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PROBLEM II.

To find on what day of the week any given day of the month will happen.

RULE. — Find by the last problem the dominical letter for the given year, and on what day in January will be the first Sabbath ; and the corresponding day in the succeeding months will be as follows : Wednesday for February; Wednesday for March ; Saturday for April; Monday for May; Thursday for June; Saturday for July; Tuesday for August ; Friday for September ; Sabbath for October ; Wednesday for November ; Friday for December. Having found the day of the week for any day in the month, any other day may be easily obtained, as may be seen in the following example.

8. Let it be required to ascertain on what day of the week was the 25th day of September, 1838.

The dominical letter for 1838 is G; therefore, the 7th of January was the Sabbath, and, by the above rule, the 7th of February was Wednesday, the 7th of March was Wednesday, the 7th of April was Saturday, the 7th of May was Monday, the 7th of June was Thursday, the 7th of July was Saturday, the 7th of August was Tuesday, the 7th of September was Friday. If the 7th was Friday, the 14th, the 21st, and the 28th were Fridays. And if the 21st was Friday, the 22d was Saturday, the 23d was the Sabbath, the 24th was Monday, and the 25th, the day required, was Tuesday.

The following distich will assist the memory in finding the corresponding days of the month:

At Dover Dwells George Brown Esquire,

Good Christian Friend, And David Friar. It will be recollected, that the initial A is for the Sabbath, B for Monday, C for Tuesday, D for Wednesday, E for Thursday, F for Friday, and G for Saturday.

Note. When it is leap year, the days of the week, after February, will be one day later than on other years.

9. Required the day of the week for the 4th of July, 1836.

We find the dominical letters to be B and C, the 3d day of January therefore was on the Sabbath, and by the above rule the 3d day of July would have been on Saturday; but as it was leap year, the 3d of July was one day later; that is, it was on the Sabbath ; and, if the 3d was the Sabbath, the 4th of July was on Monday 10. On what day of the week will be Dec. 8, 1849 ?

Ans. Saturday.

11. On what day will happen July 4, 1857? Ans. Saturday. 12. On what day will March begin in the year 1890 ?

Ans. Saturday. 13. On what day of the week was our Independence declared ?

Ans. Thursday. 14. There will be a “ Transit of Venus,” December 8, 1874; on what day of the week will it happen? Ans. Tuesday.

15. On what day of the week were you born?

SECTION LXXXIV. MISCELLANEOUS QUESTIONS. 1. What number must 73 be multiplied by, that the product may be 6?

Ans. 39. 2. What number is that, which, being multiplied by half itself, the product shall be 4:1 ?

Ans. 3. 3. What fraction is that, which, being divided by 11%, the quotient shall be 5 ?

Ans. 571. * 4. What part of 74 is 94? Ans. 294 or 1074.

5. Reduce to a simple fraction. Ans. tr. 6. Add 4 of a ton to g of a cwt. Ans. 12cwt. lqr. 841b.

7. If the earth make one complete revolution in 23 hours 56 minutes 3 seconds, in what time does it move one degree ?

Ans. 3m. 59" 20".

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Ans. 2409.

8. Multiply of gt by of of 84. 9. Divide 12147 of of 100 by 1 of 75

Ans. 18114341. 10. What number is that to which if & of be added the sum will be 1?

Ans. . 11. A certain gentleman, at the time of his marriage, agreed to give his wife of his estate, if, at the time of his death, he left only a daughter, and, if he left only a son, she should have } of his property ; but, as it happened, he left a son and a daughter, by which the widow received in equity $ 2400 less than if there had been only a daughter. What would have been his wife's dowry if he had left only a son ? Ans. $2100.

12. A gentleman being asked what o'clock it was, said that

it was between 5 and 6 ; but, to be more particular, he said that the minute hand had passed as far beyond the 6 as the hour hand wanted of being to the 6; that is, that the hour and minute hands made equal acute angles with a line passing from the 12 through the 6. Required the time of day. Ans. 32m. 18 sec. past 5.

13. A, B, and C are to share $ 100,000 in the proportion of }, }, and }, respectively; but C's part being lost by his death, it is required to divide the whole sum, properly, between the other two. Ans. A's part is $ 57,1429, and B's $ 42,8577.

14. A father devised is of his estate to one of his sons, and is of the residue to the other, and the remainder to his wife. The difference of his sons' legacies was found to be 257£. 3s. 4d. What money did he leave for his widow ?

Ans. 635£. Os. 1035d. 15. In the walls of Balbec, in Turkey, the ancient Heliopolis, there are three stones laid end to end, now in sight, that measure 61 yards in length; one of which is 63 feet long, 12 feet thick, and 12 feet broad; what is its weight, supposing its specific gravity to be 3 times that of water ? Ans. 7593 tons.

16. A burden of 2001bs., suspended on a pole 4ft. in length, the point of suspension being 6in. from the middle, is carried by two men, the ends of the pole resting on their shoulders; how much of this load is borne by each man? Ans. 125lbs. and 75lbs.

17. The new court-house in Boston has 8 pillars of granite, each 25ft. 4in. in length, 4ft. 5in. in diameter at one end, and 3ft. 5in. in diameter at the other end. How many cubic feet do they contain, and what is their weight, allowing a cubic foot to weigh 3000 ounces? Ans. 2455.03 cubic feet, 205.4 tons.

18. A father, dying, left his son a legacy, 1 of which he spent in 8 months; 9 of the remainder lasted him 12 months longer; after which he had only $ 410 left. What did his father bequeathe him?

Ans. $ 956.663. 19. A butcher, wishing to buy some sheep, asked the owner how much he must give him for 20; on hearing his price, he said it was too much; the owner replied, that he should have 10, provided he would give him a cent for each different choice. of 10 in 20, to which he agreed. How much did he pay for the 10 sheep, according to the bargain? Ans. * 1847.56.

20. A merchant sold goods to a certain amount, on a commission of 4 per cent., and, having remitted the net proceeds to the owner, he received per cent. for prompt payment, which amounted to % 15.60. What was the amount of his commission ?

Ans. $ 260.00.

21. A, of Boston, remits to B, of New York, a bill of exchange on London, the avails of which he wishes to be invested in goods on his account. B having disposed of the bill at 7} per cent. advance, he received $ 9675.00, and having reserved for himself 1 per cent. on the sale of the bill, and 2 per cent. for commission, what will remain for investment, and for how much was the bill drawn ?

Ans. For investment, $9461.58; the bill was £ 2025. 22. Bunker Hill Monument is 30ft. square at its base, and 15ft. square at its top ; its height is 220ft. From the bottom to the top, through its centre, is a conical avenue 15ft. in diameter at the bottom and about 11ft. at the top. How many cubic feet are there in the monument ?

Ans. 86,068.518+ft. 23. A hired a house for one year for $ 300; at the end of 4 months he takes in M as a partner, and at the end of 8 months he takes in P. At the end of the year what rent must each pay?

Ans. A pays $ 1834; M pays $ 83}; P pays $ 331. 24. A merchant receives on commission three kinds of flour; from A he receives 20 barrels, from P 25 barrels, and from C 40 barrels. He finds that A's flour is 10 per cent. better than B's, and that B's is 20 per cent. better than C's. He sells the whole at $ 6 per barrel. What in justice should each man receive ?

Ans. A receives $ 139161; B, $ 158174; C, $211144. 25. Bought 100 barrels of four, at $5 per barrel, and immediately sold it on a credit of 6 months. The note which I received for pay, I got discounted at the Suffolk Bank, and, on examining my money, I found that I had gained 20 per cent. on my purchase. What did I receive per barrel for the flour?

Ans. $ 6.181698. 26. Purchased for a cloak 54 yards of broadcloth, that was 1} yards wide; to line this, I purchased flannel that was yard wide, but on being wet it shrunk 1 nail in width, and i yard in every 20 yards in length. How many yards of flannel was it necessary to buy ?

Ans. 1248yards. 27. How many bricks would it require to build the walls of a house 40 feet long, 30 feet wide, and 20 feet high, admitting the walls to be a foot thick, and that each brick was 8 inches long, 4 inches wide, and 2 inches thick ? Ans. 73,440 bricks.

28. How many feet of boards would it require to cover a house, that was 40 feet square, and whose height to the top of the plate was 20 feet, the roof projecting 1 foot over the plate, and coming to a point over the centre of the house, 15 feet above the garret floor ?

Ans. 5367.7+ feet.

29. Lent a friend $ 700, which he kept 20 months. Some years after I borrowed of him $ 300 ; how long should I keep it to balance the favor?

Ans. 46 months. 30. John Lee gave half of his estate to his wife, of the remainder to his oldest son, and of the residue to his oldest daughter, and 4 of what then remained, which was $ 1500, to be equally distributed among his other children, who received $ 150 each; required the number of his children, and the value of his estate.

Ans. 12 children; estate, $ 10,000. 31. A and B set out to travel round a certain island, which is 80 miles in circumference. A travels 5 miles a day, and B 7 miles a day. How far must B travel to overtake A ?

Ans. 280 miles. 32. If 24.4 cubic inches of lead weigh 16 pounds, required the number of feet of lead pipe that can be made from 80 pounds of lead, the diameter of the pipe to be 1 inch, and the thickness of it of an inch.

Ans. 124.26+ feet. 33. How long a tube can be made from a cylinder of lead 8 inches long and 2 inches in diameter, and through the centre of which is a hole of an inch in diameter; the tube or pipe to be of an inch in diameter, and of an inch in thickness ?

Ans. 16.29+ feet. . 34. Four men, A, B, C, and D, bought a stack of hay, con

taining 8 tons, for $ 100. A is to have 12 per cent. more of the hay than B, and B is to have 10 per cent. more than C, and C is to have 8 per cent. more than D. Each man is to pay in proportion to the quantity he receives. The stack is 20 feet high, and 12 feet wide at its base, it being an exact pyramid ; and it is agreed that A shall take his share first from the top of the stack, B is to take his share the next, and then C and D. How many feet of the perpendicular height of the stack shall each take, and what sum shall each pay?

Ans. A takes 13.22+ft., and pays $28.9313431; B takes 3.14+ft., and pays $25.8311497; C takes 2.06+ft. and pays $ 23.4816134; D takes 1.58+ft., and pays $21.741546 .

35. Suppose the rails of a railroad to be 5 feet 4 inches apart at the place of the wheels bearing, and on a curve line of 1200 feet radius for the outer rail. Suppose the wheels of the car running on the rails to be firmly fixed to the axle, and that it is 5 feet from the outside of the flange of one wheel to the outside of the flange of the opposite wheel ; that from the outer side of one wheel to the outer side of its opposite wheel is 5 feet 8 inches; that the diameter of each wheel at the outside

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