Exer. 141. Find 3 of 112 and of 289: find also the sum and difference of the results. Answ. 21, 85, 106, and 64. 142. What is the number of which 42 is? Answ. 154. 12 143. Find of 576 and 17 of the result. Answ. 336 and 238. 144. Square 38 and cube 16. Answ. 1444 and 4096. 145. Find a fourth proportional to 28, 42, and 128. Answ. 192. 146. Required the prices of 64 lbs. of butter, at 101d. per fb.; and of 31 lbs. at 91d. Answ. £2 - 14 - 8, and £1 - 4 - 61. 147. Find the prices of 47 barrels of oats at 10s. 6d. per barrel, and 38 barrels of barley at 12s. 9d. per barrel. Answ. £24-13-6, and £24 - 10 - 101. 148. What cost 49 lbs. of sugar at £3 - 16 per cwt., and 48 lbs. at £3 17 per cwt.? Answ. £1 13 - 3, and £1 - 13 - 0. 149. What are the costs of 15 lbs. of beef, and 131 lbs. of mutton, the first at 7d. and the second at 6d. per ib.? Answ. 98. 01d. and 6s. 7 d. 150. Find the price of 93 lbs. of salmon at 1s. 6d. per ib. Answ.. 148. 7 d. 151. Reduce £99 19 - 2 to pence. 152. Reduce 1245 pence to pounds. 153. If of a gallon of wine cost 7s. 89 gallons? Answ. £1 and £89. Answ. 23990. 154. If of a ton cost £3-15, what cost 1 ton, and 123 tons? Answ. £6, and £76 10 0. 155. If a hundred weight of sugar cost £2 - 100, what is gained by selling it at 7d. per fb.? Answ. 15s. 4d. 156. What is gained or lost by selling 122 yards of broadcloth at 18s. per yard, the first cost and charges having amounted to £110? Answ. Lost 4s. 157. If a person drink, daily, a bottle of porter, worth 41d. what is the amount for a year? Answ. £6 - 16 - 101. 158. If 12 bottles of wine cost £17, what cost 7 dozen and 5 bottles? Answ. £10 - 0-3. 159. Reduce 742 guineas to pounds. Answ. £779 - 2 - 0. 160. If one steamer start at 12 o'clock, and sail at the rate of 10 miles per hour, and another start at half past one, and sail in the same direction, at the rate of 11 miles per hour; at what hour will the latter overtake the former? Answ. At half past ten on the succeeding day. 161. How many times greater is a square field, having each side 60 perches, than a triangular one having its base = 18 perches, and its perpendicular = 10 perches ?* Answ. 40 times. 162. What is the interest of £65 for 1 year, 5 months, at 5 per cent. per annum? Answ. £4 - 12 - 1. 163. Find the present worth of a bill for £95, due at the end of 4 months, interest at 4 per cent. being taken as discount. Answ. £93-11-6. 164. A person borrows £100, and pays £55 at the end of 7 months, and the rest at the end of a year. What has he to pay for interest at 5 per cent. per annum? Answ. £3 - 17 - 1. 165. Find the interest of £70 from the 4th of April till the 24th of July, at 6 per cent. per annum. Answ. £1-5-61. 166. Find the present worth at 4 per cent. per annum, of a bill for £43 - 6-8, which has 60 days to run. Answ. £43-0-5. 167. Required the present worth of £250, due at the end of 160 days, at 5 per cent. per annum. Answ. £243-19 - 5. 168. How often will a carriage wheel, 132 feet in circumference, revolve in going a mile? Answ. 384 times. This question will, of course, be omitted by those who are unacquainted with mensuration. THE METRIC SYSTEM OF WEIGHTS AND MEASURES. THE tables of weights and measures already given, afford a remarkable exemplification of the utter absurdity, and great, and wasteful, and dangerous inconvenience, of the variety of systems, in more or less common use in Great Britain, for the reckoning of mass and dimensions. Thus different modes of reckoning mass are employed in commerce and the arts, according as the substance is one of the precious metals, or an article of ordinary merchandise, or a medicine specified in a physician's prescription. The apothecary buys according to avoirdupois weight,-pounds of 16 of one kind of ounce (437 grains), and drams, and grains; and compounds his medicines according to apothecaries' weight,-pounds of 12 of another kind of ounce (480 grains), and drams, and scruples, and grains. The avoirdupois dram is 2711 grains; the apothecaries' dram is 60 grains. A certain multiple of the imperial unit of length, called a mile, is used for the measurement of distance travelled by land and for land telegraph wires; while another unit of length, also called a mile, which is one minute of latitude, or one minute of longitude at the equator, on the earth's surface, and is not an exact multiple of the imperial unit of length, is used for the measurement of distance travelled by sea and for the measurement of submarine telegraph wires. The length of a rope or chain is measured in yards, feet, or inches, the length of a piece of cloth in yards, quarters, or nails. These various modes of reckoning, since they have no connection with one another, and follow no method in the formation of multiples and submultiples of their fundamental units, are a source of great inconvenience to the British nation, which It might be wholly avoided by the adoption of some simple and uniform mode of reckoning with different denominations chosen according to the decimal system. Such a mode of reckoning has been long in use for general purposes in France, Germany, and Italy, and for scientific purposes throughout the whole world. owes its origin to a decree * of the French Republic passed in 1795, which, giving effect to a recommendation of a committee of the French Academy of Sciences, provided that the unit of length should be one tenmillionth part of the quadrant of the earth's circumference measured along the meridian of Paris. The work of realising this standard was entrusted to Borda, who, using the determination of the length of an arc of the meridian made by Delambre and Méchain, constructed a rod of platinum which, when at a temperature of 32° Fahrenheit, or 0° Centigrade, represented, as accurately as geodetical knowledge then permitted, the length specified by the decree. This rod has been carefully preserved in the national archives of France, and by it is defined the metre or fundamental unit of the French system now called the metric system. The length of the metre, it is to be observed, therefore, is not affected by the results of any subsequent geodesy, though more accurate than that of Delambre and Méchain; on the contrary, all such results are expressed in terms of the length of Borda's platinum rod. Thus One great convenience of the French metric system consists in the fact that the multiples and submultiples of its fundamental unit follow the decimal law. the metre, which is equal in length to 39 37079 English inches, is divided into 10 parts, each of which is called a centimetre, and each centimetre into 10 parts, each of which is called a millimetre; again, a length of 10 metres is called a decametre, a length of 100 metres a hectometre, a length of 1000 metres a kilometre, and so on. Thus any length or distance whatever can be expressed in convenient numbers; and at the same time the utmost facility of computation is obtained by the adoption of the decimal scale of numeration. Another advantage of the French metric system is * Loi du 18 germinal, an III. found in the relation of the unit of length to the unit of mass or weight adopted in that system. The French unit of mass or weight is defined as the mass of a certain piece of platinum, called the "Kilogramme des Archives," which was also made by Borda, and was intended to represent the mass of a cubic decimetre of distilled water at the temperature of maximum density, viz. 39° Fahrenheit or 4° Centigrade. Although, when the utmost strictness of definition is required, it must be remembered that the standard of mass is the mass of that one piece of platinum, in most cases no sensible error is introduced by estimating the mass of a cubic decimetre of water at 39° Fahrenheit, or at 4° Centigrade, as a kilogramme, or the mass of a cubic centimetre of water at that temperature as one gramme. A great simplification is by this means introduced into the computation of masses of different volumes of various substances from their specific gravities. The specific gravity of a substance is the ratio of the mass of a certain volume of the substance to the mass of an equal volume of water at its temperature of maximum density. Hence if the specific gravity of a substance be known, the mass of any specified volume of the substance is found by multiplying the number of units of volume by the specific gravity, and the result by the mass of unit volume of water. This last factor, which, in the English system, is always a troublesome one, is reduced to unity in the metric system by the connection explained above between the unit of length and the unit of mass. Thus the mass of a given volume of a substance is given in grammes by the product of the specific gravity and the volume in cubic centimetres, in kilogrammes by the product of the specific gravity and the volume in cubic decimetres or litres, and in French tonnes by the product of the specific gravity and the volume in cubic metres. The French tonne, or 1000 kilogrammes, is 984 of the English ton. The following tables show the relations of the various weights and measures of the metric system to one another and their values in English imperial units. |