To find the part of the Globe opposite to a given place. RULE. Take the same latitude of an opposite name for the place required, and subtract the longitude of the given place from 180°, the remainder is the longitude of the place required, but of an opposite name. EXAMPLES. 1. Required the opposite part of the globe to London, in latitude 51° 31' N. and near the first meridian. London lat. 51° 31′ N. long. 0° 00' 180 00 2. Required the opposite part of the globe to Boston. Boston lat. 42° 23′ N. long. 71° 03′ W. Opposite place 42 23 S. long. 108 57 E. 3. Suppose a ship in any of the following places, what place on the globe would be opposite to it? To estimate the distance of objects at sea. Multiply the square root of the height in feet by 11, and point off the unit's figure in the product for decimal parts, the remainder is the miles required—thus, Height. At 16 feet 25 Sq. Root. Miles. 5,7 PLANETARY MOTION. To find the velocity of a Planet's motion in its orbit. . RULE. As 1 is to 3,14159, so is the diameter of the Plan et's orbit to its circumference, and as the time of revolving is to the circumference, so is the given time to the distance required. EXAMPLE. If the Earth moves round the Sun in a ear, at the distance of 95 millions of miles, what is e hourly velocity of of its motion? 95 1: 3,14: 190,000,000 3,14+ 365)596,000,000 circumference. 24)1,634,520 Ans. 68,105 miles per hour. The distances of the other planets from the sun, and the times of their revolving round it being known, the daily and hourly velocity of their motion in their orbits may be found as in the preceding example. MISCELLANEOUS QUESTIONS. 1. If Gunter's chain of 100 links be equal to 4 rods or perches, what is the length of Î link, and how many square links in an acre? 2. In 23 chains 48 links, how many rods, &c. ? 23,48 4 93,92 12 161 4. In 534 chains, 72 links, how many miles? 80)534,72 12 2,10= Ans. 93 rds. 15 ft. 2 ins, 5. If the tunnel of a canal at the base be 18 feet, and the height 12 feet, how many cubic yards in every running yard? 18×12×3=648 3×3×3=27 24 yards. 6. How many cubic feet of water in a pond, containing 95 acres, 20 feet deep? 1 Acre 43560 ft. × 95 = 4138200 20 Ans. 82,764,000 Cubic feet. 7. What quantity of water may be retained in the following ponds, if used as reservoirs for a canal? Cubic feet. =249,163,200 L. 90,604,800 8. Suppose a loss of 1 foot by evaporation from the surfaces of these 6 ponds, how many feet in the whole ? 1 acre 43560 feet X 878 acres=38,245,680 Cubic feet Cut. qrs. lbs. 1 piece 253 ft. by 24 ft. produced 10 3 0 of hay. 2 "" 252 193 201 11 0 0 What was the produce of each equal to per acre Tons. Ans. 1 piece equal to 3 17 0 13 per acre. 2 11. The births in a certain town were 475, and the proportion 13 boys to 12 girls. What is the number of each ? Ans. 247 boys, and 228 girls. 12. How many yards of carpet, yard wide, will cover a floor 25 feet long, and 18 wide ? Ans. 50 yards. 13. How many trees, 4 feet apart every way, may grow in a nursery of one acre of ground? Ans. 2722 trees. 14. If a ship of 350 tons, chartered at 3s. a ton per month, deliver a cargo of 600 tons, what is the real rate per ton? Ans. 1s. 9d. 15. A farmer raised 43 tons 11 cwt. 3 rots on 1 acre 1 rood and 25 perches. qrs. 14 lb. of car What was it per Ans. 31 tons. 17. There are two numbers in proportion as 3 to 11, the greater is 3267, what is the sum of both? 230 Ans. 4158. 18. The Chinese wall is said to be 1200 miles in length, averaging 18 feet high, and as many thick, how many solid fathoms does it contain ? Ans. 9,504,000 fathoms. 19. Suppose a steam-boat at $1103 per share cost $25472, 50 cts. and that of it sold for $5725. Was there a gain or loss by the sale? Ans. $1141,50 loss. 20. A pile of wood 84 feet 6 inches long, 22 feet 7 inches nigh, and 23 feet 10 inches wide, is sold at $3,26 per cord, what is the amount? Ans. $1158,32. 21. Required the cost of a lot of land 62 feet 11 inches ong, and 27 feet 3 inches wide, at $1,80 per square foot ? Ans. $3093,86. 22. A. of Providence has in his hands $500 due to G. of Charleston, for net proceeds of his cotton, this is remitted to G. per bill on M. in his favour when bills on Charleston are at 2 per cent. discount. Required the amount of the bill? Ans. $510,20. 23. Suppose $984,371 was paid in New-Orleans for a bill on New-York, when the advance was 5 per cent. what was the bill drawn for? Ans. $937,50. 24. If 33865 feet of land sold in Boston in 1824 for $403, 840,121 cts. how much is it per foot, and what would be the rate per acre in Federal and also in Sterling money? Ans. $11,92 per foot, $519,453 per acre, Equal to £116,876 18 6 ster. |