Page:Transactions NZ Institute Volume 13.djvu/201

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When the nebula has become stable, that is no longer expanding, much of its elementary matter will be at a sufficiently low temperature to combine; and these compound molecules will tend to aggregate into groups, and it may be shown that these masses may ultimately become so considerable as to form star clusters, associated by gravitation but not coalescing. I propose discussing this difficult question in a paper on star clusters; but in this paper I shall simply state that these little bodies will in all probability revolve in independent orbits at all eccentricities around the centre of the mass; these and other masses will be occasionally picked up by the planet. The following problem shows that component to and from the centre tends to be destroyed, and only a circular orbit left.

Problem 4.—Given two bodies revolving in eccentric orbits in the same direction around an attracting centre, to find the effect upon the eccentricity of the new orbit in the event of their coalescing.—Let a represent the two bodies colliding, the direction of one body is along the path ab, the other along ac, the component along the diagonal ad is evidently the new direction of the coalesced body; it has evidently less velocity than the mean of the two, as the component towards and away from the sun is more or less destroyed. The position of the body is also nearer after than before, so that the total effect will be to reduce mean distance, to lessen aphelion distance, and generally to increase perihelion distance, in other words to lessen eccentricity.

There can be but little doubt that this agency of accretion will be most important in giving regularity to any system. Proctor has discussed the influence of accretion of meteors, and it is certain he is right in giving it very great value. It probably played a great part in the formation of Jupiter.

An agency whose effect it is difficult to estimate is that of the outward motion of the general mass of the nebula. The planet may meet this on its return towards the centre; if so it will directly oppose its return, acting exactly opposite to gravitation, that is, in the same manner as though the central mass were of less mass; the body will consequently not be attracted back towards the centre so far as it otherwise would be. This action will tend to lessen perihelion distance. This outrush will evidently be much less as the planet leaves the sun on its second revolution, thus the body will not be aided by it on its return, and consequently it may not reach its full aphelion; but it is extremely likely that the nebula will attain equilibrium before it could affect the planet on its return. In the event of a case of partial impact in which the two parts of the original bodies escaped into