applied such as are cited at the beginning of these pages, how can it be otherwise than that total misconception of the Moon's motion should arise? The conflicting varieties of opinion entertained on so simple a matter, which this discussion has evoked, prove how great is the confusion of ideas created. If scientific men insist on calling the Moon's motion axial rotation, let them do so; but I protest against a misleading use of that term in books of general instruction. Astronomers appear to use the term axial rotation for both motions, just as botanists call wheat and couch-grass by the same generic term, simply because certain affinities prove them to be of the same genus; but botanists also designate each species by its distinctive name, and do not persist in teaching that wheat is couch. Let astronomers do the same!

The reader will now judge for himself whether I have or have not established a claim on the writers of works for popular instruction so far to modify their definitions as to give distinct names to distinct motions, and to simplify the explanation of great truths, so that the glorious science of Astronomy-no longer the exclusive privilege of the few-may be brought down to the "level of ordinary minds," and

MADE PLAIN TO THE PEOPLE!

APPENDIX A.

Proof of the curves that would be described by any point in the Moon, if she rotated on her own axis, in the same time that she revolves round her orbit. By H. PERIGAL, ESQ., JUN.

The centre of the Moon being supposed to revolve about the centre of the Earth (assumed at rest, to avoid unnecessary complexity), in a circle called the deferent, the radius of which is denoted by D; while the Moon is supposed to rotate about an axis perpendicular to the plane of her orbit; any point of her surface at the distance from the axis of the Moon's rotation would evidently describe in space a bicircloid curve, as the resultant of such two movements, of which would be the epicyclic radius, and the line joining the centres of Earth and Moon would be the deferential radius.

If the revolution and the rotation be equal in angular velocity, and in the same direction, then

V=V,..v=1;

and the equations are in this case

x=D cos + cos 24,

y=D sin + sin 2p,

r2=x2+y2=D2+ E2+2DE cos &;

being the longitude of the Moon's centre from the primitive axis of x. Let D=1 and E=e, the values can be restored afterwards; then

2x=2 cos +2e cos 2p,

72=1+e2+e, 2 cos ;

or

2 cos 24=(2 cos 4)2—2, and 2 cos -(2-1-e13)

e

2ex+e2(1 − e2)=(x2+y2)2−(1+2e2). (x2+y2) ;

.. restoring D,

2D2Ex+E2(D2— E2)=(x2 + y2)2 — (D2 + 2E2)(x2+y2).

This equation being of four dimensions, the curve may be cut in four points by a straight line; therefore it must have an inflection or undulation.

The polar equation is

4-(D2+2E2)2-2D2Er cos 0=E2(D2-E2).

I cannot conclude without expressing my sense of the invaluable aid I have derived in this controversy from many scientific supporters, and especially to Mr. Evan Hopkins, who is now pursuing the subject with his accustomed ability and success.

J. S.

PROOFS OF THE MOON'S ROTATION.

TO THE EDITOR OF THE ENGLISH JOURNAL OF EDUCATION.

SIR,-Allow me to submit to your notice the following proofs of the Moon's rotation, which I forwarded to the Times in April, but which, in common with many others, was refused insertion.

Station a vessel at some distance from a buoy, due south of it, with the prow turned towards the buoy. Now it will be found that she may be made to go round the buoy in three ways. And, first, let her be put round with her hull keeping always the same inclination, that is, with her prow pointing continually due north. In this condition, when she arrives at the east, her larboard will be opposite to the buoy; when she comes round to the north, her stern will be towards it; on arriving at the west, her starboard will be presented to it; and on regaining her original position, her prow again comes opposite. Here she has gone round, or revolved, without rotating, and every part has come successively opposite to the buoy. Secondly, as she goes round, let her swing slowly on her centre, in such a manner as always to keep her prow opposite to the buoy. On completing the first quadrant, her prow will point to the west; at the end of the second quadrant, it will be towards the south; the third quadrant will point it to the east; and the fourth quadrant restores it to its original position, pointing north. Here the forepart of the vessel has been always opposite to the buoy, and at the same time she has completely rotated, turning her prow to every point of the compass in succession. A line, drawn from prow to stern of the vessel, represents the Moon's equatorial diameter; another, forming vertical right angles with the centre of it, her axis. This experiment exemplifies the Moon's motion ;—a slow axial rotation; a slow rotation on a progressive centre ; a gently rotating diameter on a revolving centre. Thirdly, as the vessel goes round, let her rotate continuously. She will then present all parts

of her lateral surface to the buoy as many times as she rotates, minus or plus one, according as she rotates in the direction of her revolution, or against it. This is the Earth's motion ;-a swift axial rotation; a swift rotation on a progressive axis ; a rapidly rotating diameter on a revolving centre. To prove that a rotating body will present its surface to the centre as many times as here stated, cut out two circular discs of paper, one an inch, and the other six inches, in diameter; divide the circumference of each into twelve equal parts, draw the twelve radii, and number them like the dial of a watch. Pass a pin through the centre of the smaller, from behind the disc, up to the head. Lay the centre of the smaller disc on the XII of the larger in such a manner that the XII of the smaller disc shall point to the centre of the larger. Now, while a body is supposed to revolve from the XII to the XI, let it rotate in the same direction. By means, then, of the pin, move the smaller disc from the XII to the XI of the larger, and while so doing, turn it slowly round in such manner that the I, II, III, IV, &c., point successively to the centre, and count the numbers as they pass. By the time that eleven have been presented to the centre, it will be found that the disc has completely rotated, the diameter connecting the VI and XII of the smaller disc becoming parallel with the diameter connecting the XII and VI of the larger disc, and the XI of the smaller pointing to the centre of the larger. During its progress, therefore, along one-twelfth of the larger circle, the smaller, in the presentation of its disc to the centre, falls short by one-twelfth. Now lay the smaller disc on the XII as before, and move it again from the XII to the XI; and while so doing, turn it slowly round in the contrary direction, pointing the XI, X, IX, VIII, &c., successively to the centre. It will now be found that, by the time the disc has completely rotated, thirteen of the divisions will have been presented to the centre; therefore, in this case, the smaller gains one-twelfth, precisely as the hands of a watch come together eleven times in twelve hours, and would meet thirteen times in the same period if the hour-hand moved backwards while the other advanced. To a spectator, therefore, in the centre of any orbit, in which a body rotated twelve times during a revolution, those twelve rotations would appear as eleven or thirteen, according to the order of rotation. Diminishing the number of rotations till the body is supposed to become stationary, and then reversing the motion, 3 would appear as 2, 2 as 1, 1 as 0, 0 as 1, 1 as 2, 2 as 3, &c. ; where the negative terms denote the reverse rotation. 0 as 1 represents the first case supposed, in which the hull, keeping the same inclination, appears to the spectator as a rotation. 1 as 0 represents the Moon's motion, one rotation appearing as stationary. It also explains what appears, at first sight, to be an anomaly; viz., that two rotations and no rotation both appear as one rotation. These appearances will be evident by referring to the discs. That bodies necessarily rotate in the same direction in which they revolve, unless acted upon by an extraneous force, may be shown by floating a piece of cork, about the size of a shilling, with a line marked across it as a diameter, upon some water that has been stirred round. If the motion be feeble, the cork will simply float round with a stronger motion it will rotate, slowly or swiftly, according to the force impelling it; but the rotation will always be in the direction of the current. Should the cork come in contact with the edge of the vessel containing the water, it will begin to rotate in the opposite direc

tion. The radiating force, therefore, of the Earth upon the Moon appears to be so nicely adjusted to her weight and distance, as to turn her round upon her axis once, and once only, during a revolution; whereas the superior propulsive action of the Sun upon the Earth causes her to rotate 366 times during her revolution. Arguments derived from the revolving parts of machinery have led to false conclusions, from the fact having been overlooked that the parts of such machinery are necessarily connected; whereas bodies rolling through space are unconnected. The governor-balls of a steam-engine can have no axial rotation; they are but portions of a whole, the axis of which lies in the central upright rod to which they are connected. A cut decanter or tumbler may be carried round a plate, and made to rotate like the vessel round the buoy; the axis then lies in the tumbler: let it, by any means, be connected with the plate, and the plate turned round, the axis immediately quits the tumbler, and becomes transferred to the plate. In the swings used at fairs, in which four boats are carried vertically round a circle, the boats, by reason of their weight, are disconnected from the motion of the machinery; the consequence is, they have revolution without rotation, and present every part of their surface successively to the centre.—I am, Sir, your obedient Servant, THOMAS KENTISH.

College House, Hackney Road, London.

PRACTICAL HINTS FOR SCRIPTURE LESSONS.--No. 4.

66HY did St. John write the Apocalypse in the isle of Patmos ?"

"WHY Will any rational being, twenty years hence, believe that this

question was actually and seriously asked of a very ignorant class of poor children by the clergyman of a large parish, in a school which he specially superintended? We devoutly hope not. We are full of sanguine hopes as to the progress of sound, practical, sensible education; and we trust, that in far less than twenty years' time such an example of utter ignorance of educational requirements for the poor will be so rare, that if exhumed and held up to the light, it would be deemed a fossil relic of mediæval teaching, confined to monastic days, when intelligence was illicit, and popular understandings were to be kept carefully benighted, knowledge being made unintelligible to the many, lest it should cease to be the privilege of the few. The writer of this paper has examined several hundreds of our schools for the poor, and has had rather unusually large means of knowing how religious knowledge is imparted to children of the middle and higher classes; and he has no scruple in saying, that to a very large proportion of the children no available religious instruction is imparted. The scriptural education is given exactly as any dry science would be taught,—by axioms and formulæ, together with chips and parings of history, and a due sprinkling of useless chronology. Parrots would be just as proficient, if they could only chatter enough. The Rev. Mr. Brookfield, H.M.'s Inspector for a large section of England, gives this specimen of the performance of scholars who had gone through the regular school-mill, pounded and crammed, as follows:

SCHOLAR NO. 1.-" My duty toads God is to bleed in him to fering, and to loaf withold your arts, withold my mine, withold my sold, and with my sernth to wirchp," &c. &c.

SCHOLAR No. 2 (by an "intelligent boy ")." They did promis and voal three things in my name, first, that I should pernounce of the devel and all his walks, pumps and valities of this wicked wold, and all the sinful larsts of the flesh," &c.

SCHOLAR No. 3.-" My dooty tords my nabers to love him as thyself, and to do to all men as I wed them shall do and to me-to love, onner, and suke my father and mother-to onner and bay the Queen, and that are pet in a forty under her-to smit myself to all gooness, teaches, sportial pastures, and marsters," &c. &c.

These are not merely verbal mispronunciations; they are exact copies of what was written down deliberately on slates. Mr. Brookfield makes some very sensible remarks on the matter. If these blunders were, he says, merely such as might occur by reading aloud with rapid utterance and foggy articulation, the evil would not lie very deep; but they are written errors, which nothing but entire non-apprehension of the meaning can account for. And he adds, that in all probability, had these boys repeated the same answers, vivâ voce, in a Midsummer examination, they might have carried off their spelter prize-medals for intelligence, good conduct, and general assiduity. Such is the humbug of rote teaching: and Mr. Brookfield well says of the Catechism, that "it is (most properly) required by our Church to be taught; but I do not consider that getting it off by sound fulfils the condition of teaching." Is it not monstrous that it is still necessary to repeat this palpable truth? He adds, and here is the gravamen of the evil, that he shall be prone to report the religious instruction in schools as satisfactory, when he "has the satisfaction" of the parochial clergyman's acquiescence in the verdict that it approximates to the prevailing standard! Nothing can justify this; nor can we agree that satisfaction ought to be comparative. It must be positive, and dissatisfaction also, or there is very little progressive improvement to be gained by inspection and its awards. But what shall we say of clergymen who issue these certificates, indorse these bills of health, and put their impress on counterfeit coin? This: that it is at the very root of the mischief! They, of all others, are bound to probe the religious teaching in their schools, and test whether it be a reality or a mockery. Let each priest or deacon who feels a doubt on the matter (and their doubts are prudential virtues on such a subject) go forthwith to their schools, and closely examine into the thing. Let them, discarding all rote answers, ply each child severally, especially the younger and lower-class children, with questions such as these How did Christ's death atone for sins? Would a man's death have done so? Why not? Explain atonement? Explain what is meant by a ransom for sin? Give Scripture proofs that grace is needful for salvation? Also that it is sufficient for salvation? What must we do to get the benefit of Christ's death? What is the meaning of the parable of the Ten Virgins? What does it teach us as to grace? What is meant by living waters? Prove that all may have it who will? What is the best proof of our love to God? What did Christ live for? What was the purpose of his example? How did he show us that we should forgive enemies? Whom did he forgive? Whom did he ask God to forgive? When and where? What parable teaches the same duty? What part of the Lord's Prayer? Who alone can forgive us our sins? What part of what Commandment teaches us to work hard on weekdays? Which teaches us to respect God's holy name? What part of the Lord's Prayer? What is meant by the words, "There is no health in us?" Give texts showing the frailty of human nature? Which