every inference he draws. Such habits as these will be invaluable in every Pursuit and duty of life, for they will help to make him a sounder and more modest reasoner, and therefore a wiser man. The value of the exact sciences as instruments of mental discipline has long been recognised. To omit them from any scheme of instruction, however humble, is to allow an important class of the mental faculties to remain runtrained. In the limited eurriculum of our common day schools, arithmetic holds a place analogous to the mathematics of a University course. It is the only one of the pure sciences usually admitted into snch a school, and the only instrument there available for severe and systematic logical training. It is only when looked at in this higher aspect that arithmetic can become an efficient instrument for disciplining the judgment and improving the mental powers; indeed, it has no right to be called a science at all, so long as it is limited to ciphering on a slate, and does not include a systematic acquaintance with principles as well as rules." "Many of the questions are selected from the Cambridge and London University papers, and from those proposed to schoolmasters who have been candidates for certificates of merit. The students who master the reasonings and becomes familiar with the rules in this book, will, as far as arithmetic is concerned, be competent to pass with credit the ordinary examination for the degree of B.A. at either of the Universities.

Church of England Sunday-School Quarterly, Dec., 1856. Published at the Institute, 169, Fleet Street.-We have pleasure in again calling the attention of Teachers' Associations to this Quarterly. Though not directly addressed to teachers of Day Schools, there is, nevertheless, always a good supply of matter bearing on the subject of religious teaching, which is not to be found in the ordinary educational serials.

The School and Family History of England. New Edition. By E. Farr, F.S.A. Longman and Co.-Mr. Farr's History of England is of some standing, and ranks among the best of the school histories. Beside the usual narrative of events, brought down to the end of the Crimean war, the author has judiciously added supplementary chapters on each period, for the purpose of presenting to his readers some slight information on the condition of the people in referenee to employments, marners, customs, &c. There is however wanting that strict accuracy in the statement of facts, which is so absolutely necessary in history. Mr. Farr tells us, that trial by Jury was in use among the Saxons, but our best constitutional writers deny this, on grounds which cannot be challenged ;-that Robert Bruce, the restorer of the independence of Scotland, was the son of the original competitor, whereas he was the grandson;-that the first English newspaper was published in 1588, which newspaper has been shown to be a forgery;-again, it is said that "Becket gave £5, for a dish of eels, more than equivalent to three times as much of our present money,"-the best writers say from twenty to twenty-five times as much. These and other similar errors, tend much to lower the value of a work, which otherwise is a fair history.

Infant School Manual. Infant School Depository and Groombridge and Co. The proper object of this Manual, is to present to the public for the first time, the plans adopted in the Model Infant School of the Home and Colonial School Society. This part of the Manual was done by Miss Sunter, the late mistress, aided by Miss E. Mayo. As an introduction, and to make this Manual the more complete, the work opens with a section on the school room and schoolmanagement. The chapters in the second part contain the several steps in

Lessons on Colour, Form, Objects, Number, Reading, Drawing, &c. We beg to remind our readers, that these Lessons have borne the test of long trial, and are therefore entitled to great consideration, even by those who may object to some of the detail. Of course this Manual will be patronised by all who teach in Infant Schools, but we think its usefulness is not limited to that class. No teacher in an elementary school can carefully examine these plans without profit. We recommend it strongly to all pupil-teachers.

First Steps in English Grammar. By W. Pindar. Simpkin and Co. The purpose of these thirty-four pages, we take to be to supply the compiler's pupils, with just as much text as should be committed to memory. From the number of these little compilations, it would seem as if schoolmasters found it profitable to print their own text-books.

Domestic Economy. (Gleig's School Series.) Longman & Co. The introductory part of this work contains chapters on " Commencing Housekeeping," &c. and the body of the work chapters on the Choice of a House; Domestic Expenditure; Household Work; Needlework, washing and ironing; Food, marketing, and cooking, and care of the Sick and of children. The style is attractive, the "Hints" judicious, and the work one deserving of extensive patronage.

Reflections on Church Music. By Carl Engel. London: Scheurmann and Co. The course which these "Reflections" take may be gathered from the following summary of contents. After some general remarks on Church music, the writer proceeds to discuss the essential qualities of Church Music. This is followed by rules for singing, and a chapter on congregational singing, with remarks on the kinds of music suitable for Congregational use. The concluding chapters take up the subjects of organ-playing, choir-singing, and the means of further improvement. We have read Mr. Engel's "Reflections" through with pleasure and profit, and though not at one with him on all points, we cannot but commend the devotional tone and artistic feeling, which runsthrough the entire work. These "Reflections" should command the attention of clergymen, organists, choirmasters, and other persons possessing influence in Connexion with our church music. The following extract on "The Organ Accompaniment" strikes us as singularly pertinent in a large number of instances. "It appears easy enough to accompany a hymn or chant; yet to do it well, needs more taste and judgment than is generally thought. Moreover, almost every one can perceive the great difference in the playing of the same accompaniment, by an accomplished organist and by an inferior one. As a general rule the accompaniment ought to be subordinate to the singing. The superiority of the voice to any instrument, and the circumstance that vocal music, in which poetry is wedded to music, appeals in words aud tones doubly powerfully to our heart, sufficiently account for this. The instrumental accompaniment has, so to say, to support the vocal music, and to show it to the greatest advantage. In divine worship, the subordination of the instrumental accompaniment is doubly important, on account of the words, which have, of course, the first claim to our regard. The degree, in which the accompaniment ought to be subordinate, depends upon different circumstances, with which the complete organist will know how to cope. Thus, if the congregation are but slightly acquainted with the music which they are to sing, it will probably require a more leading and louder accompaniment; while a well-prepared choir scarcely needs any accompaniment-indeed, may be better without it. Even

in cases where the accompaniment must take the lead, it ought not entirely to dominate; since, though in this way the defects of the singers may be more hidden, yet they will not be avoided; and another great defect will arise, viz., disproportion of the accompaniment to the voices.

"It may be that many of the usual defect in the playing of the accompaniment originate only from a certain nonchalance of the organist. Moreover, the very fact, that by more care they might be avoided, will sometimes make them much more annoying than the unavoidable blunders in singing, of the unmusical members of the congregation. Of such kind are generally the following:-In the middle of a piece the stops are thoughtlessly drawn out or pushed in, just as suits the momentary whim of the organist. The swell is unwarrantably and continually reverted to, by which the so-called see sawing is produced. The last verse of hymn is always sure to be accompanied with louder stops than the preceding verses regardless whether it be in accordance with the sentiments of the words or not. What can be more unseemly than resorting to the employment of many noisy stops, so that the organ overpowers and drowns the voices of the singers! In such cases the latter will either yield at once to the greater power of the former, or there will arise a kind of strife for superiority, more resembling the cries of the heathen invoking Baal, than the pious effusions of a Christian assembly."

Carrespondence.

SIR,-For the information of "A Church Schoolmaster," and other readers of your valuable pages, I beg to submit the following method for obtaining what I think to be correct, "Quarterly Results," in James Martin's (No. 2.) Class Register of Attendance, Absence, and Payments.

For the average attendance of the class during the quarter, add the weekly averages, and divide by the number of weeks.

The total number present in the "Quarterly Results," is the number who have been present at all during the quarter.

The average number of days atter.ded by each child present at all during the quarter, is the sum of "School days prssent" in the “Quarterly Total," divided by the total number present at all.

Total school fees received needs no explanation.

T. H. C. will find an answer to his question at page 15 of the Minutes of the Committee of Council on Education for 1852-3, condition 4. It is there stated "that at least seven-tenths of the whole income, including the (capitation) grant, shall be applied to the salary of the teacher and assistant teacher. This seems to be so plain, that one almost wonders at managers and teachers being ignorant of its meaning. If a teacher's stipend be less than seven-tenths of the whole income of the school, including the Capitation grant, where there is no assistant teacher, he can claim a certain proportion of the grant, perhaps, in some cases, the whole. For, suppose the income of a school, without the grant, to be £90 a year, and suppose the grant to amount to £10, and the teacher's stipend to be £60, he can, by the minute of council, claim the whole.

December 8th, 1856.

I remain, yours, &c.,

W. P.

SIR,-Having some doubts as to the exact purpose which the 2nd and 3rd pages of Martin's Class Register, No. II., are intended to serve, I would feel obliged to you or any of your correspondents for informing me, through the medium of your valuable periodical, what entries are to be made in these pages? Whence and how the materials for filling them are to be obtained? and what is the advantage of so filling them up seeing that the Register seems otherwise pretty complete in itself. I admire the generous proposal of "Senex" in your last number, for which he deserves the hearty thanks of those whom it is intended to benefit. Had I deemed my present difficulty of sufficient importance to incur the amount of trouble and correspondence necessary to obtain a solution in the way he proposes, I would gladly avail myself of the opportunity thus offered to me.

Yours, &c.,

A. D.

Up Holland Moor, December 2nd, 1856.

DEAR SIR. In your December number "A Church Schoolmaster" applies for a method of obtaining a correct "Quarterly Result," in James Martin's School Register, No. II. I beg to offer the following as a solution :

All Schoolmasters using the Registers in question will be aware that in the printed rules on the title page, there is a mistake which may lead to great error in calculation. I mean the second rule, where, instead of saying that the sum of all the total should be divided by ten (that being the usual number of attendances in a week) 2, is given as the divisor. Again, in the fourth rule, for obtaining average number of days attended by each child during the week," the correct method is to add together the days attended by each child during the week, and divide by the number of children; or what amounts to the same thing-when the children have had five whole days in school-divide the average by twice the number of children present during the week.

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To find the " Quarterly Results."

1. Add together the averages for all the weeks in the quarter, and divide by the number of weeks in that quarter.

II. Count up the names of those who attended school at all during the quarter. III. Add together the number of days each child has attended during the quarter (as filled in on the margin of the Register] and divide by the number of children who have attended at all in the quarter.

IV. Count all the names on the Class Register.

V. The pence having been previously added up for each child along the margin on the right hand side of the Register, find the total of all those sums. The Annual result may be found in a similar manner.

I am, Sir,

Yours, truly,

J. H.

Wharton School, December 6th, 1856. Sir,-Having been a constant reader of your valuable paper ever since its commencement, and having received many valuable hints from it, I beg in return to answer one or two enquiries in the December number, and offer a few remarks which may be of use to some of my fellow teachers, and if of use to one I shall feel myself amply repaid for my trouble.

The first is by a "Constant Subscriber, Wigan." He quotes from your own article "where are those bright spots, in which permission has been employed by the Board of Guardians to pay for the schooling of children who receive out-door relief." I can tell him that in the above school such children are paid for in the same way as he describes, and subject to the same regulations.

The next is an enquiry by a "Church Schoolmaster;" I use in my school the Registers published by James Martin, 9, Lisson Grove, and in order to get correct Quarterly Results in the Register (No. 2.) of attendance, absence, and payments, he must add up the numbers under each heading, and divide by the number of school weeks in the quarter. In reference to the question asked by "T. H. C.," I must say that I fully agree with the advice given by the Editor of the "Papers for the Schoolmaster to the School Managers.

I can mention a school a few miles from here, where the managers add a certain sum to the money paid by each child in the Clothing Club, upon condition that the same child attends the required number of days (176) for the Capitation Grant. In another, three shillings are given to each child upon the same conditions. In the former school the average attendance is about 150, and 42 made the required number of days, and in the latter a mixed school of about 120 not more than £12 was received for Capitation fees.

In neither case does the master receive any benefit from the Capitation Grant. Now, I believe the saddle is laid upon the wrong horse. If the managers would say to the teacher, we will give you all the Capitation fees above a certain sum which may be considered reasonable, they would find a different result. In support of my assertion, I will take my own school for example.-The number on the books last year was 105, the average attendance 75, and the number who made not less than 176 days was 61, and consequently got £15 for Capitation fees; one-half of this sum is given to me.

I have enclosed a card which I use; they are sold to the children at d. each, and are brought to the school every Monday morning, and how glad the children are to see a row of fives!

I copy the Quarterly result of attendance and payments, which I have arranged for myself as below, and it enables me to watch the attendance of the children more closely, which I do not hesitate to say will not be done by those who receive no benefit from the Capitation Grant.

I find the use of this table saves a great deal of trouble at H. M. Inspectors visit to the school, and if a similar table were added to these Class Registers, I think they would be improved. If you think the above remarks and the card will be of use to any of my fellow teachers, by inserting them in your valuable paper you will much oblige,

Yours respectfully,

A. G.