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dozens and grosses of feet, which would serve to measure buildings ; and for distances on land, the foot, dozens and grosses of feet, and a triple, or 1,000 (1,728) feet, about
of a mile, which might be called a long. The mean diameter of the earth 67,9129 miles is 11,977 longs.
In Land or Square Measure, the denominations might be,--a square foot (of twelve inches on each side), dozens and grosses of square feet (the side of which would be found by extracting the square root), and a plot, or a square of a gross feet on each side, that is, 10,000 (20,7369 square feet, a little less than half an acre.
Celestial distances might be measured by the diameter of the earth as a unit ; thus, the sun is 6,656 (11,875) diameters distant from the earth.
In Time, no change for the better could be made except that of counting the hours of the day forward to two dozen, and thus doing away with the troublesome, and to many persons unintelligible a.m. and p.m. (the former being sometimes read as a contraction signifying after morning); dividing the hour continuously into twelfths, and giving thirty (2} dozen) days to each month, with (359 to December. The last five (in leap-year six) days of the year might be considered a national festival; interest for money being reckoned the same for December as for any other month. The year should commence at the winter solstice, on the 22nd of December. The only change necessary in clocks and watches would be the division of the space between the hour figures on the dial, into six parts instead of five. Where there is a seconds movement, the seconds hand must be surrounded by the twelve numerals, and the movement adjusted thereto. Chronology in history, and the reckoning the day of the month and the year, might be brought into conformity with the new arithmetic, and a New Style inaugurated, about the year (20009 1168, or as much earlier as public opinion might demand. The oldest date in Arabic figures in this country is 1454, which is inscribed on a brass plate commemorating the death of Ellen Wood, in the church of Ware. The Arabic figures were not generally adopted in England till the sixteenth century.
Divisions, in twelfths, of the several units (hour, foot, pint, pound), to be called primes, seconds, thirds, fourths, &c. ; not discarding the additional terms half, quarter, ounce (iz of a pound), inch, line (1, of an inch), gallon, quart, drop, &c.
These would be measures of convenience, but not measures of account, except when they are twelfths.
I will now illustrate this duodecimal arithmetic by a few examples.
What is the price of a load of coal, weighing 1 ton 16 cwt. 3 qrs. 24 lbs., at (10ļd. per cwt.? The bill would be delivered as 2,490 pounds of coal (or 2 loads, 4 gross, 9 dozen pounds), at ls. 1;d. per gross (pounds). The operation is
360 = 51, nearly
1 9 2692
12 ) 369 9d. for the 9 doz. pounds
20 ) 30 9 2767
1 10 9 or 2 marks 7 shillings and 6d.
for the 3 qrs. 24 lb. 9d.
£1 11 6 There is a difference of £d. upon the two calculations, because ls. 11d. per gross is a little higher rate than 10ļd.
What is the value of 38 (44) pounds of sugar at 7d. per pound? New Method.
Present Method. 38
44 lbs. 7
218 or 2 marks 1s. and 8d.
20 ) 25 8
£1 5 8
What is the value of 132 (182) yards of cloth at 3s. 3d. per yard ? New Mcthod.
Prosent Method. 132
182 yards 33
3d. = 1 of 1s. = 45 6 4136
20 ) 591 6 or 4 doz.& 1 marks, 3s. and 6d. or 4 bancos, 1 mark, 8s. & 6d.
£29 11 6 The hour might also be divided into twelve “beats" (or primes, a beat or prime being five of the present minutes), and the beat into twelve minutes (each equal to nearly one-half of the present minute), the minute into twelve thirds, &c.
The transfer of an old number into its corresponding new expression (when it is not a high number, say not exceeding three figures), may be accomplished in an instant by dividing by twelve, decimally, and throwing out the remainders, which form the new number. Thus—What is the duodecimal expression of 907 ? Answer 637 ; thus,
For high numbers of four figures and above, re12) 907
ference may be made to a series of tables, which 12) 75 7
could be prepared, exhibiting all numbers in the two notations from unity to $1,000,000), and sold for a few pence.
To transfer a number in the new notation into the old notation, divide by ten duodecimally, and throw out the remainders, which make the old number. Fractions of a unit may be called “parts," answering to the present “decimals." To translate decimals into duodecimals, or parts, add one-fifth, cut off the first figure to the left, and continue the operation with the remainder until one figure remains : 3:14159265), the ratio of the circumference of a circle to its diameter 3:1848094.
I would enforce the advantages of this scheme of notation by the consideration that as the shadow naturally follows the substance, so should the writing of money, or the keeping of accounts, conform itself to the money, the weight, or measure, in use, in general. It would be less trouble for the few who deal in figures to learn a new
method of keeping accounts, and a new multiplication table, than for the whole nation to change its money, and all its weights and measures. An account in a ledger is, to the money which it represents, just what the inoney itself is to the property, houses, land, commodities, which it represents. It is just what written words are to spoken, and spoken words to ideas, and ideas to the affections that give them life. It is just what Nature itself is to poetry, or a man to his photograph. There is no complaint against the penny, the shilling, the pound weight, the inch, foot and yard measures, the twice twelve hours of the day, and the twelve months of the year. These have done no wrong, and caused no confusion. The trouble has arisen solely from the manner in which we combine these to make higher denominations, or divide them to make lower ones, and employ entirely different weights for a pound of tea, a pound of gold, and a pound of medicine.
Every one can aid this reform by giving precedence to the dozen over ten in all his counting. The practice of both the ten and the twelve scales by schoolboys, thus emulating the custom of our Universities, where arithmetie is practised in various scales, would be a great benefit to their reasoning and calculating powers. In thinking of what is possible in art and science, we should ever bear in mind the truism—the Future is greater than the Past.
The French system of money, weights, and measures, called the “metrical system,” in which every coin, weight, and measure, is one-tenth of the next above it, is certainly
superior to the English diversified system ; but when we si consider that to adopt it in this country we must change
every coin, weight, and measure that is now in use, the question we should ask is, whether in passing from the
good old” system now extant in England, we should
adopt the better one of France, or ask France to adopt the the best from us?
On the occasion of the second reading of the “Weights and Measures Bill” in the House of Commons, 1st July, 1863, when a majority of 35 votes was given in favour of the bill, in a thin house of 185 members, the “Times” of 2nd July, in a leading article says :—
“ The very first step,” in the proposed arithmetical revolution, or is the adoption of a new unit as the base of all other measures
of length, surface, solidity, and weight. The unit, without which it would be penal for a shopkeeper to sell the smallest quantity of tape, bread, sugar, or oil, is thirty-nine inches and thirty-seven thousand and seventy-nine hundred thousandth parts of an inch of the Imperial standard measure, and its name, we need not say, is to be ‘Metre.' We will not here insist on the principle involved in adopting a basis selected on so recondite a principle as the cal. culation of the length of a quadrant of the earth's meridian. Why that should govern all transactions in comestibles and potables, in clothing, and every other affair of buying and selling, it is impossible to say. But we let that pass. Let one yard be as good as another. We speak on behalf of the already overworked and not very quick wits of our countrymen. We tremble to think of the softening of the brain, the confusion of ideas, the mistakes, the losses, this will occasion. How is Lord Dundreary ever to make it out? His is a much larger family than is generally supposed."
Letters from correspondents, practical men, and not deficient in arithmetical science, followed in abundance, all contending against ten as the repeating number of a system of money, weights, and measures. See the “Times" for July 4th, 9th (a long and powerful letter occupying three columns), 20th, 23rd, 24th, and 1st August. The last writer, “Á Schoolmaster,” says:
“Had we single marks for 10 and 11, our language and our notation would be complete in the duodecimal scale; and when the great body of the people are educated and taught arithmetic intelligently, and not by empiric rules and formulæ, the transition to that scale will most certainly come. In the meantime, to force the decimal scale on a nation which, by the light of nature, has pronounced so unmistakably against it (not one unit in the popular measures of space, time, weight, or value being divided, or bound up decimally), would be nothing short of insanity."
The “Saturday Review” of 16th May, 1857, also contains an able essay on the superior merits of a duodecimal scale of money,
London : FRED. PITMAN, 20, Paternoster Row, E.C.
Printed by J. WARD, Dewsbury.