;

to be compelled to say it? You tell us it would "produce confusion :" the reason, and the only reason, being that the contrary has been held by astronomers; and I quite agree with you that it would confound them, were you and others to be "compelled to say" what is the simple truth, namely, that while the Moon does not rotate about her own axis, the Earth does so 3651 times in a year, with reference to the Sun, which is the only common-sense way of determining her rotation—inasmuch as the Sun, instead of any fixed star, is at the focus of the Earth's orbit. The Sun's daily appulses to the meridian are obviously the measure of the Earth's rotation, and of these there are 365, and not 366. In other words, if it be true that the Sun, instead of revolving in the ecliptic, occupies a fixed place in the centre of the Earth's orbit, the Earth's rotations must be identical in number with the 365 presentations of the same face or point in her circumference to the Sun, and not to any fixed star outside her orbit. If the Earth makes the additional rotation ascribed to her, it must be a latent one, possessed of the sin gular property of making no additional presentation of face (like the other 365) to the Sun. Now this is precisely the one rotation which the astronomers and Dr. Whewell persist in ascribing to the Moon and I am free to admit, that to deny the one is to confound the other: in fact, one blunder is upheld to support the other. The reason, as you well know, why there are 3664 sidereal days (as they are incorrectly termed) is simply that, owing to the Earth's orbital revolution, she presents the same point to the same fixed star (or, in other words, its transit over her meridian happens) in a shorter time than that in which she completes her rotation on her axis. They are, in fact, short days, and incomplete rotations. These diurnal short quantities make up in the year one additional sidereal day. To an observer in a fixed star the Earth, of course, therefore presents the same semi-cycle or side 366 times in a year, because in her orbital revolution she has turned herself once round in addition to her axial rotations. But if she were at rest in space, her axial rotation continuing precisely as it now does, it is mani fest, that whilst to the Sun she would give exactly the same 365 presentations of the same face she does now, and have the same number of days and nights, she would give one presentation less to the fixed star. Now, simply because this orbital revolution has, quoad an external object, one property in common with rotation, is it not monstrous to assert their identity? I cannot help thinking that the time is at hand when it will be deemed better for science, better for learners, and not derogatory to teachers, to be "compelled" to say what is true; even though we sacrifice cherished dogmas to facts, instead of gainsaying facts for fear they should confound dogmas.

In PARS. 6 and 7 you again affirm twice that the Moon is not attached to the Earth,‚—a fact, I am sure, that nobody disputes; though you correctly showed how similar was her motion to a revolving body having such rigid connection with the centre of its orbit, by illustrating her motion at Cheltenham with a tin ladle fastened by the handle to a pivot, a machine which I presume was "made by man.'

I am unable to perceive how the conclusion in PAR. 8 follows from the premise in PAR. 7. If you mean by "machinery" anything comprising a rigid connection, there is no such " machinery" known to astronomy, and there is no logic in your "reason;" for the same fact

will apply to all the motions of heavenly bodies alike. If you mean that the revolution of the Moon with the same face to the centre is necessarily the result of two separate motions, you are simply begging the question at issue, and assuming that the parallel motion is the only revolution without rotation, a point we shall come to presently.

I have read PAR. 9 over and over without any certainty of what you mean. Doubtless we may examine the Moon's movement in space and round the Sun, as well as round the Earth, but these are distinct things. The disputed dictum as to rotation is confined by the very terms of those who wield it to the Moon's motion relatively to the Earth; her circum-solar motion (as I replied to you at Cheltenham) is not in dispute; neither will it help you to encumber the discussion with it. The Moon moves, and each particle of her moves, solely in concentric rings (or rather ellipses) round the Earth, and in no other manner, and describing round the Earth no other path, courses, rings, or curves of any kind or description; while no point in the Moon describes a ring round any other point within her. This you are both too scientific and too truthful to deny. You are equally unable to deny that whenever a body rotates round its own axis, or about an axis within it, each particle in it must describe, with the rest, concentric circles round that axis. In the Moon none does so whilst no part of this side of her ever moves or revolves round her axis or centre. Nor can you assign any relation which any point in the Moon bears to what is called her axis more than to any other point in her. All points in the Moon move with angular velocities proportioned only to their respective distances from the centre of her orbit? Would this be so had she any axial rotation? It would not.

These are utterly distinct dynamical and geometrical properties, and the two motions thus distinguished can, I submit, with no more propriety be called by the one term of "rotation" than can an ellipse be called a circle. To do so were indeed to introduce "confusion worse confounded." It would not only upset the established definition of Barlow, in his "Mathematical Dictionary," but it would introduce a jumble into the technology of mechanics, as well as astronomy, which practical mathematicians may truly regard with the "scientific horror" affected by those who cram men for honours by the aid of formulæ of which they rarely understand the elementary principles. De Poinsot's definition has introduced a mischievous heresy on this point; and every

* Common sense and the reverse in definitions were seldom better contrasted than in this and De Poinsot's definitions. Here they are :

"Rotation; the motion of the different parts of a solid body about an axis, called the axis of rotation, being thus distinguished from the progressive motion of a body about some distant point or centre: thus the diurnal motion of the earth is a motion of rotation, but its annual motion one of revolution."

*

*

*

"When a solid body turns round an axis, retaining its shape and dimensions unaltered, every particle is actually describing a circle round this axis, which axis passes through the centre of the circle, and is perpendicular to its plane."-Barlow.

"There is no rotation when one face or a determinate section of the moving body remains constantly parallel to itself; there is, on the contrary, rotation, in the same time as the revolution, when the moving body turns constantly the same face towards the central body. This second case is that of the satellites, in moving round about their primaries."-Traité de Mécanique, par M. S. D. Poisson, 2nd edition, Tome II., pp. 179-180.

man who has had a common-sense mathematical education regards as a pedantic folly a definition which necessarily leads to the conclusion that if A revolves round B, B being a fixed point, B has rotated round A; so that the Sun rotates round the Earth.* This it is which has led to the ingenuous admission of Dr. Lardner that the Peak of Teneriffe and each individual, &c. &c., rotate on their own separate axes. The scientific writer of an anonymous pamphlet at Edinburgh † reduces this offshoot of science run mad to its climax of absurdity in the following well-put illustration :—

"They who maintain the established kindred doctrines on these three points must be prepared to assent to, and affirm, the monstrous proposition that the radius of an orbit, or the spoke of a wheel, nay, even the stick twirled round in the hand, possesses the marvellous property of turning round on both ends at once, and describing at the same time two separate circles, round different centres, separated from each other by its whole length!"

You seem to derive great comfort from the Moon's undulating path in space round the Sun. I repeat that this will not help the astronomers one bit. You may just as well attempt to eke out an argument against the palpable fact that a fly flies round and round your head in a railway-carriage, or with a given motion, because it is at the same time moving through space in nearly a straight line from Cambridge to London. I wish you had given your reasons for saying that the Moon revolves more about the Sun than about the Earth: though wholly irrelevant to the argument, they must be at least curious. But however we may lament the scantiness of your information on this and some other points, no such complaint can attach to your assurance that the heavenly bodies are not fastened to each other. We are assured of this for the fifth time in PAR. 11.

In PAR. 13 you revert to the solar and sidereal days; and having stated the number of the solar days correctly, you add that "the Earth revolves [I presume you mean rotates] 366 times on her axis with reference to the fixed stars." I have already endeavoured to show you that she does not a revolution or rotation means a complete revolution or rotation: if the revolution or rotation of a body in motion of translation be measured by the interval of time which any point on it occupies in twice presenting itself to another external point at rest, any child will perceive that such measurement cannot be equal to the period of a full rotation, the angular distance having changed.

The concluding paragraphs of your paper merely repeat the experiment by which Galileo arrived at the conclusion that a body revolving round a distant centre, preserving its parallelism, and presenting the same face to an external point and different faces to the centre of its orbit, did not rotate. Your argument is, that since this manner of orbital revolution is not rotation, the lunar motion must be. In the first place, this is a non sequitur; there is no physical impossibility in two or more modes of turning in an orbit without rotation. Mr. H. Perigal, Mr. Hopkins, Mr. D. Mushet, and the author of the Edinburgh tracts, and I dare say many other far abler reasoners than myself, have over and over again demolished this fallacy.

* Hymer's Elements of Astronomy are, I believe, founded on this doctrine.

+ "Considerations on the Established Doctrines concerning the Moon's Rotation." Armour, Edinb. 1856.

Your water experiment proves nothing. Admitting, for the sake of argument, the immobility of the water, and that it preserves its parallelism, and, if you will, that it does not turn like the Moon, how does that prove that the Moon rotates on her own axis? There is really nothing to grapple with in an illustration and argument so utterly irrelevant. Motions in mechanics being phenomena resulting from forces, the motion of the Moon is undeniably (as you assert in PAR. 14) the result of mechanical force. But of what kind of force, and of how many, you prudently omit saying. If I am right in the geometrical phenomena I have above ascribed to the relative motions of the different particles in the Moon, as being distinct from those which are inseparable from rotation, equally distinct are the mechanical forces which respectively produce them. Mathematical definitions have long been vague and unsatisfactory; but the abuse which assigns the same term to two distinct motions, is, I believe, unequalled; and not only detrimental, but discreditable to science. I could confirm this remark by the manner in which "scientific men," in their correspondence with me on this subject, have contradicted each other.

In conclusion, if it had been merely affirmed that the Moon rotated round the centre of her orbit, it would have been useless to contest that merely verbal misuse of the term rotate; but it is gravely asserted that the Moon rotates on her own axis once in addition to her orbital revolution and this is gravely assigned as the cause of her presenting the same face to the Earth, and the synchronism of these double and distinct movements is said to be an extraordinary coincidence (instead of a single motion). Since reverend philosophers at scientific associations get into very unphilosophical passions because these dogmas are "marred and murdered," it is high time that the growing requirements of common sense should be respected, and plain teaching vindicated in high places; so that such errors may be calmly disproved, firmly denounced, and completely exploded.

It is no matter of mere verbal difference. You and I heard it openly declared from the platform of the Mathematical Section at the last British Association, that the Moon rotated' on her axis as a peg-top spins. I perfectly acquit you of any direct assent to such a statement; but before you, holding the high station which you worthily fill in the University of Cambridge, indirectly support the men who are thus teaching the elements of two noble sciences, of which you are bound to conserve the purity, I humbly submit that you should be prepared with more cogent reasons for such countenance, than the remarks you volunteered in behalf of the doctrine that the Moon rotates round her own axis at the Cheltenham meeting.

I am, Reverend Sir, your obedient servant,

JELINGER SYMONS, B.A. Cant.

FEMALE EDUCATION.-No. 3.

Na preceding paper we have endeavoured to point out how woman

habits of study

will be most conducive to that end. There is, however, another branch of the subject to which we would gladly call attention in a concluding article-the manner in which she should guard the hearts and minds of others; more especially those of the younger members of her own sex, whose real education is generally committed to her care.

It is a very different thing teaching oneself, and teaching others; the latter duty requiring a far greater amount of patience and perseverance than the former.

In commencing the education of a child, we must keep always in view our one great object; which is neither to make a well-taught parrot, nor a moving automaton, but a sensible, intelligent woman, fitted to take her place in society and fulfil the duties of her station.

The mind of a child is pliant and easily moulded; let us be careful that we form it aright; remembering always how responsible is the situation in which we are placed, and that the future happiness of that child may probably depend upon the care we have bestowed upon her early years. When we look upon the subject in this point of view, we shall be struck with its vast importance, and strive more earnestly to fulfil its duties aright; recollecting that we are forming a creature not merely for time, but for eternity. Let us put our whole hearts in our work, and then we may humbly trust that the blessing of God will accompany our labours.

To be able to teach well we must be thoroughly masters of our subject, and in explaining it should endeavour to do so in as few and simple words as we can. A long history confuses the listener, who forgets the first part in listening to the conclusion. We must never, however, be weary of repeating the same lessons again and again, until thoroughly comprehended by our pupils. Precept must be upon precept, line upon line, here a little, and there a little; remembering that what seems very clear to us, may be more difficult of comprehension to another mind, somewhat differently constituted to our own. Undisheartened, we must try again, firmly resolved that our charges shall not pass by any difficulty without having first surmounted it.

over ?"

An anecdote in the early life of one of the Wesleys illustrates this patience and perseverance. His mother was one day teaching him a simple lesson which he was slow to learn; she was very patient with the child, but the father became greatly irritated. "How can you," he at length exclaimed, "tell that dull boy the same thing twenty times. Because," she replied gently, "nineteen will not do." Patience and a perfect command of temper under all circumstances are some of the most important requirements of a teacher, though perhaps at times a little difficult to maintain. It is remarkable how a single ebullition of passion will destroy the effect of all that we have been endeavouring to teach; and it does this by diminishing the respect in which our children hold the office of the teacher. If dislike and ridicule ever take the place of love and confidence, we can hope for but little success in our future labours.