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influence their understanding of many others which occur in the prosecution of an algebraical process. The advanced student who exults in the progress which the modern calculus enables him to make in the Lunar or Planetary Theories, perhaps, hardly reflects how much of the power of understanding his conclusions has been derived from Newton's general explanations.
The utility of such a work being allowed, it cannot, I think, be disputed that there exists a necessity for a
The only attempts at popular explanation in general use with which I am acquainted, are Newton's eleventh section, and a small part of Sir John Herschel's admirable treatise on Astronomy. The former of these (the most valuable chapter that has ever been written on physical science), is in some parts very defective. Thus, the explanation of the motion of the line of apses is too general, and enters into particular cases too little, to allow of a numerical calculation being founded on it. The explanation of evection is extremely defective. The explanation of variation, however, and of alteration of the node and inclination, are probably as complete as can be given. The latter treatise, besides expanding some of Newton's reasoning, alludes to the long inequalities and secular disturbances of the planets, but not perhaps with sufficient accuracy of detail to supersede the necessity of further explanation. No popular work with which I am acquainted, alludes at all to the peculiarities of the theory of Jupiter's satellites.
I have attempted in some degree to supply these defects; with what success the reader must judge. As it was my object to avoid repetition of theorems, which are to be found in treatises on Mechanics and elementary works on Physical Astronomy, and which are fully read and mastered by those who take much interest in these subjects, and which, moreover, do not admit of popular explanation so easily as many of the more advanced propositions, I have omitted noticing them any further than the consistency of system seemed to require. Thus, with regard to elliptic motion, Kepler's laws, &c., I have merely stated results; because the investigation of these are familiar to the higher students, to whom I hope the other explanations may be useful; and because without great trouble it did not appear possible to put the reasons for these results in the same form as those for other effects of force. I have, however, alluded to some of the difficulties which are apt to embarrass readers in the first instance, as much for the sake of the reasoning contained in the explanation as for the value of the results. The only additions which I have thought it desirable to make for the benefit of readers of Newton, are contained in a few notes referring to one of Newton's constructions.
To the reader who may detect faults in the composition of the work, I can merely state in apology, that it has been written in a hurried manner, in the intervals of very pressing employments. I have only to add, that, holding a responsible situation in my University, I have always thought it my duty to promote, as far as I am able, the study of Physical Astronomy; and that if this treatise shall contribute to extend the knowledge of its phænomena and their relation to their causes, either among the students of the University, or in that more numerous body for whom it was originally written, I shall hold myself well repaid for the trouble which it has cost me.
SECTION 1.-On the Rules for calculating Attraction, or the Law
of Gravitation .
3. Attraction is to be measured by the motion which it
produces 5. Attraction does not depend on the mass of the attracted
body 7. Is proportional to the mass of the attracting body 9. Varies inversely as the square of the distance
SECTION II.-On the Effect of Attraction upon a Body which is in
motion ; and on the Orbital Revolutions of Planets
and Satellites. 14. The motion supposed transversal to the direction of the
force: a simple case is the motion of a stone thrown
from the hand 15. The motion of the stone calculated by the second law of
motion 16. The same rule will apply to a planet, if we restrict the
calculation to a very short time 18. A planet or satellite may move in an ellipse, a parabola,
or a hyperbola : in fact, they all move in ellipses differing
little from circles 21. Distinction between projectile force and attractive force 25. The planets, when nearest to the sun, are in no danger of
falling to the sun, because their velocity is then neces
sarily very great 27. Explanation of terms 29. Law of equable description of arvas.
62. Disturbing force perpendicular to the radius vector, in the
direction in which a planet is moving, when the planet