58. In what time will he travel over 10 (degree) of motion : A. Is of 1 hour, or the of 60 min., 4 min. 59. In what time will he travel over" 1' (minate) of motion ? A. 1 of 1 min., or its of 60 sec., = 4 seconds. Q. By the foregoing we see that every degree of motion makes a difference in time of 4 minutes, and every minute of motion a difference of 4 seconds. Now, si ce longitude is reckoned in degrees, round the earth, can you tell me koi lo find the difference in time between one place and another, ajer knowing their difference in longitude ?, A. Multiply the difference of longitude in degrees and ininutes by 4, the product will be their difference in time, in minutes and seconds. 60. What is the dilurence in time between two places, wliose difference in longitude is 20 4' ? A. 2° 4' X 4 = 8 minutes and 16 seconds, the difference in time. 61. What is the difference in time between two places, whose difference in longitude is 5° 10'? A. 20 m. 40 sec. What, when the difference of longitude is 80 ? A. 32 m. Is 100 .A. 40 m. Is 15° ? A. 60 m. = 1 hour. Is 15° 15' ? A. 1 h. 1 m. Q. The sur travels from east to west: which place, thon, will havc thc ear. liest time? A. The one most easterly: 62. There are two places, the one situated in 10° E. longitude, and the other in 4° É. longitude; what is the difference in tine between these two places? When it is 24 minutes past 6 o'clock in the former, what hour is it in the latter ? A. 24 minutes, difference in time; then, 100 being the most casterly place, it is there 24 minutes earlier than at 40; that is, when it is 24 minutes past 6 at 109, it is only 6 at 40. 63. Boston is situated about 6° 40' E. longitude from the city of Washington; when it is 2 o'clock at Washington, what o'clock is it at Boston ? A. 26 m. 40 sec. past 2 o'clock. 64. “I recollect of reading a story once of a gentleman going to a foreign country, who had a fancy to look at a bright star every evening, at the same moment, with a certain lady whom he left behind, and they agreed to look at it at 9 o'clock ;" but, it seems that, when the gentleman was in a different longitude, the time would, of course, be different; as, for instance, whes he was in longitude differing 30° W. from where the lady was, she most probably had retired to rest, and was, perhaps, asleep while he was gazing at the star. Can you tell me what o'clocks it was, then, where she was? When he was 60° of W. longi tude from her, what hour of the night was it at the place where the lady resided ? Exercises for the Slate. 1. Write down three millions, three hundred and thrce thou sand, three hundred and three. 2. What is the difference between 50 eagles and 4599 dimes 4 $40,10. the 3. What number is that, which, being wvided by 65, quotient will be 42? A. 2730. 4. A captain, 2 lieutenants, and 30 seamon, tako ? prizo worth $7002, which they divide into 100 shares, of which the captain takes 12, the two lieutenants each 5, and the remainder is to be divided equally anjong the sailors; how much will cach man receive ? A. Captain's share, $840,24, each lieutenant's, $350,10, and each scaman's, $182,052. 5. Bring $400 into crowns, at 6 s. 8 d. each. A. 360 crowns. 6 Washington was born A. D. 1732 ; how many years old would he have been, had he lived until the end of the year 1327? and how many seconds old, allowing the year to con. tain 3654 days? A. 95 years, 2997972000 seconds. 7. The wheels of a cart are 5 feet in circumference, and that of a wheelbarrow 27 inches; how many more times will tlie latter turn round than the former, in going round the earth? How many more times in going through the earth, allowing the diameter to be of the circumference? A. 32292480 times round the earth, 10704160 times through it. 8. How many minutes is it from the commencement of the Christian era to the end of the year 1827 ? A. 960928920. 9. Jacob, hy contract, was to serve Laban for his two daughtors 1.1 years; when he had accomplished 10 years, 10 mo., 10 weeks, 10 days, 10 hours, 10 minutes, how many minutes liad he then to serve ? A. 1416350. 10. Reduce 44 to its lowest terins. A. 4*. A 8568,29705 A. ,7281+ 18. From ,l of a pound, take ,0678 of a pound. A. ,0322. 19. If you give $60 for 25 yards of cloth, what will I yard cost ? A. $2,40. 20. A merchant sold 8 bales of linen, 6 of which contained 15 pieces each, and in each piece were 40 yards; the other 2 bales contained 12 pieces each, and in each piece were 27 yards, what did the whole amount to, at $1} per yard? A. $5310. 2. A man, dying, ieft $10024 to his wife and 2 sons, to be divided as follows: to his wifo g, to his eldest son š of the remainder, and to his youngest son the rest : what is the share 1 of each? A $3759 to his wife $2506 in hes eldest son, $3751 to his youngest 22. A farmer sold a grocer 20 bushels of rye, at $,75 per bushel ; 200 lbs. of cheese, at 10 cents per lb.; in exchange for which he received 20 gallons of molasses, at 22 cents per gal lon, and the balance in money ; how much money did he re ceive ? A. $30,60. 23. A has 150 yards of linen, at 25 cents per yard, which he wishes to exchange with B for musli7 at 50 cents per yard : how much muslin must A receive ? A. 75 yas. 2. A gave B 500 yards of broadcloth, at $2,50 per yard, fu: 000 umbrellas; what were the umbrellas apiece ? A. $2.04:37.. 25. A farmer sold a grocer 20 bbls. of apples, each barrel con taining 3 buskels, al 40 cents per bushel; (24) 30 bushels of corn, at 30 cents per bushel ; (27) 500 lbs. of cheese, at ocents per pound; (40) 200 lbs. of butter, at 17 cents per pound; (34) 75 bushels of turnips, at 19 cents per bushel ; (1425) 40 bushels of barley, at $14 per bus)rel; (50) 25 bushels of rye at 95 cents per bushel ; (2375) and, in exchange, the farmer has received 2 bbls. of cider brandy, at 42 cents per gallon, (2646) 1 bbls. of flour, at $81 per barrel; (35) 60 gallons of molasses, at 34 cents per gallon ; (2010) 40 gallons of wine, at $1,50 per gallon; (60), 10 lbs. of tea, at 73 cents per pound; (7130) $49 in cash ; and he agrees to take up wha.. is still due him in rice at 7 cents per pound; how many pounds of rice must the gro cer give the farmer to balance the account? 4. 340 lbs. 9 07. 23 dr 26. What quantity of cider, at $1,20 per barrel, will buy 3 barre's of rum, at $2 per gallon? 4. 105 bbls. 27. A man exchanged 40 bushels of salt, åt $1,50 per bushcł. for 200 bushels of oats, at 25 cents per bushel ; how much wä's the balance in his favour ? A. $10. 28. A sold B 10 cwt. of sugar, at 8f cents per pound; (14784) 20 bbis of for, at $114 per barrel ; (225) 17 chests of tea, each containing 8 cwt., at 53 cents per pound;. (607296) 30 tierces of rice, at $36 per tierce; (1080) for which В gave up A his notc of $400, that had been on interest 6 yrs. 7 mo. 15 days; (5599) in addition to which В gave A 700 dozen of wax candles at $1,14 per dozen; (7:18) and for the balance A consents to take B's note, payable in 21 years, without interest ; but B, un - expectedly receiving some money, wishes to advance the casli, instead of giving his note; what sum of ready rioney ought B to pay A, discounting at 54 per cent.? A. $7181,302+: 29. A had 200 bbls. of flour, at $10,50 per bbl., for wlich B gave him $10:0 in money, and the rest in molasses, at 21) cents per gallon; how many hogsheads of molasses did he receive ? A. 80 hhds. 10 gals. price ? 30. A has linen cloth, worth $,20 per yard, but, in bartering he will receive $,30; B has broadcloth, worth $4,60 per yard, ready money: at what price ought B to rate his broadcloth, to ba in proportion with A's bartering price ? $,20 : $4,60 : : $,30 : $6,90, Ans. Or, multiply $,30 by the ratio of 20 to $4,60, that is, 23 ; thus, 23 X 30 $6,90 ; for, $4,60 being 23 times as much as 20, it is plain that 3 times $,30, A's bariering price, will give B's bartering price, A. $6,90. 31. A merchant, in bartering with a farmer for wood at $5 per cord, rated his molasses at 25 dollars per hhd., which was worth no more than $20; what price ought the farmer to have askod for his wood to be equal to the merchant's bartering A. $6,25. The last ton examples are proper questions in a rule usually called Barter. 32. What number is that, which, being multiplied by 15, will mako ? A. zb. 33. What number is that, which, being divided by 15, will make abo? A. 34. What decimal is that, which, being multipried by ,625, will make ,25? A. ,4. 35. At $,75 per bushel, how much rye can be bought for $150? (200) For $600? (800) For $75? (100) A. 1100 bushels. 36. (800+ 12 +88) • (50-5)=how many? A. 20. 37, (06 to 444) = (3,55,-55)= how many A, 21. 38. Two persons depart from one place at the same time ; the one travels 35, and the other 40 miles a day; how far aro they distant at the end of 10 days, if they both travel the same road ? and how far, if they travel contrary directions ? A. 50, and 750 miles. 39 Two men, A and B, traded in company; A put in $700 for 8 months, and P $1280 for 10 months ; they gained $500: what was the share of each ? A. A's share, $152,17%; B's sharo, $347,826 + 40. How many cord-feet of wood are contained in a load 8 feet lony, 4 ft. 6' wide, and 5 ft. 3' high ? A. ! 118 ft. or 11 ft. 9'g'. 41. What is the difference in time between two places, whose difference of longitude is 400 ? (2,40) 50° ? (3,20) 600 ? (4) A. 10 h. 42. What time iş it in 15° W. longitude, when it is 6 o'clock in 15° E. longitude ? A. 4 o'clock. 43. If a cow yield 16 qts. of milk in a day for 240 days, and 20 qts. make 1 pound of butter, or 10 pounds of cheese, how much more profitable is the making of cheese than butter, the price of butter being 35 cts. per pound, and that of cheese 81 ets. per pound A. $110,40. ? ? 58. In what time will be travel over 1° (deg A. Its of 1 hour, or the of 60 n. 59. In what time will he travel over 1' (minu A. I's of 1 min., or I's of 60 sec., Q. By the foregoing wc see that every degree of motion in time of 4 minutes, and every minute of motion a diffe: Noro, sice longitude is reckoned in degrees, round the earl koro to find the difference in timc between one place and anot! their difference in longitude ? A. Multiply the differeni in degrees and ininutes by 4, the product will be th in time, in minutes and seconds. 00. What is the diference in time between two pl: difference in longitude is 20 4' ? A. 20 4' X 4 =81 16 seconds, the difference in time. 61. What is the difference in time between two play difference in longitude is 5° 10' ? A. 20 m. 40 sec. when the difference of longitude is 80 ? A, 32 m. A. 40 m. Is 150? A. 60 m.= 1 hour. Is 15° 15' ? A. Q. The suu travels froin east to west : which place, thon, will har liest time ? A. The one most easterly: 62. There are two places, the one situated in 10° E. los and the other in 4o E. longitude; what is the difference between these two places? When it is 24 minute o'clock in the former, what hour is it in the latter ? utes, difference in time; then, 100 being the most casterly place, minutes earlier than at 40; is, wžen it is 24 minutes past 6 at 6 at 40, 63. Boston is situated about 6° 40' E. longitude of Washington; when it is 2 o'clock at Wash o'clock is it at Boston ? A. 26 m. 41) sec. past 2 0 64. “I recollect of reading a story once of a geri to a foreign country, who had a fancy to look at every evening, at the same moment, with a certa ho left behind, and they agreed to look at it at ! it scems that, when the gentleman was in a dift the time would, of course, be different; as, fg he was in longitude differing 300 W. from wh she most probably had retired to rest, and was while he was gazing at the star. Can you tel it was, then, where she was? When he was tude from her, what hour of the night was it a the lady resided ? Exercises for the Slate. 1. Write down three millions, three hundi sand, three hundred and three. 2. What is the difference between 50 ea Ą $40,10. |