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Notices of Books.

LETTERS TO YOUNG PEOPLE. BY THE LATE W. A. SHIRLEY, D.D., BISHOP OF SODOR AND MAN.

Pp. 164. (London: Hatchard.

1850.) WHILST We approve of the object of this little volume, we hardly think that the letters contained in it are such as to justify publication. It is certainly desirable for parents, and others interested in the welfare of young persons when temporarily absent, to cultivate an epistolary intercourse with them; since it may often be so managed as to be made a very powerful instrument in the formation of character. But the effect thus produced will generally arise rather from the individual character and personal influence of the writer than from anything peculiarly striking in the letters. The effective parts of the letters will generally consist of seasonable, though perhaps apparently slight, allusions to past events or future prospects, of great interest to those to whom they are directly addressed, but often barely intelligible to others. Few persons can write letters which will bear publication; and still fewer do write such letters to their children, or to young persons under their care; or such as, if practically useful to them, would be so also to strangers. And this, we think, is as true of these letters of Bishop Shirley as of those of most ordinary letter writers. To those who were acquainted with the amiable character and superior abilities of the bishop, it must be interesting to observe in these letters the affectionate care and pains which he bestowed upon his children, even in their earliest years; how he wrote to his little boy in printing characters, that the child might be able to read the letter himself, and write one like it; and how he entered into all the details of the amusements of his little folks. It may, too, perhaps be well that parents generally should know that persons of very superior attainments are not above such acts as these, but consider them of so much importance as to make a point of not neglecting them, even when fully engaged with weighty matters of professional duty. Still it seems hardly fair to publish letters of this description when written by such a man as Bishop Shirley, unless they are somewhat superior of their kind, which we think these letters can scarcely claim to be. They evidently proceed from the pen of a pious and affectionate parent, and of an honest and practical adviser; but there is little else remarkable in them. We give however two extracts, which contain advice that may be of general service, and are favourable specimens. The first is addressed to a boy at school, on the subject of receiving the holy communion; the other is a reply to a youthful correspondent who had written slightingly of repetition as a school exercise:

LETTER XXXVI.

"I hardly know what to say about the Sacrament. You have had my general advice on the subject; but I consider your present state (would that I had reason to believe it was past!) of idleness a state of sin. Your work may have been hard, perhaps rather too hard for you; but is there the least ground for thinking that you did your best? if not, you have been living in a state of sin; for your schoolwork is your present duty, and your religious

principles should be manifested by the conscientious discharge of your present duties. I do not say that the recollection of sins should keep you from the Lord's table; but certainly you should not approach that table except with deep penitence for the past, a lively faith in God's mercy through Christ to forgive and heal you, and a stedfast purpose to lead a new life. Examine yourself on these heads, and do as your conscience may dictate."

LETTER LII.

"I do not think so lightly of the repetition as you seem inclined to do, and am persuaded that the power of learning by heart accurately is a test of intellectual vigour, and that the practice is an excellent method of strengthening the mind, as it most unquestionably is of improving scholarship. I was reading lately a life of Porson, by Dr. Young; and his biographer says, that his extraordinary scholarship was mainly the effect of a wonderful memory, which had been exercised at school by his having to learn by heart every lesson he construed. The real fact is, that you are lazy; and though you will read what interests you, and make an effort for some special object, you will not do your ordinary work with steady persevering diligence. This is, however, injurious to your moral and intellectual character, and fatal to your scholarship."

CONFIRMATION DAY. BY THE REV. H. GOODWIN, M.A., LATE FELLOW OF GONVILLE and caius colLEGE, AND MINISTER OF ST. EDWARD'S, CAMBRIDGE. Pp. 58. (Cambridge: Deighton. London: Riving

tons.

THE season of confirmations, which has again come round, leads us to notice the above tract. Its title sufficiently represents its object, which the author has more fully described as being "A book of instruction for young persons; how they ought to spend that solemn day on which they renew the vows of their baptism, and are confirmed by the bishop with prayer and the laying on of hands." Its design is to assist young persons in spending, to the best advantage, one of the most important of their days. The author confines himself to the endeavour of placing the usual instruction given previous to confirmation in a practical and devotional form. This he has done very successfully, and has thus supplied a want which other clergymen as well as himself must have often experienced; namely, that of a hand-book, to serve as a sort of guide to young persons on the day of confirmation, to assist them in spending each hour of it in the most fitting and profitable

manner.

AN ELEMENTARY COURSE OF PRACTICAL MATHEMATICS: FOR THE USE OF SCHOOLS. PART II. PRACTICAL GEOMETRY AND MENSU

RATION. BY JAMES ELLIOT. (Edinburgh: Sutherland & Knox. London Simpkin, Marshall, & Co.

IN 1845, the author of this work published a "Complete Treatise on Practical Geometry and Mensuration," together with a Key containing full demonstrations of the rules, and solutions of all the more difficult or laborious exercises, accompanied by critical and explanatory remarks. These two excellent volumes form a valuable addition to the list of books on practical geometry and mensuration; for though we have several works on both subjects, yet Dr. Hutton's large treatise on

mensuration is the only work having any pretensions to completeness which is worth consulting. While adverting to these two complete treatises on mensuration, it may be useful to remark that the expressions for the solid content of the Dodecahedron and Icosahedion are not given in their simplest form in either of these works, nor in any treatise which has come under our observation. In Dr. Hutton's mensuration, as well as in Mr. Elliot's, the expressions for the solid

10

content of these two regular bodies are respectively L3(17+21√5)₺ and & L3(7+3√5)*; ; now the square root of each of these binomial surd expressions can be extracted by the usual process given in all* books on algebra; the square root of

47+21√5
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47 21 5 is

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is 1⁄2 (3 + √ 5), and substituting these results in the preceding expressions, the solid content of the Dodecahedron is L3 (15 + 7 √ 5), and the solid content of the Icosahedron is

=

5

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L3 (3 + √5), where L

denotes the length of the edge, or lineal side of the face. These expressions are much simpler than those usually given, and though the mensuration of the five regular solid bodies is not of great practical utility, still the expressions, if given at all, ought to be exhibited in their simplest form. These modified results were first pointed out by Mr. Rutherford, in the Northumbrian Mirror, vol. I., p. 153, a periodical work, published at Alnwick in 1837.

The first part of Mr. Elliot's "Elementary Course of Practical Mathematics" is " Algebra,” which was published several months ago; and the second part, on "Practical Geometry and Mensuration,” recently published, is only an abridgement of the complete treatise on the same subjects, alluded to at the commencement of this notice. In his preface to the complete treatise, Mr. Elliot recommends the scholar to go over the large print of the several parts of that work, and to solve only the large-print exercises, before he attempts to study the whole of the volume in regular succession. The abridged form consists of nearly all the large print in the larger treatise, and the numbers of the paragraphs and propositions are retained the same as in the complete work, so that in the elementary course many numbers are necessarily omitted.

By the omission of several paragraphs and propositions, the complete treatise is reduced to a very convenient-sized volume, well adapted as a class book for beginners. In the Practical Geometry we are glad to observe the insertion of several useful problems on "Geometrical Perspective," which greatly enhances the value of this part of the book. On the whole, we are much pleased with the second part of Mr. Elliot's "Elementary Course," and we think it will be found a very useful class book, abounding in original exercises on the mensuration of lines, of surfaces, and of solids, and containing much varied and practical information. The concluding chapter consists of a great

number of unresolved exercises, without answers, on every part of mensuration. Part Third," On Logarithms and Plane Trigonometry," is in preparation.

THE ELEMENTS OF MECHANISM CONTAINING A FAMILIAR EXPLANA

TION OF THE CONSTRUCTION OF VARIOUS KINDS OF MACHINERY, &c. BY THOMAS TATE, LATE MATHEMATICAL PROFESSOR IN THE BATTERSEA TRAINING COLLEGE (London: Longman & Co.)

In this fruitful age very of mechanical contrivances and inventions, it would be an herculean task to give a familiar description of even a tithe of the numerous applications of machinery, whether these applications be to the arts and manufactures, or to the more important purposes of human life. The advantages and uses of machines are apparent to every observer; for "amid the busy haunts of men," we cannot look around without observing a machine of one kind or another, either for accumulating power, or for exerting forces too great for human or animal power. With the common crane, whose uplifted front is visible on every wharf, one man can raise a weight which would require the united efforts of several horses to move; and with the coining and punching machine, which is a lever attached to a screw, and carrying heavy masses of matter at its extremities, a single man can produce the impression of the die upon the metal, or perforate the plate, which the unaided pressure of a hundred men would fail to effect. The distribution of power and motion is regulated by machines, as, for instance, by the pendulum of a clock, or by the governor of a steam engine, uniformity of the rate of motion is preserved and maintained. By the intervention of a series of wheels, the motions thereby communicated to the several parts of a machine may be modified and adjusted to the requisite speed; the direction of motion may be changed by mechanism, as in the steam engine, where the reciprocating rectilinear motion of the piston is made to turn wheels, to pump water, or to produce the various kinds of motion which may be required for special purposes; and the action of forces may be prolonged by machinery, as in the case of a watch, which continues in action for twenty-four hours after it is wound up, the winding up occupying only a few seconds. Machines are useful in registering operations, in effecting uniformity and precision in work to be done, and above all in economising time and labour.

Under the title of "The Elements of Mechanism," Mr. Tate has produced a most useful little volume. In his prefatory note, the author explains the term mechanism as it is usually employed :-" Mechanism treats of the construction and relative motions of the different pieces which compose machines, without regard to the forces which may act upon them." The work is for the use of schoolmasters and private students, being designed "to supply teachers and students of engineering with a familiar exposition of the leading principles of mechanism, and to apply them to the elucidation of the most important pieces of machinery.'

This excellent production contains 176 pages of the most useful and interesting matter, and to give the reader an idea of the value of the work, it will be sufficient to mention that from the first page to the last it is full of really useful and practical information, embodying a descrip

tion of the construction and use of a great variety of machines in common use, with about 200 diagrams for illustration. To give extracts from such a work would occupy more space than the Journal can afford, nor is it necessary to do so, inasmuch as we cannot refrain from cordially recommending every reader to purchase a copy of the work, that he may at once be both gratified and instructed by the perusal of its pages, and that he may lay up a store of interesting and useful information with reference to the various machines which are now so common in ordinary life. We must not, however, omit to mention that the concluding chapter contains a valuable collection of problems on mechanism, amounting to upwards of one hundred, chiefly intended to illustrate the advantages gained by machines. They are almost all new exercises, and the student will derive much benefit by writing out their solutions. In page 3 the answer to example 3 should be "l seconds," instead of 13 seconds."

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THE ROTATION OF THE EARTH RENDERED VISIBLE. AN experiment is now being exhibited in Paris, by which the diurnal rotation of the earth is rendered palpable to the senses, and it is certainly one of the most remarkable of the modern verifications of theory. Although the demonstration by which the rotation of the earth has been established be such as to carry a conviction to the minds of all who are capable of comprehending it to which nothing can be imagined to add either force or clearness, nevertheless even the natural philosopher himself cannot regard the present experiment without feelings of profound interest and satisfaction, and to the great mass, to whom the complicated physical phenomena by which the rotation of the earth has been established are incomprehensible, this experiment is invaluable. At the centre of the dome of the Pantheon a fine wire is attached, from which a sphere of metal, four or five inches in diameter, is suspended so as to hang near the floor of the building. This apparatus is put in vibration after the manner of a pendulum. Under, and concentrical with it, is placed a circular table, some twenty feet in diameter, the circumference of which is divided into degrees, minutes, &c., and the divisions numbered. Now it can be shown by the most elementary principles of mechanics that, supposing the earth to have the diurnal motion upon its axis which is imputed to it, and which explains the phenomena of day and night, &c., the plane in which this pendulum vibrates will not be affected by this diurnal motion, but will maintain strictly the same direction during twenty-four hours. In this interval, however, the table over which the pendulum is suspended will continually change its position in virtue of the diurnal motion, so as to make a complete revolution round its centre. Since, then, the table thus revolves, and the pendulum which vibrates over it does not revolve, the consequence is, that a line traced upon the table by a point projecting from the bottom of the ball will change its direction relatively to the table from minute to minute and from hour to hour, so that if such point were a pencil and that paper were spread upon the table, the course formed by this pencil during twenty-four hours would form a system of lines radiating from the centre of the table, and the two lines formed after the interval of one hour would always form an angle with each other of 15°, being the 24th part of the circumference. Now, this is rendered actually visible to the crowds which daily flock to the Pantheon to witness this remarkable experiment. The practised eye of a correct observer, especially if aided by a proper optical instrument, may actually see the motion which the table has in common with the earth under the pendulum between two successive vibrations. It is, in fact, apparent that the ball, or, rather, the point

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