value in farthings of pounds sterling; the following table may not be amiss. Now, it appears by the above table, that if there are three figures in the pounds, the answer must be expressed with hundreds of thousands of farthings, instead of hundreds, as in the numeration table. The reason of it is, that there are three more figures wanting to finish; and this is made up by the farthings in the remaining shillings and pence. Now, this is totally the reverse in common arithmetic; for the work must be finished before it is possible to know how to value the product; hence the beauty and utility of being able to give an answer, and in so short a space of time, that it must appear very astonishing to the best calculators; for indeed, answers may be obtained mentally in less than a fourth of the usual time, and that more correct than by the pen or pencil, when we take into consideration the liability of making errors by the common method. It may be truly said that £1 cannot be called one thou sand farthings; but, by putting to it 10d., it will become 1000; and there is a triffing exception, which will not be in any way difficult to the reader; for it will be seen afterwards that it will be almost impossible to make a mistake in valuing the product. Nor is there any occasion to learn the table by heart; but the reader may do well to refer to it, and he will find it to be literally correct. It is, however, the best table the author could invent. 2dly. It will be seen that those who are clever in practice may find the product of two factors, thus, Suppose it is required to find the square of 768; now, this is the same as 768 at 16s., (768 farthings,) and, therefore, the square must be the same in number as the farthings in £614 8s., or 589,824; and such equations as this, when performed without the aid of pen or pencil, obtain for a man the desirable character of being quick, ingenious, and clever. 3dly. That by the intervention of money tables, the reduction of weights, measures, &c., may, in a great measure, be performed by multiplication; besides many other things that would be too tedious here to mention. 4thly. Instead of burdening the memory, these rules serve in a wonderful way to relieve it, for instance, by remembering 5; it will, at once, put a person in mind of the number of feet in a mile, namely, 5280; there being so many farthings in £53. And, by multiplying this 5 by 12, because 12 inches is a foot, we have £66; and the farthings in this sum serve to remind him of the number of inches in a mile, viz., 63,360. Again: multiply this 66 by 3, and we have 198; the farthings in which will, in numbers, equal the barley corns in a mile, viz., 190,080. One more: 5, or x=£y, the farthings in which will, in numbers, equal the yards in a mile, viz, 1760. Thus, then, by remembering that which is so trifling may all the denominations in weights and measures be found. It is to be recommended to the reader to get a ready knowledge of the value in shillings of from 1 to 23 tenpences; as also the farthings in the aliquot parts of a pound; thus, in making use of those parts, when we say 6s. 8d. is the third of a £., it may be as well to accustom ourselves to say it is also 320 farthings, that is 990, and so on, with all the aliquot parts: and thus, by proceeding in this way we may easily gain a ready knowledge of the number of farthings in all the aliquot parts of a £., which will be of great service. First, we will begin with that curious branch of reduction which requires, it might be said, no calculation at all; but, from its curiosity, deserves a place here. L REDUCTION OF MONEY. A CURIOUS AND NOVEL METHOD FOR BRINGING MONEY INTO FARTHINGS. When the pence are half the number of shillings, the shillings will shew the number of half hundreds, and the pence the number of hundreds of farthings that are contained in the whole value; thus, for example, How many farthings are there in 2s. 1d.? Here the pence is 1, (which is the half of 2,) and therefore the answer is 100, or twice 50 farthings: and, by the same method of reasoning, 17s. 8d. will be 8 hundreds, or 850, which is also equal to 17 half hundreds, and so on, in like manner for any sum whatever. EXAMPLES. In 13s. 6 d., how many farthings? Answer, 6 hundreds, or 650. In 148. 7d., how many farthings? How many farthings in 11s. 51⁄2d.? Answer, 700. Answer, 550, or 11 half hundreds. Note. When the pence exceed or fall short of half the number of shillings, then add or subtract from the farthings, as the case may require. EXAMPLES. In 21s. 94d., how many farthings? Here, as in the above, we see, had the pence been 10 d., (half 21,) we should have had 1050 farthings; and therefore, by deducting the difference of 5 farthings, we have 1045. which is the answer. AGAIN. How many farthings in 22s. 11 d.? Here we see that, had there been only 11d., the answer would be 1100 farthings; but it being 3 more, we have 1103 farthings, which is the answer. When the number of shillings as compared with the pence, is considerably more in number than the shillings, observe the following Rule. From every twenty-five in the shillings, deduct 1; and add the value in pence to the pence, and proceed as before directed by this means the pence are brought nearer to half the number of shillings, and the answer thus is more readily obtained. EXAMPLES. In £3 16s. 1 d., or 76s. 14d., how many farthings? Here 76-3 (because there are 3 times 25 in 76, and rejecting the remainder)=73. And 73s. 374d.=76s. 14d. By the above means we can easily know the number of farthings, for 73s. 36 d. 3,650, and by adding the difference of 3 farthings, we have 3653 farthings the answer required. It is evident that had not the above been so disposed of, we must have proceeded in the following manner, and have said, 76s. 38d.=3800 farthings; then 38—11=363=147 farthings; this being deducted from 3800 leaves 3653, as before, which would have been very tedious. EXAMPLE. How many farthings in 55s. 74d.? Answer, 2669. To carry the above method to a great extent would be troublesome; to avoid which observe the following: Every 1000 farthings is £1 Os. 10d.; consequently, upon valuing the sum, if it is found to be any multiple of £1 Os. 10d., it will equal as many thousand farthings. The author now claims the reader's very best attention to the above, and the following rules, which will be found to be laid down in reduction of money, as multiplication, weights, and measures, &c, depends upon it. EXAMPLES. In £7 5s. 10d., how many farthings? How many farthings in £21 17s. 6d. ? Answer, 21,000. How many farthings in £11 9s. 2d.? Answer, 11,000. In £17 14s. 2d., how many farthings? Answer, 17,000. Note. If the sum be more than the nearest multiple of £1 Os. 10d., the farthings in the difference added to the thousand will be the answer. |