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faces to the starry regions by her orbital motion. Had she continued to show the same face to the same star, she could not revolve, much less, rotate. Professor Airy must mean the Moon's revolution in her monthly orbit. His explanations are totally irreconcilable with the simple action of rotation. The mere rotation of the Moon has no relation whatever to space. Were the Moon the only object seen in the heavens, her rotation or non-rotation could be ascertained with equal precision. Why then refer to the stars ?

How do we determine whether the Sun rotates or not? Do we refer. to the stars, or any other distant objects ? Certainly not. ; We simply observe the visible hemisphere, and watch the black spots moving across the disc, and thus we find that the Sun rotates, and that the period of that rotation is 25 days 7 hours 48 minutes. Had the dark patches seen on the Moon moved across, like the black spots on the Sun, we should then observe a motion resulting from her own axis—that is, rotation ; but as the Moon constantly presents the same face towards the centre of her orbit, she is equivalent to a body fixed in a ring, and therefore cannot rotate. Indeed, this is a self-evident proposition, and cannot be controverted.

All bodies that float on the ocean, in the air above, within the Moon's orbit, that accompany the Earth in its movements round the Sun, are to all intents and purposes attached to it, although the connection may be invisible. And if such bodies in moving round the Earth always present the same parts towards its centre, be those parts the keels of vessels, our feet, the feet of birds in flying, the clouds, or the face of the Moon beyond, it is precisely the same thing; they cannot, under such con, ditions, rotate on axes parallel to the revolving axes. .

The Astronomer Royal, in his second letter, May 5, fully confirms the impression, that what he means by rotation (as far as the Moon is concerned) is her revolving motion ; inasmuch as he distinctly states, that “ Every point in the Moon's body does describe a ring round the Earth, that Earth being a travelling centre.” This shows plainly the effects of a revolving motion, but what are we to make of the following observation !—“Every point in the Moon's body does also describe a ring round that axis of the Moon which is perpendicular to the Moon's orbit, that axis being a travelling axis.” If this means rings of motion round an axis in the Moon, it is in direct contradiction to the former statement; as it is utterly impossible that two such distinct circular actions of any given points on the Moon could co-exist.

The Astronomer Royal very clearly states, that, “ With reference to the Earth, the invisible half of the Moon moves with the greatest velocity,” as compared with the visible half. This agrees with her revolving motion ; but unfortunately this is again neutralized by the following remark :-“ With reference to the Moon's centre, the two halves of the Moon move with equal speed.” How is it possible to reconcile this statement with the former ? How can the inner portion of the segment of a circle travel at the same rate as the external part, or move at equal speed ?

The Astronomer Royal then proceeds to state, that “A body consisting of firmly-connected parts, if it rotate at all round any centre whatever, must (by geometrical necessity) so rotate that all points move in concentric rings relative to that centre; and the speed of each particle

relative to that centre, will be proportional to the distance from that centre. But this does not at all determine where that centre is.” The centre of rotation must necessarily be within the circles, and in the body ; it cannot be situated without, because in that case the motion would be no longer rotation, but revolution, and consequently could not describe rings on the body; the rings must, therefore, determine the position of the centre. How then can it be said, that “this does not determine where that centre is ?” Professor Airy concludes his letter with the following observations :~" Suppose it be known that a body does rotate, with reference to any specified axis, then the body may be said, with equal propriety, to rotate [revolve ?] round any other axis parallel to the former, provided that this be accompanied with a statement of the motion of translation of the new axis relative to the former.It is difficult to comprehend the meaning of this paragraph, and had it not been written by such an authority as the Astronomer Royal, it would have been attributed to the want of knowing the distinction and the true meaning of the terms rotation and revolution, and the necessary situation of their respective axes.

The following paragraphs in the second letter of Professor Airy show that the terms rotation and revolution are not employed according to their strict meaning by astronomers :—"Nobody scruples to say that the Earth revolves round its axis,” and “It is true that if the motion of any point of the Moon be laid down, conceiving the Earth to be fixed, it shows distinct circular monthly rotation round the Earth.”

If astronomers confuse these questions by employing the terms rotation and revolution as synonymous, and actually use them, as above, vice versa, we need not be surprised at the endless discussions and contradictions that have taken place on the single motion of the Moon. Her Majesty's Inspector of Schools deserves our gratitude for pointing out this error, and for his perseverance in striving to remove such a serious blot from educational astronomical books.

LUNAR MOTION.

TO ALEXANDER ELLIS, ESQ. SIR,—Though bound to deny the soundness of your science, I readily admit your courtesy, respect your useful services to education, and admire the courage with which you volunteer a defence for anonymous Wranglers, and rush into the lists in behalf of everybody's rotation round their own separate axes, whilst we all stand still on the Earth, simply because our noses point successively to different stars. I had vainly imagined, from the admissions I have received from many really scientific men, and the generally admitted fact that I have not yet been answered, that you all felt the impossibility of showing that each part, or any part of the radius of a circle, rotates round itself, as well as turns round the centre of the circle to which it belongs ; and agreeing with me as to what is the actual motion of the Moon, I began to hope you rotators had candour as well as science enough to admit that rotation round her own axis is a mis-statement of that motion. It seems, however, that we are nearer to the times of Galileo than I fancied. The Willises and Lardners of those days believed in one Aristotle just as devoutly as those eminent men believe in Herschel and W. Hopkins now. He was oracular : and among the sacred Aristotelian tenets which Galileo was bold enough to deny, was, that if a one-pound weight fell a certain height in a certain time, a ten-pound weight would fall ten times faster. This was demonstrated by problems quite as plausible as those by which you have endeavoured to refute Mr. Perigal. Unluckily for poor Galileo, he was not deterred by the “scientific horrors” of the Aristotelian Hopkinses, and had the “astounding boldness” to put his statement to the test. He accordingly assembled the Cantabs and Doctors of his day, and let fall at the same instant large and small weights from the top of the celebrated leaning tower of Pisa. Yet, with the sound of the two weights clattering upon the pavement at the same moment, they still maintained that the ten-pound weight would reach the ground in onetenth part of the time of the other, because they could quote the chapter and verse of Aristotle where the fact was asserted, just as all the lunar rotators can point to chapter and verse in La Place & Co. Now, inasmuch as it is an admitted fact that the Moon revolves round the centre of her orbit, keeping the same face always towards it (though true it is that she turns entirely round once in so doing, and of course, of necessity, presents each part of her to all points of the compass once in succession), is it not self-evident that, as far as her motion is concerned, she would perform it just the same were she and the Earth, and any other number of balls in the same line, transfixed by a rigid pole revolving, as on a pivot, round the common centre of their orbit ? If so, how can any such ball, or any part of such radius, be said to rotate round its centre? If it did, all points in the Moon, or in such bit of radius, must of necessity, as Professor Airy admits, form concentric rings round the centre of rotation within itself. I assure you, that though you affirin the contrary, no point in any ball, so revolving as to keep same face to centre of orbit, does or can describe a ring round its own centre ; and as this may be very easily tested, I consider your assertion far more inexplicable, and quite as hopeless, as that of the Aristotelians, who would not believe their own eyes or ears at the tower of Pisa. Your hammer experiment, like E. B. D.'s tin moon, and my friend's flat board and ball, admirably illustrates that the Moon can have no such second motion as rotation; for the moment the orbital revolution ceases, and the centrifugal force alone, without centripetal to counteract it, as in your hammer experiment, takes effect unchecked, the rotation begins ; and that it did not exist before, is incontestably proved by its immediately turning different faces towards the centre of the orbit! If the Moon were served in the same fashion, I have no hesitation in admitting that she would do exactly the same thing, and begin to rotate, as. your hammer begins to do after it quits the sling and takes its tangential flight. I need hardly say that I made the assertion that she would be motionless if her orbital revolution ceased, as a mere corollary to the assertion that she had but that one motion, and no rotation on her own axis : a fact capable of proof by any instrument which does not misrepresent the special character of the lunar motion. The rigid connection is that which makes the experiment analogous ; for the lunar motion is precisely, bating the librations, such as would exist were there really a rigid connection.

I assure you I did not misuse Professor Airy's statements : they are these :

1. “A body, consisting of firmly-connected parts, if it rotate at all round any centre whatever, must (by geometrical necessity) so rotate that all points move in concentric rings relative to that centre.”

2. “Every point in the Moon does describe a ring round the Earth, that Earth being a travelling centre.”

I deduced from this (see page 19 of “ Lunar Motion "), that as in no revolving body (and I used the term advisedly, as the most comprehensive, but “rotating body ” will do as well) can any points by any possibility form concentric rings round more than one centre,* the Earth, according to Professor Airy, is the only centre round which the Moon forms such rings, and revolves, or can be said to rotate.

If you and other rotators choose to pick out other passages in Professor Airy's letters by which you think you can show that he holds inconsistent views, that is your affair. But you are not helped in your difficulty in escaping from this syllogism by laying stress on the words “ firmlyconnected parts.” Professor Airy did not apply this expression as you represent to the Moon and to the Earth,—or he would not have said “a” body; for the Moon and the Earth are two bodies. Neither will the “ travelling centre” help you ; for both the Moon and the Earth have centres which, though “travelling,” travel together, the one being in the centre of the other's orbit. Therefore their dynamical relation to each other is as if the Earth were at rest. Thus it is that all attempts to support the doctrine of rotation by references to fixed points or lines in space are futile. The Moon's motion as to rotation or non-rotation could be determined, as I said, even if her centre were at rest, and she alone in creation, by the rotation or non-rotation of points in her around her centre, moving in concentric rings—a fact requiring no reference whatever to any external objects. You are misled, like every one else who is still against us, by the palpable fact that she turns different faces to fixed stars or points of compass; and of course the pin in the disk you suggest (p. 330) will twist in any one's hand who holds it from outside the circle of orbitation ; but surely you need not be told that as this results from any revolution, it is no proof of the rotation of a body round its own axis. Draw a line, dividing your disk into two hemispheres ; one will be within, the other without the centre. Make it revolve, and you will find that no point in the inner hemisphere ever rotates or turns round the centre. How, then, can it be correctly said that the whole body rotates round the centre, if one-half of it does not? The fact is, that the centre turns round the inner hemisphere. But to reduce the non-rotation of the body of the Moon to a practical proof, substitute a single point for the Earth, at the centre of the Moon's orbit, and without changing the motion of the Moon, bring that point in her edge which is nearest the centre of her orbit into 'exact coincidence with it; she will then revolve round it, that point being at rest. Are you prepared to say that a sphere, having one point of its circumference at rest, is rotating ?

* If you really question this, try to draw a diagram in which they do. a geometrical phenomenon, which I should like to see.

It will be

Mr. Perigal wishes me to tell you, that if you like to call upon him, he will show you how bicircloidal and other curves are formed by instruments which he has had constructed for the purpose. Like myself, I presume he is unable to comprehend your geometrical proofs without a diagram. When, however, in the case which represents lunar motion, you say, that “ as 0'-=0, there will be no rotation of O P relative to 0 P, although O P really rotates once for each rotation of OP,” it is plain that you use the word rotation to express what we assert to be simple orbital revolution ; and that, so far from proving it to be rotation, you are reduced to the necessity of simply affirming it to be so.--I am, Sir, with much respect, yours truly,

J. SYMONS. P.S.—Dr. Lardner, I observe, is sorry that I copied his correct dynamical statement : the day will come when he will regret that he withdrew it. How much better it would be for modern astronomers (notwithstanding their Cambridge tethers) to say, “ We have for some generations copied La Place, who made a mistake. We understand the real lunar motion correctly enough by rotation ; but as it must mislead others, we will drop it, and define the lunar motion as the revolution of a sphere once round a distant centre, keeping the same face towards it." All the world would agree in the accuracy of this, and it would have the additional advantage of being intelligible to all the world. I may, perhaps, be permitted to add, that I do not think it necessary to write more on this subject. Some instruments and diagrams are, however, being prepared, which, by aid of the magic lantern, will enable some who are interested in setting this question at rest, to give such lectures on the whole subject of the Moon, including the recent discoveries by Mr. Breen and others, as may elucidate this interesting branch of astronomy, and explode the misuse of “rotation” from astronomical books.

THE MOON'S MOTION. TO THE EDITOR OF THE ENGLISH JOURNAL OF EDUCATION. SIR,—Concerning the Moon's motion, the solution of the difficulty seems to be, that axial rotation ought to be regarded as either absolute or relative, according as it is independent or dependent on the body's revolution about a distant centre. For example : if a ball be stuck on each leg of a pair of compasses, and one leg be fixed while the other describes a circle, each ball will turn all its points successively about its axis towards a fixed point in space,—the North, for instance. This appears to be the strictly mathematical notion of axial rotation ; only the ball on the fixed leg, however, has absolute rotation on its own axis, the axial rotation of the other being dependent on its revolution about its companion.-I am, Sir, your obedient Servant, H.M.'s Dockyard, Pembroke.

SAMUEL A. GOOD.

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