18 cwt. 3 qrs. 17 lb. 7 oz. was 47. 14s. 6d. the custom and fees, 21. Ss. 6d. Freight, 11. 2s. Sd. Factorage, 4s. 6d. Pray how must I sell it per cwt. so that I may gain 51. 10s. by the whole? (30) A certain tower projected upon level ground a shadow to the distance of 63 yards 1 foot, when a staff 3 feet in length, perpendicularly erected, cast a shadow of 6 feet 4 inches. From hence the height of the tower is required. (31) Suppose a person travel 285 miles in 6 days 4 hours, at what rate is that per hour, allowing 12 hours to the day? (32) Suppose I gave 441. 2s. for one pipe of wine, at what rate did I give per pint? (33) The globe of the earth, under the equinoctial line, is 360 degrees in circumference; and this body being turned on its own axis, in the sidereal day, or 23 hours 56 minutes, at what rate an hour are the inhabitants of Bencoolen, situated in the midst of the torrid zone, carried from west to east by this rotation? (34) What is the value of one grain of gold, when one ounce costs 5 guineas? (35) If 12 apples are worth 21 pears, and 3 pears cost a halfpenny, what will be the price of fourscore and four apples? (36) It is a rule in some parishes to assess the inhabitants in proportion to eight-tenths of their rents. What is the yearly rent of that house which pays 87. 10s. to the king under this limitation, at 4s. in the pound? (37) If 19 yards of yard-wide stuff exactly line 14 yards of silk of another breadth, how many yards of the latter will line 184 pieces of the former, each piece holding 28 yards? (38) In 117 times 406 pieces of coin, worth 3s. 8d. a piece, how many rees at 20 for 3d. English? (39) A merchant bought 274 ells Flemish of Holland, for 4s. per ell, and sold it again for 7s. 10d. per ell English. What did he gain by the whole? (40) A May-pole 50 feet 11 inches long, when the sun is on the meridian, will cast a shadow 98 feet 6 inches long; I would thereby find the breadth of a river, that runs due E. and W. within 20 feet 6 inches on the north side of the foot of a steeple, 300 feet 8 inches high, which at the same time throws the extremity of its shadow 30 feet 9 inches beyond the stream. (41) If 2 men in three days will earn 15s. how much will seven men earn in the same time? (42) How far will one be able to travel in 9 days 8 hours, at the rate of 12 miles every four hours, allowing 12 hours to a travelling day? (43) What will 1000 yards of walling amount to, at the rate of 4s. 6d. per rod? (44) A factor bought 64 pieces of Holland, which cost him 3521. at 5s. 6d. per ell Flemish. I demand how many yards there were in all, and how many ells English in each piece. (45) If 100l. in 12 months gain 41. 15s. what will 40l. 10s. gain in the same time, the interest being at the same rate? (46) If 12 yards of yard-wide stuff exactly line 8 yards of silk of another breadth, how many yards of the latter will line 24 pieces of the former, each piece containing 20 yards? (47) What is the quarter's rent of 240 acres of land, at 17. 19s. 6d. per acre per annum? (48) A person owes 1000l. but not being able to pay the whole, compounds with his creditors to pay half-aguinea in the pound. How much does he pay his creditors? (49) When the sun is in the meridian at Soho-square, in what time will it be so at Tyburn, lying due west of it at the distance of a measured mile, in the latitude of 51 degrees north, where a degree of longitude measures 37 miles, 2 furlongs, 37 poles, 5 feet, and 6 inches, known by the diurnal rotation of the earth to pass in 4 minutes' time? (50) How many pieces of Holland, each 33 ells Flem. 1 qr. 2 na. can I have for 118. 17s. 74d. when 4 ells English cost 11. 7s. 10d.? (51) I laid out 1007. upon serges and shalloons: the total value of the shalloons was 60l. and the total quantity of serge 236 yards; also, for every two yards of serge, I had three of shalloon. How much shalloon was there, and what was the value of one yard of each sort? (52) If 1 s. will buy 8 lb. of tobacco, how much will 47. 19s. 14d. buy at the same rate? (53) What will the carriage of 20 cwt. 2 qrs. 16 lb. come to at 7s. per cwt. ? (54) Bought a pipe of Port wine, for which I gave 251. 4s. but it leaked out 12 gallons; the remainder I sold at the rate of 18d. per quart. What was my gain or loss in the whole ? (55) If 7l. 4s. 9d. be paid for the carriage of 20 cwt. 2 qrs. 16 lb. at what rate is that per pound? (56) How many bricks, 9 inches long, and 4 inches wide, will floor a room that is 20 feet square? QUESTIONS for Exercise at leisure Hours. (57) I am dispatched on a commission from London to Edinburgh, distant by computation 350 miles, and my route is settled at 22 miles a-day; you, four days after, are sent after me with fresh orders, and are to travel 32 miles a-day. Whereabout on the road shall I be overtaken by you? (58) In the year 1582, Pope Gregory reformed the Julian calendar, ordaining, that as the year is found to consist only of 365 days, 5 hours, and about 49 minutes, in order to prevent the inconvenience of carrying the account of time too forward, by taking the solar year at 365 days and 6 hours full, which in a series of years must bring Lady-day to Michaelmas, that the Christian states for the future should drop three days in account every 400 years: that is to say, for each of the three first centuries in that space of time, the intercalary day in February should be omitted, but retained as formerly in the last century, beginning with the year 1700, when 10 whole days were sunk at once, by which artifice the variation of time will not, at least for a long space, be very considerable; according to his regulation, it is required to know in what year of Christ, the New Style, as it is called, will be twenty days, as it is now only 11, before the Old Style, which makes no such allowance. (59) Suppose the sea allowance for the common men to be 5lb. of beef, and 3lb. of biscuit a-day, for a mess of four people, and that the price of the former be to the king 24d. per lb. and of the latter 1d.: such was the ship's company, that their meat cost the government 12 guineas per day; pray what did it pay for their bread per week? (60) A. set out from London for Lincoln at the very same time that B, at Lincoln set forward for London, distant 135 miles; at eight hours' end they met on the road, and then it appeared that A. had rode 24 miles an hour more than B. At what rate an hour did each of them travel? (61) A. can do a piece of work in 10 days, B. alone in 13. Set them both about it together, in what time will it be finished? (62) B. and C. together can build a boat in 18 days; with the assistance of A. they can do it. in 11 days. In what time would A. do it himself? (63) In some parishes in the country they take off 31. one year in 17, from the rents, in assessing the farms. What will the landlord receive net out of a farm of 1401. a-year in those places, when the king's tax is 4s. in the pound? (64) A tradesman begins the world with 1000l. and finds that he can gain 1000l. in five years by land trade alone, and that he can gain 1000l. in eight years by sea trade alone; and likewise that he spends 10007. in 2 years by gaming. How long will his estate last if he follow all three? (65) If I leave Exeter at ten o'clock on Tuesday morning for. London, and ride at the rate of 2 miles an hour without intermission; you set out of London for Exeter at six the same evening, and ride three miles an hour constantly the question is, whereabout on the road you and I shall meet, if the distance of the two cities be 170 miles. : (66) If the Sun move every day one degree, and the Moon thirteen, and at a certain time the Sun be at the beginning of Cancer, and in three days after the Moon in the beginning of Aries, the place of their next following conjunction is required. (67) As I was beating on the forest grounds, Up starts a hare before my two greyhounds: OF SOUND. SOUND not interrupted is, by experiments, found uniformly to move about 1150 feet in one second of time. (68) How long after firing the warning-gun in Hyde-Park may the same be heard at Highgate, taking the distance at 53 miles? (69) If I see the flash of a piece of ordnance, fired by a vessel in distress at sea, which happens, we will suppose, nearly at the instant of its going off, and hear the report a minute and three seconds afterwards, how far is she off, reckoning for the passage of sound as before? OF THE LEVERS— There being three orders of levers, or three varieties wherein the weight, prop, or moving power, may be differently applied to the vectis, or inflexible bar, in order to effect mechanical operations in a convenient manner. For the First Order, see page 71. Of the Second and Third Order of LEvers. In mechanics, a lever of the second order is, where the power acts at one end, the prop fixed directly at the other, and the weight somewhere between them. In this order of levers their force is in a contra proportion to their length. In a lever of the third order the prop is planted at one end of the bar, the weight at the other end, and the moving force somewhere between. (70) If a lever be 100 inches long, what weight lying 7 inches from the end resting on a pavement, may be moved with the force of 168 lb. lifting at the other end of the lever? (71) A water-wheel turns a crank, working three pumprods, fixed just six feet from the joint or pin; by which their several levers, each nine feet in length, are fastened, for the sake of the intended motion, at one end. The suckers of the pumps being worked |