the distance. The rigorous validity of this law has, in recent times, been doubted; but its extraordinary approximation to the truth is unquestionable. Consequently, without going into the question as to whether the law is rigorously valid, I will endeavor to verify it. The propagation of light through interstellar space shows that this space cannot be absolutely vacant. It is filled with a material, the condition of which we assume to be like that of a gas of extraordinarily rare density. The barometer-formula gives, for the density of air at an altitude, h∞, which, therefore, corresponds approximately to the density of the interstellar medium, DoD, 10-346, * Translated from Astronomische Nachrichten by E. F. CODDINGTON. where D, designates the density of air at sea level. Evidently this formulæ is not exact, since MARIOTT's law, on which it is based, holds good only for a finite pressure and therefore for a finite altitude. Nevertheless, this value can be regarded as an approximate measure for the density of the interstellar medium. We can also assume that the matter of bodies is composed of a very large number of very minute particles, whose dimensions are exceedingly small compared with the space between them. Suppose we consider a single particle of the Sun and one of a planet. The particles of the interstellar medium move, according to the kinetic theory of gases, with an enormous velocity among each other. If we imagine a body particle, a, it will be struck on all sides by particles of the medium; therefore will receive an equal pressure on all sides and will remain at rest. If there exists a second particle, b, a will not be struck in the direction ba, and likewise b will not be struck in the direction ab. Therefore, the impulses acting on a in the direction ab and those acting on b in the direction ba, will tend to push the two particles together; that is, there will seem to be an attractive force between them. The question is, whether this force will act according to NEWTON'S law. First of all it is clear that a body consisting of a particles will receive n times the number of impulses, and, therefore, the moving force will be proportional to the mass, provided the single particles are far enough apart not to cover each other from impulses, and that each particle is struck just as often as it would be if it existed alone; or, in other words, provided the interstellar medium can go through the celestial bodies without apparent resistance. Evidently it can and must happen that in a certain element of time some body atoms will cover others, but in the same or equal elements of time other body atoms will receive many impulses. Therefore, according to the theory of probabilities, since the number of particles is assumed to be infinitely large, there will be a constant value for the number of impulses which lies within the limits of our perception, and which is proportional to the number of body atoms or to the mass. The phenomenon of the diffusion of gases seems to give additional evidence that we can assume such a free passage of the interstellar medium. According to the investigations of GRAHAM especially, the diffusion volume (V) of a gas is inversely proportional to the density of the gas; that is; In fact, this law is easily explained from molecular structure. The less dense the particles of a gas are, the more of the same will pass through resisting bodies without striking them. That is, the number n of gas particles going through each row of body particles, is inversely proportional to the density of the gas. But if the number of particles passing a row be increased v times, the number passing a cross-section and also the volume will be increased v2 times, and the ratio of the volumes will be inversely as the square root of the densities. According to this law, it is evident that the ability of the celestial bodies to allow such a free passage of the interstellar medium of the above-mentioned minimum density must be such that the above-made assumption will appear correct. it will not be maintained here that the passage of the world particles (as we will name those of the interstellar medium) occurs accurately according to GRAHAM's law; rather it will only be shown that the assumption of this perviousness of the celestial bodies for the world particles in the assumed measure contains no inconsistency or improbability. We come then to the consideration of the question, whether the power produced by the interstellar medium must act inversely proportional to the square root of the distance. For this purpose we make the assumption that the density of this medium is constant within an attraction system (solar system), if not in the whole universe. This assumption is certainly allowable, since there is no evidence for the opposite assumption of unequal densities; and if there should be inequalities of densities, they would become equalized by expansion in finite distances and in a finite length of time. Moreover, it is not absolutely excluded that in other attraction systems, at an infinite distance away, there cannot exist temporarily other densities. We see that, of the world particles, only those have a dislocating effect upon the body particles which move in a line connecting the two particles; or that the planets are pushed towards the Sun only by those world particles which move in directions radial to the Sun. The number of these motions is independent of the distance from the Sun; therefore, an equal number of world particles will rebound radially against the surfaces of spheres which surround the Sun concentrically. Therefore, the number of impulses received by a surface unit is inversely proportional to the square of the distance, as NEWTON's law requires. I will illustrate this point in another way. gas upon the side q of the inclosing vessel is, The pressure of a where m is the mass of a gas particle, u its velocity, n the number of particles, and 7 the length of the enclosing vessel to the opposite side q. we can use the density of the gas 8, n For A 1 whereby we become independent of the assumption of finite enclosed space. Therefore, the pressure of the interstellar medium upon the surface units of two spheres described about the Sun with radii r and r' is, According to NEWTON'S law, the following relation should hold: P r2 P, and, therefore, & must equal d'. That is, NewTON'S law is satisfied if the density of the interstellar medium is constant within the attraction sphere. It is also easily seen by a simple geometrical representation, without applying mathematical formulæ, that the pressure directed radially toward a center must be inversely proportional to the square of the radius. Within other attraction-spheres in which other densities of the interstellar medium reign, NEWTON's law of gravitation would still be valid, but the gravitation constant for the unit of mass would have different values. Possibly the remarkable mass and distance relations reigning in some of the systems, such as Algol, are due to these conditions. At places of transition, where the density of the medium is variable, a stable system is as a rule impossible. Since the conceptions given in the above lines will probably meet many objections, I may be permitted to discuss some of the expected ones. To the assumed rare density of the interstellar medium, comes the objection that the number of single impulses of the world particles in the unit of time is far less than that of a particle of gas (earthly), whereby its effect must be correspondingly diminished. But this decrease of effect would |
