a circle. The following is the great law regarding the eccentricities of the planets:—"If the mass of each planet be multiplied by the square of the eccentricity, and this product by the square of the mean distance, the sum of these quantities will always retain the same magnitude." The purport of this is, that all the disturbances of the various planets, taken together, can never exceed a certain amount, and that a small one. The planets are so related, that if one has a large share of eccentricity, another must have a small one. The case may be familiarly illustrated by supposing that a certain quantity of wine is given to be shared by several individuals, the quantity being so small, that even though it were consumed by one individual, instead of being divided equally, it would do no harm. There is, thus, only a small fund of eccentricity out of which the various planets can draw, and though one should monopolise that fund, the equilibrium of the system would not be endangered; much less can there be danger when each enjoys a share of the eccentricity. A like law has been proved in regard to the inclinations of the orbits to one another. They can never vary much from their mean position, as they draw out of a common fund, which is a small one.
The stability of the system would be destroyed by an unlimited change—first, in the dimensions of the orbit; secondly, in the form, or eccentricity; and, thirdly, in the inclination; but in all these, compen-
