in that magazine twenty years ago, so will be new to the present generation. The story is certainly wonderful, and there seems no reason to doubt its authenticity. There is one weak point in the narrative, however. The ghostly lady sits opposite Mr. Heaphy at dinner, invisible to the rest of the party, but nevertheless eats beef and drinks claret. The unprejudiced mind naturally asks the question, who carved the beef and who poured out the claret?

'Dolly Dear;' or, the Story of a Waxen Beauty. By Mrs. Gellie (M. E. B.). Griffith

and Farran.

The little girl who finds among her Christmas gifts a prettily bound book with the above title will read with delight the adventures of the model doll, almost as large as a real baby, who plays so important a part in the lives of her young mistresses, and we venture to say that once begun it will not readily be laid down.

The interest of the tale is well sustained throughout, and it contains many truths and useful lessons which, laid to heart and practised by the reader, may have as good an effect upon her as 'Dolly Dear' herself had upon Eileen and Lizzie when ill in bed.

St. Aubyn's Laddie,' and the Little Wouldbe Soldier. By E. C. Phillips. Griffith and Farran.

The little hero of this pathetic tale is Cyril St. Aubyn, always known by his pet name of Laddie,' and the would-be soldier is his cousin Alan, who is of the same age as himself, and has such a devoted affection for the little crippled invalid that he even gives up his cherished wish of being a soldier, and promises to remain with Cyril all his life. He is a high-spirited, determined little fellow, and though only seven and a half when he makes this promise, he keeps it faithfully, although at the cost of some tears; and when Cyril a few days before he dies wants to release him from his promise, he refuses, saying, 'No; if you don't want me to write your letters for you, I'll be an army doctor, and cure the sick and wounded soldiers, and be doctor to their wives and children when they are ill. Wouldn't that be nice?'

This satisfies Cyril, and Alan, glad to have made his cousin happy, says he never means to change again.

Cyril himself is a model of patience and thoughtfulness for others, and his influence his felt by all who know him. The story is one which will be read with interest by all who like this style of sorrowful literature.

The Belton Scholarship. By Bernard Heldmann. Griffith and Farran.

A story that will interest boys, treating as it does of school life, and coming from the pen of one already well known to them as a writer of similar tales.

The chief incident of the book is, of course, the competition for the scholarship; but there are many other scenes introduced that boys will appreciate, and in particular the account of the paper chase in Chapters VI. and VII. is very exciting, while the tragic affair of Charlie Stewart and the bull will arouse the sympathy of the reader.

In Belton school, as in other establishments of the kind, there are to be found boys of all tastes and temperaments, good and bad dispositions; for a school is a little world in itself, and the child is father to the man.

George Denton, the hero, is not faultless, but he has many good qualities which are brought out strongly when, by a reverse of fortune, he has to depend on himself, and industry and perseverance take the place of laziness and discouragement at his inability to learn as quickly as his companions. How he succeeds in his efforts, and who in the end wins the Belton, we leave our boy-readers to discover for themselves.

The Baby's Museum. Griffith and Farran.

A perfect collection of the 'rhymes, jingles, and ditties' which have lived and laughed in our nurseries from gene

ration to generation, profusely and humorously illustrated. Quite the book for our little ones, and in the multitudinous woodcuts especially useful to rub out wrinkles from older foreheads.

White's Grammar School Texts. The Epodes and Carmen Sæculare of Horace, with an English Vocabulary. Longmans.

One of the numerous series in Greek and Latin classics issued in the interests of educational literature by Dr. White. A short account of Horatian metres precedes the text, which is followed by a full vocabulary: the whole comprising a most compendious manual for the numerous happy students of these easier times. What would not an old Carthusian or Etonian have given for such a troublesaving help up Parnassus !

Longmans' Magazine. No. 2. December,

1882. London: Longmans, Green, and Co. This is an excellent number, and promises well for the Dr. future of this new candidate for public favour. Smiles' John Harrison the Chronometer Maker,' and Mr. Froude's Norway Fjords,' are alone worth double the price of the magazine. We cordially recommend our readers who have not already seen 'Longmans' Magazine' to get a copy.

A Short Treatise on the Greek Particles, etc. By F. A. Paley, M.A., Editor of the Greek Tragic Poets, and Examiner to the University of London. Deighton, Bell and Co.

A learned, if so-called elementary, handbook for scholars who study the Greek classics microscopically. Mr. Paley is known as a distinguished educationalist, and has contributed several volumes to the series of Bibliotheca Classica, published by the eminent firm of George Bell and Co. This treatise is claimed by its author to be ' entirely original,' and he adds that as a concise manual it is probably unique, as explaining correctly the doctrine of the Greek particles. In this connection one cannot help remembering-and quoting-the famous triumph of rhyme and rhythm, Browning's Grammarian's Funeral,' where it is written

'So, with the throttling hands of Death at strife,
Ground he at grammar;

Still, through the rattle, parts of speech were rife;
While he could stammer

He settled Hoti's business-let it be !

Properly placed Oun

Gave us the doctrine of the enclytic De,
Dead from the waist down!'

That Mr. Paley himself has full sympathy with such enthusiasm, let this extract from his preface suffice,

viz. :

'To my mind, then, so far from being a dry, unimportant subject, the combinations of the Greek Particles are full of the highest interest, as being, so to say, an elaborately finished part of a most complex and beautiful machinery. That a few inflected monosyllables should determine so completely the tone and meaning of a sentence is in itself a curious phenomenon of language. Believing that, from long and careful observation, I understand them myself, I have tried to make others do the same; and I only hope they will have the same pleasure in reading which I have had in writing this small work.'

Ivanhoe. Edition de Luxe. Part I. Ward and Lock.

This, perhaps the romance-masterpiece of Sir Walter Scott, is here so splendidly printed and so spiritedly illustrated as to be indeed what it professes, a luxury of literature. The excellence of the ancient matter 'goes without saying,' and the profuse modern embellishments by several French and English artists are worthy of the

text. The whole novel is to be issued in ten parts at a shilling, and it is hoped will amply recompense the enterprising' House of Warwick,' now transferred to Salisbury Square.

Christmas and New Year's Cards. London : M. Ward and Co.

We have received from Messrs. Marcus Ward and Co. an excellent assortment of seasonable cards.

Songs for Little Singers. Composed by Henry King Lewis. Hodder and Stoughton. 'Songs for Little Singers' is a book of words and music well expressed by such a title. The words comprise forty-four selected hymns and pretty rhymes, mostly by well-known authors, and the musical settings to them, all composed by Mr. Lewis, are simple and tasteful if not very scientific. Those which please us most are ' His Little Child,' 'Thy Kingdom Come,' 'Benediction,' 'Little Things,' and 'Alice's Supper.' Some of the airs are more original than others, but, on the whole, we can heartily recommend this pretty book as supplying a want that has long been felt in giving the children songs to sing which they can understand and enjoy, and which express the real feelings of childhood.

The Teachers' Diary and Pocket Book. London: Jarrold and Sons.

Many a hard-worked teacher will thank the Messrs. Jarrold for the timely issue of this admirable, and, we might add, much-needed volume. If regularly used, it will save no end of trouble and worry. Its comprehensiveness may be gathered from the fact that it is adapted to the wants of either master, mistress, or pupil-teacher.

'The head master, by using it, will have always at hand any information he may require, without having to turn first to one page and then to another of the Code and the Instructions to Inspectors; all the information bearing on the same subject being put together.

He will also find useful the form on which to enter the time table for each standard; and the space for observations on the work of the standard, results of his examinations, etc., during the year.

The head mistress, in addition to the above, will find the needlework requirements for each standard, together with the exercises that may be set on the day of examination.

'The Assistant or Pupil Teacher will find in it :—

(a) The work of his class set out, whatever standard he may be taking;

(6) Information from the "Circular to Inspectors," as to
what will secure a pass in each subject;

(c) A form on which to enter the time table of his class;
(d) A space for entering notes on the work of his class; and
(if a pupil-teacher),

(e) A full statement of what he has to study in each subject
for his own examination, not only for the year, but
right up to the time when he goes to the Training
College.'

We heartily recommend 'The Teachers' Diary and Pocket Book' to every elementary teacher in the country.

[Several Reviews are unavoidably left over for want of space.]

Publications Received.

Christmas Cards

(1) Marcus Ward's Christmas Cards. Marcus Ward and Co. Classics

(1) Horace. Epodes and Carmen Seculare (White's Grammar School Texts). Longmans.

Diagrams

(1) Johnston's Standard Series of School Diagrams. No. 1. Chemical Apparatus, mounted on rollers. A. Johnston. (2) Johnston's Illustrations of Natural Philosophy. Sheets No. and 7 with Handbooks. A. Johnston.

VOL. II.

(1) Shakespeare's Julius Cæsar. Longmans. (2) Selections from Julius Cæsar. Longmans. Mechanics

(1) Garnett's Elementary Mechanics. G. Bell and Sons. (2) Besant's Hydro-Mechanics. G. Bell and Sons. Mensuration

(1) My First Mensuration. By M. H. Senior. Greenwell. Miscellaneous

(1) Heroes of Maritime Discovery. Gall and Inglis. (2) The Belton Scholarship. Nelson and Sons. (3) Tommy Greedygrab and Wriggletum. John Heywood. (4) Universal Instructor. Vol. II. Ward, Lock, and Co. (5) Our Dolly. Griffith and Farran. (6) St. Aubyn's Laddie. Griffith and Farran. (7) Won from the Waves. Griffith and Farran. (8) The Teachers' Diary and Pocket Book. Sons.

Jarrold and

Blackie and Son.
Griffith and Farran.
Wesleyan Methodist Sunday

(14) Two Illustrated Readings. Wesleyan Methodist Sunday School Union.

(15) Philip Phillips' Story of His Life. Wesleyan Methodist Sunday School Union. No. I. Wesleyan Methodist

(16) School-Room Placard.

Sunday School Union.

8. PUZZLED.-A tradesman has on his books 960 customers, whose monthly custom averages in each case £5; he sends out his bills at the close of each month and allows 5 per cent. discount to each who pays ready money, but charges 23 per cent. interest for each complete calendar month for all outstanding bills; at the end of a certain month one-half of these bills have been outstanding for one month, one-third for two, and the rest for three months; find the ratio cady-money customers to the others, if the discount paid to them is equal to the interest charged to the others. (Certificate, 1880.)

Discount on ready-money payments=2% of (£5× No. of ready-money customers);

Interest on outstanding bills for 3rd month

= of (£5× No. of other customers)
+ 2% of (£5 × 33

+% of (£5 × &

Interest on outstanding bills for 2nd month

=% of (£5×4 No. of other customers) + 2% of (£5 × }

Interest on outstanding bills for Ist month

);

= of (£5 × No. of other customers); ..Total interest on outstanding bills

=% of (£5× No. of other customers) + of (5x No. of other customers) +% of (£5 × & No. of other customers)

= £5× {(4% of §) + (r% of }) + (1 of 1).

of No. of other customers

= £5× (x2+35+) of No. of other customers
= £5×12 No. of other customers;

No. of ready-money customers
=5x No. of other customers;

..No. of ready-money customers: No. of other customers

II. NO NAME.-There are two vessels, one containing 12 gallons of water, and the other 6 gallons of wine; if a gallon be taken out of each, and poured into the other, and if this be repeated 4 times, find how much water and wine will be in each? (Johnstone's Arithmetic).

After first exchange

13. ANXIOUS. The price of £100 bank stock which pays 6 per cent. is 1853. £6,250 of this stock is transferred to the three per cent. consols at 92; find the alteration in income. Interest on Bank stock = £(624×64) = £406 5s.;

Amount of stock in consols = £(6,250 × 1851)

923

=(406 5s. - £375) decrease =£31 58. decrease. Ans.

NOTE. Writing pretty fair, but too thick.

14. KAPPA.-Two settlers in New Zealand own adjoining farms of 3,000 and 5,000 acres respectively. They unite their farms, taking at the same time an additional partner, who pays them £8,000, on the understanding that a third share of the land shall in future belong to each. How is the £8,000 to be divided between the original owners?

Size of each farm after division=

.. Value of an acre=

3000+ 5000 acres =2,6663 =2,6663 acres ; £8,000÷2,666}

= £3;

Quantity taken from first settler = (3,0co-2,6663) acres

=3331 acres ;

... First settler should receive (333) × 3) £

Let ABC be the given triangle, and let the triangle DEF be formed by drawing lines through the points of trisection of the sides adjacent to the angles.

Then the triangle DEF shall be equal in all respects to the triangle ABC.

Proof.-Because GB is double of AG,

.. triangle GHB is double of triangle AHG;

similarly, triangle HGG is double of triangle AHG;
.. triangle GHB is equal to triangle HGC;
wherefore GH is parallel to BC. (I. 39.)

Therefore the triangles DEF has its sides respectively parallel to the sides of the triangle ABC.

In the triangles AHG, KHE,

the angles HAG, AGH= angles HKE, KEH, each to each,

and side AH-side KH,

... side AG = side KE; (I. 26.)

(I. 29.)

similarly, it can be proved that LK = KE, and FL=LK; ÉF is treble of EK, and therefore equal to AB. Similarly, it can be proved that DE BC, and DF=AC. .. Triangle DEF is equal to triangle ABC in all respects. Q. E. D.

As the square of m2+n2 is equal to the sum of the squares of m-n2 and 2mn, the lines representing those units will therefore form a right-angled triangle. (I. 47.) Q. E. D.

3. EGS. Given two points, find two other points that shall be at the same given distance from each of them. What is the least possible length of the given distance? (Scholarship, 1876.) Let A,B be the two given points, and C the given distance. Join A B, and bisect it in D. (I. 10.)

Draw EDF at right angles to AB. (I. 11.) From A as centre with C as radius cut EF in E and F, then E, F shall be the two points required.

Join A E, B E, AF, BF.

Proof.-In the triangles ADE, BDE,

=

the two sides AD, DE = the two sides BD, DE, each to each, and the angle ADE = the angle BDE, (Ax 11) therefore AE BE; (I. 4.)

Similarly it can be proved that AF

and AE, AF

=

=

BF; the given distance C, (Def. 15.) Therefore E, F are the two points required. Q. E. F.

The least possible length of the given distance is half the line joining the two given points, and then the two points coincide.

4. PUZZLER PERPLEXED.-Draw a line DE parallel to the base BC of a triangle ABC, so that DE is equal to the difference of BD and CE.

Produce BC to K. (I. 9) meeting in F. (I. 31.)

Bisect angles ABC, ACK by BF, CF Through F draw FED parallel to BC.

Then DE shall be equal Proof.--The angle DBF and the angle CBF .. the angle DBF wherefore BD =

=

=

to the difference of BD, CE.

the angle CBF, (Con.) the angle BFD, (I. 29.) the angle BFD (Ax. 1); DF; (I. 6.)

Similarly it can be proved that CE

Now, DF = DE and EF,

=

BD =

wherefore DE =

DE and CE ;

DE and CE;

= EF.

the difference of BD and CE. Q. E. F.