instead of one, apparently offered,—a course, I am afraid, too many would be likely to follow, at least until they were convinced of its foolishness,—the master would show him the impropriety of his conduct, by bidding him consider how such unfair proceedings are regarded by Him whose eye is on us at all times. He might ask him if he would not consider such conduct in another as cowardly and dishonest; and he might further question him as to which he thought was the best cipherer, the boy who had only twelve or fourteen sums, but had worked them all fairly, or he who had twenty, but had worked only eight or ten. If this method were adopted, the child would rarely be guilty of a similar offence a second time. The best time to make these observations is after they have finished ciphering, when all the class may profit by them; for it is a difficult matter to draw their attention from the sums during the lesson.

I do not profess to have anything new to offer on the theory of arithmetic. No doubt it is very necessary and important that the children should be taught the reason and use of what they are doing; but do not many persons misapply much valuable time in attempting to explain the reasons for operations which the children are unable to perform? If they cannot do it, there surely can be little or no use in telling them why it is done; it can hardly be expected that they will understand such explanations, or be interested by them. I never think of saying anything of the reason for the operation in addition, until the child can work " case fourth" of that rule tolerably quick; and so of the other

rules.

I will here mention, what, perhaps, I ought to have stated before, that the names of the figures are taught in the same manner as the alphabet, as described in your last number; and that for teaching the children to make figures, I employ a set of papers with six figures on each; in using the latter, two assistants are necessary, the same as in teaching the alphabet; the duty of the teacher is to guide the hand of the learner while making the figures. The learners read the figures to the hearer from the slate, and not from the paper.

Although I cannot speak with certainty of the time children will take to master all the cases I enumerated in the former paper; still I have good reasons for believing, that in general those who begin at about six years of age, will have accomplished the task by the time they have completed their ninth year; some considerably before.

Few, I imagine, will deny, that when these cases have been gone through in the manner I propose, the real difficulties of arithmetic will have been overcome; all that they will afterwards require will be explicit and intelligible rules; these, I am sorry to say, are still desiderata in works on arithmetic. Writers on the subject generally appear more desirous to give the reasons for the rules in algebraic formulæ, which not one reader in fifty understands, than they are to impart perspicuity to the rule itself.

When the children have passed through the cases just mentioned, I could put them to cipher one half hour a day, from a guide, taking care it should be one without answers to the questions; the question with its answer, but not the work, should be entered in a book; this would

be a useful exercise in writing, and something for them to take home to their parents. They should commence with the first rules of arithmetic. The other half hour they would cipher in other sets of separate sums, which I have prepared, viz., four of reduction, one of simple and one of compound proportion, four of duodecimals, &c.

Clerkenwell.

Your obedient servant,

THOS. JEFFERY.

REV. SIR,-Permit me, through the columns of your useful Journal, to recommend the "Separate Sum System,' of Mr. Jeffrey, described in your November number.

I have partially adopted it in my own school, having been made acquainted with it by him whilst at the "Training Institution;" there is no reason, however, why it should exclude the usual method for the purposes of explanation, illustration, &c. I think the class might be more effectively instructed in the mode of working the various rules from the slate or black board. I also differ from my friend with respect to allowing the children to use their fingers in computing. I should by all means encourage this, without the use of tables for addition and subtraction, multiplication, &c. The children in my own school provide themselves with small table books," thus doing away with the trouble of constructing tables for them.

I write my "answers" on stiff card-board, the same size as one of the sums, on both sides, and tie them all together with a red tape, or wrap them, i.e., a set, in a strip of parchment of a proper size previously. To teach arithmetic well is an object of much importance; it is a great inducement for parents to send their children.

I hope Mr. Jeffrey will be able to induce others to try his system, that, many joining, the sums might be printed, to save the time and trouble of copying.

Kingston.

I am, Rev. Sir, your obedient servant,

R. FLOYD.

LONG TIME TABLES FOR NATIONAL SCHOOLS,

WITH A VIEW TO THE MASTER'S TEACHING EACH CLASS IN TURN.

MR. EDITOR,- -One of the most useful features of your Journal is the ready and kind admission given to the practical suggestions of men engaged in the arduous business of education. These suggestions, for the most part individually of great importance, are in their accumulated mass, of the most sterling advantage to the schoolmaster, who, in duly appreciating them, and in carrying them out, takes the surest way to invest his own plans with success. With a view of contributing a mite to this department of your publication, I request the insertion of the subjoined.

In your number for February last are inserted some time tables for national schools. In these, and in many others with which I am acquainted, there appear to me to be two very serious, even radical defects:-1st, the time generally allotted to a lesson is too limited for that lesson, either to be well taught, or well learned; and, 2nd, each day's lessons being similarly arranged, they only admit of the master's general superintendence, and not of his regular and systematic teaching of all the classes at proper times.

The first of these defects is, doubtless, the chief cause of the want of success in some schools, and obstructs the attainment of complete success in others, where the indomitable energy and incessant application of the master surmount in part the difficulty. It is erroneous to suppose that these extremely short lessons, and the rapid, incessant change from one to another, are necessary to keep up the interest of the scholars. On the contrary, I have found them to be quite opposed to the fostering of this feeling. Generally, the minds of children need time to be well instructed; and, if the time allowed be too little, the lessons must necessarily be very imperfectly attained. Being blamed for having accomplished too little, the scholars become disheartened, and weary of attempting to do what, in fact, the shortness of the period prevents their doing thoroughly. Besides, "a thing well done," says an old adage, "is twice done; ill done, not done at all." Then, the additional time lost, and noise made in so many changes of lessons; and the small scope, considering the number of classes, given to the master's actual superintendence, are all reasons, and strong ones, against the short-time

tables.

The constant teaching, the stated and systematic examination of each class by the master, in sufficiently prolonged periods, and this only, can ensure success. It is possible so to arrange the time tables, as that every kind of lesson shall have its proper time assigned, according to its relative importance; and that the master may direct his exertions in equalized periods to the teaching each class, and each lesson. Rigidly confining himself to such a system, the master enforces by example, as well as precept, the order and discipline of the school, and this is no slight matter. And, on the one hand, while he teaches a class, he also examines it; so, on the other hand, each class, knowing that its progress in every respect must necessarily come under his regular cognizance, is rendered anxious to prepare for such examination. The firmest hold over the boys is thus given to the master, and extended to the monitors. He is, by this regulation, able to commend whatever he deems worthy, and to correct firmly, but temperately, whatever may be wrong, in teacher or boy. In short, he becomes in truth, by this simple arrangement, the focus whence radiate the life and activity, the order and success of his school.

It would be easy, Sir, to point out many evils resulting from the opposite plan; but, in my present communication, I must pass to the time tables given underneath. I do not pretend to offer them as models; but, at any rate, they will be allowed to evince an anxious desire to make the master's labours less irksome and more effective :

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