(16.) Compound interest on £125, at 10 per cent., for 5 years? (17.) What is my gain per cent. by selling goods at 32s. per cwt., for which I gave d. per lb. ? (18.) How much wine, at 54s. a dozen, must I receive for 3 boxes of cigars at £1. 2s. 6d., so as to make a profit of 3 per cent.? (19.) I lose 7 per cent. by selling an article for 10s. 6d.; what did I give for it? (20.) What is the solid content of a cistern 6 feet long, 3 ft. 2 in. broad, and 351⁄2 in. deep? METRICAL SYSTEMS. NOTATION, as was explained in § 1, is the process of representing numbers by figures. This is effected by setting down the figures in a line, and estimating their value according to their relative position, right and left of each other. As we move a figure from right to left, its value increases by a regular multiple; the one commonly employed being ten. Thus, in the number 54321 (fifty-four thousand three hundred and twenty-one) the 2 is ten times as large as if it stood where the 1 is; the 3 is ten times as large as if it stood where the 2 is; and so on. This multiple is called the base of the system; and the system whose base is 10 is called the decimal system. When we come to the notation of concrete quantities we might, if we chose, represent them in the same metrical manner. Thus 7 yards 2 feet 5 inches" might be represented as "725 inches," if there were a regular base throughout, and if one denomination (such as the inches above) were invariably regarded as the unit of that particular system. But as our systems of weights and measures are different, and as the bases vary in almost every case, we are clearly unable to adopt this very convenient method of representing concrete quantities. Thus 725 inches" does not stand for the same thing as 7 yards 2 feet 5 inches," because 2 feet are not ten times as much as 2 inches, and 7 yards are not ten times as much as 7 feet. 66 It has often been proposed to reduce all our systems of notation, both of abstract numbers and of concrete quantities, to one and the same system, having a common base throughout. There would be many advantages in this uniform metrical system; and we will now proceed to explain what its nature would be. The French nation has already adopted such a system, with ten for the common base; and the most serviceable manner of illustrating the special features of a metrical system will be to explain that which is employed in France. It may, however, be remarked that, in adopting ten as the common base, we should lose the very great advantage of being able to employ weights and measures which are one-half and one-quarter of others; whilst to employ any other base than ten, after it has been used for abstract numbers so long, would be practically impossible. Hence the reason why no country, except France, has thought it worth while to adopt a uniform metrical system-decimal or other. The French Metrical Systems. The following are the tables of money-value, weights and measures, now used in France : (This table is manifestly insufficient, and therefore the following coins are also employed ; 5 centimes = 1 sou. 20 francs = 1 Napoleon. A franc is worth about 93d. of English money. The precise value at any particular time is subject to arrangement amongst the money-changers. It is generally safe to reckon a hundred francs as worth £4. A decime is nearly worth an English penny, and will as a rule pass as such in England.) (The prefixes to the word gram in the seven words above given are derived from the Latin and Greek, and express ten, and multiples of ten. Thus deci, Latin, and deka, Greek, denote ten; centi, Latin, and hecto, Greek, denote a hundred; milli, Latin, and kilo, Greek, denote a thousand; myria, Greek, denotes ten thousand. The Latin prefixes are used to express fractional parts of the unit; and the Greek prefixes to express integral multiples of the unit. A milligram is one-thousandth of a gram; a myriagram is ten thousand grams. *From this example it will be at once manifest that the process of reduction of concrete quantities disappears from the metrical system. All that it is necessary to know is the value of the unit in any number before us: thus, 357 centimes = 3 francs 5 decimes 7 centimes; = 35 decimes 5 decimes 7 centimes. A gram is the weight of one cubic centimetre of distilled water. The same prefixes are employed in the remaining French tables; therefore, when these are once mastered, no further difficulty will be met with. The column on the right hand of the table will illustrate the great simplicity of a complete metrical system, in which both abstract and concrete quantities can be expressed upon a common base of notation.) EXAMPLE OF NOTATION:-69342158 milligrams (One metre is about 31 inches longer than the English yard. One kilometre is nearly five furlongs. Though the metre is theoretically the unit, long distances are usually reckoned by kilometres. In land-surveying the dekametre is found most convenient. The French chain, divided into fifty links, is one dekametre in length. Thus 1 link 2 decimetres about 7.9 inches.) = = EXAMPLE OF NOTATION:-89307.541 metres As our number contained an integer and a decimal fraction, the word "metres" served to define the integral unit 7 as a number of metres. |