upon a length of 10 metres. This standard is called an ARE, and is nearly equal in area to 120 square yards. The standard of solid measure is a cube whose edges are each a metre in length. This standard is called a STERE, and represents a little more than 35 cubic feet. The standard of capacity is a cubical vessel whose edges are each one-tenth (1) of a metre in length. This standard is called a LITRE, and represents about a pint and three-quarters. The standard of weight is the quantity of distilled water which, at a certain temperature,* would fill a cubical vessel whose edges are each one-hundredth (100) of a metre in length. This standard is called a GRAMME, and represents a little more than 15 grains.† Of the standards just mentioned, decimal multiples are taken for higher, and decimal submultiples for lower denominations. In connexion with the names of the standards themselves, the Greek words for 10, 100, and 1,000 are employed, as prefixes, to express the higher denominations; whilst the corresponding Latin words are similarly employed to express the lower denominations. Thus,-deka, hekaton, and chilia being the Greek words for 10, 100, and 1,000, respectively,—a length of 10 metres is called a deka-metre; a length of 100 metres, a hecto-metre ; and a length of 1,000 metres, a kilo-metre: whilst—decem, centum, and mille being the Latin words for 10, 100 and 1,000, respectively-one-tenth (1) of a metre is termed a deci-metre; one-hundredth (16) of a metre, a centi-metre ; and onethousandth (1.00) of a metre, a milli-metre. So with regard to the other standards.‡ The following are the details of the Metric system : Even the FRANC, the French standard of value, may be said to be based upon the metre, being equal in weight to 5 grammes. The franc is a silver coin,-of which 9 parts out of 10 are pure silver,—and is equivalent to about 10d. British. 66 The only exceptions are- -"millier" (1,000,000 grammes) and quintal" (100,000 grammes). § From myria, the Greek word for 10,000. NOTE. The Kilometre, in terms of which long distances are usually expressed, represents nearly 5 furlongs: a Kilometre containing 39,371 inches (nearly), whilst in 5 furlongs there are 39,600 inches. SURFACE. Hectare Centiare 100 Ares 119.6033 square yards. NOTE.-The Hectare, in terms of which large areas are usually expressed, represents nearly 2 English acres: a Hectare containing 11,960 square yards, whilst in 2 English acres there are 12,100 square yards. Decigramme = = 15:4323487 grains one-tenth (1) one-hundredth (1) of a Gramme one-thousandth (1,000) NOTE.-The Kilogramme, in terms of which the weights of heavy articles are usually expressed, represents about 2 Avoirdupois pounds: a Kilogramme containing 15,432 grains, whilst in 2 pounds (Avoir.) there are 15,400 grains. It will be seen that, in the Metric system, there are no Compound Rules-the numbers employed to express lengths, surfaces, &c. being all simple numbers. Thus, metres. 2 kilometres 4 hectometres 6} would be written 2468 dekametres and 8 metres grammes. 3 decigrammes 5 centigrammes would be written *357 and 7 milligrammes ares &c. mes} centi-} ares. 908.07 &c. It will also be seen that, in this sytem, Reduction is performed by the mere removal of the decimal point. Thus, for the reduction of kilometres to hectometres, dekametres, or metres, the point is simply removed to the right-one place, two places, or three places, as the case may be; whilst, for the reduction of litres to dekalitres, hectolitres, or kilolitres, the point is removed one, two, or three places-as the case may be-to the left: 67.89 kilometres=678.9 hectometres=6789 dekametres= 67890 metres; 2345 litres=2345 dekalitres=23:45 hectolitres=2.345 kilolitres; &c. Even the numbers which the French employ in expressing sums of money—that is, "money of account"-are simple numbers: a smaller amount than a franc being always written as so many "centimes," or hundredths of a franc. Thus, 234 francs and 56 centimes would be written 234'56 francs.* The following illustrations will enable the student to appreciate the advantages of the Metric system: I. A vintner sold 3 hectolitres 5 dekalitres 7 litres and 9 decilitres of wine on Monday; 2 dekalitres 4 litres 6 decilitres and 8 centilitres on Tuesday; 8 dekalitres 9 litres and 7 decilitres on Wednesday; 2 hectolitres 4 litres and 6 centilitres on Thursday; 7 dekalitres 6 litres 5 decilitres and 4 centilitres on Friday; and 4 hectolitres 6 dekalitres 8 decilitres and 3 centilitres on Saturday: how much did he sell during the week? By means of Simple Addition we find the answer to be: I kilolitre 2 hectolitres I dekalitre 3 litres 7 decilitres and I centilitre; in other words, 1,213 litres and 71 centilitres. 357'9 24.68 89.7 204.06 76.54 460.83 121371 * There is no special name for a sum of 10, or 100, or 1,000 francs; just as there is no special name for £10, or £100, or £1,000. The French have a coin called a "decime," equal in amount to 10 centimes or the tenth part of a franc, and of about the same value, therefore, as the British penny. The number of decimes is expressed by the figure in the first decimal place. II.-Off a piece of cloth measuring 5 dekametres 6 decimetres and 7 centimetres, a draper cut a length of 8 metres and 9 centimetres; how much remained? : By means of Simple Subtraction we find the answer to be 4 dekametres 2 metres 5 decimetres and 8 centimetres; in other words, 42 metres and 58 centimetres. 50.67 8.09 42.58 III.-A farm is divided into 4 fields, each containing 6 hectares 5 dekares 4 ares and 32 centiares; what is the area of the farm? By means of Simple Multiplication we find the required area to be: 26 hectares I dekare 7 ares and 28 centiares; in other words, 2,617 ares and 28 centiares. 654.32 4 2617.28 IV. A quantity of silver, weighing 5 hectogrammes 9 dekagrammes 2 grammes 5 decigrammes and 9 centigrammes, was made into Ŏ spoons of equal weight; what did each spoon weigh? 6)592'59 By means of Simple Division we find the answer to be: 9 dekagrammes 8 grammes 7 decigrammes 6 centigrammes and 5 milligrammes; in other words, 98 grammes and 765 milligrammes. 98.765 V. The price of a metre of cloth being 18 francs and 60 centimes, what would a length of 7 metres and 4 decimetres cost? Multiplying 18.6 by 7.4, we find the answer to be 137 francs and 64 centimes. 18.6 7.4 744 1302 137.64 VI.—The rent of a farm containing 13 hectares 5 dekares 7 ares and 90 centiares is 3,394 francs and 75 centimes; what is the rent per are? Dividing 3,394'75 by 1,3579, we find the answer to be 2 francs and 50 centimes. 13579)3394'75 2.5 13579)33947-5 27158 67895 67895 The Metric system of Weights and Measures has been introduced into most of the countries of Europe; and, except in the case of the Stere and its decimal multiples and submultiples, the adoption of the system has been rendered "permissive" (but not made compulsory) throughout the British Empire by an Act of Parliament passed in 1864. It is to be feared, however, that, in the absence of a decimal system of British money, this Act will not be productive of much practical good. The issuing of the florin or two-shilling piece was a step in the direction of a decimal system of money: but there are still required—(1.) a coin, which it has been proposed to call a cent, equal in amount to one-tenth of a florin; and (2.) a coin, which it has been proposed to call a mill, equal in amount to one-tenth of a cent. The cent would be a silver coin, not quite as large as the present three-penny piece; whilst the mill would be a bronze coin, a little less in size than the present farthing. The coins of account would then stand thus:— So that a pound being regarded as the standard-3 pounds 5 florins 7 cents and 9 mills would be represented by the simple number £3.579. Conversion of Shillings and Pence into a Decimal of a Pound, and vice versa. A tenth of a pound being a florin (2 shillings), any number of tenths will represent the same number of florins : £1=28.; 2=48.; £*3=6s.; £4=8s.; £5=10s.; &c. As, when the unit is a pound, 5 in the first decimal place represents 5 florins or 10 shillings, 5 in the second decimal place—that is, 5 hundredths-represents 10 times a smaller amount, or I shilling: £5=10s.; £'05=18. A pound, which is worth 960 farthings, farthings. thousandths. 24 = 25 being divisible into 1,000 thousandths (or 40)960=1,000 "mills"), we have 960 farthings=1,000 thousandths, and (dividing by 40) 24 farthings 25 thousandths. So that, in writing farthings as thousandths, we add 1 for every 24; whilst, in writing thousandths as farthings, we reject 1 for every 25. I EXAMPLE I.-Express 14s. 53d. as a decimal of a pound. In the given amount there are 7 florins, for which we write seven tenths of a pound (£7). In the remainder of the amount (5d.) there are 22 farthings, for which—the number being |