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graph 5.) In this passage, the generally received opinion is attempted to be proved; but in No. 1, "The Planets," paragraph 18, he says,—" No law of matter would have prevented the Earth from receiving any other rate of rotation more or less rapid. It might have made a Single Rotation a year; in which case the alternations of day and night would have been six months, or," &c.
In direct opposition to these statements (save the last), I hold, that though the Moon in her orbital revolution round the Earth, keeps nearly the same face always towards it, she does so because she has no rotation on or round her own axis; that her movement, excepting her librations, of which more presently, is exactly analogous to that of any portion of the outer ring of a wheel; and that inasmuch as the centre of rotation is outside of and distant from the revolving body, it is not only a misnomer to apply the term axial rotation to the lunar movement or mode of revolving, but that axial rotation is, as these astronomers clearly imply, a totally distinct and additional movement having different dynamical forces, and distinguished by different geometrical conditions and phenomena. In other words, and shorter terms, I hold that a body does not rotate round its awn axis, when that axis is not within it; and that in order that a body should rotate round its own axis, every part of that body must rotate,' revolve, or turn round that axis: which is demonstrably not the case with the Moon.
There are three distinct modes of motion in which the Moon or any body may revolve.* As a vast deal of this discussion has arisen from the popular misconception that there are but two, I beg to illustrate these three motions by the first set of diagrams (A.) on the opposite page. No. 1 represents such movement as would exist if the Moon always preserved the same face towards any given point of the horizon, in which case she would present all her sides successively to the Earth and to the centre of her orbit. This she does not do. No. 3 presents the Moon keeping the same face towards the Earth and centre of its orbit, without any rotation in addition on her own axis; and No. 2 represents the Moon revolving and rotating round her own axis once during one orbital revolution, which is the double motion assigned to her by the authorities above cited; and in which cases she must, as I contend, present all her sides once successively to the Earth during her orbital revolution.
My opponents range themselves in two perfectly distinct classes, and are a house divided against itself: one, the least scientific, standing up manfully for the double movement; others, who may be termed the mathematical men, maintaining the same movement I ascribe to the Moon, but holding with equal confidence that it ought to be termed axial rotation. It is obvious, therefore, that the arguments by which each set of objections are to be met must, like the objections themselves, be strictly distinguished.
It being conceded that the Moon always keeps the same face to the Earth as it revolves round it, it is easy to give two balls exactly such movement as observes these conditions, and therefore so far represents
* To avoid ambiguity and tautology, I shall exclusively use the terms revolve and revolution for circular movements which I deny to be rotation; and rotate and rotation for those which comply with my definitions of rotation round the revolving body's own axis.
the motion of the Moon. Now this may be perfectly accomplished by a simple instrument such as this :—
A represents the Earth, which, as far as affects this question, may be taken as the centre of the Moon's orbit;* the bar C is simply a means of keeping B, which represents the Moon, in its orbital revolution. B is attached by a pivot or axis to the outer end of C, and C turns on the axis of A: and when moved round without turning £ also (as far as affects any point in dispute), the ball B correctly represents the Moon's motion by revolving round A, and always presenting the same face, marked x, towards A.
The number of letters I have received from educated people is almost incredible, insisting upon it, that in order that a ball revolving round a distant centre should present the same face to that centre, it must also twirl round on its own axis, like a teetotum. I have witnessed the astonishment of many such people, to whom this instrument or any similar test has been shown, on discovering their mistake. Let the ball B be now made to twirl or rotate on its own axis ever so little, and it immediately presents a different face to A; and it is palpable to the senses, that this is a distinct, separate and additional motion given to B. The great majority of those who allow themselves to try this experiment are convinced; but there are a still larger number who disdain to do it, and simply seek for all kinds of modes of supporting the astronomical axiom, with that peculiarly English idolatry of an established dogma, which reminds one forcibly of Sterne's description of it in "Tristram Shandy." "It is in the nature of an hypothesis, that when a man once begets it, from the hour of its birth, he appropriates to it, as proper nourishment to its growth, everything he sees, reads, or hears for the future. This is very convenient."
The first resource is to lay hold of the rigidity of this or any instrument by which the lunar motion is illustrated. The Moon moves freely in space: the Moon is not connected by a bar to the Earth; therefore, the instrument misrepresents the state of the facts; therefore it fails to prove l/iiU site, does not rotate on her aids, &c. This conclusion is an obvious non sequitur from the premises. It would be just as sensible to say that the balls are infinitely less than the Earth and Moon, and that therefore they do not represent the facts, and prove nothing. Let it be shown wherein they misrepresent the motion in dispute: if they fairly
* These are not quite identical; the centre of the Moon's orbit, owing to the slight gravitation of the Earth towards the Moon, is near the Earth, but not identical with the Earth's centre.
show it, they do all they are designed to do, and all that it is in the least requisite that they should do for the support of my theory. They illustrate perfectly the dynamical law disputed by the objectors. To make good their objection to the bar, they are bound to show in what respect the bar gives the model of the Moon a different motion to that which the Moon has. The more scientific objectors will reply, that it does not represent the ellipticity of the Moon's orbit. But I do not dispute the ellipticity of the Moon's orbit. They aver that it fails to show the Moon's librations. I admit the Moon's librations. It represents neither of these: but neither is it in the least necessary that it should. It represents and proves the fact that if the Moon or any other globe or body revolve round a distant centre as the Moon does, always presenting or keeping the same face towards that centre, it Cannot rotate round its own axis also. This is all I aver; and it is just as irrational to object to a mechanical or rigid illustration of that fact, as it would be to object to the resemblance of a portrait, because the person it represented was not, like the picture, composed of canvass and paint.
The non-scientific objectors get into a blunder on this subject, by first convincing themselves correctly that the Moon does not move as in So. 1, Fig. A, and then by jumping to the conclusion incorrectly, that there is no other way in which she can possibly revolve, except by rotating on her own axis: in which case she must present, if she rotate once during her orbital revolution, the motion represented by Fig. 2, turning exactly opposite faces to the Earth at opposite sides of her orbit. If she rotates more slowly or faster, a similar result, different only in degree, will ensue. To prove this by another instrument is, though a little more costly, equally easy. Construct a circular board of a foot diameter, standing on three or four short legs ; to a vertical spindle, immovably fixed in the centre, attach a revolving bar similar to C in the above woodcut, so that it may revolve round the spindle as a pivot, with a ball on it to represent the Earth; immediately above the bar fix a cogged wheel of four or five inches diameter, by means of a square socket, on the spindle; at double this distance from the spindle, place another spindle and another cogged wheel of the same dimension and number of cogs on the bar, to play into the central wheel, and so fixed that its spindle may rotate with it; on the top of this spindle place another ball to represent the Moon, so that its equator shall be in the same plane with that of the central ball. If the bar be now moved completely round the wooden disc by its handle or projection, it will be found that the ball representing the Moon complies exactly with the description of the Moon's motion given by the abovecited authorities; it will in precisely the same period as it completes its orbital revolution, have also rotated once on its own axis, and it will by means of this revolution, plus rotation, present when it has gone round one-half its orbit the opposite face to that which it presented to the ball in the centre at starting ; presenting the same face again as at first on its return to the starting-point; and similarly in succession it will present all ita sides during its revolution. Now take the outermost wheel out of gear, so that the Moon's model no longer rotates on its pivot, and it will present the same face to the centre all round its orbit.
Thus the Moon may be demonstrated to have no axial rotation, in the sense in which mankind at large use that term. The theoretical diffi.culties in comprehending how this should be, vanish on seeing it done. I thought I should make this clear, and at any rate provoke the experiment by the letter in the Times of the 12th April, in which I said :—
"Arrest the Earth in its revolution round the Sun, and it will still rotate on its axis, for it has axial rotation. Arrest the Moon in her revolution round the Earth, and she will he motionless, because she has no axial rotation. To put this question to a practical test, let an orrery be constructed so that the Moon shall rotate on her axis, as we are told she does, in the same period in which she revolves round the Earth. Let this period be ten minutes. I affirm that at the expiration of five minutes after the orrery is put in motion, the Moon will present to the Earth exactly the opposite hemisphere of her surface to that which she presented to it at starting. If I am right in this, the question is settled, and the Moon has no axial rotation; for at whatever rate she rotates, a similar result will ensue."
This, I know, has convinced many ; but a writer signing himself E. B. D. asserted the contrary, whose anonymous insolence would have rendered any further notice of him out of the question, had not the counter-experiment he suggested* been adopted in a modified form by a friend of mine, who is well known as an astronomer, and whose suggestions are entitled to respectful consideration.
This gentleman has constructed a strong flat board, a foot wide, screwed in the middle to a strong vertical axis; at one end of this board, which revolves horizontally, a ball, nine inches in diameter, six or seven pounds in weight, is inserted, so that it can rotate on its own axis, the lower end of which is delicately poised on glass. Having balanced this ball nicely, a "rapid " motion is given to the board ; the ball will, Mr. — affirms, "present different sides to the Earth, till the friction of the pivots gradually brings it to present the same face. Then stop the board suddenly, and you will find the Moon spin on its axis, by the rotary motion it has gradually acquired by the action of the said friction, till the friction again conversely reduces it to rest. The first part shows, by simple experiment, that if there be no original rotary movement, and the centre of gravity be made to revolve, different faces will be turned to the centre. The second shows, that when the model Moon is revolving, and at the same time turning the same face to the centre, if it be 'arrested' in its orbit, it will rotate and present different faces."
I have no doubt whatever of the accuracy of this statement, and only wonder that so much ingenuity has been expended in showing what the Moon does not do. It being admitted on all hands that she constantly preserves the same face towards the Earth, what possible advantage can there be in experiments which represent other motions? While the ball presents the same face to the centre of rotation, this gentleman may
* It was this i—" It [the experiment] will answer perfectly with a mere disc of tin for the Moon, hollowed a little in the middle to make it balance easily on a strong needle, stuck point upwards, near the end of a bar of wood revolving horizontally. You can hold the disc with your finger while you turn the bar, so as to keep some mark upon the disc facing the axis on which the bar turns, and let it go just before you stop the motion of the bar. [If this be done steadily, and without an impetus or jerk, the disc remains motionless on the needle.] In the converse experiment, you have only to turn the bar, leaving the disc alone; and then it will not revolve (except on its orbit), but will present all its circumference in succession to the axis of the bar [It will do exactly the reverse], thus showing that an additional force was necessary to make the Moon turn on its axis besides turning round the Earth."—This experiment has been tried frequently, and entirely confutes the statement it is designed to support.