Biography of Percival Lowell

by A. Lawrence Lowell

In a paper presented to the American Academy in April, 1913, and printed in their Memoirs[38] Percival explained the “Origin of the Planets” by the same principle of commensurate periods. In addition to what has already been said about the places where these periods occur coming closer and closer together as an object nears the planet, so that it is enabled to draw neighboring small bodies into itself, he points out that in attracting any object outside of its own orbit a planet is acting from the same side as the Sun thereby increasing the Sun’s attraction, accelerating the motion of the particle and making it come sunward. Whereas on a particle inside its orbit the planet is acting against the Sun, thereby diminishing its attraction, slowing the motion of the particle and causing it to move outward. “Thus a body already formed tends to draw surrounding matter to itself by making that matter’s mean motion nearly synchronous with its own.” These two facts, the close—almost continuous—commensurate points, and the effects on the speed of revolution of particles outside and inside its own orbit, assist a nucleus once formed to sweep clear the space so far as its influence is predominant, drawing all matter there to itself, until it has attained its full size. “Any difference of density in a revolving nebula is thus a starting point for accumulation. So soon as two or three particles have gathered together they tend by increased mass to annex their neighbors. An embryo planet is thus formed. By the same principle it grows crescendo through an ever increasing sphere of influence until the commensurate points are too far apart to bridge by their oscillation the space between them.”

So much for the process of forming a planet; but what he was seeking was why the planets formed just where they did. For this purpose he worked out intricate mathematical formulae, based on those already known but more fully and exactly developed. These it is not necessary to follow, for the results may be set forth,—so far as possible in his own words. “Beyond a certain distance from the planet the commensurate-period swings no longer suffice to bridge the intervening space and the planet’s annexing power stops. This happens somewhat before a certain place is reached where three potent periodic ratios succeed each other—1:2, 2:5, 1:3. For here the distances between the periodic points is greatly increased....

“At this distance a new action sets in. Though the character of its occasioning be the same it produces a very different outcome. The greater swing of the particles at these commensurate points together with a temporary massing of some of them near it conduces to collisions and near approaches between them which must end in a certain permanent combining there. A nucleus of consolidation is thus formed. This attracts other particles to it, gaining force by what it feeds on, until out of the once diffused mass a new planet comes into being which in its turn gathers to itself the matter about it.

“A new planet tends to collect here: because the annexing power of the old has here ceased while at the same time the scattered constituents to compose it are here aided to combine by the very potent commensurability perturbations of its already formed neighbor.

“So soon as it has come into being another begins to be beyond it, called up in the same manner. It could not do so earlier because the most important deus ex machina in the matter, the perturbation of its predecessor, was lacking.

“So the process goes on, each planet acting as a sort of elder sister in bringing up the next.

“That such must have been the genesis of the several planets is evident when we consider that had each arisen of itself out of surrounding matter there would have been in celestial mechanics nothing to prevent their being situated in almost any relative positions other than the peculiar one in which they actually stand....

“It will be noticed that the several planets are not quite at the commensurate points. They are in fact all just inside them.... Suppose now a particle or planet close to the commensurable point inside it. The mean motion in consequence of the above perturbation will be permanently increased, and therefore the major axis be permanently decreased. In other words, the particle or planet will be pushed sunward. If it be still where” the effect of the commensurateness is still felt “it will suffer another push, and so on until it has reached a place where the perturbation is no longer sensible.” He then goes on to show from his formulae that if the particle were just within the outer edge of the place where the perturbation began to be effective it would also be pushed sunward, and so across the commensurable point until it joined those previously displaced.

“We thus reach from theory two conclusions:

“1. All the planets were originally forced to form where the important and closely lying commensurable points 1:2, 2:5, or 1:3, and in one case 3:5, existed with their neighbors; which of these points it was being determined by the perturbations themselves.