THE MOON DOES ROTATE ON HER OWN AXIS.

EFINITION.-"Rotation is the motion of the different parts of a body about an axis called the axis of rotation." Thus it is defined by Barlow, and similarly by Grier and others, in their dictionaries and works on mechanics.

Let S represent the sun, (fig. 1.) with unity as a semi-axis major s as a focus, and 0.0168 as eccentricity, describe the arc 1, 2, 3, &c., of an ellipse, which let be divided into parts, each equal to 29·1 degrees, by the points 1, 2, 3, &c. These will represent, very nearly, the positions of the moon's centre at intervals of 29-53 days. Select two points on the moon's surface, at opposite extremities of a diameter, for instance the point known by the name Insulasinus Medii, and the point O. Let these be represented by I and O, on the circumference of the small circles representing a section of the moon. Let the points 1, 2, 3, &c., be those occupied by the moon's centre when she is said to be full moon, and we know, from observation, that then the point I is nearly in the line between O and S. Similarly we know that when the moon's centre occupies the positions a, b, c, &c., about midway between the points 1, 2, 3, &c., the point is in the line between I and S. Consequently the diameter I O rotates about an axis passing through the section at right angles, or nearly so, to the plane of that section. Similarly every diameter of the section rotates, and as the same reasoning applies to every section parallel to the one here considered, it follows that the moon does rotate on her own axis, for by the definition, "Rotation is the motion of the different parts of a body about an axis, called the axis of rotation."

Thus, in so far as the definition requires us to show the satisfying of conditions, the proof is complete, but, like all or most definitions of scientific terms given in dictionaries and popular treatises, it is imperfect, quite true, so far as it goes, but incomplete. To render it sufficiently comprehensive for this inquiry, there ought to be added the words, the motion of the parts being continuous in the same direction, through at least 360 degrees, or words of similar import; otherwise an oscillatory rotation through half a circle backwards and forwards, would satisfy the conditions of the definition. Let these conditions, then, be added to the original definition, and we now show that these also are satisfied by the moon.

Let the adjacent circle (fig. 2) represent that hemisphere of the moon of which the point I is known to be near the centre; and we know from observations that certain known points, here represented by 1, 2, 1, 4, 5, are successively turned towards S, the sun, and also from S, in the same order as they are here set down. Now as this could not be with an Oscillatory motion, it follows that the moon's rotation is complete, continuous, and in all respects similar to the rotation of other heavenly bodies. It differs from them in nothing but velocity, and so does each body differ in this respect from all the rest. Thus, the number of times that each rotates during one of its own revolutions around S we find to be as follow:Saturn 24,619, Jupiter 10,479, Mars 669, the Earth 366, Venus 230, Mercury 87, and the Moon 13. It is quite true that the moon does not coincide all round, with the ellipse 1, 2, 3, &c. It crosses it twice every 29.1 days, but as it never departs from it more than the oth part of S a it is quite unnecessary to let this consideration complicate the question.

The path of the moon is nowhere convex towards S, and its motion is always direct. Its velocity along, or near to, the ellipse varies slightly, having a maximum and minimum value every 29.1 days, but its motion is never retrograde. To assist such persons as are but little accustomed to consider large numbers and small ratios, I have projected so much of the moon's path as she describes during one lunation, as truly as it can be drawn, and I have found the study of it contribute more to clearness of ideas than any amount of popular illustrations. See figure 3. The firm line represents the moon's path, projected on the plane of the ecliptic, and the dotted line the ellipse described by the earth. These two bodies move onwards continuously, the earth moving nearly uniformly, while the moon changes her velocity, and is at one time a little before, and again a little behind the earth, but never more distant from it than the distance between the two curves (the 4 of an inch in the projection), while the centre of the curve (S in our first figure) is 10 inches distant. By considering the points 1, a, and 2, in figure 1, to be the same as 1, a, and 2 in this, and that at these points the sun, moon, and earth are in line, the clearest possible ideas will probably be obtained of the relative positions of these bodies, and the difficulty of perceiving the analogy between the rotation of the moon and the rotation of other heavenly bodies will at once disappear.

With respect to the proposition that the sidereal day is the measure of the earth's rotation, we ought to agree, in the first place, in respect to some definition of the term measure. Mathematicians generally, I believe universally, use it thus. If A vary directly, or inversely, as B, B is said to be a measure of A. Now we know that the two quantities, the velocity of the earth's rotation, and the duration of a sidereal day, vary inversely as each other; that is, were the velocity of the earth's rotation to become double, or half, of its present value, the sidereal day would become half, or double, of its present duration. This must be true, whatever may be the velocity of revolution, and therefore the latter is a measure of the former. But it will not follow that the solar day is a measure of the earth's rotation, for let the velocity of rotation and that of revolution become equal, and the solar day would become infinite in duration, hence the propriety of selecting the sidereal day as the measure of the earth's rotation.

Again, if we use Barlow's definition, "Measure denotes any certain quantity assumed as unity with which other homogeneous quantities are compared,' we find ourselves at liberty, from the words "any certain quantity," to use either solar, sidereal, or any certain quantity as the measure we seek; but such definitions were, in short, never framed to serve the purpose for which we require definitions, to settle disputed questions.

Southampton,

14th January, 1857.

J. STEEL.

HOW TO WRITE ENGLISH.-No. 2.

COME specimens of style-and some very different ones in all respects were given in my last article, which was of course designed as an introductory one to the whole subject, and was therefore rather discursive: most readable papers are so. It would be very easy to methodise this series of articles, by means of the usual process of classification, and divisions and sub-divisions. This is the mechanism of treatises; and it has its uses, greater or less, according to the subject matter. It, however, rarely conduces to the interest of the reader. Now this subject of How to write English does not seem to me to require classification much. I am doubtful whether a disregard of it altogether may not aid my object, and impress what I wish to say 'more strongly and lastingly on the reader's mind. If so, it will chime with the general aim of those who now govern and support this JOURNAL; namely, that of bringing down knowledge to the level of ordinary apprehension, and as far as possible adapting it to popular taste. Nothing is so injurious to education as distasteful modes of imparting it; nothing so helpful to ignorance as the untoward vehicles of knowledge. By the set phraseology and stiff didactic wisdom in even sensible educational essays and articles and books which abound just now, and always have abounded, more or less, since teaching came into fashion, it happens that much knowledge escapes men, which, if more pleasantly strewn before them, they would more readily take. A vast deal of information is also wasted by the diffuseness of books, and their much verbiage, as well as prolixity of exposition and manifold repetitions; so that Lord Bacon's advice is far more to be followed now than even in his own time, when writers wrote more tersely, and were not, as now, paid for the quantity they enabled the publisher to make the public buy. "Some books," said Bacon, "are to be tasted, others to be swallowed, and some few to be chewed and digested." Very few are worth this latter process now-a-days certainly. The multiplication of books is an evil as well as a benefit. As no one can, even on a given subject, read all books, a skimming of them ensues, which often grows into a bad habit of superficial reading.

Before citing more specimens of style in later times, I would fain supply an early one that I accidentally before omitted. It is that of Chaucer's prose. Now though Chaucer was truly a poet, he was also a great pattern of style. And that was the reason why he was and is, after nearly four centuries, so eminently famed as a poet. His descriptions are so admirably terse, truthful, and life-like. He dealt out his vivid impressions of what he saw or heard in such simple and vigorous words, and in sentences so Saxon in mould and expression, that it is no wonder he won the English heart and taste of his times. It was his triumph to raise the mother tongue out of the disesteem into which the Conquest cast it, with its long lived sequel of foreign fashions. By making the rugged national language the vehicle (as has been well said) of his graphic and minute descriptions, his playful fancies, his tender and kindly thoughts, Chaucer not only

I think it probable that this word is not in Todd's Johnson; I cannot tell and do not care. I and some more writers intend to use a few new words; if they signify their meaning plainly, and are otherwise useful and needful, good grammarians will forgive and peradventure assist their adoption.

struggled successfully with and greatly improved the elements of a tough half-formed language, but he enshrined its best parts and handed them down to become, as they now are, the strongest materials of our modern English, and the back-bone of its frame-work. He laid the basis of a national literature. A little modernised, here is an extract of his descriptive prologue to the Canterbury Tales:--

There was also in our company a nun, a Prioress called Madame Eglantine, a demure and simply smiling lady, whose sharpest speech was "By Saint Eloy !" She could chant by heart the whole of the divine service, sweetly twanging it through her nose. She was mistress of the French language, as it is spoken at the school of Stratford-leBow; but the French of Paris was to her unknown. Her conduct at meals was precisely well-bred and delicate, all her anxiety being to display a courteous and stately deportment, and to be regarded in return with esteem and reverence. So charitable and piteous was her nature, that a dead or bleeding mouse in a trap would wring her heart. She kept several little dogs, which were pampered on roast meat, milk, and the finest bread. Bitterly would she take on if one were ill-used or dead; in short, she was all conscience and tender heart.

To speak of her features, her nose was long but well shaped, her eyes light and grey as glass, her mouth delicately small, soft and red, and her forehead fair and broad. For dress she wore a neatly made cloak and a carefully crimped neckerchief: on her arms a pair of beads of small coral, garnished with green, from which depended a handsome gold brooch, with a great A engraved upon it, and underneath the motto-"Amor vincit omnia."

Here is another picture :

A sergeant at law, cautious and shrewd, who had often been at consultation, was there also. A prudent and deferential man; he had been frequently appointed justice of assize, by patent and commission. Many were the fees and robes with which he had been presented, on account of his great legal knowledge and renown. There was no purchaser like him, and his dealings were above suspicion. He was the busiest of men, and yet he seemed more busy than he was. He had at his fingers' ends all the terms, cases, and judgments from the time of the Conquest, and in his indictments the man was clever that could detect a flaw; he knew all the statutes by heart. He rode in a plain coat of mixed cloth, fastened with a narrow striped silken girdle.

A country gentleman, commonly called a Franklin, was in our company. He had a fresh coloured rosy face, and a beard as white as a daisy. A sop in wine was his favourite morning beverage; for he was a true son of Epicurus, believing that the most perfect happiness consisted in perfect enjoyments. He possessed a noble mansion, and was the most hospitable of entertainers. He dined at quality hours-always after one o'clock, and so plenteously stored was his table that his house may be said to have snowed meat and drink, fish, flesh, and fowl; and of these the daintiest. His suppers were furnished according to the season. Many a fat partridge had he in his preserve; and stewed bream or pike was a common dish at his board. Ill befell his cook if the sauce were too pungent, or the dinner not punctually served. He kept open house, and the dining table in hall remained covered the whole day.

He had been at several times justice of the peace, sheriff, steward of the hundred court, and knight of the shire. Among all the country gentlemen round there was not his compeer. At his girdle, which was as white as morning milk, hung a dagger and a silken purse."

There is scarcely a living writer, after all the fresh light and experience of the intervening ages who could paint portraits so perfect or vivid as these in as few words. The force of this style is derived from its extreme simplicity. If there were the least effort for effect, the smallest search for fine expressing or ornament in figure or phrase, the virtue of this writing and its point and nerve would be seriously damaged. The power of this simplicity of style is wonderfully great; few ever achieve it. Even Cobbett, who was among the greatest of English classics who ever wrote, sometimes erred in using too many expletives. He fell into this mistake, perhaps, by passion. He so frequently wrote abusively and dealt