2, 3, 4, 6, 8, 12; for it is divisible exactly by all these numbers, and these numbers are submultiples or divisors of 24.* (To be Continued.) F. CURIE. A HELP TO TEACHERS IN SETTING SUMS. REV. SIR,-A correspondent favored us in the July number, with a key to the quotient of a division sum. As such keys unquestionably offer facilities to teachers, perhaps you may not deem it foreign to your purpose to insert the following " method of setting sums in simple and compound addition, showing the answer without the trouble of working the sum." Your readers will understand that the method lays no claim to novelty. Simple Addition. Set down any line of figures, as for instance, 864326. Let the next line be composed of numbers, each of which added to the figure above it, shall make nine, and in the unit's place, ten. Thus :- 1 3 5 6 7 4 Set down another pair of lines on the same principle. Thus :- 5 4 2 0 9 2 Now add another linet composed of any figures, and this last line will be the answer. * Let it be required to divide m by n, and let y be the quotient, then the type or formula of division will be m n y, or m÷ n = y. Again, let it be required to divide 6 a 2b by 2 a; then, because division is equivalent to the cancelling of a factor to divide 6 a 2b by 2 a, is to cancel the factors 2 and a; so that 6 a 2b ÷ 2 α = 3 ab; for 6 a 2b 3.2.a.a b = 2 a.3 a b; and by cancelling the factor 2 a, we have 3 a b. Frequently we cannot cancel all the factors, and in this case the division is even a more simple process than before. Surely it would be better, in order to avoid detection by the pupil, to add two lines, varying in position, the addition of which would not give much trouble to the teacher.-[ED.] The figure 2 on the left hand indicates the number of pairs of lines, minus the last, of which the sum is composed. If three pairs be set down, 3 will be substituted for 2; if four, 4; and so on. It will be evident on examination that the line of figures placed last in the above example, may, to avoid detection, be put in any other situation. All that is necessary is to form the pairs independently of it. Compound Addition (of Money). Set down any line as before, £ 8. d. Thus :- 342 The next line must be composed on the following plan. Beginning with the farthings, let as many be added as will make a penny, in this case three-farthings: which set down under the farthing. Passing to the pence let as many be added as will make eleven pence, in this case 5d., put it down under the 6d. Going forward to the shillings, let as many be added as will make nineteen shillings, in this case 6s. The pounds must now be treated in the same manner as in simple addition, each figure making nine with the one placed under it. The first pair of lines will then stand thus ; Proceed in the same manner to form another pair of lines (or any number of pairs), and add a last line of any figures, as in simple addition, which will be the answer. Let the pairs correspond upon the same principle as before. Suppose the first line to be the lbs. making 28; the qrs. 3; the cwts. 19; and the tons as in simple addition. In the above example the key is placed in a different situation from those that preceded it; and the figure 3 on the left of the answer shows that there are three pairs of lines. Wrexham. Your obedient servant, P. G. ENGLISH GRAMMARS. SIR, I have recently seen in the English Journal, some judicious observations by "H. B." on English grammars. Permit me to suggest, that the republication of Dr. Lowth's (which is now out of print) would meet most of his notions. No modern school grammar, with which I am acquainted, exhibits such a comprehensive, accurate, and systematic view of the principles and practice of the English language. The critical remarks are exceedingly valuable, and have been the storehouse from which the materials of more recent publications have been taken. Some slight alterations and additions, in order to adapt it to improvements in tuition, might be made. The observations and critical remarks, instead of being printed at the foot of the pages, might be put in their appropriate places in the body of the text, and in small type; in some cases they might be compressed, and in others of less importance, omitted. This would save space, and have the advantage of marking out two distinct courses of instruction, if it should be deemed necessary. The verbs also might be arranged with greater simplicity; a chapter on the derivation of words (a branch of education now deservedly attracting much attention), would be desirable. These, with a more copious illustration of syntactical principles, which have received much elucidation since Lowth's time, and a few pages of parsing lessons, consisting of entire passages from our best writers, would, in my opinion, render the book more useful and worthy of general support. The method which Dr. Lowth has adopted, of "teaching what is right by showing what is wrong," is, I think, sound in principle; but, in addition to this, would it not be highly useful* to have, at the end of [* We have our doubts about this point. As to the republication of Lowth's grammar, we ventured to make this suggestion in our first number.-ED.] each chapter, a few passages in which inaccurate expressions occur, for the pupil to correct, which he may be fairly expected to do, with the aid of the critical remarks on similar passages in the preceding text? With these views I have been for some time engaged on a new edition of Dr. Lowth's grammar, which I expect to publish before ChristF. mas. Notices of Books. Plain Sermons, addressed to a Country Congregation. By the late Rev. Edward Blencowe, M.A., Curate of Teversal, Notts, and formerly Fellow of Oriel College, Oxford. Foolscap 8vo., pp. 412. (Bell.) It was observed by a correspondent in a recent number, that the exhortation addressed by the church to sponsors, enjoins that they " shall call upon" the child for whom they have answered, "to hear sermons," in order that it may the better know the things which its sureties have promised in its name. Such an injunction can leave no doubt upon the minds of those to whom the church has committed the teaching of her youthful members, as to whether the hearing sermons should form a part of religious instruction. The main question for their consideration will be the kind of sermons best suited to this purpose. The motto of the volume before us, namely, that "reality appears to be the most conspicuous feature of the scripture method of instruction; the second being, perhaps, affectionateness;" and, as we conceive, the exemplification of this in the sermons themselves, seemed calculated to throw some light upon such a question. Reality and affectionateness appear to us to mark the happy medium between a cold constrained form of language on the one hand, and exaggerated statements and unwarranted excitements on the other. Sermons of the former cast cannot, under any circumstances, be expected to produce much effect, especially upon the young; and although, as regards the latter kind of sermons, it is very certain that great immediate (apparent) effect may be produced by a high-strained and vehement tenor of discourse, yet still the question arises, whether the judgment must not be enlisted on the side of truth, in order to produce the true and lasting power of godliness. But here it may be asked, what share is the judgment likely to have in regulating the opinions or conduct of the young? or what is the standard to which it is most probable that their judgment would appeal? To such questions our answers must necessarily be brief, and will consist in assertions rather than in proofs. To the first, then, we reply by expressing our belief that, in the case of the young, the judgment is of necessity exercised (whether rightly or not) much more than is generally supposed, and only apparently less on account of the operations of of the feelings being at an early age more conspicuous. Our reply to the second, is, that we believe real life to be the standard to which the young are continually, though perhaps unconsciously, appealing. And hence we would infer that, whilst it is peculiarly necessary in the case of the young that the preacher should manifest personal concern, which is essential to engage their affections, it is no less necessary to the last ing efficiency of his teaching, that it should approach as nearly as possible to reality, or a true connection with life, and aim at constantly bringing home to the judgment the conviction that "true religion is a silent inward principle, of operation like to that of leaven, capable of spreading through the whole mass, both of the individual in whom it is, and of society in which it ought to be;" that "it is the very life blood circulating through every vein of the whole moral and social system; the moving, vital spirit of man's daily life, and its unceasing, uniform, and universal guide;" that "it is (for instance) in worship, devoutness; in business, diligence and honesty; in suffering, patient resignation; amidst enjoyment, temperance and sobriety; (and so on, through the chain of christian graces, religion being the perfection of each), all springing equally from a sincere belief in what the Saviour of the world has done for us, in the fulfilment of His Father's will." Discourses which, in a natural and affectionate manner, thus enforce the belief of the gospel as the foundation of daily conduct, and as the framework into which all acts, thoughts, hopes, affections, and desires are to be cast, and thereby moulded,—such discourses are models of instruction for all periods of life, and especially for youth. It is not because the sermons in the volume before us are more particularly addressed to the young, but because, as we conceive, they possess merits of this description, that we would recommend them to the notice of the readers of a “journal of education." We conclude with a few extracts: The first sermon upon the text, Job, ch. vii, v. 6, My days are swifter than a weaver's shuttle," affords an instance of the successful application of peculiar local circumstances to the purposes of religious instruction. "The words of Job fitly and strikingly describe the quickness with which the days of our life glide away. Have you ever seen, brethren, the weaver at his frame? Have you ever watched how swiftly he throws the shuttle from side to side, backwards and forwards, and how every throw leaves a thread behind it, which is woven into the piece of cloth he is making? If you have, you will feel how well Job compared human life to the shuttle's motion; and if you have not, yet it is a thought you can all understand. Something like it you may see going on in many a cottage around us here. "The truths brought before our minds, and which may God's grace and holy spirit bless to us, are the following:-1. The swiftness of our days. 2. That each day as it goes adds a thread to the web of life. 3. That what we weave in time, we shall wear in eternity. 66 Hence, how needful it is for us to consider what sort of thread it is that our days are weaving in the web of life! Is it dyed in the light of heaven? When God at last shall cut it off, will it appear that we have been doing His work? Will He accept it for Christ's sake? Shall we be found clad in our Redeemer's righteousness—in the garments of salvation ?" (pp. 1, 2.) In the 16th sermon, on Matt. ch. vii, v. 13, 14, the 'broad way" is thus graphically described, and practically applied to real life : “It is broad, because it admits of many paths, all forming, however, but one road, and all leading but to one end. The ways of sin are various; the devices of Satan, for man's destruction, are manifold. All we,' says the prophet, 'like sheep have gone astray; and he adds, we have turned every one to his own way. Suppose an army of soldiers marching across a country to a certain spot. 6 X |