It is demonstrated by mathematical analysis that these variations are periodical, and confined within narrow limits, in such wise that "the planetary system can oscillate only round a certain mean, from which it never departs except by a very small quantity." But may not this very mean, which we have taken to be constant, oscillate round a more distant and still more constant mean? Observation had long ago detected a continual acceleration in the movement of Jupiter, and a not less certain diminution in the movement of Saturn. Now, to say of a star that its velocity augments, is to declare that it draws nearer its centre of movement. To say that its velocity decreases, is to affirm that it is retiring from that centre. It would seem, therefore, that Jupiter,[88] the greatest of our planets, is destined to be swallowed up, or absorbed, in the incandescent mass of the Sun, while Saturn,[89] with its belt and eight satellites, will gradually wander further and further into the mysterious infinity of space. It is true enough that these catastrophes are very distant,--distant to a period of time which the human imagination cannot even grasp,--and the "common herd" will certainly feel no anxious apprehension about an event which will not take place until myriads of years have elapsed. Yet, in the last century, the question excited the curiosity of certain scientific societies, and they directed the attention of the geometers to these formidable perturbations. Euler and Lagrange spent their keen intellects upon them to no profit. Laplace discovered that between the mean velocities of Jupiter and Saturn the ratios are simple, and capable of calculation; five times the velocity of Saturn perceptibly equals ten times the velocity of Jupiter. These terms, which, in the regularly-decreasing and indefinite series, might have been neglected, have acquired a value which was worthy of being taken into consideration. From thence result, in the movements of the two planets, those perturbations whose complete development necessitates a period of upwards of nine hundred years.... This will be, then, another periodic inequality. But, independently of the centres, which we suppose to be in themselves variable, may there not exist, in the space traversed by our planet, some cause of perturbation? Is our system so isolated in the universe that it neither receives nor loses aught of that which constitutes its force and matter? Is there no solidarity between its different worlds? And if this solidarity exists, is not their transformation a necessity?] [Footnote 88: The equatorial diameter of Jupiter in English miles is 56,065; its density is ·24 of the Earth's; its distance from the sun, 494,270,000 miles; inclination of its orbit to the ecliptic, 1° 18' 51".]