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ASTRONOMY

associated with, the zodiacal light, which, on rare occasions and under the most favourable conditions, some observers have thought could be traced near midnight all the way across the heavens, forming a complete arch from east to west. In that case the Gegenschein would be a small patch in this zodiacal arch, slightly brighter than elsewhere. Of the various explanations which have been propounded no one can be considered as sufficiently probable to merit acceptance. An ingenious suggestion, and one which it is equally difficult to prove or disprove, is that it is composed of nebulous matter thrown off from the earth, forming a tail to the latter like that of a comet. The quantity of such matter necessary to produce the phenomenon would be minute in the last degree. Similar appendages, if carried by the planets, would be entirely ih visible to us, and that of our earth would be visible only because we see through it endways and on a dark sky. Intimately associated with this subject is the question of the conditions necessary to the permanence of an atmosphere round a planet. Dr Johnstone atinotary Stoney kas recently investigated these conditions, spheres, taking as the basis of his work the kinetic theory of gases {Trans. Roy. Dubl. Soc. vi. p. 305). On this theory every molecule of a gaseous mass is completely disconnected from every other and is in rapid motion, its velocity, which may amount to one or more thousand feet per second, depending on the temperature and on the atomic weight of the gas. At any temperature the velocities of individual molecules may now and then increase without any well-defined limit. If at the boundary of an atmosphere the velocity should exceed a certain limit fixed by the mass and force of gravity of the planet, molecules might fly away through space as independent bodies. The absence of hydrogen from the atmosphere of the earth, and of an atmosphere from the moon, may be thus explained. If the fundamental hypotheses of Dr Stoney’s investigations are correct and complete, it would follow that neither the satellites and minor planets of the solar system nor Mercury can have any atmosphere. If the separate molecules thus flying away moved according to the laws which would govern an ordinary body, they would, after leaving their respective planets, move round the sun in independent orbits. The possibility is thus suggested that the matter producing the zodiacal light may be an agglomeration of gaseous molecules moving round the sun; but several questions respecting the intimate constitution of matter will have to be settled before any definite conclusions on this point can be reached. It is not to be assumed that a molecule would move through the ether without resistance as the minutest known body does, and there is probably a radical difference between the minutest particle of meteoric matter and the molecule of a gas. The relations of identity or difference between such finely-divided matter as smoke and atmospheric haze and a true gas have yet to be fully established, and until this is done a definite and satisfactory theory of the subject does not seem possible. II. Gravitational and Theoretical Astronomy. The fundamental hypothesis of modern theoretical astronomy is that the motion of each heavenly body is determined entirely by the gravitation of other bodies. Assuming such to be the case, it will be possible to predict the celestial motions with entire precision, if certain fundamental data are given. Such data would be the mass of each body, and its position, velocity, and direction of motion at some given instant. The problem ould then be the construction of general formula by which the position of each body at any moment whatever could be expressed in terms of the time. In practice we

do not use as fundamental data positions and velocities, but the elements of the orbits, including mean distance, eccentricities, position of orbit in space, mean position of the planet at a given moment, and other quantities which do not vary with the time. When the differential equations expressing in a general way the effects of gravitation are integrated, the elements appear in the solution as arbitrary constants, to which values may be assigned at pleasure. The astronomer has then to assign such values that the observed positions of the bodies, whether planets or satellites, shall be accurately represented by the formulae. The mathematical processes by which the equations are integrated, values assigned to the elements, and the results compared with observation, are perhaps the most difficult and most complicated with which the mathematical astronomer has to deal, and only in comparatively simple cases can he be sure that the minute deviations of the actual movement of a body from his predictions do not arise either from errors in his process or from errors of observation. The frotn the equations of motion can be integrated only in law of the form of an infinite series of complex terms of gravltawhich all below a certain magnitude have to be tiondropped, and the difficulty is to be sure that no terms are omitted which could have a sensible value. Generally, it is possible to secure the necessary precision, but in some cases the question whether every possible term which could affect the result has been included may be an open one. One of the most interesting problems of the astronomer at present is whether the motions of the heavenly bodies, as determined by our most refined methods of observation, go on in rigorous accordance with the law of gravitation. This question cannot be settled by a mere comparison of the predicted motion with observations. When differences are found, the question will arise whether they may not be due to errors either in the fundamental elements or in the theoretical computations; in several instances supposed deviations have been found due to the latter cause. One notable case in history is that of the motion of the moon’s perigee. This motion was found to be twice as great as was at first supposed to be due to the Newtonian theory, but Clairaut showed that when more rigorous methods were adopted the observed motion was represented. The general rule has been that, whenever an observed deviation has been well made out, it has been traced to the omission of some term of the algebraic formulae expressing the motion of a planet. To this rule there are two notable exceptions:— (a) In 1845 Leverrier found that the centennial motion of the perihelion of Mercury derived from observation was greater by 35" than it should be from the Motions gravitation of the other planets, and his result 0f the has been more than confirmed by subsequent planetary investigations, the most recent discussion of perihelia. observations showing the excess of motion to be 43" per century. In this case there can be no question as to the correctness of the theoretical result, since the computation of the secular motion of the perihelion is a comparatively simple process. It follows that either Mercury must be acted upon by some unknown body or the theory of gravitation needs modification. The most natural explanation, and that offered by Leverrier, attributes the discrepancy to the action of a group of intra-Mercurial planets. For some time, therefore, careful search was made for these planets. One or more has been thought from time to time to be detected, but every observation of the kind has been disproved by critical examination. The simplest and surest method of discovery is afforded by the consideration that these bodies, if they exist, must