should find that I could be given 59 different times to each of the II persons, and that the number of pounds then remaining would be 9. Taking 118. as often as possible from 1948. (9 148.), we should next find that is. could be given 17 different times to each person, and that the number of shillings then remaining would be 7. Taking 11d. as often as possible from 93d. (78. 9d.), we should next find that id. could be given 8 different times to each person, and that the number of pence then remaining would be 5. Lastly, taking 11 farthings as often as possible from 22 farthings (5d.), we should find that 4d. could be given 2 different times to each person, and that nothing would then remain to be distributed each person's share being thus found to be, as before, £59 178. 8d. EXAMPLE II.-How many lengths of 2 ft. 8 in. each could be cut off a ribbon 17 yds. long? 87. Rule for Compound Division, (a) when the Divisor is an abstract number: Divide the several denominations successively-beginning with the highest-by the divisor, taking care, when a portion of any denomination is left as "remainder," to include this portion, after having reduced it, in the next (lower) denomination. (b) When the Divisor is a concrete number, reduce it and the dividend to the lowest denomination which occurs in either, and then find the quotient by Simple Division. NOTE 1.-When the divisor is an abstract number greater than 12, but resolvable into a pair of factors of which neither exceeds 12, we can proceed as in Simple Division-first dividing the dividend by one of the factors, and afterwards dividing the resulting quotient by the other factor. If, for instance, it were required to divide £365 178. 11d. by 72, we could resolve 72 into the factors 8 and 9, and proceed as follows: 72 { £ s. d. 8)365 17 112 9)45 14 83+7 5 1 71+5 5×8+7=47; 47f.=113d. NOTE 2.-When the divisor is an abstract number greater than 12, and not resolvable into factors, we proceed as directed by the Rule. Thus, if it were required to divide 365 178. 11d. by 47, the quotient (£7 158. 84d.) would be obtained in the way shown below: METRIC SYSTEM OF WEIGHTS AND MEASURES. "The great diversity of Weights and Measures which has existed in all countries has principally arisen from the lesser communities of which they were originally composed having each adopted its own system. In process of time these lesser communities were amalgamated into separate nations, with whose increase of population and trade the inconvenience of a variety of Weights and Measures soon made itself apparent, and the desire of establishing uniformity arose. France was the first country to relieve itself from its barbarous multiplicity of Weights and Measures, by adopting a uniform system. Louis XVI., at the recommendation of the Constituent Assembly, invited, by a decree, all the nations of Europe, and particularly the King of Great Britain, to confer respecting the adoption of an international system of Weights and Measures. No response being given to this invitation, France committed the consideration of the subject to some of the most learned men of the age, who devised what is called the Metric system: the most simple, convenient, and scientific system of Weights and Measures in existence."* The Metric system is so called from the circumstance that it is based upon the METRE, which is the standard of Length. The metre is the ten-millionth (10,000,000) part of the distance-measured upon the meridian of Paris-between the equator and the pole, and is longer by about 3 inches than the English yard. * The standard of Superficial measure is a square described Report of Parliamentary Committee on Weights and Measures of United Kingdom: 1862. 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 () 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 (1) of a metre in length. This standard is called a GRAM,† 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 (déra), hekaton (exaτov), and chilioi (xilio) 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 () of a metre is termed a deci-metre ; one-hundredth (1) of a metre, a centi-metre; and onethousandth (1,01‰ō) of a metre, a milli-metre. So with regard to the other standards.§ The following are the details of the Metric System : * About 39°, Fahrenheit. +In France, and in other countries on the Continent, the word is spelled "gramme;" but in the British Act of Parliament referred to at p. 130 the spelling is "gram." Even the FRANC, the French standard of value, may be said to be based upon the metre, being equal in weight to 5 grams. The franc is a silver coin,-of which 9 parts out of 10 are pure silver,— and is equivalent to about 10d. British. § The only exceptions are “millier" (1,000,000 grams) and quintal" (100,000 grams). WEIGHT. Centimetre = one-hundredth (100) of a Metre Millimetre = one-thousandth (1,000). 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 Are Centiare = 100 Ares = 119.6033 square yards one-hundredth (130) of an Are. 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. Dekastere = 10 Steres CAPACITY. SOLIDITY. Kilogram Gram Decigram Centigram = Milligram 10,000 15 4323487 grains one-tenth (o) of a one-hundredth (100) Gram = one-thousandth (1,000)) *From myrioi (μúpio), the Greek word for 10,000. |