[Sidenote: The cause of Kepler's laws.] These calculations were founded upon the hypothesis that the moon moves in a circular orbit with a uniform velocity. But in the "Principia" it was demonstrated that when a body moves under the influence of an attractive force, varying as the inverse square of the distances, it must describe a conic section, with a focus at the centre of force, and under the circumstances designated by Kepler's laws. Newton, therefore, did far more than furnish the expected solution of the problem of elliptical motion, and it was now apparent that the existence of those laws might have been foreseen, since they arise in the very necessities of the case. [Sidenote: Resistless spread of the heliocentric theory.] This point gained, it is obvious that the evidence was becoming unquestionable, that as the moon is made to revolve round the earth through the influence of an attractive force exercised by the earth, so likewise each of the planets is compelled to move in an elliptical orbit round the sun by his attractive force. The heliocentric theory, at this stage, was presenting physical evidence of its truth. It was also becoming plain that the force we call gravitation must be imputed to the sun, and to all the planetary bodies as well as to the earth. Accordingly, this was what Newton asserted in respect to all material substance. [Sidenote: Perturbations accounted for.] But it is a necessary consequence of this theory that many apparent irregularities and perturbations of the bodies of the solar system must take place by reason of the attraction of each upon all the others. If there were but one planet revolving round the sun, its orbit might be a mathematically perfect ellipse; but the moment a second is introduced, perturbation takes place in a variable manner as the bodies change their positions or distances. An excessive complication must therefore be the consequence when the number of bodies is great. Indeed, so insurmountable would these difficulties be, that the mathematical solution of the general problem of the solar system would be hopeless were it not for the fact that the planetary bodies are at very great distances from one another, and their masses, compared with the mass of the sun, very small.