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Sir J. In this instance, at least, they were visionary enthusiasts.

Sir G. But I wonder, W., that, with your veneration for the decimal scale, you should have confined your attention solely to our monies. Sir J. I was not the less sensible that, in the divisions of the units of weight and extension, the greatest and most perplexing irregularity is found.

Sir G. And that the simplest operations are hence involved in an intricacy which no ingenuity has been able to remove.

Sir J. That follows, Sir G. There is, however, an irregularity which is even beyond the power of a Parliament to alter.

Sir G. Ay, what may that be? Sir J. Those divisions of units which have their origin in nature, or are determined by an authority which all must revere.

Sir G. You are pleased to be oracular, Sir J.

Sir J. I mean simply, that, whatever improvement may be hoped for in the progress of society, the number of days in a year and in a week are irrevocably fixed.

Sir G. And yet the French, in their enthusiasm for system, divided time into decades, or periods of ten days.

Sir J. To have been consistent, they ought also to have divided their year into ten, or a hundred decades!

Sir G. Well thrust, Sir J.; but the same necessity does not adhere to any of the divisions of weight or extension.

Sir J. Or money, you might add. Sir G. Certainly. They have all been formed without any regard to general principles, and apparently with no other motive than present

convenience.

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a certain number of

Sir G. Very true; and we have fractions, as well as integers, as terms in our system.

Sir J. For example, there is the puncheon of 14 hogshead, the hogshead of 14 tierces, and the tun of 2 pipes.

Sir G. Ay, and the nail of 2↓ inches, the yard of 3 feet, or 4 quarters, the ell of 5 quarters, the pole of 5 yards, and the fathom of 6 feet.

Sir J. And the wey of 6 lods, and the clove of 7 pounds.

Sir G. Yes, and the ale-firkin of 8 gallons, the beer-firkin of 9, and the anchor of brandy of 10 gallons. Sir J. And there we may stop. Sir G. What! because the varieties are exhausted?

Sir J. No, C.; but because they are exhaustless.

Sir G. They are so, when we consider also the varieties of units with similar names.

Sir J. Such as the pound Troy of 5760, and the pound Avoirdupois of 7000 of the same grains.

Sir G. And the Scots Troy pound of 7616, and the old Tron pound of 102164.

Sir J. And the wine-gallon of 231 cubic inches, the ale-gallon of 282, the corn-gallon of 268, the corn-bushel of 21504, and the coal-bushel of 22174.

Sir G. And, in Scotland, the alepint of Aberdeen, of 108.89 cubic inches, of Argyle 109.866, of Ayr 110.624, of Banff 105-284, of Dumbarton 105.5, of Dumfries 114, of Elgin 105.438, of Inverness 115.161, of Renfrew 109.877, and of Roxburgh 110.

Sir J. A pretty catalogue, to be sure! But you did not mention the ale-pint of Edinburgh.

Sir G. That county and Linlithgow employ the standard pint, which is 103.404 cubic inches; but, from a principle of liberality, I suppose, the pint-stoups are generally made to contain 105.

Sir J. Well, all this diversity must be insufferably inconvenient.

Sir G. The corn varieties of Scotland are, however, much more so. Almost every individual county employs one measure for wheat, and another for barley; and there are

nearly as many of these duplicate measures as there are counties.

Sir J. It is full time, certainly, as one of your great experimenters has said, to restore the sobriety of reason.

Sir G. It is so. An uniformity of our weights and measures has been long anxiously desired by all classes of the United Kingdom.

Sir J. And the Legislature (how liberal!) has conceded, that all local varieties ought to be abolished.

Sir G. And I have no doubt, Sir J., that this concession will be carried into effect.

Sir J. Well, when it is, the internal commerce of the country will be much facilitated, by having only one general system.

Sir G. And the labours of calculation will be greatly lessened in those cases, in which a comparison of local varieties would otherwise be required.

Sir J. But calculation and commerce would still be impeded by the irregular divisions of the units employed.

Sir G. I am well convinced of the intricacy they occasion.

Sir J. And, in the greater part of the country, there would be the change of a bad system for one equally bad.

Sir G. I grant you there would. Sir J. And there would therefore be much reason to regret, that, for the sake of partial and present convenience, a favourable opportunity had been neglected of giving harmony and consistency to calculation, and of raising arithmetic to its proper rank among the other sciences.

Sir G. I confess that something more is required for facilitating calculation, than the simple adoption of a regular system.

Sir J. And that something is The perfect adaptation of the units to the decimal scale.

Sir G. I am half inclined to be of that opinion.

Sir J. If you were wholly so, you would think that object of so much importance, that, for the attainment of it, no present inconvenience ought at all to be regarded.

Sir G. But Mr W., you recollect, did not seem to perceive the advantages to be derived from decimal divisions.

VOL. XIV.

Sir J. It requires so very limited a knowledge of numbers to perceive them, that I am disposed to question the sincerity of his assertion."

Sir G. I can see that, if the decimal scale were introduced, the value of a compound quantity, in terms of any denomination, would be known at once by a simple inspection.

Sir J. Exactly; thus of French monies, 573 cents are equivalent to 5 francs 73 cents.

Sir G. That is simple enough, truly.

Sir J. Another advantage isthat, as the tens of any denomination would express units of the next higher, any operation upon compound quantities would be precisely the same as upon simple numbers.

Sir G. That is equally clear. To multiply 5 francs 73 cents by 8, for instance, is the same thing as to multiply 573 cents by 8; and therefore the product is 4584 cents, or 45 francs 84 cents.

Sir J. And so in every case. But this improvement would also have the effect of very much lessening the number of arithmetical operations.

Sir G. Many of these, I know, have been invented for the purpose merely of avoiding the tediousness of a more direct procedure.

Sir J. And as the cause of their introduction was the irregularity of the divisions, they would be entirely excluded from the real business of life.

Sir G. Or only find a place in those works on arithmetic in which a complete developement of the science was intended to be given. Sir J. Exactly so. Sir G. But you would not advise an entire change of units?

Sir J. That would not be necessary; and indeed that alteration would be most generally acceptable, by which the least violence was offered to established habit.

Sir G. And the most effectual way, I conceive, by which this would be avoided, would be to retain as units of the decimal system, one of each kind of units already employed.

Sir J. That is precisely my opi

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Sir J. At last they acted otherwise. To determine the real figure and magnitude of the earth, a considerable portion of the meridian had been actually measured, and they assumed the mètre, or ten millionth part of the quadrant, as a unit of extension.

Sir G. And by employing this mètre as the standard from which all their weights and measures were to be derived, they thought they had formed a system for all nations.

Sir J. But they failed in even creating one proper for themselves. They were not aware that no standard is proper to be adopted, the length of which may not at all times be easily ascertained.

Sir G. And they did not perceive that the length of the pendulum was certainly more proper, since, by means of it, they confessed, the mètre, if lost, must eventually be restored.

Sir J. There is no doubt, Sir G., that the length of the pendulum is the most convenient standard.

Sir G. But not that this standard should also be a unit of length?

Sir J. Assuredly not. If the foot were retained as a unit, its length might always easily be determined, from a comparison with the pendulum.

Sir G. And would you retain the foot in preference to the yard?

Sir J. Unhesitatingly-and the ounce avoirdupois rather than the pound.

Sir G. And why, Sir J.?

Sir J. Because a cubic foot of pure water, at the temperature of 564 degrees of Fahrenheit's thermometer, weighs exactly 1000 ounces avoirdupois.

Sir G. That is a very remarkable coincidence.

Sir J. And a very fortunate one for our present purpose. By retaining the foot and the ounce as units of the decimal system, a beautiful harmony would obtain among our weights and measures.

Sir G. And the different kinds of units be derived from each other, without employing fractions at all in the operation.

Sir J. True. A cubic foot of water would give 1000 ounces; and, conversely, 1000 ounces would give the cubic foot.

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Sir G. What is the principle of your nomenclature ?

Sir J. I retain such of the present names as are variable in their significations. The stone, for instance.

Sir G. There is no lack of variety in that unit, from the stone of glass of 5 lb., to the stone of Scotch wool of 24 lb. But the dram?

Sir J. Is nearly an arithmetical mean between the dram avoirdupois and the apothecaries' dram. The former is 0625, and the latter ⚫1371, of an ounce avoirdupois.

Sir G. And the mean is 0998, or only a five-hundredth part less than a tenth of an ounce. The new ounce, you say—

Sir J. Is the ounce avoirdupois ; and the new carat is not a tenth part more than the troy carat.

Sir G. And the new grainSir J. Is to the grain avoirdupois as 12 to 25, and to the grain troy as

7 to 16.

Sir G. Well, there are small and large grains in nature, and why not in weight? But the pound is variable, and yet you have adopted the mark?

Sir J. To avoid the ambiguity which so often arises from applying the term pound both to weight and value.

Sir G. And why quintal, and not hundred-weight?

Sir J. Because the latter term has yet been applied only to 112 pounds, while the former is as various as there are countries on the Continent.

Sir G. I am now satisfied, Sir J., that these units should be introduced.

Sir J. For every weighable article, I hope?

Sir G. Yes, for silver, and senna, and groceries, and gold. I think,

with the late Professor Playfair, that "the simplicity and accuracy of the system would be sacrificed by any partial exceptions."

Sir J. I am glad you think so. But, even to goldsmiths and apothecaries, the inconvenience of the system would be scarcely felt. They might have the aid of tables of comparison.

Sir G. They might; and as they use the same pounds, ounces, and grains, one table would suffice for

both of these classes.

Sir J. Exactly. And, moreover, as the new and avoirdupois ounces are the same to merchants in general, a table would hardly be necessary.

Sir G. In any case, the required reductions would be extremely simple. To convert new grains into grains troy, you would multiply by 7, and divide by 16?

Sir J. Or it would be simpler to take, from half the number of new grains, one-eighth of that half.

3752

1876

Sir G. Let me see; to reduce 37 52 new grains into grains troy, I must, from the half, 1876, take the eighth, 2344 and reckon the difference, 1641, as troy grains?

234

1641

Sir J. Precisely; and to convert troy grains into new grains

Sir G. You would add, to double the number of troy grains, oneseventh of that double?

Sir J. I would-as, for example, to reduce 16414 grains 1641×2 troy into new grains; to 3283 the double, 3283, I add 469 the seventh, 469, and the sum, 3752, is new grains. 3752

Sir G. This is all very clear; and I see, that, to reduce the units of avoirdupois weight into the new units, it is only necessary to reduce them to ounces, or decimals of an ounce ?

Sir J. That, C., is all. To change, for instance, 3 lb. 15 oz. 8 dr. into new units, you reduce this quantity to 63, or 63.5 oz.; and you have, of the new units, 6 marks 3 oz. 5 dr., or 63 oz. 5 dr., or 635 dr.

Sir G. And the converse of this is equally plain. To reduce 6 marks 3 oz. 5 dr. into avoirdupois units, I have, by simple inspection, 63.5 oz., or 3 lb. 15 oz. 8 dr.

Sir J. You are right. And now for the lineal measures.

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W., in the names of the units?

Sir G. You make no innovations,

Sir J. No; but in the values of all, except the foot.

Sir G. And I am willing to accept them all for the sake of this exception! The foot is the foot of little importance. the three kingdoms, and all else is of

is,

Sir J. I should think so.
Sir G. Well, your pole is 10 feet.
Sir J. Yes; and the offset staff

in England, 6 feet, and in Scotland 7; the statute pole is 161; the Devonshire 15, the Dorsetshire 15, the Cornwall 18, the Lancashire 21, and the Cheshire 24.

Sir G. Yet more; in Scotland it is 18, and in Ireland 21; so you have precedents enough for your variety. But your chain

Sir J. Is 100 feet; while the English one is 66, and the Scotch 74.

Sir G. That is, the English chain is a third, and the Scotch a fourth, less than your proposed one.

Sir J. Nearly so; and there are the same relations between the respective furlongs.

Sir G. But you advance no farther than 1000 feet; which is your furlong?

Sir J. For surveyors and landmeasurers this is surely far enough. Sir G. Ay, but for measurements on a large scale ?

Sir J. If the furlong won't do, there is the English, or the geographical mile-either would very easily be converted into new units.

Sir G. Or, what think you of making the statute mile 5000 feet? The distance of the sun from the earth would then be 100 millions of miles!

Sir J. That would be an inducement! The quadrant of the terrestrial meridian is nothing to this!

Sir G. No; the French system is grand, but this would be sublime!

Sir J. It would, however, be much more magnificent to make our mile 10,000 feet; and then, not only would the regularity of the system

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Sir G. You have beat me, C.; and I therefore had better return to your inch.

Sir J. The proposed inch would be a fifth more than our present one; and

Sir G. You need not go lowerartists and artificers are already practised in dividing their inch decimally. But as to the conversion of the systems

Sir J. That is an easy affair. The present measures must be reduced to feet, or decimals of a foot. Sir G. I see it, W.; and now for your square measures.

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Sir J. Here they are: The sq. furl. of 100 sq. chains=1,000,000 The sq. chain of 100 sq.poles The sq. pole of 100 sq. feet The sq. foot of 100 sq. inches= The sq. inch.........

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Too Sir G. You are right, W. in making the units of square measure to correspond with the squares of the

lineal units.

Sir J. We have thus a clearer idea of the surface meant. The centesimal scale is, moreover, as simple as the decimal.

Sir G. Equally so; it is as easy to say 75 square feet, as 8 square yards 3 square feet. But the word square

Sir J. May in general be omitted. When I say that such a field contains 3 chains 26 poles

Sir G. I know you to mean 3 square chains 26 square poles; and SO "the sound will sometimes seem an echo to the sense."

Sir J. Nay, almost always. Sir G. Well, your square foot is the English square foot?

Sir J. And the Scots and the Irish too.

Sir G. I know that, W.; and that your square pole is 100 square feet, or the artificers' square of flooring; and that your square chain

Sir J. Is 10,000 square feet, or about a twelfth part less than the English rood.

Sir G. And your square furlong isSir J. A million of square feet, which is about a fourteenth part less than the French hilare.

Sir G. That is, your furlong is

nearly 23 acres, the hilare fully 241. And now, W., all is plain.

Sir J. The reductions, you perceive, are made through the common medium of the square foot.

Sir G. I am aware of that; and I am therefore ready to attend to your cubical units. Sir J. They are, The cub. furlong The cub. chain The cub. pole The cub. foot

of 1000 cub. chains. of 1000 cub. poles. of 1000 cub. feet.

of 1000 cub. inches. Sir G. We take now the cubic foot as the medium of comparison? Sir J. We do; the English lineal foot was retained.

Sir G. And of course the square and the cubical. But you make the cubical pole 1000 cubical feet?

Sir J. And the cubical chain a million; and the cubical furlong a thousand millions.

Sir G. It is, however, with your foot and inch chiefly that we have any concern.

Sir J. With respect to measures of capacity, you mean?

Sir G. Yes; and for that purpose you propose to interpolate the tenth and hundredth of a foot?

Sir J. And the tenth and hundredth of a pole.

Sir G. Then your units of capacity are, one, ten, and a hundred cubical inches; and one, ten, and a hundred cubical feet?

Sir J. Unquestionably; but recollect that the cubic inch is the 1000th, and not the 1728th of a foot. Sir G. I meant it so.

Sir J. In other words, the proposed units are, in cubic feet, the thousandth, hundredth, tenth, one, ten, and hundred.

Sir G. And these you mean for both liquid and dry substances?

Sir J. For corn, wine, and oil; milk and honey; and malt, and malt liquors.

Sir G. And coals and potatoes. Sir J. And for every article that can be poured into a vessel. The units of capacity are:

The last of 10 tierces
The tierce of 10 ankers
The anker of 10 gallons
The gallon of 10 pints
The pint of 10 gills
The gill~~~~~~~~

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