ing 20 or 30 degrees from it, thus giving a tendency to deviate to one side of the correct plane of its range.

The steadiness with which these shots preserved their longer axes in the line of flight, so as always to keep their solid end in front, suggested, as has been already stated, that this principle might be made available for exploding bombshells on their striking the object they fall upon, by placing an exploding-cap on a metallic spindle in the line of the axis of the shell, and retained in that position by a firm spiral spring, that would not permit the momentum of the spindle to drive the cap home for explosion, unless the shell were going with greater velocity than its fall by accident from any ship's deck, or the height of any ordinary building, would generate. The requisite strength of these springs, to be subjected to the test of falling from this given height in such a manner as to ensure their perpendicular action without exploding their caps, before they are certifiled to be fit for use,

A drawing of a 9-inch shell on this principle, with all the requisite strength of parts, so far as calculation might aid a first experiment, was sent by me to a scientific friend, who ultimately placed it in the hands of the Master-general of the Ordnance; and the select committee at the office of the grand depôt, Woolwich, were obliging enough to invite me to their meeting on the 5th of November, 1841, further to explain this shell; but I was in Yorkshire at the time, which prevented my attending it. The use of a mortar and powder was obligingly offered, if I would furnish the shells; but I declined entering upon a troublesome and expensive range of experiments in which I had no more personal interest than any other Englishman in preventing foreigners from possessing more efficient instruments of war than ourselves. It was offered merely as a suggestion, warranted by experiment, and so it still remains. The forms of all the shots here described were also sent to the select committee, as the steps which led to this result.

I shall close this communication by observing, that although there is a striking similarity of form between the shot H, fig. 4, and the sugar-loaf shot used in the rifle by the Messrs. Lancaster, yet there is an essential difference in their modes of action. In the rifle-shot the rotation

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on its axis is communicated in the gun; hence, even if the hinder portion of the shot be the heaviest, yet the front part will preserve its lead, and hence it may be made considerably heavier than a round shot filling the same bore; and if the same velocity be communicated to it, from its greater momentum and elongated form, it will take a much more extended range, its resistance being diminished and its power to overcome resistance increased.

To enable the pear-shaped shot H, fired from an ordinary gun, to preserve its axis in the line of its flight, its hinder portion is made hollow: the whole weight is the same as the round shot, and, though it obtains the precision of a rifle by its spinning through the air, yet its resistance is only diminished by meeting it more obliquely on the sides of the conical part than on the more obtuse face of the round shot: hence, though the range is in some measure increased, that increase is by no means in the same ratio as that of the solid elongated rifle-shot.

It should, however, be observed, that it will require a greater charge of powder to give an equal velocity to these more weighty shots, and to have guns made proportionably stronger. Sugar-loafed leaden shots, with rifled cannon, may, no doubt, be made greatly to exceed in range any of our present shot, but the cost would be considerably increased: this, however, may be no object on some particular occasions, and to lessen it, the main parts of the shots might be made of cast-iron, and only a groove round the part that fits the bore filled with lead, so as to take the threads of the rifle.

At the time the hollow shots were thought of, the idea was limited to what could be attempted with guns of the ordinary strength; and hence their weight was limited to that of the round shot; but the elongated-rifle shot will require guns adapted to their weight; and if the plain-bored guns were likewise made proportionally stronger, then by increasing the weight of these hollow shots in their solid part in front, more secure steerage would be obtained, and with equal initial velocities their range would probably much exceed that of the round shot.

The hollow shots might be taken advantage of to convey combustible materials and fire when required, especially the one represented at fig. 3; and they

show at least some approximation to the best form of a shot that can be used from the ordinary gun.

Fig. 5 shows, in full size, the construction of a spring explosion bolt for a bomb-shell, to be screwed into the hinder part of it in the line of its longer axis. A is the bolt, firmly restrained from moving by the spring B; C is a nipple on which a copper cap of good size can be placed, and firmly secured by pinching down the top into a groove, and wrapping it with fine copper wire. A piece of parchment may also be tied over the touch-hole of the nipple, the better to secure it from getting clogged or rusted up.

Should it be found that the weight of the charge rendered the steerage of such shells uncertain, probably a couple of yards of rope, coiled as wadding behind the shot, and fastened to a ring at D, might complete the steerage.

G. CAYLEY.

20, Hertford-street, June 26, 1846.

INSOLUBILITY OF CARBONATE OF NICKEL IN STRONG ACIDS.

Sir,-Wishing to prepare some salts of nickel, I purchased some carbonate of various eminent operative chemists of undeniable scientific acquirements; but to my mortification I found it impossible to form a perfect solution, not even on boiling the mixture for hours together. The strong acetic acid exerted no more action on it, than water would do on sand or pebbles. The sulphuric, nitric, and muriatic acids each became slightly tinged green, but nothing like a decided formation of a sulphate, nitrate, or muriate did occur, the carbonate always settling to the bottom of the vessel, like fine sand.

It has never been recorded in the annals of chemical science that the carbonate of nickel requires to be recently precipitated, and still moist, to dissolve in acids; so that, if the young chemist prepares it under the conviction that he can put it to any use, at any time, he will find himself, as I have been, most grievously mistaken. In fact, oxides with this unexplained peculiarity ought always to be preserved in a moist state, and used as speedily after making as possible, else they will turn out to be utterly useless for anything but blowpipe experiments or fusions. Yours truly,

E. V. HART.

YOUNG'S THREE LECTURES ON THE ADVANTAGES OF MATHEMATICAL STUDY.* On merely looking at the title-page and preface of this little book, it might be thought to be too limited in its nature and objects to attract the attention of the great body of readers, or to repay them for its perusal. Such an opinion would, however, be erroneous; the work abounds in sound instruction, rendered delightful by appropriate language and copious illustration; and the value which cannot but be attributed to its contents by the generality of thinking persons, justifies us in regarding a notice of it as within the legitimate scope of this Magazine.

It was for the most part to theological students that the Lectures were addressed, and it is scarcely possible, nor, indeed, would it be proper, to omit considering them in this point of view. We present, therefore, our readers with the following extract from the work, without comment, merely premising, that, in the observations preceding it, the Professor has, after showing the importance and utility of the mathematical sciences, and giving results of a highly interesting nature, made a happy transition to the moral world. He then proceeds in the following eloquent strain:

"Newton, indeed, was too well accustomed to reason from analogy to suppose that his Creator would lift the veil from the face of nature, and so largely unfold to him the laws by which He governs the material universe, and yet leave him in the dark respecting all that concerned the moral go. vernment of himself; or that he should be gifted with light to perceive the mystic links which connect this dark and distant earth with the glorious source of light and heat, and yet be furnished with no ray to reveal to him the connection between the eternal purposes of God, and the immortal destiny of his own soul.

"As connected with these remarks, it may not be out of place to advert here to the fact, that some persons, but imperfectly versed in scientific subjects, have fancied that they have discovered, in the inspired writings, statements which directly militate against the conclusions of modern astrono

* Three Lectures, addressed to the students of Belfast College, on some of the advantages of mathematical study, to which is added An Examination of Hume's argument against miracles; by J. R. Young, professor of mathematics. London: Souter and Law; Greer, Belfast; and Milliken, Dublin

my. Thus, they point to the earth's standing still, and justly argue that if such an event had ever occurred, the earth must necessarily have been drawn into the sun, and have been incorporated with its mass, provided the Newtonian law of attraction existed. But surely He who had power to put that law in action has also power to suspend it. There was not, however, any occasion for the exercise of such power; the event might have been effected, and no doubt was effected by much simpler means, without the slightest interference with existing laws; for it must be recollected that the miracle consisted in arresting the apparent diurnal motion of the sun, or of prolonging his apparent presence above the horizon. Now, it is well known that when rays from any luminous body enter a dense medium, they are bent downwards, or so as to proceed in a direction more nearly perpendicular to the surface of the medium after they enter it than they did before; an eye, therefore, situated within this medium, and receiving the bent rays, will refer the luminous body to a place above its real situation, and the greater the density of the medium is, the greater will be the distance between the true and apparent place of the body.

"It is this refraction, as it is called, which causes the sun, whose rays, upon entering our dense atmosphere, are bent downwards, always to appear higher than he really is; so that we see him in fact long after he has sunk below the horizon. To cause the sun, therefore, to appear stationary while he is actually descending, nothing more would be necessary than to gradually increase the density of the atmosphere, which, by bending the rays more and more, would keep the sun's apparent place stationary, and thus prolong the day. A still further increase in the density of the atmosphere would cause the sun to appear to retrograde, and, as in the case of the dial of Ahaz, the shadow of an object would go backward. These events unquestionably imply a special exercise of Almighty power, but certainly no suspension of a law of nature."

With equal ability is this part of the subject treated in the second lecture, where Professor Young rescues the mathematical sciences from the charge of rendering the mind unfit for the reception of Divine truth; and, in the third lecture, we would recommend as particularly worthy of attention, the ideas suggested to him by the consideration of imaginary quantities. We regret that want of space will not allow of our giving further extracts from those parts of the

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work which bear more immediately on theology; but, as may be inferred from the above, while they teem with philosophic views, they in no degree breath a rationalistic spirit. It is the more necessary to make this remark, inasmuch as there are those of all creeds and sects-nay, even among that class of persons supposed in all persuasions to be more especially devoted to questions of this sort-who (some from motives, possibly, of honest bigotry, others again from a desire to avoid having their indolence tasked or their competency tested) discourage all arguments of this description, and even go the length of questioning the faith or the orthodoxy of both the parties engaged in them. But let us hope that that school of divinity is rapidly declining which, in questions that are the subjects of legitimate controversy, substitutes anathema for argument, and abuse for refutation. Who that peruses the work of Mr. Babbage, or the little volume now before us, can help experiencing a feeling of melancholy when he reflects on the contrast between the defence of Divine truth as conducted by the man of science, and as it has too often been carried on by the minister of religion?

In the following extract, Mr. Young vindicates the claim of the mathematics to a high place among the sciences, on the ground of practical utility, and, we think it will be admitted, successfully:

"It is not uncommon to hear people say; 'Acquaintance with the principles of geometry and mensuration, and with so much mathematical analysis as may be required in the ordinary routine of practical affairs, may be all very necessary for professional men; but where is the use, even to them, of pushing these inquiries so far, and of occupying so much time with subjects which, after all, are little else than matters of barren speculation.' Before replying to this objection, I would first inquire which of the numerous applications of mathematical science to practical affairs did not at one time appear to be but matter of barren speculation? The conical pendulum of Huygens was certainly little better than a subject of barren speculation to him; but when, in the succeeding age, it was applied by Watt as a governor to the steam-engine, it proved to be one of the most efficient contrivances for equalizing the supply of steam that could

possibly have been devised. The remarkable theorem of the Flemish mathematician, Albert Girard, technically known by the name of the Theorem for the spherical excess, was certainly to him, and no doubt to thousands of others, a matter of barren speculation. It was, however, after the lapse of 150 years, at length called from its repose among speculative truths by General Roy, at the suggestion of the late Professor Dalby, of Sandhurst, and successfully applied by him, during the great trigonometrical survey, to abridge certain laborious computations which occurred in reducing the observations.

"And what were the researches of the ancients, respecting the conic sections, but barren speculations to them and to many succeeding ages? The properties of the ellipse and parabola were as well known in the days of Apollonius as in the time of Kepler and Newton, yet it was not discovered till then that these hitherto unappropriated properties were necessary to the true explication of the celestial motions.

"It was by contemplating a certain problem which appeared to be but a barren speculation, and to offer no reward except the gratification of solving it, that Descartes was led to the discovery of his beautiful system of analytical geometry, one of the most useful inventions of modern times, to which the continental mathematicians are much indebted for their recent rapid progress in mathematics and mechanical philosophy. Our celebrated countryman, Dr. Brook Taylor, to whom we owe the remarkable theorem which bears his name-Taylor's Theorem-little suspected the practical importance of that theorem when engaged in its investigation; and, indeed, it was by British mathematicians generally regarded for upwards of half a century as little more than a barren speculation. But upon this very theorem, so long neglected in the land of its birth, the French mathematicians have founded a most extensive body of science, as full of valuable applications as of beautiful theories.

"These few instances may serve to show that mathematical inquiries, even as regard their practical application, should not be condemned as useless, merely because the state of our practical science is such that they do not find their immediate application. What to one age may appear but barren speculation, may to the next furnish information of the highest practical importance.'

Admirable as is the style and matter of these lectures, there is, nevertheless, one point as to which we feel bound to express our dissent from, or rather perhaps to sug

gest an implied limitation to the views of the learned author. At pp. 32, 33, in speaking of the experimental processes by which Ferguson convinced himself of certain geometrical truths, the professor says:

"Those who receive the doctrines of arithmetic upon the same kind of partial experimental proof, are in the same predicament; their knowledge is always uncertain and insecure; and, in acquiring this imperfect knowledge, they acquire at the same time a habit likely, as in the case of Ferguson, to indispose the mind to the pursuit of truths by the more slow but more certain path of logical deduction. When properly taught, the study of arithmetic forms an excellent preparative to that of algebra and geometry; that is, when its theoretical principles are conveyed as well as their practical application, when the rule is shown to harmonize with the reason, and when the judgment and reflection are called into exercise as well as the memory.'

Were it practicable, there can be no doubt of its being desirable to convey in all cases the reason and the result simultaneously. That the professor has found it practicable among the class of students with whom he has to deal at Belfast College, can be as little doubted. But the methods to be pursued must, as it appears to us, be modified according to the age of the persons instructed. In the case of students of an advanced order, we may safely presume that the judgment is sufficiently developed to enable them to see the reason of rules which it may be, nevertheless, desirable to commit to memory. But is the reason always obvious and intelligible in proportion to the simplicity and practical utility of the rule? Take, for want of a better instance, the method of proving the correctness of operations in the four fundamental rules of arithmetic by casting out the nines. So long as the memory is more easily impressed than the judgment, ought we not to administer the draught of knowledge by that inlet,—not to the exclusion of the other, but bearing in mind the importance of storing the former faculty while the mind is young and plastic? It is the total exclusion of reflection and judgment which has heretofore prevailed, (which Mr. Young very properly animadverts upon in the paragraph following,) that

called forth the remarks last quoted; and, possibly, in those which we have just made, we are only setting out those limitations which the acute and experienced author would himself impose. We cannot conclude without recommending the notes which are appended to the lectures to the reader's attention, and also the list of works at the end.

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THE NEW THEORY OF THE PRISMATIC COLOURS."

Sir,-Your correspondent, in p. 510, vol. 44, considers that in my last communication I have done "J. M.," of Battersea, injustice. I suppose that no one else will think so.

If it is intended to assert that different rays are impressed with different velocities at the origin of light, the paragraphs marked 2nd, 3rd, 4th, 5th in my last communication must be refuted.

If we are to suppose that light has different velocities at distances from the origin of light, we must have before us reason to believe that there acts upon light some extraneous force.

I can hardly imagine that "J. N." does not perceive that, according to the received theory, the different colours are produced by a difference in velocity of a disturbance perpendicular to the direction of a ray; while by that of "J. M.," of Battersea, the same effect is supposed to be produced by a difference of velocities in the direction of the ray.

To prevent confusion I shall subscribe myself J. M'G.

Trinity College, Cambridge.

NOTES AND NOTICES.

Miniature Statuary. - During a recent visit in Boston we were shown specimens of the production of a wonderful piece of mechanism, which were, indeed, truly astonishing. They were miniature busts of Daniel Webster, Abbot Lawrence, and Levi Woodbury; being perfect fac-similes of their distinguished originals, and wrought out of beautiful American marble, and by a machine which has been invented by Mr. Thomas Blanchard, of Boston. This inven tion certainly establishes a new era in the art of sculpture, and promises to dispense, almost entirely, with the deep thought, and classic study, and indefatigable labour of the artist, in his efforts to put life and poetry into the marble; for nature, art, every thing tangible, can be copied by this machine, with a precision which defies the chisel, even when guided by the most skilful band and directed by the most gifted talent. The machine, too, can be graduated so as to give reduced copies of any statuary, which

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shall, in their miniature, be perfect and exact copies of the originals in everything else but the size; preserving every line, furrow, and dimple, and giving prominence to muscles and veins, and every particular lineament and feature, in exact proportion. By the same machinery the most correct and perfect bas-relief profile likenesses may be cut, on the hardest material, and of any size required, from half an inch to full lifelike size. We saw a strikingly exact cameo profile of Henry Clay, as perfect a head of that statesman as we have ever seen in any of the busts or casts to be found, and of the fashionable size for a lady's breast-pin. Among the specimens shown us, too, were the heads of several of our acquaintances, cut in cameo and ivory, the proper size for setting in pins, the first glimpse of which called before our minds the originals as readily as the most perfect daguerreotype or pencilled miniature would have done. We are assured that the best of Greenough's and Persico's productions, which have cost them years of study and effort, can be copied by this apparatus with most positive accuracy; and the block of shapeless marble put into its power will, in a few hours, stand forth a perfect copy of the most beautiful and animated statuary the greatest sculptors ever produced. And, what is most wonderful, this machinery may be readily graduated to increase or diminish the copy, so as to furnish a colossal or a miniature figure, with equal precision, and in all respects exact proportions.-American paper.

American Patents.-It appears from the last annual report of the American Commissioner of Patents that the number of patents applied for in 1845 was 1246, and number issued 502, making the total number of patents granted by the United States since the establishment of their independence up to January of the present year 14,526.

The Electric Telegraph in America.The Americans appear to be going rather ahead of us in this branch of enterprise. Washington, New York, Boston, and Baltimore all now communicate with one another by electric currents. The New York Sun gives the following account of some very extraordinary phenomena connected with this system of communication, which occurred on the New York and Baltimore branch :-"Three thunder storms, each some thirty or sixty miles from the other, were all coming east on the telegraph route about the same time, and every discharge of electricity from either was fully recorded by the lightning itself in the telegraph-office at Jersey city, Philadelphia, Wilmington, or Baltimore. The wire became altogether unmanageable, and the operators being obliged to withdraw the batteries used for writing,