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article. Mr. Bennoch, of Wood-street, Cheapside, for whom thousands of such costs are calculated every year, states his belief, in his evidence before the Committee, that results which now take minutes to produce would take only a fraction of a minute, if the proposed system were introduced :

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Cost of 37} gross, 8s. 01d. per gross. £14 19 81 In the first six lines, no money result is perfectly exact: nor is any such thing necessary. The prices are all in even pence, and this is mainly for facility of calculation. A decimal system, instead of forcing fractions of coinage upon those who do not want them, would give great power of introducing fractions to those who do want them, and who cannot with sufficient ease make them available under our present system. Not only would the mil become much more common than the farthing is now, but the minute fractions of a penny, which are sometimes spoken of, would be supplanted by the decimil, or tenth of a mil, and the centimil, or hundredth of a mil.

We now come to the banker, bill-discounter, &c.; and here we shall find that more than a farthing is wilfully neglected. Every one knows that the Bank of England, and the private bankers, recognize nothing under a penny: but this is not all. We heard, some time ago, of a sententious individual who, by way of damaging a particular place of education, said, “I asked a boy educated at

what was the difference between interest and discount, and he answered that they were the same; which of course is wrong." Some of the opponents of the pound system have followed this worthy man in drawing ideas from old school books, instead of from actual business in our own day. The boy was right; interest and discount ought to be different things, but for ease of calculation are made the same.

When a bill of £100 has three months to run, it is discounted at 4 per cent., by deducting three months' interest from £100, leaving £99. This, in three months, amounts to £99 19s. 9d., not to £100: what ought to be paid is £99 Os. 27d. This twopence-halfpenny is cheerfully abandoned, to save a little amount of calculation.

In truth, all this difficulty about neglecting, during the change, a portion of the lowest coin in use, is of that disposition to exaggerate trifles which always arises during discussion, acting upon imperfect knowledge of actual business. An advocate of decimal division, Lowe (not the member for Kidderminster, but quite a different person, Solomon Lowe, who published on arithmetic in 1749), says, speaking of the error committed, “... if it is brought so low as to be less than any quantity of that kind which is usd (for example, the smallest real coin, or weight, &c., that has any name or distinct being in society), then the defect is not to be complained of ... And this is, and always was, the common sense of the question; and nothing but a strain upon the cleverness, such as is caused by party discussion, ever brings out any opposition to it.

Before proceeding to the third point, we shall venture a little further into arithmetic, to show how very easily, and by headwork alone, any degree of approach towards a perfect reconciliation between the two systems may be made. It is due to the member for Kidderminster that we dare venture on such a thing; for he paraded the rules of reduction of common into decimal fractions, and such results as .00104166666 ad infinitum, as necessary for apple-women. Surely, then, we are justified in showing our readers, whom we can trust to turn 4 d. into mils, how much less than Mr. Lowe's allowance of arithmetic for an apple-woman will do for the highest clerks in a bank.

On our lowest scale of conversion, twenty-five new farthings to the half-shilling, we need only further remark that the man who has nothing to do with accounts needs no more. To him the florin is but a two-shilling piece, and the cent is but a coin of 10 new farthings, a new twopence-halfpenny. He exchanges these coins, but he does not reckon with them. No one can teach him half so well as he will teach himself, upon the basis of the words in italics.

The second step will suffice for ordinary book-keeping. It runs thus :-Mils are farthings below sixpence, with a Parliament mil put on at sixpence. Not a Parliament mill, Mr. Lowe ! we cannot afford a column for debates. The victim, as the

penny wise would call him, must manage, below the shilling, to turn pence and farthings into farthings; he must be clear in a moment that 9 d. is 39 farthings: Equally ready must he be at adding on to 50 anything less than 49, he must be strong in the power of seeing that 50 and 39 make 89. Is he too much of a victim ? The penny wise, if they had him, would draw harder upon him. We put down the requisites which the two systems require, headwork both, to obtain equal expertness in converting old money into new. Pound System.

Farthing System. He must be able to turn pence He must be able to turn pounds,

and farthings, under a shilling, shillings, pence, and farthings into farthings: to add less into farthings. than 50 to 50, and thus to arrive at any number under

99. He omits a fraction of a mil, His answer is perfectly exact.

which we shall show how to supply, when needful, at much less trouble than that of turning mixed sums into farthings.

Our book-keeper must learn to allow 100 for each florin or pair of shillings, 50 for the odd shilling, if any, and mil for farthing on the rest, with the Parliament mil at sixpence. Say it is, in old money, £42 11s. 9fd. Here we see 5 florins and an odd shilling, say 550; 39 farthings, say 39 mils, with the Parliament mil, 40 mils; altogether 590 mils. Accordingly,

421. 11s. 9 d.=421. 590m.= 421. 5f. 9c. Om.=42,590m. Suppose the farthing system established, what then? Turn £42 ils. 9fd.into farthings-in the head, if you can,--but turn it into farthings. The answer is 40,887 farthings. Accordingly, the given sum is 40 new pounds, 8 new florins, 8 doits, and 7 farthings.

If the fraction of a mil be worthless, as it will be in almost every case, we stop here. But what is this fraction of a mil ? As many 24ths as there are farthings above sixpence, or, if not a whole sixpence, above the shillings. We put down a few examples, and we ask Mr. Lowe, as an honest man who knows the trouble of canvassing-assuming always that men may be honest who have gone through that mill-whether any member would not cheerfully work three dozen of them to get a single vote. Old Money.

Approximate new Fraction of a Numbers employed
mil omitted.

in the process. Os. 7d. Of. 3c. lm. 6 twenty-fourths 30, 1. ls. 2 d. Of. 6c. lm. 11

50, 11. 2s. O d. If. Oc. 2m.


100, 2. 17s. 10 d. Sf. 9c. 4m. 19

800, 50, 43, 1. 18s. 6d 9f. 2c. 5m. 0

900, 24, 1. 19s. 11 d. 9f. 9c. 8m. 23

900, 50, 47, 1.

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A great many persons will not readily bring themselves to write in mils, that is, put down 925m. instead of 9f. 2c. 5m. They will distrust such facility : they will doubt if it can be lawful alchemy which turns copper into gold and silver without real tough division. That 41. 3f. 7c. 9m., and 43f. 7c. 9m., and 437c. 9m., and 4379m., and 41. 379m., and 43f. 79m., &c., should be obtained by reduction at sight, instead of by the good old multipliers 4, 12, 20, will seem almost too easy to be true. And we have sometimes been amused by hearing advo. cates of the pound system settling how to provide by Act of Parliament for the manner in which people are to read. We feel pretty certain that, any act to the contrary notwithstanding, they will read in pounds, florins, and mils.

When one banker's clerk now checks another, the latter reads £53 11s. 4d. as fifty-three, eleven, four : in the decimal system, 531. 2f. 6c. 3m. will probably be read short, fifty-three, two, sixty-three, as if it were 531. 2f. 63m.

However it may be, opinion and not law will settle the matter.

The conversion into mils, above described, will serve ordinary purposes. But it will occasionally happen, for a time, that the rejected 24ths of a mil are wanted by the higher order of book-keepers in tenths, hundredths, &c. of a mil, or in decimils, centimils, &c. Those who want to make this conversion in their heads, must become quick at the multiplication table of fours up to 4 times 23. Tell this to the representative of Kidderminster, and let him set the House in a roar, which he will not fail to do, by representing us as demanding this acquisition from apple-women and members.

But we can point out how such multiplication is within the power of numerical expertness of a degree far below that of an ordinary clerk.

When children first count, they sometimes forget to take a new departure from ten, and go on as in twenty-nine, twentyten, twenty-eleven, &c. In adding, say thirty-four to fifty-nine, in the head, the best way is to imitate the children; call it eighty-thirteen, and then ninety-three. Similarly, four times 17 is forty-twenty-eight, or 68; four times 19 is forty-thirtysix, or 76; and so on. Having mastered this by practice, the method of treating the rejected fraction of a mil is as follows: - Take four times the number of farthings above the shillings, or above the odd sixpence, if there be one, and add one for every complete six which that number contains; the result is the number of centimils, a fraction of a centimil being rejected. For example, 17s. 10 d. As already described, using 800, 50, 41, 1, we have 892m. Above the sixpence we have 44d., or 17 farthings (having 2 complete sixes). Four times 17 and 2


make 70, whence 179. 10 d. is only a fraction of a centimil (cm.) above 892m. 70cm., or 89,270cm. Again, 14s. 8 d. gives (700, 35, 1) 736m. to begin with: 4 times 11 and 1 is 45, and 14s. 8 d. is 736m, 45cm., or 73,645cm. Suppose now that a wholesale trader who has sold at 2 d. a piece, old money, wants to price the goods in new money, so as to be within onehundredth of a farthing. Here 24d. is llm. and a fraction : 4 times 11 and 1 is 45; so that 11m. 45cm., or 1145cm. is the price. This means Of. lc. lm. 4 dm. 5cm. a piece, or 11. 1f. 4m. 5dm. per hundred, or 111, 4f. 5m. per thousand. This may be his mode of sale, and the hundred or the thousand will soon supplant the gross: while 1145cm. will be his mode of pricing the single article. But so long as he continues to use the gross, he will use 1145 x 144, or 164,880cm. the gross; that is, stopping at mils, 11. 6f. 4c. 8m. per gross.

We have now got to what the learned call five decimal places, denominated, for the higher sort of arithmeticians, florins, cents, mils, decimils, centimils. But Mr. Lowe will not let us stop here; he parades his interminables ad infinitum ; so that, to diminish the terror which he excited, we shall show how easily all the following places are obtained. Strike out all the shillings and every three-halfpence out of the pence. If no farthings be left, say 000. ... ; if 1 farthing, say 1666. ...; if 2 farthings, say 3333. . . ; if 3 farthings, say 5000... if 4 farthings, say 6666....; if 5 farthings, say 8333. . . .

A fair trial given to these rules will show that the method of turning old money into new can hardly be said to involve calculation up to mils, and can be carried with great ease, and without any writing, except of the result, up to any fraction of

But if the country were to be burdened with the farthing system, it is easily shown that in turning old money into new, the shortest method would be to pass through the pound system by the preceding rules. Deduct 4 per cent. from the representation in the pound system, and the result is that in the farthing system the five places will be sufficient. For example :

£136 135. 43d. is £136 66979 CM.
4 per cent. of this is 5 46679

a mil.

Difference £131 203

Hence £136 13s. 4d., present money, is, in the farthing system, 131 new pounds, 2 new florins, and 3 farthings. The given sum contains 131,203 farthings.

Thus it appears that the preference of the farthing to the pound system would be, so far as business calculations are

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