sions for the Variations of the Mean Distance, the Eccentricity and the Longitude of the Perihelion: the Variation of the Ec- centricity expressed by means of partial Differential Coefficients of the Quantity (R) dependent on the Disturbing Force: the same Form of Expresssion extended to the Variations of the Deduction of the constant Parts of the Development of R. Ex- pressions for the Secular Variations of the Elements. Varia- tions of the Eccentricities of the Orbits of Jupiter and Saturn. Theorem for shewing that their Eccentricities can neither in- crease nor decrease beyond certain Limits. Diminution of the Eccentricity of the Earth's Orbit. It is the Cause of the Acce- leration of the Moon's Mean Motion. Its Value computed from the disturbing Forces of the Planets. Thence, the Secular Equation of the Moon's Acceleration computed. Variation of the Longitude of the Perihelion: sometimes a Progression, at other times a Regression. The Progressions of the Perihelia of Jupiter and Saturn computed. Variations of Inclination and of Node. Theorem for shewing that the Inclinations of the Planes of Orbits oscillate about a mean Inclination. The Mean Motions of Nodes, with reference to the Ecliptic, sometimes Pro- gressive, at other times Regressive: but, with reference to the Orbit of the disturbing Planet, always Regressive. The Moon's Nodes. The Quantity of their Regression computed. Variation of the Obliquity of the Ecliptic: Progression of the Equinoxes; both caused by the disturbing Forces of the Planets: their Quantities computed. The Length of the Tropical Year affected by them. 407 Stability of the Planetary System with regard to the Mean Distances. The Mean Distances subject only to Periodical In- equalities and not to Secular. Stability of the Planetary System with regard to the Eccentricities and Inclinations. Theorems On the Method of determining the Masses of Planets that are accompanied by Satellites. Numerical values of the Masses of Jupiter, Saturn, and the Georgium Sidus. The Earth's Mass determined. The Methods for determining the Masses of Venus, Mars, &c. and, generally, of Planets that are without Satellites. The Masses of Satellites and of the Moon determined............. 466 PR E F A C E. IT must be in compliance with custom, rather than from any distinct view of good likely to result, when an Author begins his Work by defining the Science he means to treat of. A definition is not easily laid down. It is not difficult, indeed, to define a branch of science in general terms; but such are seldom intelligible to the Student. If we enumerate what is too summarily expressed, and explain a general statement by detailing certain cases comprehended under it, we, probably, forestall what belongs to the body of the Work. We attempt to do immaturely what, it is almost certain, will be done imperfectly; and this without an adequate advantage; for, a definition such as we allude to, entailing no consequences, is not required in the beginning of a Work: at the end it is unnecessary. But if a Student does not require, as essential to the perusal of a Work, a formal definition of its drift and nature, an Author will gladly be absolved from giving one. He cannot but wish to avoid such slippery ground. For, should he restrict himself, as it is usual, to few terms, he is in danger of defining too largely, or too partially, or too vaguely. If it be said, the object of Physical Astronomy is the explanation of heavenly phenomena, the definition is too wide: if merely of the laws of the motions of the Stars, too restricted if of those laws on mechanical principles, too vague and indistinct: if of their causes, too presumptuous and illusive. : Even Newton's Theory, perfect and excellent as it is, and on which Physical Astronomy is founded, does not pretend to exb plain the causes of the phenomena of the heavenly bodies. It rather explains why they may be reduced to the same class; which is an object more simple and distinct. The two points on which the theory rests, are, first, that every particle of matter attracts, and, consequently, that two particles mutually attract each other; the second point is, that, if the distance between the particles vary, the attraction will vary proportionally to the inverse square of the distance. The first of these is called the Principle, the second the Law of Gravity. But the terms Attraction and Gravity, although they seem borrowed from the language of Causation,. are not meant to signify any agency or mode of operation. They stand rather for a certain class of like effects, and are convenient modes of designating them. One of these effects is the space fallen through by a heavy body at the Earth's surface: another is the deflection of the Moon from the tangent of her orbit towards the Earth; and, in every case, gravity, or attraction is expounded by a like space or deflection. If, on analysing a phenomenon of a revolving planet, we can detect such space or deflection taking place towards the attracting body, we have found out all that is meant by attraction. If, for instance, we can so resolve an arc of the Moon's orbit into the elements producing it, that two of them being the Moon's velocity and direction, the other two shall be spaces or deflections towards the Earth and Sun respectively: the former distance proportional to the Earth's mass and the inverse square of the distance of the Earth and Moon, the second proportional to the Sun's mass and the inverse square of the distance of the Sun and Moon, we have found out all that is necessary to be understood by the Earth's attracting the Moon, and the Sun's attracting the Moon: or, in other words, by the Moon's gravitating to the Earth, and gravitating to the Sun: although the latter part of this expression, so applied, is contrary to the technical and conventional language, which, for the sake of distinction, it is found convenient to employ. It is thus, by resolving a phenomenon, that we may form a notion of gravity and attraction: and we may obtain an equally distinct notion by the reverse process. Draw, for instance, from the Moon towards the Earth and Sun, two lines, representing, respectively, according to the prescribed conditions, (see p. 10.) the attractions of the Earth and Sun: then combining these with the lines representing the Moon's velocity, &c. according to the principles of Dynamics (those principles by which we estimate a body's motion in a parabolic curve, and the oscillation of a pendulum) the result will be the described arc of the Moon's orbit. According to Newton's Theory, like results take place throughout the planetary system: each planet is attracted by all the rest, and their attractions are to be expounded similarly to the attractions that have just been spoken of. This is a general statement which is easily made; but the actual finding of the results, must, it is plain, be a most difficult research. The attracted and attracting bodies, both with regard to their relative situation and the intensities of their mutual attractions, are in a state of perpetual change. Their Configuration, as it technically is called, is for ever varying: and whether we investigate the arc of an orbit, or a change in its dimensions, the result must be the modified effect of many forces, that, during unequal times and with varying intensities and directions, have been sometimes conspiring, and at other times counteracting each other. This may give us some idea of the difficulties of Physical Astronomy, they are indeed so great, that, if met in their full extent, they cannot be completely overcome. But there are various means for lessening and avoiding them: some devised, others naturally presenting themselves. The Moon's motion, for instance, we have considered to depend on her velocity and direction, and on the forces of the Sun and Earth. But, according to Newton's Principle of Universal Gravitation, every planet in the system must, like the Sun, attract the Moon. Each planet, however, attracts so much less forcibly, |