absence of eccentricity. All that we could do would be to declare the divergence from the circular form to be inappreciable. Delambre was unable to detect the slightest ellipticity in the orbit of Jupiter’s first satellite, but he could only infer that the orbit was nearly circular. The parabola is the singular limit between the ellipse and the hyperbola. As there are elliptic and hyperbolic comets, so we might conceive the existence of a parabolic comet. Indeed if an undisturbed comet fell towards the sun from an infinite distance it would move in a parabola; but we could never prove that it so moved.
Substitution of Simple Hypotheses.
In truth men never can solve problems fulfilling the complex circumstances of nature. All laws and explanations are in a certain sense hypothetical, and apply exactly to nothing which we can know to exist. In place of the actual objects which we see and feel, the mathematician substitutes imaginary objects, only partially resembling those represented, but so devised that the discrepancies are not of an amount to alter seriously the character of the solution. When we probe the matter to the bottom physical astronomy is as hypothetical as Euclid’s elements. There may exist in nature perfect straight lines, triangles, circles, and other regular geometrical figures; to our science it is a matter of indifference whether they do or do not exist, because in any case they must be beyond our powers of perception. If we submitted a perfect circle to the most rigorous scrutiny, it is impossible that we should discover whether it were perfect or not. Nevertheless in geometry we argue concerning perfect curves, and rectilinear figures, and the conclusions apply to existing objects so far as we can assure ourselves that they agree with the hypothetical conditions of our reasoning. This is in reality all that we can do in the most perfect of the sciences.
Doubtless in astronomy we meet with the nearest approximation to actual conditions. The law of gravity is not a complex one in itself, and we believe it with much probability to be exactly true; but we cannot calculate out in any real case its accurate results. The law asserts that every particle of matter in the universe attracts every other particle, with a force depending on the masses of the particles and their distances. We cannot know the force acting on any particle unless we know the masses and distances and positions of all other particles in the universe. The physical astronomer has made a sweeping assumption, namely, that all the millions of existing systems exert no perturbing effects on our planetary system, that is to say, no effects in the least appreciable. The problem at once becomes hypothetical, because there is little doubt that gravitation between our sun and planets and other systems does exist. Even when they consider the relations of our planetary bodies inter se, all their processes are only approximate. In the first place they assume that each of the planets is a perfect ellipsoid, with a smooth surface and a homogeneous interior. That this assumption is untrue every mountain and valley, every sea, every mine affords conclusive evidence. If astronomers are to make their calculations perfect, they must not only take account of the Himalayas and the Andes, but must calculate separately the attraction of every hill, nay, of every ant-hill. So far are they from having considered any local inequality of the surface, that they have not yet decided upon the general form of the earth; it is still a matter of speculation whether or not the earth is an ellipsoid with three unequal axes. If, as is probable, the globe is irregularly compressed in some directions, the calculations of astronomers will have to be repeated and refined, in order that they may approximate to the attractive power of such a body. If we cannot accurately learn the form of our own earth, how can we expect to ascertain that of the moon, the sun, and other planets, in some of which probably are irregularities of greater proportional amount?
In a further way the science of physical astronomy is merely approximate and hypothetical. Given homogeneous ellipsoids acting upon each other according to the law of gravity, the best mathematicians have