So-LESSON,

Your enemy, however hardened, application of kindness and generosity against you like the metal-by feeding like fire under, around the sides, and on him when hungry when thirsty the top, will certainly accomplish. giving him water to drink-by continuing these kindnesses in every variety of ways and at all times.

You will thus, as it were, have "heaped coals of fire upon his head;" and accomplished in the Moral what takes place in the Natural world. You have subdued and gained your enemy; he will be melted under your overwhelming kindness.

kindness to an enemy.

that "heaping coals of fire on the head of their enemy" will just be following the spirit and example of Christ; who "when reviled, reviled not again," shed his blood for his enemies, "even unto death," and prayed for his murderers.

From "Bible Emblems" by David Stow, Esq.

Educational Intelligence.

WENTWORTH CHURCH OF ENGLAND SCHOOLMASTERS' AND SCHOOLMISTRESSES' ASSOCIATION.

The members met on Saturday, 6th February, at the Hoyland School, when after tea, the usual business of the Association being disposed of, Mr Hornby the Schoolmaster read a Paper on "Reading, and how to teach it ;" in which the Synthetical and Analytical Methods were compared, and the Cheltenham mode of teaching this subject favourably noticed. The different points of the Paper were discussed, and the Meeting broke up a little before 8 o'clock.

The next Monthly Meeting was appointed to be held at Mr. Loane's the Parkgate School, on which occasion Mr. L. proposes to read a Paper on "Timetables."

NATIONAL SCHOOL CHORAL FESTIVAL-1858.

The expectations of the Committee, as to numbers, have been more than realized. At the first rehearsal of Teachers and Pupil Teachers, on the 6th, at Exeter Hall, a large number were unable to gain admission. Between seven and eight hundred intending participators in the Festival applied to the Secretaries for tickets for the next rehearsals. Indeed, so numerous are the volunteers, that could the orchestra at Sydenham be so enlarged as to hold seven thousand, instead of three thousand five hundred, not the slightest difficulty would be experienced in filling it.

To Thomas Rember, on the completion of his apprenticeship in the National School, Hartfield, Tunbridge Wells,-an elegant portable Writing Desk, by the Clergy and Teachers; also a neat sliding Book-stand, of Tunbridge ware, by the l'upil Teachers and Scholars.

EXTRACTS.

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 occur 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.

or 5 yards = 1 rod or pole,

from which is deduced 4 poles or 22 yards = 1 chain.
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.

or 6 tods 1 wey.

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:1 clove

7 lbs. avoirdupois.

1 stone 2 cloves.

1 tod =2 stones.

1 wey = 6 tods or 13 stones.
1 sack 2 weys.
1 last = 12 sacks,

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. advoirdupois 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 (258458) 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 (1) being a prime number.

1000

12 29

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 aeason of principle, but to have arisen from accidental and arbitrary causes. There is no apparent benefit in connecting our highest coins by 3 and 5, the iutermediate 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 appearanca of an entire want of principle in their construction.

The introductien of an additional prime has the effecting 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 system 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. It is more necessary or convenient to divide by 3 than 5, duo-decimal 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 decimas scale.

The investigation which we have been pursuing is therefore, first, in favour of decimal measures, weights, and coins; and secondly, supports the view 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. letter to the Chancellor of the Exchequer, dated 21st September, 1841, he maintains the following positions:

In his

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 it multiplies 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 any where appear in the tables."-British and Foreign Schoo Record.