Will you excuse a stranger taking the liberty to suggest (in the same spirit that dictated my hope that your long-established character as an earnest, and talented labourer in the cause of education should not be allowed to suffer from such attacks) that you would either call upon the Editor to insert my letter, or that some more influ ential among your scientific friends should be requested to vouch the correctness of your views under the sanction of their signatures.

Apologizing sincerely for this intrusion upon an affair which may be of little importance to you personally, I have the honour to be, your very respectful Servant, WM. HAWKES LANGLEY, M.A., Ch. Ch., Oxford,

TO THE EDITOR OF THE "TIMES."

J. U. S. CLUB, 14, ST. JAMES'S SQUARE, 11th April.

SIR, It is said that those who are in the wrong require friends, not those who are in the right. This is, doubtless, the view taken by the scientific world of Mr. J. Symons. He is perfectly in the right. His feeble and intemperate opponents, from a confusion of ideas, imagined that, because a body rotating upon its axis presents the same face successively to every point of the compass, therefore a body which presents the same face successively to all those points rotates upon its axis; not perceiving the difference between rotating on an axis (its own) within itself and one without. If this be true, it is equally so that, as the Earth rotates on her axis, every particle of matter composing her substance, except those on the line of her axis, rotates on its own axis. AMICUS.

SIR, It is pretty well understood at College that a man may be a tolerable mathematician and yet know but little of mechanics. An example of this appears in the letter signed "A Wrangler," inserted in your Journal of the 9th. The letters also from your other correspondents seem to be equally unsound; and some of their modes of illustration for showing that the Moon does rotate about her axis prove how inadequately they have studied the subject. I shall confine myself to merely one, so as not to trespass on your valuable space.

We are told that a man has only to walk round a table, with his eyes directed towards its centre, and he will see at once that he has performed a rotation about his own vertical axis! Now, this I think is quite a misconception of the case; the man's body has performed a REVOLUTION round the table, just as a bead would do moved round a circular wire; but it has no more rotated about its own axis than the bead has, for his back has all the time been turned away from the table; and this is just the case with the Moon, which always keeps one and the same hemisphere away from us, and we therefore never see it. Now, what is really meant by rotation? An example or two will be sufficient: a spinning-top is an instance of rotary motion; a quoit hurled from the hand is another. But perhaps a better for our present purpose, is the diurnal rotation of the Earth in its course about the Sun; and what is the effect produced? Why this-that it presents all its sides diurnally to the Sun ; instead of which the Moon presents to the Earth nearly one-half of its circumference, and that always the same half; how, therefore, is it possible that she can rotate about her axis? Strange, however, to say, all astronomical works agree in telling us that she has a rotation, and that it is performed in exactly the same time that she goes through one revolution in her orbit. Now, it is very remarkable that not one of them (of all the works that I have read) has ever given us any-the least proof of it and yet they are always clear enough in the evidences which they produce of the rotation of the Sun, and also of that of the Earth; and equally so as to the Planets, Mars, Venus, Jupiter, and Saturn! But why have astronomers contented themselves with merely ASSERTING the Moon's rotation; they who, of all men, are usually so exact? It is for them to answer that question, and I hope that one of them will do so; in the mean time, I entirely agree with your correspondent, Mr. Symons, and have been for years of the same opinion, namely, that the Moon is decidedly not a rotatory body.

We have to thank Mr. Symons for the trouble which he has taken in bringing a subject of so much astronomical importance before the public; and I can but pity some of his opponents, whose want of temper and modesty of bearing says but very little for them.

VINDEX.

SUMMER HILL, BIRMINGHAM, 12th April, 1856.

SIR, I trust a stranger will be forgiven for addressing you on a subject which, doubtless, at this moment, must occasion you some uneasiness. I allude to letters in the Times newspaper, having reference to the Moon's rotary motion. In the first place, you may console yourself that the writers were not THEMSELVES philosophers; nor simply desirous to test the truth of the dogma suggested. With regard to the question betwixt you, there must of necessity be some MISUNDERSTANDING. No man in his senses could possibly suppose a distant body to make one entire turn on its own centre, without showing different phases; and hence I presume, that as we evidently see only one portion of the Moon, you must necessarily be quite right in your conclusions. The arguments adduced against you are, to my own mind, frivolous, rude, and obscure; but I do hope, from its publicity, you will find some in high quarters who will take up the question, and support you. I have myself found the difficulties attending the introduction of new theories, more especially if they clash with longestablished and settled notions. I have suffered insult and contumely; but in the hands of a man like yourself I anticipate better treatment; and shall feel obliged if (at your leisure) you will give me your candid opinion of the work I herewith forward. I remain, Sir, your obedient Servant, CHARLES HOPKINS.

BIRKHAMSTEAD SCHOOL, April 14th, 1856. SIR,-As one of those who were startled with your letter denying the rotation of the Moon, I venture to address a few remarks in reply to your last communication to the Times.

We both admit that the Moon, in accompanying the Earth round the Sun, presents every side to the Sun in a month, and keeps the same side always towards the Earth. You maintain this to be the result of the Moon's motion round the Earth, while astronomers have generally considered it to be the result of a proper rotation of the Moon on its own axis. In support of your view you say, that if the Moon were arrested in its course round the Earth, its rotation would instantly cease. I take this to mean, that if the Moon moved in an orbit parallel to that of the Earth, and accordingly presented only one phase, when viewed from the Earth, there would then be no rotation of the Moon on its own axis, and it would always present the same side to the Sun. You will excuse me for thinking this a petitio principii. For argument's sake, let me assert that the Moon would continue to revolve once in 655 hours and 44 minutes. Upon whom does the onus probandi justly fall? For the common theory of rotation explains the actual phenomena satisfactorily, and neither hypothesis is evidence either way. Your objection, that the Moon is not an oblate spheroid, somewhat surprised me. The centrifugal force acting on the equatorial zone of the Moon's sphere, in consequence of the Moon's monthly rotation, is, if I am not mistaken, so very much less than the centrifugal force which elevates the equatorial zone of the Earth, that no micrometrical measurement could detect the difference between the equatorial and the polar axis of the Moon arising from that cause.

I must confess that I cannot understand your argument, from an orrery so constructed that one ball should pass round another in ten minutes, and rotate on its axis in the same time. I should fancy it would illustrate the common theory.

The analogy of machinery may be incomplete; but I would venture to suggest that no heavenly body rotates without moving through space, and I am not aware of any fixed law requiring the rotation to be in a certain proportion to the diameter of the sphere, or the space described during the time of one rotation. For example, that the Earth should rotate once in describing an arc of 200 diameters. Upon the whole, it is a question about a word, and not about a fact. If we take a circle of some twenty feet diameter to represent the Earth's orbit, and project upon it the Moon's path, by laying off the angular distance of the Moon from the Sun, for any given month, we shall find the curve which the Moon describes always concave to the Sun; and in describing a certain arc of this orbit, she will have presented every side to the Sun. Now, we can say precisely the same of the Earth. That body describes a

curve always concave to the Sun, and in describing a certain arc of that curve it presents every side to the Sun; the only difference being that the Earth does this in an arc of about 200 terrestrial diameters in length, while the Moon does so in something under 12,000 lunar diameters.

The really interesting question is, Why should the lunar rotation be precisely synchronous with its apparent revolution round the Earth ?*

There is no doubt that the centrifugal force of the Moon in her orbit round the Earth is enormously greater than the centrifugal force of the Earth round their common centre, which I take to be a point within the sphere of the Earth, not fixed, but revolving round the Earth's centre; and in examining the amount of centrifugal force and terrestrial attraction on the opposite sides of the Moon, we find the difference so great that it may give rise to an accumulation of matter on the side of the Moon away from the Earth, so as to make the equatorial axis in that direction much longer than the polar axis. Is it possible that the excess of centrifugal force in her orbit, acting on the parts away from the Earth, just equilibrates the centrifugal force of her axial rotation, so as to keep the centre of gravity of the Moon on the other side of the apparent centre of her sphere, and allow an accumulation of atmosphere and fluid and vapour on the side which we never see? This is, I admit, a most interesting inquiry, and I shall rejoice if the discussions which your letters have aroused may lead to the advancement of our knowledge on these points.

I am, Sir, your obedient Servant,

JELINGER SYMONS, Esq.

J. R. CRAWFORD.

2, FORRES STREET, EDINBURGH, April 15th, 1856.

SIR,-As I admire the bold way in which you have stepped forward to denounce the palpable scientific fallacy, which has so long been maintained, and is still clung to, on the pretended rotation of the Moon on her axis, I beg leave to send you the following copy of a letter I addressed to the Times, which the Editor has not thought proper to publish; the more unfairly, I think, that he inserted many of those of your opponents, and has thereby left the public to imagine that no man in the kingdom backed your opinion.-I have the honour to be, Sir, your obedient Servant, JELINGER SYMONS, Esq. G. MACDONELL, Lieut.-Col., late of 79th Regt.

SIR,-As Mr. Jelinger Symons seems to have brought a hornet's nest about his ears, for daring to deny the Moon's rotation on her axis, allow me to suggest to him a different exemplification of his theory. Let him perforate a small ivory ball to represent the Moon, pass a wire through it, and bend this wire into a circle of a foot in diameter, and then push the ball round the circumference. Will there then remain any doubt of her not rotating on her axis The very fact of her ever showing the same face is proof that she does not revolve on her axis. If I turn completely round on my heel, I revolve on my axis, and you see my back in the course of the gyration. Whoever saw the back of the Moon? I know well this is heresy to Cambridge Wranglers, and indeed to all astronomers; but I say Mr. Symons is quite right, and if it were not so heterodox, I would say more. G. M.

To this I appended, for the Editor's satisfaction, my signature and rank in the army, as also my address. You are at liberty to make use of this letter in any way you please.

G. MACDONELL.

14, GLOUCESTER PLACE, NEW ROAD, 16th April, 1856.

SIR,-Having forwarded to the Editor of the Times a letter on the subject of the supposed rotation of the Moon, which appears to have been either not worthy of insertion or to have arrived too late, I take the liberty of sending you a copy. My

* Naturally enough, for its motion is nearly as if it were fixed to a circular plane, of which the Earth was the centre.-ED. E. J. E.

object in doing so is merely to show that I am one of those who entirely agree in your opinion.

There is a letter in yesterday's Times, signed “ W. B. D.," in which the writer asks, "Why does the Moon show both her sides to the Sun?" How strange that he does not see that the answer must confute his own opinions!

I am, Sir, your most obedient Servant, JELINGER SYMONS, Esq.

A. F. MACKINTOSH.

LONDON, 17th April, 1856.

SIR,-It must be admitted that you have received most unfair treatment from those who have professed to answer your letter in the Times, on the subject of the Moon's motion; but I think they would have been silenced had you stated that the Moon no more rotated on her axis than St. Paul's on its axis; the fact being, that, according to their notion of the meaning of the expression " rotation on axis," everything that can be imagined on the Earth's surface rotates on its axis, from Mr. Goodeve's head or nose to the Monument, or St. Paul's, or the hippopotamus in the Regent's Park Gardens,-in fact, not only everything on the Earth, but every subdivision to an infinite extent; every grain of sand on the sea-shore, and every part of those grains. They appear also, in their virulence, to have forgotten to deny that the Moon may have a lesser convexity on this side and a greater on the other; or, in other words, be oblate on this side and prolate on the further; whereas, if it rotate on its axis, properly so called, it should be an oblate spheroid.

The plain question which should be put is this:-Do St. Paul's, the Monument, London Bridge, Snowdon, the Pyramids, the Archbishop of Canterbury, and Cardinal Wiseman, one and all, rotate on their axes?

Wishing you well through the discussion, I am, yours, &c.,
To J. SYMONS, Esq.

F. R. A. S.

UNITED SERVICE CLUB, PALL MALL,
April 17th.

SIR, I addressed a few lines to the Editor of the Times on the subject of the asserted axial rotation of the Moon, containing one of the following arguments, though expressed in different terms :-I propose to show that, presenting the same face to the Earth, she cannot have axial rotation; and also, that a body rotating, like her, round a distant axis, and having, like her, the same face always to it, does not move upon its own axis. Two spheres in contact, and rotating in the same direction on their axes, must alter the position of their surfaces relatively to each other; but they may rotate round a distant axis, and not alter them. Let there be another Moon in contact with the Moon, having the same motion as she has, and they may rotate round a distant axis, and present always the same face to it, which they could not do if they rotated on their axes. For, let A B be a straight line passing through the point of contact, and extending (at right angles) to their axes. If they have axial rotation, the line A B is broken into A D and B C, and the points of intersection, F G, which are the centre of the Moon's face, as presented to the Earth, are also altered; but as the face presented to us is always the same, it follows that she has not axial rotation.

Again, place a globe upon the Earth's equator, it will rotate on the Earth's axis, presenting always the same face to it; and presenting all sides successively to the Sun, as the Moon does; yet it does not rotate upon its own axis. This is true of every particle of matter of which the Earth is composed, except those which are on the line of its axis, obviously.

If you perceive any error in these arguments, and will communicate it, you will very much oblige your obedient Servant,

CHARLES AGNEW, Major.

8, CUMBERLAND MARKET, REGENT'S PARK, LONDON, April 18th, 1856.

SIR-It is with considerable diffidence that I now address you on the subject of the Moon's motion, as I am neither astronomer nor mathematician, but simply a mechanic, and that in not a very learned sense. When, however, I read your first letter in the Times, and bestowed a little thought on the subject of it, I thought it was the result of discernment when I acquiesced in the position you took; and the subsequent cor

respondence which has taken place has by no means caused me to change my opinion. It was not, however, to tell you this that I have written to you, but to bring before your notice (if you have not detected it already) a singular contradiction which occurs in Dr. Lardner's "Museum of Science and Art," upon this very subject. In No. 28, "The Moon," occurs the following passage:" While the Moon moves around the Earth, we find, by observation of its appearance, that the same hemisphere is always turned towards us. Now, in order that a globe which revolves around a centre should turn continually the same hemisphere toward that centre, it is necessary that it should make one revolution upon its axis in the time it takes so to revolve. For, let us suppose that, in any one position, it has the centre round which it revolves north of it, the hemisphere turned towards the centre is turned towards the north. After it makes a quarter revolution, the centre is to the west of it, and the hemisphere which was previously turned to the north must now be turned to the west.

As the same hemisphere is successively turned to all points of the compass in one revolution, it is evident that the globe itself must make one revolution on its axis in that time.”—Paragraph 5. In this passage, the generally received opinion is attempted to be proved; but turn to 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. Now, this is, I apprebend, the very result you affirm would take place did the Moon rotate once on its axis during its revolution round the Earth, allowing of course that the Earth would not cause day and night. This, then, is directly the opposite of what he says in No. 28; it is impossible that both can be right. The only effect that can be produced by rotation on its axis seems to me to be this which Dr. Lardner here says. This I thought might not be altogether unworthy of your notice, the more especially

as Sir David Brewster calls his work "accurate."

I hope you will pardon me for saying a word or two on the means by which I have attempted to describe the Moon's motion. I have drawn a rough diagram, illustrating my idea. I supposed that a point, anywhere but in the axis of a globe which has both circular and rotating motions, would have two motions; but in the case of the Moon, no point on its surface has two motions. A point on its equator, nearest the Earth, moves through less space than any other point on its surface, and preserves uniformly that position; while a point exactly opposite it, on the outer side, uniformly passes through a space equal to two circumferences of the Moon more than the inner point; and the centre has an acceleration of one circumference. This proportional increase of speed destroys the necessity for axial motion. Another method of testing the existence of this second motion was, by supposing two Moons formed in the diameter of the larger one. I conclude, that if there were any motion on their axes, there would be a rubbing, of necessity, of the two surfaces which were in contact; this of course is not the case, and hence I would argue no axial rotation.

The great mistake seems to be in placing the Moon in the same category with the planets. Dr. Lardner may very justly say, in regard to the Earth, that no law of matter would have prevented it having a different rate of rotation, that not agreeing in any way with its motion round the Sun. But he cannot say that of the Moon; we may regard the motion of the Earth on its axis as directly emanating from Divine beneficence, to fit the Earth for man; but I apprehend the law of gravitation must have to do with the motion of the Moon. It is too much to suppose that the Moon has an independent motion on its axis identical with that on its orbit; such an exactness does not exist with any of the planets in regard to the Sun. It would appear to me, then, that the motion of the Moon is due entirely to centripetal and centrifugal motion, acting on a body whose centre of gravity is not in its centre. One difficulty, however, remains: How does this theory agree with the statement of Dr. Lardner, that the Moon's axis inclines five degrees? I would have supposed that it would have been exactly at right angles with the plane of its orbit. Here, Sir, I am reminded how little I know, and that, presuming you have read thus far, I may have been wasting valuable time. Pray pardon my boldness in having thus addressed you, and believe that it is not to thrust myself upon you, but merely to bring to your notice that which is to be found in that certainly useful work, on the question, so contradictory. You have my thanks at least for your publication of your ideas on this interesting subject.-I remain, Sir, your obliged Servant,

Mr. J. SYMONS.

MATTHEW KER.