The undisturbed revolution of a planet around the sun, in conformity with Kepler's law, would assure for that planet permanent conditions of climate. The earth, for instance, if guided solely by Kepler's laws, would return each day of the year exactly to the same position which it had on the same day of last year. From age to age the quantity of heat received by the earth would remain constant if the sun continued unaltered, and the present climate might thus be preserved indefinitely. But since the existence of planetary perturbation has become recognised, questions arise of the gravest importance with reference to the possible effects which such perturbations may have. We now see that the path of the earth is not absolutely fixed. That path is deranged by Venus and by Mars; it is deranged, it must be deranged, by every planet in our system. It is true that in a year, or even in a century, the amount of alteration produced is not very great; the ellipse which represents the path of our earth this year does not differ considerably from the ellipse which represented the movement of the earth one hundred years ago. But the important question arises as to whether the slight difference which does exist may not be constantly increasing, and may not ultimately assume such proportions as to modify our climates, or even to render life utterly impossible. Indeed, if we look at the subject without attentive calculation, nothing would seem more probable than that such should be the fate of our system. This globe revolves in a path inside that of the mighty Jupiter. It is, therefore, constantly attracted by Jupiter, and when it overtakes the vast planet, and comes between him and the sun, then the two bodies are comparatively close together, and the earth is pulled outwards by Jupiter. It might be supposed that the tendency of such disturbances would be to draw the earth gradually away from the sun, and thus to cause our globe to describe a path ever growing wider and wider. It is not, however, possible to decide a dynamical question by merely superficial reasoning of this character. The question has to be brought before the tribunal of mathematical analysis, where every element in the case is duly taken into account. Such an enquiry is by no means a simple one. It worthily occupied the splendid talents of Lagrange and Laplace, whose discoveries in the theory of planetary perturbation are some of the most remarkable achievements in astronomy. We cannot here attempt to describe the reasoning which these great mathematicians employed. It can only be expressed by the formulae of the mathematician, and would then be hardly intelligible without previous years of mathematical study. It fortunately happens, however, that the results to which Lagrange and Laplace were conducted, and which have been abundantly confirmed by the labours of other mathematicians, admit of being described in simple language.