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and has had his eyes open for the discussions that The Advanced Reader. (Nelson's School Series.) take place in various journals on the etymology of London : T. Nelson and Sons, Paternoster Row; words. And he has given the results in a compact, Edinburgh ; and New York. 1866. practicable form. We do not know a manual of the same size in which so many of the results of modern We have no hesitation in pronouncing this the philology are accurately given. And there are les. best “ Advanced Reader” that we know; and the sons not merely on etymology, but on the affinities reasons that we have for this opinion are, that the of the Arian languages and the laws of changes. work is formed on an idea, that the idea is a right one, Besides all this, there are collections of Latin, and that it is successfully carried out in the book. French, and Italian, phrases in common use, an ex- There cannot be a doubt that the observing faculplanation of names, and a quantity of other curious ties are the faculties which ought to be cultirated matter. The work can be confidently recommended with the greatest care in the earlier stages of educato teachers, as likely to be exceedingly useful to tion. It is not till a comparatively late period that them in the instruction of their classes.

we can expect to see the reflective powers in full

operation. It follows from this that the readings of Chambers's Readings in English Prose: A collection young people should be such as to train and ennoble of specimens from our best Prose Writers, from the observing powers. This is the idea on which A.D. 1558 to 1860, chronologically arranged, with the book is based. The extracts presented are such biographical notices and explanatory notes, and

as will form to the mind of the reader pictures, and an Introduction, containing specimens from English

he is supplied with these pictures from striking writers from the earliest times to 1558. William events in the history of individual men, and from and Robert Chambers, London and Edinburgh.

the sublime and beautiful scenes of nature. These

individual pictures are so arranged, that they do The title of this work states clearly what is to be not distract by their endless diversity, but they form found in it. The men who take the foremost placés parts of a unity. And the reader is thus interested in the history of English literature, are here repre- more and more by each lesson, and the knowledge sented by one or two extracts of the length of a page he receives coalesces with what he has already or two. Sometimes the extracts are a little longer. received. The plan, however, would have failed enFor the most part only one extract is given from tirely, had an attempt been made to convey knoweach author. The extracts are generally well-known ledge simply; or in other words, to convey pure and favourite passages; the biographical informa- scientific truth. It is not pure truth that sustains tion is drawn up with care; and the whole book is the mind. The truth must be presented in its Deatly got up. The extracts from the Anglo-Saxon living beauty, it must be joined with its native and early English writers are printed in very small goodness, and thus truth, beauty, and goodness sink type, and they occupy fourteen pages. It is singu- together into the soul. The extracts selected have lar that no enterprising publisher or school-book therefore been made from the writings of those who writer has got up a good text-book out of Chaucer combined a scientific knowledge of nature with a and his contemporaries.

poetic eye; in other words, of those who have the

gift of word-painting in a high degree. And their First Lessons in the Evidences of Christianity. By prose descriptions are enlivened and impressed by

B. B. WOODWARD, B.A., F.S.A. Second Edition. extracts from our best poets relating to the same London: Jackson, Walford, and Hodder, 27 Pater

subjects. noster Row.

The work consists of five parts. In the first we have

scenes from human life, as it exhibits itself in variThis is an admirable little book. It is written in ous places and stations. Thus we have the Death language so simple, that a comparatively young per- of Little Nell, the Elder's deathbed, Hector and son can easily understand it; and the matter is pre- Andromache, and other such scenes. Alongside of sented in a lively interesting manner. And it sug- these are instructive articles on man and the indusgests no doubts. “ In this little book," the author trial arts, the eye, the pleasures of knowledge, the says, “ the attempt has been made to treat the sub- dignity of labour and other such subjects. ject without any reference, explicit or implicit, to Parts second, third, fourth, and fifth, present vari. an opponent of the convictions regarding the Bible ous aspects of nature in different parts of the world ; and the gospel of which it speaks. It has been the mighty deeds which throw a lustre round them, thought possible truthfully to prepossess the minds and the poems which celebrate them. Thus in part of children with the Evidences of Christianity; and second we have descriptions of the Torrid Zone, the 80 to forearm them against the assaults to which the Equator, the Amazon, a Brazilian Forest, the Pacific faith of most persons, in this active age, is exposed.” Ocean, and other grand scenes of nature in PolyWe think the author has acted wisely in this matter, nesia and in India ; and poems are given which harand has succeeded in his aim.

monise with these prose pictures, such as the Ancient

od

а

VOL. II.

Mariner of Coleridge, the Shipwreck of Byron, and we can warmly recommend it to parents, as being the Unknown Isles by Wilson, Part third takes healthy and instructive reading for their children. us to Egypt and the Holy Land. Part fourth gives The Butterfly's Gospel" and " Benaiah” are two us pictures of Greece and Rome and Spain. And of the tales that have appeared in Merry and Wise. part fifth gives us some of the most famous English They have been reprinted separately, and done up and Continental scenes. Occasionally are intro- in an elegant style, with illustrations, for Christmas duced extracts on more general subjects, such as presents. We can very strongly recommend them. “ The Origin of Mountains and Valleys," and the “ The Butterfly's Gospel" is a perfect gem in its way, reader is taught to reflect in such extracts as “ Man and so is the other story in the volume, “ The Rose in unison with the Creation."

of Jericho.” And the picture of a girl worth ber The book is one of deep interest from beginning weight in gold, which is added to these two tales, is to end, and will be read by the teacher as well as admirably drawn, and tells at once on the young the pupil with growing pleasure. Very large poeti- mind. cal extracts are given from our best poets, but all “ Benaiah" is a tale of the captivity. A good the extracts are well worth knowing, and being en- deal of historical matter is introduced, and it abounds graved on the memory.

in vivid pictures of scenes in the life of the Jews

during their captivity, and on their return to Jeru. Merry and Wise. A Magazine for Young People. salem. It is also deeply interesting.

Edited by OLD MERRY. 1865. London : Jackson, Walford, and Hodder, 27 Paternoster Row.

The Advanced Lesson Book : Consisting of Reading The Butterfly's Gospel, and other Stories. By Frede- Lessons in History, Geography, Literature, and

RIKA BREMER. Translated by MARGARET Howitt. Science. Together with a complete course of London: Jackson, Walford, and Hodder, 27 Pater

examples in the higher parts of Arithmetic and noster Row. 1865.

Mensuration. For the use of advanced classes in Benaiah: A Tale of the Captivity. By Mrs WEBB, Schools and Institutes. By E. T. Stevens, asso

Author of “Naomi,” &c. London : Jackson, ciate of King's College, and CHARLES HOLE, Walford, and Hodder, 27 Paternoster Row.

Head-Master of the Loughborough Collegiate and

Commercial School, Brixton. Editors of “ The There are two things required in a good serial for

Grade Lesson Books," &c. London: Longmans, the young. It is essential that it be interesting to

Green, and Co. 1866. those for whom it is intended; and it is also essential that it meet the approbation of critics of riper

The title of this work states exactly its nature. years.

“ Merry and Wise" fulfils both conditions. It is needless to say that the lessons are interesting, Its appearance is looked forward to with intense plea for they have almost all been selected from the best sure by the youthful members of our household, and writers on the subjects of which they treat.

Notes and Queries.

II. MATHEMATICAL.

NOTES, 14.-The rain which fell during a shower on the roof of a rectangular building 20 yards long and 8 yards broad, is collected into, and fills a cistern, 8 feet long, 6 feet deep, and 3 feet broad; How many tons of water fell during that shower on an adjoining field, whose area is 6 acres ? Solution by A.On 8.20 square yards there fell.

3.6.8 cubic feet.

3.6.8 1

8.20

3.6.8.6.4840 6 acres (= 6.4840 sq. yds.) there fell

8.20 and taking the weight of 1 cubic foot of water at 1000 oz., the weight of water, in tons, falling op

3.6.8.6.4840.1000 3.9.25.121 6 acres =

7291', tons. 8.20.16.112.20

112 (Solved also by H. C. and Nevis.)

22

91

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15.-
(1.) Prove the formula sin. 6 + cos. 6a =

5 + 3 cos. 4a.

8 Solution by H. C.

Cos. 2a + sin. *a = 1,

sin. 2a = cos. 2a,
.:. 2 cos. a It cos. 2a,

(1.)
and 2 sin. ?a=1.
cos. 2a.

(2.)
Similarly, 2 cos.? 2a=l+ cos. 4a.

(3.)
Cubing (1); 8 cos. Ra=1+ 3 cos. 2a + 3 cos. 2a + cos. 2a.

Cubing (2), 8 sin. &a=1 – 3 cos. 2a + 3 cos. 2a cos.' 2a.
.: 8 (cos. 6a + sin. $a) = 2 + 6 cos.? 2a.

But 6 cos.? 2a 3 + 8 cos. 40; (3) 3.
:: 8 (cos. 6c + sin. 6a) 5 + 3 cos. 4a,
and cos. 6a + sin. $a =

5 + 3 cos. 4a

8 (Solved also by A, Ricardo, J. A, J., and Nevis.)

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2

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Solution by H. C.

m cos.

= n tan. y, .. ma cos.? no tan. y.

(1.) Sec. y=1+ tan.? ¥= (sin. o + cos. ®)?,

= sin. o + cos.' 0 + 2 sin. Ø cos. Q,

=l+ 2 sin. cos. P;
.. tan.' ¢

2 sin. Ø cos. p.
By substituting this value of tan.4 in (1) we get, m2 cos. O 2n sin. cos. Q,

and cos. o (ma cos. p. 2n2 sin. p)=0;

.. cos. P = 0. Also ma cos.

2no sin. p, mi cos.' ¢ 4n* sin. O,

Ant

4n* cos.? p; :: (m + 4n“) cos.? - An“,

2n?

and cos. p =

[ocr errors]

By substituting these values of cos. o in sin. 8 = m cos. Q, we get,

2mn (Sin. 0 = 0, or sin, o

I Am2 + 4n2

(Solved also by a., Ricardo, I. A. J., and Nevis.)

16,

(1.) Given a fixed right line BC, a fixed point B in the line, and a fixed point A not in it. Find a curve such that the tangent at any point in it, and a parallel to the tangent through A, may cut BC in T and T'respectively, so that BT? + BT 2. = a constant quantity.

Solution by A.

Taking B as the origin of rectangular co-ordinates, BC as axis of x; let h, k be the co-ordinates of the

y' — y=p(*" — 2) (1.) (p=)

(2.)

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k

[ocr errors]

(5.)

given point A, and yi f (2) the equation of the required curve. The equation to the tangent at any point x,y of this curve is,

dy
(x' 2

dir
and the equation of a parallel to this tangent through A, is y' - k=p(x' h), (

hp - K
Putting y' O in (1) and (2) we find, BT

P

P .:. by the given condition (rp y) + (hp k)? cop (3.) Andfrom this differential equation of the first order, and the second degree, the rolation between 1 and y is to be determined. Arranging differently, we have,

y = xp Ve?p? (hp k)2 (4.) differentiating with respect to x,

dp (e h) p + hk dp
p = p + x
dx Vc*p* (hp

k)?

doc

dp
(5) is satisfied by 0. (6.)

dx
(ca — ha) p + hk

(7.)
Vcp (hp - k)?

? From (6) we get p = constant = a, and substituting this in (3) we get,

y = ax - Na ca (ah ko (8.) which represents a straight line.

This is the general solution of the differential equation (3); and the particular solution is obtained by eliminating p between (7) and (3), which, after several reductions, leads to P - koza + 2hkxy + (co ha) ya + c*K?

O (9.) This equation represents a hyperbola having its centre at the origin, which is consequently the required

x2 ya If h= 0, that is, if AB is perpendicular to BC, (9) becomes

ca k

1, representing a hyperbola with axes = cand k. Note.—The connection between the general solution y= ax — Vac2

(ah k)? (8), and the particular solution k?x2 + 2hkxy + (CS ha) ya + cok? = 0 (9), may be thus explained: the hyperbola represented by (9) is the envelop of a system of straight lines, each straight line in the systein being determined by giving a special value to the arbitrary constant a in (8).

or x =

curve.

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n + 2 2

2" and sum to infinity 2.

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B

с 18. Proposed by A.–From any point 0 of the circle circumscribing the triangle ABC, straight lines Da, Ob, Oc are drawn so as to make equal angles with the sides BC, CA, AB respectively; Shew that b, c lie in a straight line.

19. Proposed by A. –The area of any triangle ABC is equal to the radius of the circumscribing circle multiplied by the semi-perimeter of the triangle abc, formed by joining the feet of the perpendiculars As, Bb, Cc.

20. Proposed by Ricardo.—Find the centre of gravity of a semicircle, in which the weight of each particle varies as its distance from the centre.

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The long-established custom that newly appointed UNIVERSITY INTELLIGENCE.

professors should receive the congratulations of the OXFORD.-17th October. It is likely that there University at an inaugural lecture has been broken will be no Bampton Lectures next year. Mr Had through in the case of the last two nominees to dan, of Trinity, who was elected in the spring to Regius Professorships. Censorious persons hesitate preach them, has been compelled by ill-health to whether to ascribe this to indifference to or fear of resign; and the trust-deed is said to provide no the public verdict. machinery for the appointment of a substitute. Professor Wall, of Palliol, has been elected a

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