retention of the British foot would be hailed by nearly all artisans as a great convenience, as still preserving the inch and the yard. The scale would thus be conveniently decimalised from a foot unit The division of the foot into 100 decimal parts at once gives a name to the lowest denomination as "parts," and each part will be, of course, the 1 of an inch. 365 feet 96 parts 1000 will be denoted by 365.965 feet. Decimal "parts" will answer every purpose of reference and calculation. Acreage, mileage, whether nautical or terranean, as well as the divisions of the circle, will probably be handed over to another generation, unless the country is determined to accept the French mètre, devoid of all natural subdivisions into thirds, fourths, sixths, &c. &c. All the complicated cross multiplication of duodecimals will be at once extinguished by the use of the foot and its decimal parts. Ten feet might be called a rod, and a hundred feet something else; but it is doubtful whether such a measure would serve any useful purpose, except in calculation. It may be shrewdly suspected that any further upward change in the foot will inevitably lead us to adopt the French mètre whole and undivided. APPENDIX. THE tables in this appendix have been carefully calculated and verified by reversing the process. In that for equivalents of grammes, it will be seen that 11 grammes equal 1703 English grains, within the 6-1,000th of a grain. In the table of English and French equivalents of measures, I have calculated them to eight places of decimals, so as to be accurate for seven at least. It hardly seemed desirable to convert litres into pints in a tabular form, and, conversely, gallons or pints into litres. The relation of the KARAT to the pound avoirdupois being precisely similar to that of the gramme to the kilogramme, a table has been calculated to eight places of decimals for purposes of reference. No. I. The facility and power of the notation may be considered in the following example : Example: The value of 250 tons (500 demi-tons) 5 cwt. 93 lbs. 9 ozs. 9 drms, at 587. 4 florins 6 stivers 3 farthings per ton, may be ascertained by common multiplication— Result 29266-226 or 2,9667. 2 fl. 2 st. 6 far. This can be reduced into francs by multiplying by 100 and dividing by 4, if 25 francs 11. 29266.226 4)2926622.6 731655.65 731,655 francs 65 centimes. Again, if the demi-tons be reduced to lbs., by moving the decimal points three places to the right, the amount will be reduced to kilogrammes by multiplying it by the reciprocal of the number of lbs. to the kilogramme. Thus: 5 demi-tons 0 cwt. 5 lbs. 9 ozs. 3 drams. Example: Interest on 98,8657. 9 florins 8 stivers 3 farthings, at 33 per cent., is thus quickly obtained by the new coinage proposed, and thus expressed :† 98865.983 100)370747-43625 3707-47413625, which denotes 3,7071. 4 florins 7 stivers 4 farthings, easily converted by the table of money into 3,7071. 9s. 6d., where of necessity the shilling, being the twentieth part of 1,000 farthings, contains 12 pence and a halfpenny, conveniently to be represented by a demi-florin or five stivers. If greater accuracy be required, the multiplier should contain as many places of decimals as the result contains figures, the complete decimal to eight places being ·45359266. † Conversely, 3,7077. 4 florins 7 stivers 4 farthings can thus readily be reduced into francs and centimes Old-fashioned people (probably past sixty) will long adhere to their favourite sixpence and shilling, and perhaps will in time regard a shilling as the spurious half of a florin; but the sooner both shillings and sixpences, fourpennies and threepennies, cease to be coined, the sooner will the decimal money fight its way into general use. No. III. We may write, according to the new notation-as 1 pint = 7000 grams or 1000 karats. 960-8699 karats or 9608-699 pints; or, if a pipe be exactly 100 gallons, this will be expressed in either pipes, gallons, pints, or karats— Gallons or pipes are here expressed both by weight and measure, the karat being equally a measure of capacity or of weight. Again, since 1 karat = 1 1000 part of a pint or pound, P. 12 pipes 80 gallons 9 pints 0 ounce 9 drams 9 karats which, at 120.95 francs per pipe, = = 12-809099, 12.809099 × 120.95 4)1549-2605 francs Divide by 10)387-315 £38.7315, or 381. 7 florins 3 stivers 1 farthing. A remarkable instance of the power of the new notation, concise and selfinterpreting, without reduction. The great advantage of using reciprocals for multiplication, instead of dividing by the constant, is shown by the following examples : or 45 lbs. 359 karats are equivalent to 99.999 kilogrammes. By division, five places of decimals must be used-and we get Reciprocal number is such a number or fraction or decimal as multiplied by the number makes unity. Thus is the reciprocal of two, of 250. 1 250 |