78. What is the area of a circle 1 mile in circumference?

79. If the diameter of the sun is 887000 miles, what is its surface?

80. If the diameter of Jupiter is 86255 miles, what is its solidity?

81. A conical stack of hay is 20 ft. high, and its base 15 ft. in diamete what is its weight, allowing 5 lbs. to a cubic foot?

82. How many bushels will a cubical bin contain whose side is 9 ft. ?

83. How many hogsheads will a cylindrical cistern 10 ft. deep and 6 ft. diameter contain?

84. How far from the end of a stick of timber 30 ft. long, of equal size from end to end, must a lever be placed, so that 3 men, 2 at the lever, and 1 at the end of the stick, may each carry of its weight?

85. How many different ways may a class of 26 scholars be arranged?

86. If 100 eggs are placed in a straight line a rod apart, how many miles must a person travel to bring them one by one to a basket placed a rod from the first egg?

87. What is the sum of the series 1, 1, 2, 2, 3, &c., to 50 terms?

88. A blacksmith agreed to shoe a horse for 1 mill for the first nail in his shoe, 2 mills for the second nail, and so on: the shoes contained 32 nails: how much did he receive?

89. Said a mule to an ass, if I take one of your bags, I shall have twice as many as you, and if I give you one of mine, we shall have an equal number: with how many bags was each loaded?

90. What number taken from the square of 48 will leave 16 times 54 ? 91. Divide $1000 between A, B, and C, and give A $120 more than C, and C $95 more than B.

92. A person being asked the hour of the day, said, that the time past noon was of the time till midnight: what was the hour?

93. A, B, and C, can trench a meadow in 12 days; B, C, and D, in 14 days; C, D, and A, in 15 days; and D, B, and A, in 18 days. In what time would it be done by all of them together, and by each of them singly?

94. Suppose A, B, and C, to start from the same point, and to travel in the same direction, round an island 73 miles in compass, A at the rate of 6, B of 10, and C of 16 miles per day: in what time will they be next together?

95. At what time between 12 and 1 o'clock do the hour and minute hands of a common clock or watch point in directions exactly opposite?

96. In how many years will the error of the Julian Calendar involve the loss of a day?

97. A man's desk was robbed 3 nights in succession; the first night half the number of dollars were taken and half a dollar more; the second, half the remainder was taken and half a dollar more; the third night, half of what was then left and half a dollar more, when he found he had $50 left: how much had he at first?

THE END.

ANSWERS TO EXAMPLES.

NOTE. At the urgent request of several distinguished Teachers, who have received Thomson's Higher Arithmetic with favor, the publishers have issued an edition of it, containing the answers in the end of the book. It is hoped that pupils, who may use this edition, will have sufficient regard to their own improvement, never to consult the answer till they have made a strenuous and persevering effort to solve the problem themselves.

N. B.-The work without the answers is published as heretofore.

DIVISION.-ART. 127.

13. 56977. 25. 3679.

14. 382345.

15. 416654. 27. 508301. 36. 1387805

16. 2127627. 28. 630.
17. 12152. 29. 235.

31. 26710179.. 38. 90009000

32. 563.

33. 8826211

34. 23434402

402

PROPERTIES OF NUMBERS.-ARTS. 162, 163.

1--9. Given. 13. 2024122. 18. 707961.

10. 20212331.

11. 2350147.

20. 9753020.

122. 1614386.

14. 1522365. 19. 1036993. 23. 118620366. 15. Given. 24. 387909012. 1331124. 16, 17. Given. 21. 360913096. 582.