“2. Each planet was at the same time pushed somewhat sunward by perturbation.”
He then calculates the mutual perturbations of the major axes of the outer planets taken in pairs and of Venus and the Earth.
“From them we note that:
“1. The inner planet is caeteris paribus more potent than the outer.
“2. The greater the mass of the disturber and, in certain cases, the greater the excentricity of either the disturber or the disturbed the greater the effect.”
As he points out, the effect of each component of the pair is masked by the simultaneous action of the other, and refers to the case of Jupiter and the asteroids, where the effect they have upon it is imperceptible, and we can see its effect upon them clearly.
Thus he shows that a new planet would naturally arise near to a point where its orbit would be commensurate with that of the older one next to it. But the particular commensurate fraction in each case is not so certain. In general it would depend upon the ratio of the two pulls to each other, for if “the action of the more potent planet greatly exceeds the other’s it sweeps to itself particles farther away than would otherwise be possible”; if it does not so greatly exceed it would not sweep them from so far and hence allow the other planet to form nearer. Now of the four commensurate ratios mentioned, near which a planet may form its neighbor, that of 3:5 means that the two planets are relatively nearest together, for the inner one makes only five revolutions while the outer makes three, that is the inner one revolves around the Sun less than twice as fast as the outer one. The ratio 1:2 means that the inner one revolves just twice as fast as the outer; while 2:5 means that it revolves twice and a half as fast, and 1:3 that it does so three times as fast. Thus the nearer equal the pulls of any pair of forming planets the larger the fraction and the nearer the relative distance between them. Relative, mind, for as we go away from the Sun all the dimensions increase and the actual distances between the planets among the rest.
Venus is smaller than the Earth, but her interior position gives her an advantage more than enough to make up for this, with the result that the pulls of the two are more nearly equal than those of any other pair, the commensurate ratio being 3:5. The next nearest equality of pull is between Uranus and Neptune, where the commensurate ratio is 1:2; the next between Jupiter and Saturn, and Venus and Mercury, where it is 2:5; the least equality being between Saturn and Uranus, where it is only 1:3. Mars seems exceptional for, as Percival says, from the mutual pulls we should expect its ratio with the Earth to be 1:3 instead of 1:2 as it is, and he suggests as the explanation, “the continued action of the gigantic Jupiter in this territory, or it may be that a second origin of condensation started with the Earth while Jupiter fashioned the outer planets.”
He brings the Memoir to an end with the following summary:
“From the foregoing some interesting deductions are possible: