2. Had I £24.50 more, I should have £100. What money have I ?

3. The smaller of two numbers is 2675.894, and their difference is 11.896. What is the larger number?

4. What is that number, which being multiplied by .55, the product is 65.8 ?

5. The remainder of a number divided by 25 is 12. Express its decimal value.

6. Express the quotient of 24.589 by 73, correct to five decimal places.

7. By what number must 12.668569 be multiplied so that the product may be 50.674236 ?

8. The gain arising from a speculation is £127.55, which is one-sixteenth of the money received. How much was at stake?

9. At a dinner, every guest paid 2.875 shillings, and the whole receipts were £3. 17s. 74d. How many persons partook of the dinner?

10. What is the half of the fourth part of twenty-one times 224.56?

11. 155 yards of cloth are sold for £178.25. will be sold for £74.75 ?

How many yards

12. The expenses of 18 persons, half of whom were men, and the other half women, are 130.50 shillings; each man pays 4.50 shillings more than a woman. What does each person pay?

13. A person promised to pay 6s. to the poor every time his money was doubled; this was repeated three times, and he had nothing left. How much had he at first?

14. Bought, 3 cwt. 1 qr. 17 lb. it again at shillings per lb.

sugar for £13.38643, and sold How much did I gain?

15. The circumference of every circle is 3.1416 times its diameter. If the circumference of the earth be 24857 miles, how much is its radius?

16. Find the value of £.8+.2635 shillings+.5 guinea.

17. The length of the true year is 365.242264 days. What will be the error in five centuries, if the years are taken at 365 days?

18. What decimal, multiplied by 54, expresses the sum of, 1, 12, 11?

89

19. Divide the difference of 11.229587 and 3.816243 by 274.

20. Air is 770 times lighter than water, and mercury 13.598 times heavier than water. How many times is mercury heavier than air?

21. One degree Fahrenheit is 1.80 degrees centigrades. How many degrees centigrades are 17.5 degrees Fahrenheit ?

22. Simplify the expression 4.56+15.037-4; also, (4.73+15.6) × (36.1—14.72.)

23. Determine the value of 123 ×(128-357+36).

27. Simplify

2.127

X

28. Reduce

9

22

1 1.27 .538461

(43+3)-15 × († 3—1)

36+1+Xx (81-34

29. Find the value of .2083 of .3428571 of 1 cwt.

30. Required, the value of .846153 of .081 of £6.50.

31. How much money must a person distribute who wishes to bestow £.375 a piece on 248 poor persons?

32. Add together §,,, .09375 and 2.40 by vulgar fractions and by decimals.

33. Subtract .6495 of 1 guinea from .8735 of £1.

34. Reduce to a decimal, accurate to 7 places: 1++

1

1

1×2

35. Reduce £24. 16s. 44d. and £167. 10s. 6d. f. to decimals of pounds, and find the quotient of the first divided by the latter.

36. The solar year consists of 365.242264 days, and the sidereal year of 365.256383 days. Express the difference of these years in minutes, seconds, &c.

37. Required, in decimals and in common fractions, the sum of the following quantities: 3, 3, 3, 4, 3, &; and find, also, the product of both results.

38. A bar of iron expands 1.472 inches for every yard, when brought to a certain temperature. How much would a bar 7 yds. 2 ft. 10.34 inches expand at the same temperature ?

PART V.

TABLES OF MONEY, WEIGHTS AND MEASURES. COMPOUND QUANTITIES.

215. In the preceding parts it has been shown that when it is necessary to consider quantities smaller than unity, this unity is supposed to be divided into a certain number of equal parts, which are treated as other units. But in order to facilitate dealings, it has been found convenient to have large units and small units; for instance, when speaking of long distances, we take a mile as the unit, and where it is required to express smaller distances, we take the yard, foot, or inch as unity; thus, if instead of dividing the mile into a great number of equal parts, and saying of a mile, or Tao of a mile, the difference between which would be difficult to appreciate, I were to say, this road is four yards broad, and that five yards, the mind would at once form an idea of the real dimensions.

What strikes every one, when looking at the tables of money, weights, measures, &c., is the confusion, the want of system, which exists almost throughout. They are the offspring of unscientific minds, of different epochs; they are like patchworks placed in the way of youths to puzzle them and retard their progress. It is astonishing, that in a country so enlightened as England is, some steps are not taken to improve this extraordinary labyrinth. This improvement appears the easier since. some continental nations, and scientific men in this country, have already adopted the whole or part of the decimal system, which is the only rational one.

TABLES OF MONEY, WEIGHTS, AND MEASURES.

The coins not in circulation, but frequently mentioned, are the groat=4d.; tester = 6d. ; noble = 6s. 8d.; angel=10s.; halfguinea=10s. 6d.; mark=13s. 4d; guinea=21s.; Carolus = 23s.; Jacobus = 25s.; moidore=27s.

The pound is generally called pound sterling, to distinguish it from the weight called a pound; also from foreign coins, and from stocks, shares, &c.

The standard gold coin of this kingdom is made of 22 parts of pure gold and two parts of alloy (copper). From a pound Troy of this metal are coined 4628 sovereigns = £46. 14s. 6d.; so that the weight of each is 5 dwts. 3131 grs. = 123.274 grs. ; and the value per ounce of the standard gold is £3. 17s. 10d., whilst the value per ounce of pure gold, at the Mint, is £4. 4s. 11 d.,

The standard silver coin consists of 37 parts of pure silver and three parts of alloy (copper). From a pound Troy of this metal are coined 66 shillings, so that the weight of a shilling is 3 dwts. 15 grs.; and at the Mint, the price of standard silver is 5s. 6d. per oz., and of pure silver 5s. 1143d. Silver coins are not legal tender for more than 40s.

24 pence are coined from a pound of copper avoirdupois, so that a penny weighs 103 dwts. avoirdupois, or 2913 grs. Troy. Copper coins are not legal tender for more than 12d.

This weight, which was formerly used for weighing articles of every kind, is now applied to gold, silver, jewels, liquors, and in philosophical experiments.

A grain of wheat is said to be the original of all weights used in England. It was gathered out of the middle of the ear, and being well dried 32 of them were to make one pennyweight;