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Blackwood fSons.) Since the publication of our August number we have had the pleasure of perusing this excellent and useful work. We say the pleasure, because, as our pursuits do not generally lie among parapets and ditches, ramparts, bastions and barbettes, we conceived that Lieut. Yule's book would prove somewhat tedious and uninteresting in the reading. On the contrary, we must do it the justice to remark, that we have read some novels and many a poem which did not possess the interest of this volume; and we verily believe that even those who are habitually light readers, were they to“ screw their courage up," and elevate their thoughts and views to the lofty heights of some of Lieut. Yule's ramparts and bastions, and sit down with the heroic daring of resolution required by such readers for the study of ramps and traverses, flanks and curtains, gorges bastions and demigorges, as well as the various systems of Vauban and Coehorn, would rise much gratified with the result of their courage, and would have gained some insight into the covered-way, with all its secret recesses, tunnels, and staircases.

It is stated, in the preface, that " a small impression of a work containing the substance of this was printed last year, for the use of the Scottish Naval and Military Academy at Edinburgh, which met with the approval of some interested in the subject." The approbation bestowed on the first impression suggested its publication in the present enlarged form. The aim of the author, in this essay, has been “to give principles and essential details in a natural and readable order, and freely to use biographical and other illustrative notices, with the view of giving something of life-like interest to a study which is too often vaguely regarded by soldiers as a dim compound of strange angular diagrams and technical jargon."

In a preliminary chapter, the author commences with some geometrical problems of frequent occurrence in plan-drawing, which ought to be well understood before proceeding with the practical part of the study: he then proceeds with the definitions of the various terms used in fortification, which are given with much clearness; and with the principles of outline and general rules, which are also treated in a very perspicuous manner. After a lucid description of the various forms of field-works, the calculations necessary for the construction of such works are given in detail; and in the interesting discussion of “extended systems of works” which follows, the author introduces notices like these :-" The camp which Frederick II. fortified in the vicinity of Schweidnitz, in 1761, when hemmed-in by the Austrian and Russian armies, was the means of saving him from destruction at the most critical period of his history, and had great fame in the last century as a specimen of field-fortification on a large scale. The camp was of an oblong form, and consisted of a great number of detached works on a chain of low hills, covered in front by rivulets, which left few points exposed to attack." Again, “One of the most remarkable instances in history of the use of the field-engineer's art, is that naturally so oft referred to by every English

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writer on military subjects—the lines which Lord Wellington threw up to cover Lisbon, and behind which, retiring after the victory of Busaco (1810), he baffled the endeavours of the French, under the Emperor's ablest lieutenant.” By the introduction of similar notices, the author illustrates the principles of field-fortification in a very pleasing and instructive manner.

In permanent fortification, the author commences with a description of " Vauban's First System,” and, after a brief explanation of the modes of attacking and defending a fortress, he adverts to the “Modern System,” as well as to the systems of Coehorn, Montalembert, Carnot, and Bousmard. Fifteen portraits, executed in a very creditable manner, of these and other eminent men, are interspersed throughout the volume; and an ample appendix contains interesting biographical sketches of all those celebrated men whose portraits have been given in the work. This appendix will be read with much interest, as also the Glossary of Military Terms,” with which the volume closes.

In the eight large plates, illustrative of the principles of fortification, there are given the plans of several fortifications both at home and abroad.

Of this volume we must observe, that while it is well calculated to aid the student in the acquisition of the principles of military science, it is, at the same time, more than ordinarily attractive by the introduction of so many interesting historical notices.





Mr. Gleig did well to secure for his School Series the services of two such men as Mr. Tate and Mr. Hughes; their reputation is a guarantee that the volumes to which their names are attached deserve the confidence of the public.

The first of the two works above-mentioned appears to be a reprint of Mr. Tate's “ First Three Books of Euclid's Elements of Geometry, after the text of Dr. Robert Simson,” which has already been for some time in the hands of schoolmasters. In its present shape we can give it our hearty commendation, as it has been considerably reduced in price. Now that the Committee of Council on Education encourage an acquaintance with Euclid in preference to mechanics, mensuration, and astronomy, this cheap edition of the First Three Books will be particularly acceptable to pupil-teachers.

Of Mr. Hughes's Geography, as a book " for the use of beginners,". we cannot speak too highly.

The author has very properly aroided any general account of the physical geography of the world, and after giving the most indispensable preliminary notions of the figure and surface of the earth as an “ Introduction,” has confined himself to a description of the separate portions of the land. This plan is one of the greatest merits of the book. It enables the author, without any constrained arrangement of the subject, to follow out what we may call the natural method, commencing with our own country, and proceeding from that to the nations situated nearest to us, and so on to those that are most remote. The child's ideas about the world in which he lives are thus gradually expanded, until he is prepared to take in the whole of it at one view; whereas, if the opposite course is pursued, he is puzzled and confused by the novelty and vastness of the subject so suddenly presented to his mind, and his progress is literally backwards, for he is made to pass from the difficult to the simple. One of the surest tests of the utility and judgment of a teacher is the manner in which he lays out the matter of instruction, in regard to quantity, arrangement, and relative importance; and this, in like manner, is the surest test of the merit of an elementary school-book.

The manner in which Mr. Hughes has carried out his plan is worthy of notice. He first treats of the Physical Geography of each of the great divisions of the land, and then proceeds to give a separate account of each of its National Divisions. “ Physical geography,” says he,

66 is the most important branch of the subject ; both because the natural features of the earth are liable to little change and in most respects continue the same through all ages, and also because they exert a powerful influence over the development of human industry. That is to say, the occupations

any people will in a great degree depend upon whether the country which they inhabit is maritime or inland, mountainous or level—whether it contains rivers, or is generally arid and sterile; as well as upon what are its climate and its natural productions--whether belonging to the mineral, the vegetable, or animal kingdom.” The limits of his space have not allowed him to trace this connection, nor indeed to account for

any of the phenomena wbich he describes; but the facts are given in their proper consecutive order, and it will be the duty of the teacher to point out more particularly the relation in which they stand to one another. What we ought to have in class-books is not so much actual detailed instruction, as a good framework of facts for the teacher to


fill up:

The book is admirably adapted for use in elementary schools, and we trust that it may also find its way into our middle schools, where some of the old class of geographies, consisting chiefly of lists of names, still maintain their ground against the improved works that are now published.



Ques. 111.--Proposed by P. T.
A silver shield in the form of an octagon weighs 150 oz.,

and is .09 inches thick; required the length of the side. Answered by Mr. Herbert, Mr. Righton, Mr. Henry, Mr. Dyer,

and the Proposer.

150 x 1728 No. c. in. in the shield


150 x 1728 ... Surface of the shield

275.07 sq. in.

10470 x .09 Let x =

the length of the side, then we have from the formula for the area of the polygon,


180° x cot

= 275.07 ;

whence we find, x = 7.547 inches.

Ques. 112.-Proposed by Mr. Draper, Rochester. Given a and b the parallel sides of a trapezoid inscribed in a circle, and the obtuse angle double the acute angle; to find the area of the trapezoid.

Answered by Prismoid, Mr. Cock, H. P., and Mr. Hill. Of the two parallel sides let a be the greater; then because the opposite angles are together equal to two right angles, therefore each acute angle

of 180° 60°.

Let the sides which are not parallel be produced until they meet; then the triangles thus formed will be equilateral, the side of the greater being a, and that of the smaller one b. Hence we have,

Area trapezoid difference of the areas of the triangles,

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* 13 *

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Ques. 113.–Proposed by Mr. O'Clazy, Durham. Being a friend of the cold-water system, I intend to make a circular pond in the front of my house, and a circular island in the centre, raised a feet above the surface of the water, which is to be d feet deep: I request the aid of my Journal friends, to tell me the breadth of the water, so that the excavated earth may just raise the island to the height required. Answered by Mr. Sheppard, Mr. Dyer, Mr. Salter, Mr. Sothern,

and the Proposer. Let r = the radius of the smaller circle, or island; and x = the width of the water,

* See Tate's Mensuration, &c. p. 150.

Area ring=T (2r + x) *;
.. Content of earth to be excavated=rd (2r + x) x.

Earth to form the island=gul x a.
Hence we have by the question,

ad (2r + x) x=r god a,

ar2 •. 24 + 2r x=


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LIST OF MATHEMATICAL ANSWERS. Mr. Herbert, Wootton, ans. 111, 112, 113; Mr. O'Clazey, Durham, ans. 111, 112, 113; Mr. Sheppard, ans. 111, 112, 113 ; Prismoid, Tewkesbury, ans. 111, 112 113; H. P., Newcastle, ans. 111, 112, 113; G. J., Alnwick, ans. 111, 112 ; Mr. Sothern, Burton Wood, ans. 111, 112, 113; T. V. Henry, ans. 111, 112, 113; H. Heppingstaed, Manningham, ans. 111; E. Carthew, Roehampton, ans. 111, 112, 113; J. Salter, Durham, ans. 111, 112, 113; Mark, ans. 111, 112, 113; J.T. Cock, St. Ives, ans. 111, 112, 113; W. Righton, Jun., ans. 111, 112, 113; Sam Dyer, Wanstead, ans. 111, 112, 113; E. Rutter, Sunderland, ans. 111, 112, 113 ; R. Thompson, Berwick, ans. 113; J. B., O. Malton, 111, 112, 113; J. Rowlatt, Evercreech, ans. 111, 112, 113; G. Morris, Gosport, ans. 111, 112, 113; H. Hill, Mortlake, ans. 111, 112, 113; A. M., ans. 111, 113.

To Be ANSWERED IN OUR Number for December, 1851.

Ques, 114.- Proposed by Mr. O'Clazey, Durham.
If a person

travel round the earth at the equator, how many square miles of its surface may he see, supposing the earth to be a perfect sphere, 8000 miles in diameter, and the height of the person's eye five feet ?

Ques. 115.- Proposed by Prismoid, Tewkesbury. To determine an expression for the area of an octagon in terms of the side.

Ques. 116.-Proposed by Mr. Sheppard. A wheel 6 feet diameter is obstructed by a stone 3 inches high. Required the force necessary to surmount this obstacle, supposing the line of traction to pass through the axis at an angle of 30° to the horizon, and the load upon the axis to be 10 cwt.

To Correspondents.

R. A. The paper was published in an early number of the “Educational Magazine,” and is already in the hands of many of our readers. We are obliged for the Examination Papers, but they are hardly suited for us.

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