A History of Science, vol 3 by Henry Smith Williams (sites to read books for free TXT) 📕

There the case rested till 1845, when a Prussian amateur astronomer named Hencke found another asteroid, after long searching, and opened a new epoch of discovery. From then on the finding of asteroids became a commonplace. Latterly, with the aid of photography, the list has been extended to above four hundred, and as yet there seems no dearth in the supply, though doubtless all the larger members have been revealed. Even these are but a few hundreds of miles in diameter, while the smaller ones are too tiny for measurement. The combined bulk of these minor planets is believed to be but a fraction of that of the earth.

Olbers’s explosion theory, long accepted by astronomers, has been proven open to fatal objections. The minor planets are now believed to represent a ring of cosmical matter, cast off from the solar nebula like the rings that went to form the major planets, but prevented from becoming aggregated into a single body by the perturbing mass of Jupiter.

The Discovery of Neptune

As we have seen, the discovery of the first asteroid confirmed a conjecture; the other important planetary discovery of the nineteenth century fulfilled a prediction.

Neptune was found through scientific prophecy.

No one suspected the existence of a trans-Uranian planet till Uranus itself, by hair-breadth departures from its predicted orbit, gave out the secret. No one saw the disturbing planet till the pencil of the mathematician, with almost occult divination, had pointed out its place in the heavens. The general predication of a trans-Uranian planet was made by Bessel, the great Konigsberg astronomer, in 1840; the analysis that revealed its exact location was undertaken, half a decade later, by two independent workers—John Couch Adams, just graduated senior wrangler at Cambridge, England, and U. J. J. Leverrier, the leading French mathematician of his generation.

Adams’s calculation was first begun and first completed.

But it had one radical defect—it was the work of a young and untried man. So it found lodgment in a pigeon-hole of the desk of England’s Astronomer Royal, and an opportunity was lost which English astronomers have never ceased to mourn. Had the search been made, an actual planet would have been seen shining there, close to the spot where the pencil of the mathematician had placed its hypothetical counterpart.

But the search was not made, and while the prophecy of Adams gathered dust in that regrettable pigeon-hole, Leverrier’s calculation was coming on, his tentative results meeting full encouragement from Arago and other French savants. At last the laborious calculations proved satisfactory, and, confident of the result, Leverrier sent to the Berlin observatory, requesting that search be made for the disturber of Uranus in a particular spot of the heavens. Dr. Galle received the request September 23, 1846. That very night he turned his telescope to the indicated region, and there, within a single degree of the suggested spot, he saw a seeming star, invisible to the unaided eye, which proved to be the long-sought planet, henceforth to be known as Neptune. To the average mind, which finds something altogether mystifying about abstract mathematics, this was a feat savoring of the miraculous.

Stimulated by this success, Leverrier calculated an orbit for an interior planet from perturbations of Mercury, but though prematurely christened Vulcan, this hypothetical nursling of the sun still haunts the realm of the undiscovered, along with certain equally hypothetical trans-Neptunian planets whose existence has been suggested by “residual perturbations” of Uranus, and by the movements of comets. No other veritable additions of the sun’s planetary family have been made in our century, beyond the finding of seven small moons, which chiefly attest the advance in telescopic powers.

Of these, the tiny attendants of our Martian neighbor, discovered by Professor Hall with the great Washington refractor, are of greatest interest, because of their small size and extremely rapid flight. One of them is poised only six thousand miles from Mars, and whirls about him almost four times as fast as he revolves, seeming thus, as viewed by the Martian, to rise in the west and set in the east, and making the month only one-fourth as long as the day.

The Rings of Saturn

The discovery of the inner or crape ring of Saturn, made simultaneously in 1850 by William C. Bond, at the Harvard observatory, in America, and the Rev.

W. R. Dawes in England, was another interesting optical achievement; but our most important advances in knowledge of Saturn’s unique system are due to the mathematician. Laplace, like his predecessors, supposed these rings to be solid, and explained their stability as due to certain irregularities of contour which Herschel bad pointed out. But about 1851 Professor Peirce, of Harvard, showed the untenability of this conclusion, proving that were the rings such as Laplace thought them they must fall of their own weight.

Then Professor J. Clerk-Maxwell, of Cambridge, took the matter in hand, and his analysis reduced the puzzling rings to a cloud of meteoric particles—a “shower of brickbats”—each fragment of which circulates exactly as if it were an independent planet, though of course perturbed and jostled more or less by its fellows.

Mutual perturbations, and the disturbing pulls of Saturn’s orthodox satellites, as investigated by Maxwell, explain nearly all the phenomena of the rings in a manner highly satisfactory.

After elaborate mathematical calculations covering many pages of his paper entitled “On the Stability of Saturn’s Rings,” he summarizes his deductions as follows:

“Let us now gather together the conclusions we have been able to draw from the mathematical theory of various kinds of conceivable rings.

“We found that the stability of the motion of a solid ring depended on so delicate an adjustment, and at the same time so unsymmetrical a distribution of mass, that even if the exact conditions were fulfilled, it could scarcely last long, and, if it did, the immense preponderance of one side of the ring would be easily observed, contrary to experience. These considerations, with others derived from the mechanical structure of so vast a body, compel us to abandon any theory of solid rings.

“We next examined the motion of a ring of equal satellites, and found that if the mass of the planet is sufficient, any disturbances produced in the arrangement of the ring will be propagated around it in the form of waves, and will not introduce dangerous confusion.

If the satellites are unequal, the propagations of the waves will no longer be regular, but disturbances of the ring will in this, as in the former case, produce only waves, and not growing confusion. Supposing the ring to consist, not of a single row of large satellites, but a cloud of evenly distributed unconnected particles, we found that such a cloud must have a very small density in order to be permanent, and that this is inconsistent with its outer and inner parts moving with the same angular velocity. Supposing the ring to be fluid and continuous, we found that it will be necessarily broken up into small portions.

“We conclude, therefore, that the rings must consist of disconnected particles; these must be either solid or liquid, but they must be independent. The entire system of rings must, therefore, consist either of a series of many concentric rings each moving with its own velocity and having its own system of waves, or else of a confused multitude of revolving particles not arranged in rings and continually coming into collision with one another.

“Taking the first case, we found that in an indefinite number of possible cases the mutual perturbations of two rings, stable in themselves, might mount up in time to a destructive magnitude, and that such cases must continually occur in an extensive system like that of Saturn, the only retarding cause being the irregularity of the rings.

“The result of long-continued disturbance was found to be the spreading-out of the rings in breadth, the outer rings pressing outward, while the inner rings press inward.

“The final result, therefore, of the mechanical theory is that the only system of rings which can exist is one composed of an indefinite number of unconnected particles, revolving around the planet with different velocities, according to their respective distances.

These particles may be arranged in series of narrow rings, or they may move through one another irregularly. In the first case the destruction of the system will be very slow, in the second case it will be more rapid, but there may be a tendency towards arrangement in narrow rings which may retard the process.

“We are not able to ascertain by observation the constitution of the two outer divisions of the system of rings, but the inner ring is certainly transparent, for the limb of Saturn has been observed through it.

It is also certain that though the space occupied by the ring is transparent, it is not through the material parts of it that the limb of Saturn is seen, for his limb was observed without distortion; which shows that there was no refraction, and, therefore, that the rays did not pass through a medium at all, but between the solar or liquid particles of which the ring is composed.

Here, then, we have an optical argument in favor of the theory of independent particles as the material of the rings. The two outer rings may be of the same nature, but not so exceedingly rare that a ray of light can pass through their whole thickness without encountering one of the particles.

“Finally, the two outer rings have been observed for two hundred years, and it appears, from the careful analysis of all the observations of M. Struve, that the second ring is broader than when first observed, and that its inner edge is nearer the planet than formerly.

The inner ring also is suspected to be approaching the planet ever since its discovery in 1850. These appearances seem to indicate the same slow progress of the rings towards separation which we found to be the result of theory, and the remark that the inner edge of the inner ring is more distinct seems to indicate that the approach towards the planet is less rapid near the edge, as we had reason to conjecture. As to the apparent unchangeableness of the exterior diameter of the outer ring, we must remember that the outer rings are certainly far more dense than the inner one, and that a small change in the outer rings must balance a great change in the inner one. It is possible, however, that some of the observed changes may be due to the existence of a resisting medium. If the changes already suspected should be confirmed by repeated observations with the same instruments, it will be worth while to investigate more carefully whether Saturn’s rings are permanent or transitory elements of the solar system, and whether in that part of the heavens we see celestial immutability or terrestrial corruption and generation, and the old order giving place to the new before our eyes.”[4]

Studies of the Moon

But perhaps the most interesting accomplishments of mathematical astronomy—from a mundane standpoint, at any rate—are those that refer to the earth’s own satellite. That seemingly staid body was long ago discovered to have a propensity to gain a little on the earth, appearing at eclipses an infinitesimal moment ahead of time. Astronomers were sorely puzzled by this act of insubordination; but at last Laplace and Lagrange explained it as due to an oscillatory change in the earth’s orbit, thus fully exonerating the moon, and seeming to demonstrate