Galileo and His Judges

by F. R. Wegg-Prosser

The same thing is exemplified by the small machine called the gyroscope, where a heavy disc, so adjusted as to revolve freely in any given direction, independently of the frame in which it is placed, will continue, when once set in rapid motion, to spin in the same plane, directed, for instance, to any one star that happens at the time to be due north or due south of us, while the frame moves round it with the rotation of the Earth.

I think, then, on the whole, we may say that those persons who, in the present state of our knowledge on the subject, are not convinced that the Earth revolves on its own axis, would not be satisfied by any evidence whatever.

Returning now to the general question of Copernicanism, we find that for some time after the trial of Galileo, things remained much in statu quo; unless we except the observation of the transit of Venus, in 1639; but, as that eventful seventeenth century was drawing to its close, there came on the scene some thoughtful and able astronomers, who could not only utilise the knowledge of their predecessors, but could also guess, with more or less accuracy, what that law—hitherto unknown—might be, which governed the planets and our own Earth in their movements. It was about this time that the Royal Society was founded in London, and a stimulus was thus given to investigation and to experiment. The third law of Kepler, which states that in all the planetary orbits the square of the periodic time of revolution is in a constant proportion to the cube of the mean distance, suggested the existence of another law, not yet discovered, a law of attraction, on which this itself depended. Among the astronomers of that day three names deserve special mention, Wren, Hooke, and Halley, because each of them guessed with some accuracy at the true doctrine—as it is now known to be—that the planets are attracted to the Sun by a force which acts inversely as the square of the distance. Hooke, in particular, deserves the credit of having applied this law to the path of a projectile, under certain circumstances, as well as to the planetary orbits; but though he thus lighted upon true conclusions, he appears to have been deficient in mathematical skill, and therefore unable to verify his results. It is, however, only just to the memory of Horrox, who was carried off by an early death, to mention that the true theory of the identity of terrestrial and astronomical gravity had occurred to his mind; if he had lived twenty or thirty years longer, he might have survived in history as the discoverer of the great problem.

Be this as it may, there now arose another man greater than his predecessors, and greater than all his contemporaries; he also was an Englishman, by name Isaac Newton. What others guessed, or concluded on insufficient evidence, became, in his powerful hands, clear and well-grounded truths, proved, so far as such things could be proved, by rigid mathematical reasoning, and established on a solid basis, which time has not shaken, and which subsequent investigation has confirmed. Others had supposed the existence of the law of attraction by which the Sun acted on the planets; many persons had understood the existence of terrestrial gravitation. Newton showed that these two are identical; and, moreover, that every particle of matter attracts every other particle mutually, and according to the one universal law, that of the inverse square of the distance; so that a vast planet revolving round the Sun obeys the same law as a pebble dropped from one’s hand to the Earth. The popular story of his having been suddenly led to this conclusion by the sight of an apple falling is apparently fabulous; and what really occurred is this: he sat alone one day in a garden, and fell into a speculation (as men of scientific mind are apt to do) on the power of gravity, that is, of gravity as we feel it here on the Earth. Then it struck him that however high you ascend, even on the loftiest mountains, no sensible diminution in this remarkable force takes place; so, he said to himself: why not as high as the Moon? If so, perhaps she is retained in her orbit by this very power. And again if so, what then? To which question his active mind gave the just and true answer, that it was probably one and the same force that acted at the surface of the Earth, at the distance of the Moon, and finally, as regulating the action of the Sun on the planets.

It seems that there was an error, which it is unnecessary to explain in detail, in Newton’s first calculations; but that when, after a lapse of time and with the error corrected, he again returned to them, he found the motion of the Moon to be exactly accounted for by his theory.

Again, in dealing with the complicated problem of the action of the heavenly bodies one upon the other, that is, when the disturbing force, for instance, of a third body is brought to bear on the motions of two others, although Hooke and others had as a conjecture put forth the existence of such mutual action, yet Newton was the first who thoroughly grappled with it.

The mutual attraction of matter, so far as things terrestrial are concerned, had occurred to the inquiring intellect of Francis Bacon; but it was left for Newton to propound it as the great principle that governs the physical universe.

Now let us see how all this bears on the truth of the Copernican system. Newton proved—and I may add that the improved methods of mathematics which have been adopted since his day make the proofs more simple and easy—that if any body moves in an ellipse, or indeed, in one of the other conic sections, the law of force, tending to the focus, is that of the inverse square of the distance.[26] Conversely, he proved that a body under the action of a central force, varying in intensity as the inverse square of the distance, will move in a conic section.

Then if the Moon moved in an ellipse, as it was easy to perceive that she did, and if her motion corresponded precisely with what it would be on the theory of universal gravitation; if also, as seemed evident, the planets revolved in ellipses, then the inference that the law of gravitation, as stated by Newton, was true became irresistible; not susceptible, as before stated, of direct and absolute proof, but established conclusively by a sound and legitimate induction.

What I have just stated shows that Kepler’s first law corresponds with Newton’s discovery; but the same is true of the two other laws. It would of course be out of place here to go minutely into all the evidence which can be gathered in support of the doctrine of universal gravitation. I may briefly state that all of Kepler’s laws are simply explicable by that hypothesis, and that the evidence derives additional confirmation from the following curious fact: observation shows that Kepler’s laws, though approximately true, are not strictly and accurately so; if the planets were mere particles revolving round the Sun, they would then be quite rigidly true, but the planets have a certain mass (though very small compared to the Sun) and so do in some measure attract the Sun as well as being attracted by him, and they, moreover, exercise a disturbing influence on each other. These perturbations, however, have been calculated, and the result is that they agree with what ought reasonably to be expected, supposing the theory of universal gravitation to be true. This confirmatory proof has been acquired, I need not add, since the time of Newton by the labours of astronomers, Laplace and others, who have succeeded him, and who have had the advantage of that more manageable method of mathematical calculation to which I have just alluded.