EXPLANATIONS. £ s. d. qr. 6972 8780 2563 3 10 0 0 £20 1210 1 As before, you have first to place the same denominations directly under each other; as, farthings under farthings, pence under pence, &c. Beginning with the lowest denomination, the farthings, you must say, 3 and 2 are five, that is, five farthings; you must divide the amount, the 5, by 4, because four farthings are equal to, or make one penny, and you will find that the quotient will be one, and the remainder 1; and you must set down the 1, the remainder, under the column of farthings, and add, or carry, the one, the quotient, to the next column, the pence, the next higher de- ' nomination, because four farthings are equal to one penny. Thus, one penny added to the 6, in the column of pence, makes seven, 8 make fifteen, and 7 make twenty-two, that is, twenty-two pence; you must divide the amount, the 22, by 12, because twelve pence are equal to, or make one shilling, and the quotient will be one, and the remainder 10; and you must set down the 10, the remainder, under the column of pence, and add, or carry, the one, the quotient, to the next column, the shillings, the next higher denomination, because twelve pence are equal to one shilling. Thus, one shilling added to the 10, in the column of shillings, makes eleven, 5 make sixteen, 7 make twenty-three, and 9 make thirty-two, that is, thirty-two shillings; you must divide the amount, the 32, by 20, because twenty shillings are equal to, or make one pound, and the quotient will be one, and the remainder 12; and you must set down the 12, the remainder, under the column of 1 shillings, and add, or carry, the one, the quotient, to the next column, the pounds, the next higher denomination, because twenty shillings are equal to one pound. Thus, one pound added to the 3, in the column of pounds, make four, 2 make six, 8 make fourteen, and 6 make twenty, that is, twenty pounds; and you must set down the whole number 20, as pound is the highest, or largest denomination in sterling money. You must add the column of pounds, as in Simple Addition, and set down the whole amount, and then the work is done. In order to pursue this new course with advantage, it will be necessary to attend to the sort of notation which is used in Compound Arithmetick; and, indeed, this is nearly all that you have now to learn, if you have learned the Arithmetical Tables thoroughly, to be able to perform every operation in this branch of Arithmetick. In the notation of which I have before treated, you will remember, that every advance in the value, or in the station of figures, is by tens, that is, in that notation we count from one to nine, and the next higher number is expressed by one with a cipher after it. In short, in the former part of Arithmetick, in that which we call Simple Arithmetick, in contradistinction to this, which we call Compound, we count by tallies of tens; and, indeed, on this principle is all numeration, all notation, and all calculation, carried on in Simple Arithmetick. But when we come to Compound Arithmetick, as, for instance, in counting sterling money, we begin with farthings, and as soon as we have four, (not ten,) we come to one, that is, one penny: then we count on to the next denomination, which is twelve pennies, and we call one, that is, one shilling: then, again, we count on to twenty, when it becomes one again, that is, one pound. Thus, in the notation of sterling money, instead of counting on to ten, and then changing, we count first to four, then to twelve, and then to twenty. If we wish to count by our measure of inches, feet, yards, &c., we count first twelve inches make one foot, then, three feet make one yard, and so on. If we wish to count by our ordinary weights, we count sixteen, twenty-eight, four, and twenty, that is, sixteen ounces make one pound, twenty-eight pounds make one quarter of a hundred-weight, four quarters make one hundredweight, and twenty hundred-weight make one tun, and so on. Thus you will perceive, that each sort of money, each sort of weight, and each sort of measure, has its peculiar notation; and this peculiarity must be known, and kept in mind, when you work figures descriptive of any of these several quantities. I must also inform you, that you must divide, or separate, by means of a dot or two, a comma, or a space, the figures descriptive of the different sorts of money; and that, in order to show that certain figures are employed to describe pounds in sterling money, we write before, or over it, this character £; that over figures descriptive of shillings, we write a small s; over those for pence, we write a small d; and over farthings, we write qr. This description of the notation of sterling money, contains, and illustrates the principle on which the notation of all money, of whatever country, of all measures, and of all weights, is conducted. The PRINCIPLE of this is very plain. The POUND STERLING is the whole; the SHILLINGS are regarded merely as parts of the POUND, that is, twentieths; the PENNIES the twelfths of the shilling; and FarTHINGS the fourths of the penny. Hence it is, that when you have twelve pennies, you call them a shilling; and when you have reckoned up twenty shillings you call them a pound: but the pound being the WHOLE, you count pounds, and reckon them as I have just stated, as you learned to treat whole numbers in Simple Arithmetick; and thus it is to be in all your reckonings, that is, when you deal with the highest denomination, whether of money, of weights, or of measures, you must treat it as you would treat the same sum in Simple Arithmetick. Whenever, therefore, you have to state, or to reckon any sort of money, weights, or measures, the principle on which you have to proceed is this, to ascertain what is the whole number, and what are the parts into which the money, the weights, or the measures, of which you have to treat, have been divided; and then you will know how to proceed. You have been told how to proceed in the notation and addition of sterling money. The We will take an example of the treatment of our larger WEIGHTS. The TUN is the largest weight to which we reckon; it is, therefore, the whole number, and it is broken down, or divided, into HUNDREDWEIGHTS, twenty of which make one tun. hundred-weight being composed of a hundred and twelve pounds,. a sum inconveniently large, it is divided into QUARTERS, of twenty-eight pounds each; `and for still greater convenience, the POUND is divided into sixteen ounces, so that the numeration of our larger weights is, sixteen ounces make one pound, twenty-eight pounds make one quarter, four quarters make one hundred-weight, and twenty hundredweight make one tun. The marks used to describe these several weights, are T., cwt., qr., lb., oz., as you have already learned in the Arithmetical Tables. The several sorts of weights and measures are differently divided, and have names varying from each other. But you must not startle at the multiplicity of these things; for you must remember, that you are furnished with the principle on which they are all to be treated and managed. You have seen, that all you have to do, on proceeding to work figures descriptive of any of them, is to know, first, what is its whole number, or, as it is commonly called, its largest denomination, and then to know how that is divided. These things are all stated in the Arithmetical Tables. As before stated, the principles of Compound Arithmetick do not materially differ from those of Simple Arithmetick. Thus, in Simple Arithmetick you carry one for every ten; but in Compound Arithmetick you carry by the number that it takes to make, or equal one in the next higher denomination; this is all the difference. By paying particular attention to the preceding EXPLANATIONS, you will be able to work any sum in Compound Addition; and I wish you to bear in mind continually, that the object of these EXPLANATIONS is to explain to you the principles upon which the rules are founded. As sterling money is but very little used in this country, I shall merely give you a few sums for exercise, and pass to the next part of the subject. Note.-To TEACHERS. The teacher should be very particular in requiring the learner to place the figures in each column with great accuracy; as, farthings under farthings, pence under pence; ounces under ounces, pounds under pounds; pints under pints, quarts under quarts, &c.; for neglect in this particular would very naturally lead him into errour in performing the operation. |