considerations which ought to modify, if they do not remove this first impression. In the first place it should be considered how much all children require right training as well as good teaching; how unspeakably important it is for them to be subjected to healthy moral influences, and to receive such information as they obtain in the right way. Now, an undisciplined, ill-organized school, conducted by a weak, a tyrannical, an ignorant, or otherwise incompetent teacher, is very often a school of vice. No opportunity should ever be lost of practically enforcing the doctrine, that teaching is not the whole of education; but that right principle, systematic discipline, and wise moral supervision ought to be found in every place deserving the name of a public school. The second consideration is, that even under present arrangement, teachers too often neglect the lower portion of a school, leaving the little ones without proper employment or superintendence, while they confine their attention to the upper classes, from whom they hope to gain more credit. There is no doubt that the tendency to do this will be much encouraged by the general adoption of an examination scheme. Any natural desire on the teacher's part to pass a good number of elder children, will almost necessarily increase the disposition to bring all his teaching power to bear on them, and to consider them the most important portion of the school. Thus, the younger children will be likely to suffer, at an age too when their habits are forming, and when, if possible, they require that even more thought and judgment be bestowed on them than near the completion of a school course.

Of course, these difficulties might be met by refusing to receive any candidate whose term of attendance has not been passed at a school which is certified by some competent authority to be properly officered, well organized, and efficiently taught; to be, in fact, a place where right moral discipline is possible, and where the mass of the school does not suffer for the proficiency of the elder children. If the necessities of the case could be met by any contrivance which will seem less harsh than this restriction, of course a great point would be gained; but to overlook the necessity of some effectual precaution on this point, would be fatal to the moral value, and, ultimately, to the success of any prize or certificate scheme whatsoever.

To sum up the conditions which have thus been separately enumerated :—the candidate for examination should be not less than twelve years of age; should have been in regular attendance at the same school for not less than two years; should have entitled himself to a testimonial of good conduct from the master, and of religious knowledge from the clergyman, teacher, manager, or other responsible person; and should, besides this, have received his education at a good and efficient school.

There can be no doubt that to insist on all these conditions would be to narrow the range of available candidates. It would also, at first, involve the exclusion from the advantages of the plan, of many boys who appear to be entitled to certificates. Nevertheless, it should not be forgotten that any such scheme, if carried out, is sure, indirectly, to exercise a most important influence on the character of primary schools generally; and that it is of the highest importance to secure that this influence is of the best kind. It is far better that a few individual scholars should suffer an apparent injustice, than that the whole tone of our public schools should be lowered, their religious character discountenanced, or their general usefulness diminished.

On the subject of the examination itself, it will suffice to make two observations. First: the examination should not be too stereotyped, either as to its form or matter; a certain liberty of choice should be left to teachers in relation to all subjects beyond good reading, writing, and arithmetic. These, of course, are indispensable, but excellence in some one department-history, or geography, or language-should even, at an early age, have more value attached to it than a smattering of all three. If we want to make the teaching in our elementary schools really intelligent, and to

enlist the sympathies and even the enthusiasm of teachers in such a design as this, we must beware of fettering them by prescribing very formal conditions as to instruction. What is greatly to be dreaded is, that when any course of examination is officially laid down, and its limits prescribed, teachers may be beguiled into a mechanical routine, just good enough to fulfil the conditions of the examination, but lifeless and dull, nevertheless. All examinations of this kind have a tendency to encourage cramming, in just the proportion in which they are definite. It would be wrong to say that this is a reason for making the nature of the examination indefinite, but it is a good reason for imposing no needless restraints; and for specifying rather the limits beyond which the examination will not extend, than the particular mode in which that limit should be reached.

One other point will also be found to deserve a little attention. In examining adult students, reliance is generally placed upon the test of written answers to questions. Of course, the plan is the best in their case; and whenever accuracy of technical or book-knowledge has to be tested, best even with children. But, although it is of course to be desired that the youthful pupils in our elementary schools should learn the habit of committing their thoughts to writing, it is also requisite that vigorous oral questioning should be encouraged in those schools, and that readiness, facility of expression, and general mental activity should be promoted in them by every possible means. The children of the educated classes, accustomed to the conversation of intelligent persons at home, have many opportunities of exercising their minds upon the subjects of school instruction, and for them it is enough if the school gives solidity and exactness; society makes their knowledge available, and cultivates the power of speech and reflection in relation to it. The children of the poor are in an altogether different position. Their homes and out-of-door associations do little to stimulate thought about the things which are to be learnt in books; and it is, therefore, the business of the school, in their case, to do this for them. It is not their memory only, but their intelligence which needs cultivation. Now the character of the examination will always determine, to some extent, the character of the teaching; and if it be decided to hold examinations by the help of written exercises only, written exercises will in time become the main feature of school-work. On the other hand, if the examination be to a considerable extent vivá você, oral questions and answers will still, as at present, be employed as the main instruments in teaching. We cannot afford to dispense with, or even to discourage, the vigour and life and animation which have hitherto characterised the best elementary schools; although we may well desire to bring some of the work which is done in this way to the test of written examination.

The other conditions under which certificates ought to be granted are, for the most part, matters of detail, which practical men may be safely left to adjust. Our object in these papers has been to call attention to one or two matters of principle which seemed to us to possess some importance, and to be entitled to the distinct consideration of benevolent persons, who are engaged in establishing and promoting examination schemes.

We have pleasure in calling attention to the particulars respecting a certificate scheme recently put forth by some of the leading friends of education in the neighbourhood of Banbury, which embodies in a great measure the conditions we have laid down. It will be found on the next page.

It is a sad reflection for teachers, but there can be no doubt that the bewildering contrasts which children notice between precept and practice in them is the reason why so much labour in training runs to waste. If our conduct do not point uniformly, under all circumstances, in the same direction as our precepts, we cannot be surprised that the children's dispositions acquire no fixed bent.-Currie's Principles of Infant School Education.

EXAMINATION SCHEME FOR THE BOYS AND GIRLS OF SCHOOLS WITHIN THE BANBURY DISTRICT.

President B. Samuelson, Esq. Committee-The Mayor of Banbury; Revs. W. Wilson, W. T. Henderson, W. Best, J. D. Fish, Dr. Tandy; Messrs. H. Austen, J. B. Austin, J. H. Beale, J. Cadbury, T. Clarke, T. R. Cobb, J. Fortescue, F. Francillon, R. Goffe, T. Hunt, J. B. Looker, W. Munton, W. P. Payne, R. H. Rolls, and J. Shaw.

The object of this scheme is to induce parents to keep their children at school longer and more regularly than is at present the custom, and to hold out to the children themselves an additional motive for diligence and good conduct.

CONDITIONS.

1st. Candidates to be pupils, not being paid assistants, who must be at least eleven and not more than fourteen years of age.

2nd. They will be required to produce a certificate from their teachers that they have attended some Day School for at least three years, and from the teacher of the school at which they are receiving instruction, that they have attended it at least 176 whole days during the twelve months ending the 1st of ( ) preceding the examination; also a certificate from the authorities of the school, that they bear a character for truthfulness, industry, honesty, and general good conduct throughout the year: so that mere ability and cleverness, without good conduct, shall in no case be rewarded.

3rd. Supposing that £70 be contributed to this fund,

That there be 20 rewards offered, of the value of 20s. each,

20 of the value of 10s. each,

10s.

}

For attainments accompanied by

good conduct.

To be called Special Prizes, for industry and good conduct.

Each reward to be in money or books, at the option of the prize holder.

4th. That no pupil shall receive the 10s. prize, who cannot read with correctness and intelligence -write in a fair hand, and correctly from dictation, a simple passage work correctly any sum in a simple or compound rule-distinguish readily any of the parts of speech-and answer simple questions in Geography and English History.

5th. That no pupil shall receive the 20s. prize, who shall not be able to read with fluency-write in a good hand and from memory, with correct spelling, a simple narrative previously read to him slowly -work sums in Proportion, Practice,* Vulgar and Decimal Fractions-evince a fair attainment in three of the four following subjects, viz., Geography, Grammar, English History, and Drawing.

6th. That the Special Prizes shall be awarded to such Pupils as shall be specially recommended to the examiner by their teachers, for perseverance and general good conduct. That such Special Prizes may be taken in conjunction with a 20s. or a 10s. prize, but shall not be awarded to any Pupil who shall not take a prize of at least the lower sum; nor at all, except in recompence of remarkable diligence, since they are intended as a special encouragement to the diligent, whether their mental gifts be great or small. These Special Prizes to be placed at the disposal of the schools adhering to this scheme, in the ratio of the number of pupils in each.

7th. That pupils who have taken the 20s. prize cannot present themselves again for examination; and those who have taken a 10s. prize are disqualified for the same a second time, but may receive the 20s. prize at a subsequent examination.

8th. That these rewards be accompanied with a handsomely-printed Certificate of Merit, furnishing the pupils with a testimonial, to which constant reference can be made in after-life, as to conduct,, regularity, and attainments during their pupilage.

9th. That the examiners shall be either the Government Inspectors of Schools for the district, or persons appointed by them; and tliat, having due regard to the resolutions already passed, the whole of the details of the examinations, and the responsibility of the award of prizes, shall rest in the hands of the examiners.

10th. That the liberal offer of B. Samuelson, Esq., to contribute annually the sum of £50, until a portion of that sum may be raised from other sources in the town of Banbury, be accepted; and be considered the foundation of a general fund for the support of the proposed prize scheme; and that further additional annual subscriptions be requested from the neighbouring towns and villages to the same fund.

11th. That (for the present year) any school which is situated within eighteen miles of Banbury shall be admitted to the benefits of the examination, on the contribution of at least £1 for every 100 scholars attending the school, to the general fund.

12th. That the present committee, appointed at the last meeting, continue during the first year, and receive into its number one member from every school admitted to the benefit of the examination at the appointment of their managers.

*In the examination, Girls will substitute Needlework for Vulgar and Decimal Fractions.

ON THE USE OF PRIME NUMBERS IN ENGLISH MEASURES, WEIGHTS, AND COINAGE.

THE following paper has been communicated to us by Mr. J. Yates, F.R.S., and will be found to contain some useful and practical hints :

On examining the tables of the measures, weights, and coins used throughout England, it is found that the prime numbers used in their composition, and of the most frequent occurrence, are 2, 3, and 5. Of these, 2 occurs as a factor by far the most frequently-indeed, twice or thrice as often as either 3 or 5. Seven makes its appearance in the following weights and measures :—

Eleven is used in one case only, but that is an important one viz.,

LONG MEASURE.

11

or 5 yards

=

1 rod or pole,

=

I' chain.

from which is deduced 4 poles or 22 yards

The furlong, the mile, and the acre are also multiples of this fundamental number. Thirteen also comes in once as a factor, viz., in

Wool weight is curiously compounded. No less than four primes, 2, 3, 7, 13, are used as factors, producing only six denominations, which are as follows:

Only one other prime number requires notice, and that is found in a very conspicuous position, and where perhaps it was little to be expected, viz., in a recent Act of Parliament. The law now in force, and known as the Weights and Measures Act, fixes the number of grains in the lb. avoirdupois by the use of the number 7, and goes on to determine the relation of the pound troy to the standard linear measure, by declaring that a cubic inch of distilled water "is equal to 252 grains and 458 thousandth parts of a grain." If this number (2535) be divided by 2, it will be found that a cubic inch of water weighs 126,229 five hundredth parts of a grain, the numerator of this fraction (1262) being a prime number.

500

1000

As the result of this analysis, it appears that the primes used in the English measures, weights, and coins are the following:-2, 3, 5, 7, 11, 13, and 126,229. I propose to offer a few remarks respecting the aptitude of these numbers for the functions which they are appointed to perform.

The adoption of them does not appear to have been determined in any case, so far as we can judge, by reason or principle, but to have arisen from accidental and arbitrary causes. There is no apparent benefit in connecting our highest coins by 2 and 5, the intermediate by 2 and 3, and the lowest by 2 only. No advantage arises from measuring land by elevens, and weighing wool by sevens and thirteens. No reason can be assigned why seven should be brought into avoirdupois weight, and excluded from troy weight; or why 3 should be excluded from avoirdupois weight, whilst it plays an important part in troy weight and apothecaries weight. In short, all our tables present the appearance of an entire want of principle in their construc

tion.

The introduction of an additional prime has the effect of making our weights and measures more complex and multiform: it ought, therefore, to be avoided, unless some necessity can be shown in its favour. Hence it would seem to be expedient to abolish from these calculations all primes except 2, 3, and 5; and here an important question arises, namely, should these be retained, or shall we be satisfied with 2 and 5, omitting 3?

=

We are thus brought to one of the great discussions of the present day-the expediency of decimalizing our measures, weights, and coins. The consequence of the simple fact, 2 × 5- 10, is that all decimal systems are also binary and quinary, the principal quantities expressed by tens, hundreds, thousands, &c., being divisible by 2 and by 5 without remainder, so that their doubles and their halves can be introduced and reckoned without the least difficulty or inconvenience. But such systems do not readily admit the number 3, because in the majority of cases the quantity cannot be divided by 3 without a remainder, and in many cases the division by 3 produces a repeating decimal. This is the ground on which many persons have insisted on 12 as a multiplier for measures, weights, and coins, rather than 10. But it is to be observed, that if 10 cannot be divided by 3, on the other hand 12 cannot be divided by 5 without remainder. Hence it seems to follow that the choice must be made between decimal and duo-decimal modes of computation, according as a preference is given to 3 or to 5 as a divisor. If it is more necessary or convenient to divide by 3 than 5, duodecimal methods are entitled to the preference, so far as this circumstance is concerned. I cannot, however, discover any reason for making this assumption. I think it probable that division by 5 is required as frequently as by 3; whilst every other consideration is decidedly in favour of the decimal scale.

The investigation which we have been pursuing is therefore, first, in favour of - decimal measures, weights, and coins; and secondly, supports the views of those who think that the subordinate multiples and divisions should be made by 2 and 5 only, and not by 3.

In this conclusion I have the satisfaction to observe that I am countenanced by the authority of Mr. Drinkwater Bethune, one of the commissioners appointed by the present Lord Monteagle, when Chancellor of the Exchequer, to consider the steps to be taken for restoring the standards of weight and measure. In his letter to the Chancellor of the Exchequer, dated 21st September, 1841, he maintains the following positions

1. "That the tables of weights and measures now in use are complex and inconvenient, and that it is very desirable to get rid of inconvenient multipliers, such as the factor 7, which connects the pound avoirdupois with the stone, and thereby with its multiples, the cwt. and ton; and the factor 11, which connects the yard with the chain, and thereby with the mile and acre."

2. “That it is desirable that no numbers which are not multiples either of 2 or 5 should anywhere appear in the tables."

PHYSICAL SCIENCE. THE DISCIPLINE OF THE ELEMENTARY SCHOOL.-For young people between the ages of 15 and 20, I believe that there are no studies so well calculated to call forth and sustain efforts of thought, and so to cultivate the judgment, as the study of language and mathematics. Where, accordingly, there is a likelihood of education being prolonged to any period between those ages, I can understand that for the sake of the future edifice, it may be well to occupy a large part of the preceding years, from 10 to 15, in laying the ground-work of those studies. But when a child's period of schooling is sure to close before his 15th year, it may be worth considering whether it is wise to commence a structure which will never be finished, whether we cannot find for him some other study, more directly connected with the outer world, with which a healthy child of that age is in a state of intense sympathy; whether, for instance, the study of some of the experimental sciences may not be equally well calculated to promote accurate observation, patient thought, and right judgment. My conclusion is, that in elementary schools the study of natural philosophy, as exemplified in the common things of daily life, is well adapted for this purpose.-Rev. J. P. Norris.