୧

where the unit of a is arbitrary and that of e and ▲ may be assumed if the unit of is determined in conformity therewith. We then may take for our earth a=100, g=10, A=1; then the unit of will be known as soon as the amount of resistance or the density of the ether is given. Neither being exactly known, we must be satisfied with an estimate; and thus (12) easily shows that if our earth approaches the sun annually by ten feet, the unit of age 9 is ten thousand millions of years.

It will be seen that, as soon as the annual approach of our earth is known, the unit of will be determined.

By means of (10') or its equivalent (12) we are now enabled. to calculate the effect of resistance on the motions of any planet at any age, both in future (+) and the past (-9). We now proceed to a comparison of the results of this analysis with observation, using the following data'

giving by (12) the following distances from the sun at the ages

indicated.

For a 95,000,000 × 528, or about 50,000,000,000 ten-feets, hence a-x= 49,999,999,999 ten-feets; consequently by (12)

hence 91 for 10000000000 years.

• Cosmos, Harper's ed., iv, 119; the density of Venus as given by Babinet, l'Institut, 1857, p. 94.

AM. JOUR. SCI.-SECOND SERIES, VOL. XXXVI, No. 109.—JAN., 1864.

These numbers are represented in the annexed diagram, which thus shows the variations in the distance of the planets.

As the configuration of the solar system hereby appears to be continually changing in time-even the order of sequence suffering alterations-it is idle to speculate concerning "the harmony of the heavens" without taking the element of resistance into account; for it is obvious that the true primitive law, which alone can have been harmonious, will long ago have been profoundly modified by the continued action of resistance.1o

In order to make a useful application of this table, permitting the test of actual observation to be applied to the results deduced, we will try to estimate the relative age of the planets by means of these modifications in their position.

The dislocation of strata of rocks is no fact; we simply see similar parts in irregular position, and conclude by induction that they once formed a continuous stratum; but would it not be equally just to conclude that the heavenly strata, i. e., the planetary orbs, are dislocated, if we can show that, 1st, they approach to a definite law, as the terrestrial strata in being parallel;

2nd, The assumption of the force of resistance fully explains the deviations from that law, as the assumption of internal action explains the dislocation of geological strata?

We think the analogy is about as close as can be, and therefore will venture the attempt.

It is a well known fact that the so-called law of Titius or Bode, is pretty correct for all planets from Venus to Uranus; only Mercury and Venus deviate considerably from the duplication of the successive mutual distances. This law-only in the case of Mercury deviating from the above named-may therefore well be compared to the original level of terrestrial strata, if the laws of resistance as developed in the preceding suffice to explain the actual deviations from it.

It is even a priori highly probable that some simple law prevailed at the time of the development of the heavenly spaces, although it is now almost entirely lost; for in like manner the regular stratification of the earth's crust has been disturbed

so the regular distribution of the leaves in the young plant is almost entirely lost in the arrangement of the branches of the tree--so even the human features lose their regularity by age. Yet in all cases matter seems to arrange itself according to simple laws; as we see it in the minute crystal, we must infer it for the heavenly spaces.

10 Plato, in Timæus, simply estimated the distances-having no means of testing his estimates by observation; Kepler also speculated much on the law of planetary distances, and gave as his final opinion that "the old planets are altered a little in position." (Humboldt, Cosmos, iii, 440; Harper's edition, iv, 110.) This seems to be another instance of Kepler's divination of scientific results.

Taking now x according to this law as the original distance, we find the age ✈ by (12), viz:

Although there is considerable variation in each separate group, the mean gives a decidedly higher age to the exterior planets than to the interior ones, about in the ratio of one to three.

But if this law is correct, it demands that the relative age of the planets increases with their relative distances from the sun (supposing no interchange of place yet to have occurred). Consequently our determination of the age of the single planets appears to be very uncertain, since Jupiter figures with the same age as Neptune! But it is easy to show that this is simply a consequence of our taking constant, whilst it not only is greatly varying, but even varying in different degrees for different planets. For, considering as constant," and for a certain former period g=ng, (g, being the present value of g), the constancy of the mass gives 93A 93,A, or A,=n3A, i. e.

δ

ν

38 3 δ

= -n2=v, n2, 89A 89,4,

บ

(13)

or, the greater the body, the greater is the value of v, as is self-evident. If now all planets had exactly the same masses, their cooling or condensation would be entirely parallel, and might be considered as nearly constant; but as there are great differences between the masses of the planets we must remember, that, cæteris paribus, the larger mass cools slower, i. e. keeps longer the greater value of corresponding to its longer remaining of larger size; it will consequently fall with a greater velocity than calculated on the supposition of constant, or, what is the same, will have a smaller age than calculated.

We must therefore apply a subtractive correction to our calculated age increasing with the mass of the planet. By doing so in general we found the equations of condition pretty well satis fied by taking this correction proportional to the mass. For the superior planets we may have (the constant being assumed 0·1) "These distances seem to afford a good average; the law is rigorously applied, for 80-60-20, 120-80=40=220, 200-120-80-240, etc. The series is,

m, m+n, m+2n, m+4n, m+8n, etc.

12 It is probable that d is not constant, either in time or in space; the only means for trying it will be to see whether the velocity of light remains constant in time, whereby we are carried through different parts of the heavenly space (aberration).

This is already a much more regular series; the mean of the corrected ages for Jupiter and Saturn is 9, for Uranus and Neptune 18, or, whilst the uncorrected age of the former was greater than that of the latter, by this (very imperfect) correction for mass it is as one of Jupiter-Saturn to two of Uranus-Neptune. The conclusion seems therefore well-founded, that a more thorough investigation of the variation of in time, if possible at all, would give the age of the different planets as regularly increasing with their distance from the sun.

This result is in itself already important; but it also gains much by its connection with the following considerations.

Now, as the outer planets are older than the inner ones, we must find the different parts of our solar system in very different conditions of age: and this again may be tested by direct observation. By attentively contemplating the annexed diagram, representing the effect of resistance or time on the configuration of our solar system, we shall find the following four laws:

First Law. The nearest secondary approaches its primary with advancing age.-Expressing these distances in radii of the central body, we have:

thus showing a decrease with age. Uranus, having its moons differently situated, is not comparable. Yet it must not be omitted, that this mode of comparison is not free from objections. The subsequent three laws are, however, nearly absolute. Second Law. The entire system of orbits becomes closer by advancing age. The ratio of the mutual distances will be the most proper measure of the closeness. We have: