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10 cents per lb. more than it costs him, against sugar, which costs Swift 15 cents per pound, but which he puts at 20 cents per pound; what was the first cost of the tea?
Ans. $ 0.30
Ib. 65. Q and Y barter; Q makes of 10 cents 12į cents; Y makes of 15 cents 19 cents; which makes the most per cent., and how much? Ans. Y makes 15 per cent. more than Q.
66. A certain individual was born in 1786, September 25, at 27 minutes past 3 o'clock, A. M.; how many minutes old will he be July 4, 1844, at 30 minutes past 5 o'clock, P. M., reckoning 365 days for a year, excepting leap years, which have 366 days each?
Ans. 30,386,283 minutes. 67. The longitude of a certain star is 3s. 14° 26' 14", and the longitude of the moon at the same time is 8s. 19° 43' 28''; how far will the moon have to move in her orbit to be in conjunction with the star?
Ans. 6s. 24° 42' 46''. 68. From a small field containing 3A. IR. 23p. 200ft., there were sold 1A. 2R. 37p. 30yd. 8ft. ; what quantity remained?
Ans. 1A. 2R. 25p. 21yd. 5ft. 36in. 69. What part of of an acre is f of an acre ?
70. A thief was brought before a certain judge, and it was proved that he had stolen property to the value of 1£. 19s. 11fd. He was sentenced either to one year's imprisonment in the county jail, or to pay 1£. 198. 11d. for the value of every pound he had stolen ; required the amount of the fine ?
Ans. 3£ 19s. 11d. Ogtoqr. 71. My chaise having been injured by a very bad boy, I am obliged to sell it for $68.75, which is 40 per cent. less than its original value; what was the cost ? Ans. $ 114.584
72. Charles Webster's horse is valued at $ 120, but he will not sell him for less than $ 134.40; what per cent. does he intend to make ?
Ans. 12 per cent. 73. Three merchants, L. Emerson, E. Bailey, and S. Curtiss, engaged in a cotton speculation. Emerson advanced $3600, Bailey $ 4200, and Curtiss $ 2200. They invested their whole capital in cotton, for which they received $ 15000 in bills on a bank in New Orleans. These bills were sold to a Boston broker at 15 per cent. below par; what is each man's net gain?
Ans. Emerson $990.00, Bailey $1155.00, Curtiss $605.00.
74. Bought a box made of plank, 3} inches thick. Its length on the outside is 4ft. 9in., its breadth 3ft. 7in., and its
height 2ft. llin. How many square feet did it require to make the box, and how many cubic feet will it hold ?
Ans. 7024 square feet, 294 cubic feet. 75. How many bricks will it require to construct the walls of a house, 64 feet long, and 32 feet wide, and 28 feet high? The walls are to be 1ft. 4in. thick, and there are also three doors 7ft. 4in. high, and 3ft. Sin. wide; also 14 windows 3 feet wide and 6 feet high, and 16 windows 2ft. Sin. wide and 5ft. 8in. high. Each brick is to be 8 inches long, and 4 inches wide, and 2 inches thick.
Ans. 167,480 bricks. 76. John Brown gave to his three sons, Benjamin, Samuel, and William, $ 1000, to be divided in the proportion of }, à, and 3, respectively; but William, having received a fortune by his wife, resigns his share to his brothers. It is required to divide the whole sum between Benjamin and Samuel.
Ans. Benjamin $571.42%; Samuel $ 428.577. 77. Peter Webster rented a house for one year to Thomas Bailey, for $ 100; at the end of four months, Bailey rented one half of the house to John Bricket, and at the end of eight months, it was agreed by Bricket and Bailey to rent one third of the house to John Dana. What share of the rent must
Ans. Bailey $615, Bricket $ 277, and Dana $11}. 78. I have a plank 424 feet in length, 24 inches wide, and 3 inches thick; required the side of a cubical box that can be made from it?
Ans. 48 inches. 79. D. Small purchased a horse for 10 per cent. less than his value, and sold him for 16 per cent. more than his value, by which he gained $21.84; what did he pay for the horse ?
Ans. $75.60. 80. Minot Thayer sold broadcloth at $4.40 per yard, and by so doing he lost 12 per cent.; whereas he ought to have gained 10 per cent. ; for what should the cloth have been sold per yard ?
Ans. $5.50. 81. A gentleman has five daughters, Emily, Jane, Betsey, Abigail, and Nancy, whose fortunes are as follows. The first two and the last two have $19,000; the first four $19,200; the last four $20,000; the first and the last three $20,500; the first three and the last $21,300. What was the fortune of each?
Ans. Emily has $5,000; Jane $4,500; Betsey $6,000 ; Abigail $3,700; and Nancy $5,800.
WEIGHTS, MEASURES AND MONEY. The tables in this work are intended to afford the learner a knowledge of the various weights, measures and moneys used in different countries, sufficient for the ordinary purposes of business and of practical arithmetic. It is here proposed to supply some items of information, such as are not found in popular works of this kind, nur, it is believed, in any compact or easily accessible form.
WEIGHTS AND MEASURES. The use of weights and measures can be traced back to a very early period of the world. Josephus, the Hebrew historian, asserts, that they were invented by Cain, the tiller of the ground and the first builder of a city. Whatever authority is to be attached to this statement, we learn from the Book of Genesis that the cubit was employed in designating the dimensions of Noah's ark; and it is reasonable to suppose that several other measures, and a few simple weights, such as were demanded by the common intercourse and employments of mankind, were in use among the antediluvians.
In the time of Abraham, we find mention made of measures of capacity, (measures of meal,) and also of money. With the latter, the patriarch bought a field of Ephron, the Hittite, for which he paid him four hundred shekels of silver. This sum was weighed out to Ephron, a circumstance plainly indicating that the value of money was then reckoned by its weight, as has been that of coins in all ages.
But though the use of weights and measures can be referred to an origin thus remote in time, we are not to suppose that they were at first employed with the accuracy and uniformity of modern times. On the contrary, as men's ideas of distance, quantity and value were, in the early stages of society, vague and indefinite, so also were their standards of comparison.
When it was first proposed to establish some measure by which small distances should be estimated, it was natural to have recourse to some parts of the human body, as the arm, the foot, the hand;. and hence the origin of the cubit, the length of the arm from the elbow to the end of the longest finger; of the foot, the length of a man's foot ; and of the palm or handbreadth, the width of a man's hand. The span was the distance from the end of the thumb to that of the little finger, when extended ; and the fathom the space between the extremities of the outstretched arms.
When a longer distance was to be measured, the mind would easily fix upon some familiar object of greater length, as a rod or pole, cut from the forest ; and when a shorter distance was to be expressed, it could be done either by dividing the foot or palm into any number of small equal parts, or by employing, as a unit, some minute natural object, as a grain of wheat or barley. In this way the pole, perch or rod, probably came into use, as it is certain did the barley-corn and inch, the latter being the twelfth part of a foot.* It may also be mentioned in this place, that among the measures of the Hindoos, a people with whom there has been little change for many centuries, we find the bambu-pole and the staff, which doubtless originated in a manner similar to the use of the modern rod or pole. The former of these is reckoned at twenty cubits and the latter at four.
The names of several other modern measures clearly indicate their origin, as a mile, from the Latin mille - - one thousand — that is, one thousand paces; furlong, from the Saxon, far or fur, and long, or, as some etymologists say, from furrow and long, that is, the length of a furrow. In some instances, distances have been reckoned by the space through which an arrow could be shot, or a stone thrown, and hence the terms bow-shot and stone's-cast or stone's-throw, with which we occasionally meet.
One of the most indefinite standards ever in use among any people, would seem to be the Chinese unit of linear measure, which is said to be the lih, and to denote the distance which a man's voice will reach in a level country, when thrust forth with all his might.
The instances thus adduced are sufficient to establish two points ; first, that the measures of antiquity originated from the use of some familiar natural objects, as standards of length or distance; and, secondly, that men's ideas and estimate of space were, at an early period, vague, inaccurate, and destitute of uniformity.
But it is evident that such vagueness and diversity could not con tinue. They could neither satisfy the desire of the human mind for accuracy, nor meet the demand for it created by advancing civilization. As men came to have more intercourse and business with each other ; to exchange commodities, fix upon the boundaries of lands, and erect numerous and contiguous buildings; in a word, to live in society, and satisfy their necessities by the barter, sale and purchase of different articles in common use, there would be needed more definite and exact standards by which they might compare one commodity with another, and express its relation and value. Such standards would be necessary in order that equality and justice might be had in common business transactions. And the history of weights and measures is little else than the history of the human mind, in its efforts to devise means and instruments by which commercial intercourse might be conducted on principles of reciprocity and just equivalents.
The importance of uniformity in weights and measures has been felt by all civilized nations ; and to prevent fraud by any alteration of the
* The word inch is said to be from the Latin, uncia, which signifies a twelfth part of anything.
proper standards, or any departure from them in practice, these have usually been kept in the custody of the government. Among the Jews they were committed to the care of the priests, and in Rome they were deposited in the temple of Jupiter. In England they are kept in the exchequer, and in the United States they are in the charge of the national treasury.
So careful are the people in the different states of the Union that due weight and measure shall be given in all trade, that in most, if not in all of them, laws have been enacted requiring those who sell to have their weights and measures sealed, that is, tried or adjusted by some standards kept by public authority for the purpose. In some states this is done as often as once a year.
With the desire of introducing a uniform standard of measure among the people of his kingdom, Henry I., in the year 1101, ordered that the ulna, or ancient ell, should be of the exact length of his own
On this all other measures were to be founded ; and it is worthy of remark, that this very measure, the length of king Henry's arm, has remained, without sensible variation, to this day, and is the present English and American standard yard.
For the last one hundred years, science has been at work to devise some system of weights and measures which should be accurate and intelligible in all its parts, and not liable to change or variation. For this purpose the Royal Society and the parliament of England have combined their efforts, and the result of their labors is a system of Metrology in which the “IMPERIAL YARD” is made the standard of all measures, linear, superficial and solid; and ultimately, as we shall see, of all weights. The law by which this was made the legal standard was passed in 1824, and is entitled, the “ Act of Uniformity.” This yard is represented by a solid brass rod, kept in the exchequer, about an inch square, in which, about an inch and a half from each end, is inserted a gold pin or stud, the space between these pins being 36 inches. This distance is the Imperial yard. That this standard may not be lost or mutilated, it was enacted that it should bear a fixed and definite proportion to the length of a pendulum, vibrating seconds, in a vacuum, in the latitude of London, at the level of the sea, and at the temperature of 62° Fahrenheit. This proportion was to be that of 36 to 39.1393. A third part of this yard was to be the legal foot; a thirty-sixth part the legal inch; five and a half such yards a rod, &c.
The manner in which the legal measures of capacity are founded upon the legal yard is as follows. The “Imperial gallon,” which is the proximate standard of capacity, contains 277.274 cubic inches, each solid inch being raised upon a thirty-sixth part of the Imperial yard. The law, however, allows that the gallon may be deterinined by weight, and then the measure containing a gallon must hold 10lbs. Avoirdupois weight, of distilled water, weighed in air, at 62° Fahrenheit, with the barometer at 30 inches.
By the present law of England, the pound Troy contains 5760 grains, and this pound is the standard of all legal weights. But this pound itself is determined by a reference to the Imperial yard. The compar