FOR

OR SALE, an excellent REFLECTING TELESCOPE, focal length 7 ft., aperture 7 inches, mounted so far Equatorially that with a little care it may be turned on a star or planet in the day-time.-Four Eye-pieces.-Price £20 only (less than the cost of the stand), the proprietor having mounted a larger instrument.

[11]F

TO BE SOLD, an excellent 8-in. SILVERED GLASS SPECU

tube: also a Flat Mirror. The Mirror will be sold cheap, the advertiser intending to set up a larger instrument. The Speculum will easily divide Zeta Cancri, and occasionally Gamma 2 Andromeda.-Apply to W. Matthews, Hill House, Gorleston, Yarmouth.

INSTRUMENTS, &c. WANTED.

Equatorial Stand Wanted-adapted for a 5 ft. Refractor, with graduated circles; second-hand, at a moderate price. [35] Monthly Notices of the Royal Astronomical Society. The third volume wanted: a good price will be given.

SILVERED GLASS SPECULA
OF THE PARABOLIC FORM,

Of all Apertures up to 13 inches.

[26]

Persons requiring these admirable Reflectors can be supplied at a moderate cost. Apply to Mr. F. BIRD, General Cemetery, Birmingham.

We can in no case insert communications from correspondents with whose names and addresses we are unacquainted.

E. Pieraggi. The paragraph as to the 'Spectrum Analysis of an Eclipse' will be found on p. 170, lines 9–15.

P. Vallance. The Bedford Catalogue has been long out of print. See Astronomical Register, vol. i. pp. 112, 123, 138, 151; vol. iii. p. 210.

W. G. Mackay. We beg to thank our correspondent for the information. Received. Adolph's 'Simplicity of the Creation.' Reddie's Current Physical Astronomy Critically Examined and Confuted.'

The Astronomical Register is intended to appear at the commencement of each month; the Subscription (including Postage) is fixed at Three Shillings per Quarter, payable in advance, by postage stamps or otherwise.

The pages of the Astronomical Register are open to all suitable communications: Letters, Articles for insertion, &c., must be sent to the Editor, Mr. S. GORTON, Samford Villa, Downs Road, Clapton, N.E., not later than the 15th of the month.

TO AMATEUR OBSERVERS.

We beg to direct special attention to the following invitation, given by the President of the Royal Astronomical Society to the Amateur Astronomers of Great Britain and Ireland, to send him a short account of their means of observation; and, in order that a somewhat methodical arrangement may be adopted by those of our readers who are practical observers, we forward to them a form with a few queries, so that points of interest in the instruments employed may not be omitted.

We trust that not only those who have fixed observatories and extensive means, but all who are in the habit of using instruments, however small, will respond to this intimation, which will tend in a particular manner to show the progress making by the science throughout the country. The Editor will be happy to hand to Mr. De la Rue any particulars forwarded to him by those who are not Fellows of the Royal Astronomical Society :—

"AMATEUR OBSERVERS.-Amateur astronomers of Great Britain and Ireland are invited to send to the President of the Royal Astronomical Society, Somerset House, a short account of their means of observation: for example, the nature of the instruments they possess, stating (in the case of telescopes) whether they are refractors or reflectors, their aperture, focal length, and form of mounting; also, whether the instruments are placed in observatories or used in the open air."

ASTRONOMICAL REGISTER: APPENDIX TO No. 35.

THE MOON CONTROVERSY.

TO THE EDITOR OF THE ASTRONOMICAL REGISTER.

Sir,-Anyone who will take the trouble of wading through the mass of correspondence which has taken place, even in your Register, upon the question of the Moon's Rotation, must feel how hopeless is the prospect of its being brought to a conclusion by any of the customary methods of treating it. He will see that almost the very same examples that are brought forward in proof of rotation are also brought forward in proof of non-rotation, and that each one fancies his own way of proving his case unanswerable and convincing ("Tu quoque," he will probably say). Most of the arguments and proofs

on either side are good so far as their premises support them; but they only leave the question in the old school-boy condition of "Yes, it is ""No, it isn't." Both sides admit all the actual facts, and from them, and them alone, draw directly opposite conclusions. On the one side it is said, "This is the moon's movement, and it is evidently revolution with rotation." On the other side it is said, "True -this is the moon's movement, but it is decidedly revolution without rotation." What, then, is to be done? Apparently nothing but to go, if possible, to the root of the matter at once, and compare the two descriptions of rotation and revolution, as given by the respective parties, and the grounds on which they base them. One, to whom the present controversy owes, I believe, its origin, laid it down as a law or axiom that "in axial rotation, all points in the circumference of the rotating body must successively intersect the radius vector.” This, however, would only apply to the case of a body revolving as well as rotating. To make the definition generally applicable, it should be differently worded, as thus: "In axial rotation, all points in the circumference of the rotating body must successively intersect' a line drawn from its centre to some given point. This would meet every case that can occur. Taking this, then, as a general definition of rotation, the two parties, from this as a starting point, at once branch off into interpretations widely separating from each other. The reforming party, as we may designate them, take some point at a finite distance; the conservative, some point at an infinite distance. Were the question simply of rotation without revolution, this would be a distinction without a difference, as the direction of the given point in either case would be unchanging, and the measure of one rotation the same, viz. 360°; but the question being of rotation with revolution, an essential difference immediately arises, for the finite line is continually changing its direction, while that of the infinite line, on the contrary, remains unchanged. The result is, that, under the conservative interpretation, any point in the circumference of the rotating body, in turning once round, or making one rotation, will have described exactly 360° in every case; while, under that of the reformers, it will have described either something more or something less than 360°, according to the direction of its movement in revolution; and that while the conservative rule requires one only point of reference, and in an unchanging direction, for all cases that can occur, without exception, the reforming rule requires an especial point at a different distance, and in a differently changing direction, for each case individually.

But one of the most distinguished and persevering of the reforming party has recently written: "The Moon controversy may be resolved into the question-Whether parallel motion in a circle is a single or a double movement." Now, this, although the principle involved is the same, puts the question upon a somewhat different and more hopeful footing. It can hardly be called a correct statement of the case, but it is a very near approach to it. He then adds: "The mathematicians assume that it is a single movement, but we prove that it is a compound one." This, however, is going a little too far. Whether "mathematicians" do or do not assume thus much, it is not for me to say: I can only answer for myself, that I do not; but

this I maintain, that parallel motion in a circle is a less compound movement than that which presents always the same face towards the centre of revolution, for reasons which I now proceed to give; and to this end must compare the descriptions and modes of action of the forces which cause, on the one hand, rotation; on the other, revolution.

One single force cannot, of itself, cause a body simply to rotate. If applied centrally, it will give it only a progressive.movement; if tangentially, it will give it a rocking motion in addition to progressive movement. To produce rotation only, there must be an equal force acting tangentially on the opposite side and in the opposite direction; or, which is the same thing, a reaction of the same force on the opposite side, by means of the body itself as a lever, on the centre as a fulcrum. Here, then, we have simple rotation, in which the opposite sides of the body turn round in opposite directions, describing circles exactly equal to the circumference of the body rotating; the body changing its angular position, but not changing its place. Secondly: one single force, of itself, cannot cause revolution; there must be at least two: one moving, the other controlling; commonly called centrifugal and centripetal-the one which would cause the body, if otherwise uninterrupted, to move continually in a right line; the other merely diverting the body from its rectilinear path, and retaining it within a certain distance of the centre of revolution. The moving force being applied once for all on the body as a whole, communicates one and the same velocity to all the several parts. The controlling force acting on the body as a whole, and in the direction of the line joining the centre of the body with the centre of revolution, or at right angles to its path, cannot, in any way, either increase or diminish the velocity, whether of the body as a whole, or of any of its parts individually. As all parts, therefore, of the revolving body move with the same velocity as its central point, they describe equal circles. Here, then, we have parallel motion in a circle, the body changing its place, but not changing its angular position. Thirdly: let the body, describing with its centre the same circle with the same velocity, so far change its angular position as to present always the same point towards the centre of revolution. Immediately we see that the outer side describes a larger circle or longer path, and the inner side a smaller circle or shorter path than it did before; the portion added to the one and taken away from the other being each exactly equal to the circumference of the revolving body. The velocity, and consequently the force required to produce it, of the outer side, are proportionally increased, and those of the inner side in the same degree diminished. Now, these differences in the lengths of path, in the velocities, and in the moving forces of the opposite sides of the revolving body, caused by this change of movement, are exactly equal to the actual lengths of path, velocities, and forces of the opposite sides of the body when it simply rotates. Hence that motion by which a body revolving presents always the same point towards the centre of revolution is, in its composition, exactly equal to the force of the two other motions—namely, parallel motion in a circle, and simple rotation; or, in other words, that motion which exhibits change of place with change of angular position, and the forces which

cause it, are exact combinations of those of the other two-namely, that which exhibits change of angular position without change of place, and that which exhibits change of place without change of angular position.

To put it in another way. Let a body revolve round a given centre describing with its central point a circle whose circumference may be represented by L, in a given time T. Let V represent its velocity, Fits moving force. Then, in the case of parallel motion in a circle, since L and T are the same for all its parts, V and F are necessarily the same also.

Let the same body, the centre remaining at rest, rotate in the same time T. Then, if 7 equal the circumference of the body, +,+v, ±ƒ, may be taken to represent the lengths of path described, the velocities, and the moving forces of the opposite sides respectively.

Next, let the body describing with its central point the same circle as before, in the same time T, revolve in such manner as to present always the same point towards the centre of revolution. Then, since the opposite sides describe the same lengths of path as before, the circumference of the body itself, therefore the lengths of path become respectively L +1, their velocities Vv, and, consequently, their moving forces F+f. Hence, also, it appears that in this case the spaces described, the velocities acquired, and the forces employed, are exactly equal to those required for parallel motion in a circle +those required in simple rotation.

We are now, therefore, in a position to compare the respective merits of the two theories. The conservative rule requires the less number of forces to produce the motion which they call revolution without rotation, and the greater number for that which they call revolution with rotation. The reforming rule reverses the case, requiring the greater number of forces for that motion which they call revolution without rotation, and the less number for that which they call revolution with rotation. Now, there does seem certainly something rather paradoxical in the reformers' rule; and there must be, one would think, some grievous misapprehension, on their part, of the true character of the two distinct motions of revolution and rotation. I will endeavour to show how this may have arisen. They have themselves partly suggested the cause, by calling the conservative view the "mathematical one. They themselves, on the contrary, have treated it too mechanically. The mathematical view looks chiefly to the causes, and from them describes the consequent effects. The other view looks chiefly to certain movements, and from them draws the description, ignoring, to a great extent, the forces which produce them. Mathematically, all forces are free to act, and their effects calculated accordingly; mechanically, on the contrary, many of them are prevented acting, or are insensibly engaged in overcoming the resistance caused by rigid connection. Mathematically, all forces acting must be strictly taken into calculation, in order to account for effects produced; mechanically, on the contrary, compulsory and transmitted action so far supplies the place of true forces as to cause them to be overlooked or wrongly assigned. And herein, I take it, lies the chief reason of failure in all experimental and mechanical illustrations. Mathematically, a body once started in a right line