Tare on all other goods paying a specific duty, is allowed according to the statement of the same in the Invoice of the goods, which is considered the actual weight of the box, bag, cask, &c.

The importer may always have the invoice tare allowed, if he make his election at the time of making his entry, and obtain the consent of the collector and naval officer.

For leakage, 2 per cent. is allowed on the gauge, on all merchandise in casks paying duty by the gallon.

For breakage, 10 per cent. is allowed on all beer, ale, and porter in bottles, and 5 per cent. on all other liquors in bottles; or the importer may have the duties computed on the actual quantity by tale, if he so chooses at the time of entry.

The common-size bottles are estimated at the Customhouse to contain 2 gallons per dozen.

1. What is the neat weight of 40 hogsheads of sugar weighing gross 8 cwt. 3qr. each; draft and tare as in the tables?

40 X 4 =

12 per cent. of 39040 is 4684.8

39200 lb. gross weight.

160 lb. draft.

39040

4685 lb. tare.

34355 lb. neat weight.

2. What is the neat weight of 25 bags of pepper, weighing gross 1 cwt. each; draft and tare as in the tables? 3. Find the neat weight of 6 chests of Souchong tea, weighing gross 98 lb. each, tare 22lb. per chest.

4. Find the neat weight of 12 casks of raisins, weighng gross 130 lb. each; draft as in the table, tare 12 lb. per cask.

5. What is the neat weight of 8 chests of green tea, gross weight 102 lb. each, tare 20lb. per chest?

6. What is the neat weight of 9 bags of coffee, weighing gross 114 lb. each, draft as in table, tare 2 per cent.?

7. What is the neat weight of 4 casks of glauber salts, gross weight as follows; the first 150 lb.; the 2d. 175lb.; 3d 228 lb; 4th. 264 lb.; draft and tare as in tables?

S. What is the neat weight of 4 hogsheads of madder, weighing gross 11 cwt. 2qr. each; draft being allowed as in the table, tare lcwt. 2 qr. per cask?

DUTIES.

The duties paid on goods imported from foreign coun⚫ tries into the United States, are either ad valorem or specific.

The ad valorem duty is a certain per cent. of the actual cost of the goods in the country from which they are brought.

The specific duty is fixed at a certain sum per ton, hundred weight, pound, gallon, square yard, &c.

Observe that the allowances for tare, draft, &c. are to be made, before the duties are computed.

9. What is the duty on an invoice of silk goods, which cost in Canton 4836 dollars, at 10 per cent. ad valorem? 10. What is the duty on an invoice of woollen goods, which cost in England 5729 dollars, at 44 per cent. ad valorem?

11. Compute the duty on 6 boxes of chocolate, weighing gross 1 cwt. per box; draft and tare as in the tables; duty 4 cents per lb.

12. Cast the duty on 12 boxes of Windsor soap; gross weight 84 lb. per box; cost in England 1 dollar per lb.; tare as in the table; duty 15 per cent.

13. Calculate the duty on 5 boxes brown Havana sugar; gross weight as follows; the first, 7 cwt. 2qr.; 2. 8cwt. 3qr.; 3d. 9cwt. 1qr.; 4th. 10cwt. 3qr. 20lb.; 5th. 11 cwt. 1qr. 14lb.; draft and tare as in the tables; duty 2 cents per lb.

14. What is the duty on a cargo of 148 tons of iron, at 30 dollars per ton?

15. Compute the duty on 4 pipes of wine; allowance for leakage as in the table; duty 7 cents per gallon.

16. Cast the duty on 10 gross of London porter, allowance for breakage as in the table; duty 20 cents ner gallon.

17. What is the duty on 10 boxes of Spanish cigars, containing 1100 each; duty $2.50 per 1000?

18. Compute the duty on 4 casks of Rochelle salts, invoiced at $10 per cwt.; gross weight of 1st cask 1 cwt. 2qr. 12lb.; 2d. 1 cwt. 1 qr. 17 lb.; 3d. 2 cwt. 3qr. 7 lb.4th. 4 cwt. 1qr.; draft as in table; tare 8 per cent. dutv 15 per cent. ad valorem.

XXV.

RATIO.

RATIO is the mutual relation of two quantities of the same kind to one another.

By finding how many times one number is contained in another, or what part one number is of another, we obtain their ratio. Thus, the ratio of 2 to 4 is 2, because 2 is contained 2 times in 4; and the inverse ratio is 2 because 2 is of 4. Both these expressions of the ratio of 2 to 4 amount to the same thing, which is, that one of the numbers is twice as great as the other.

By the ratio of two quantities is meant only their relative magnitude; for, notwithstanding the absolute magnitude of 2 pounds and 8 pounds is much greater than that of 2 ounces and 8 ounces, yet the relative magnitude or ratio of the two latter is just the same with that of the two former; because, 2 ounces are contained just as many times in 8 ounces, as 2 pounds are in 8 pounds; or, 2 ounces are just as great a part of 8 ounces, as 2 pounds of 8 pounds.

It is evident that only quantities of the same denomination can have a ratio to one another; for it would be absurd to inquire how many times 1 dollar is contained in 4 rods, or what part of 4 rods 1 dollar is.

A ratio is denoted by two dots, similar to a colon: thus, 39 expresses the ratio of 3 to 9. The former term of a ratio is called the antecedent, and the latter the consequent. Thus 6.: 12 expresses the ratio of 6 to 12, in which 6 is the antecedent, and 12 the consequent

Since a ratio indicates how many times one number is contained in another, or what part one number is of another, it is a quotient resulting from the division of one of the terms of the ratio by the other, and may be expressed in the form of a fraction: thus, the ratio 6: 3 may be expressed by the fraction, or conversely.

When any two numbers are multiplied, each by the same number, the ratio of the products is the same with the ratio of the multiplicands. Thus, take 3: 6, and multi ply the antecedent and consequent, each by 5, and the products 15 and 30 have the same ratio with 3 and 6; that is, 15 is contained just as many times in 30, as 3 is in 6; or 15 is the same part of 30, that 3 is of 6.

Also, if two numbers be divided, each by the same number, the ratio of the quotients is the same with the ratio of the dividends. Thus, take the ratio of 9: 18, and divide each term by 3, and the quotients 3 and 6 have the same ratio with 9 and 18; because 3 is contained as many times in 6, as 9 is in 18; or 3 is the same part of 6, that 9 is of 18.

A ratio resulting from the multiplication of two or more ratios together, that is, the antecedents into the antecedents, and the consequents into the consequents, is called a compound ratio. Thus, 6: 48 is the compound ratio of 1:2, 3: 4, and 2: 6; because 6 is the product of all the antecedents, and 48 of all the consequents. This is expressed in fractions with the word "of " between them: thus, making the antecedents the numerators, of 3 of 3 ; making the consequents the numerators, of of. Two ratios may be equal to one another, as well as two quantities. The equality of two ratios is denoted by the sign placed between them; thus, 2:43:6 signifies that the ratio of 2 to 4 is equal to the ratio of 3 to 6.

PROPORTION.

The equality of 2 ratios is called a PROPORTION, and the terms are called proportionals; and in a proportion, the first and fourth terms, that is, the antecedent of the first

ratio and the consequent of the second, are called the extreme terms; and the second and third terms, that is, the consequent of the first ratio and the antecedent of the second, are called the mean terms. Thus, in the proportion 3 : 9=4 : 12, 3 and 12 are the extreme terms, 9 and 4 the mean terms.

If the antecedent of the second ratio be the same with the consequent of the first, the terms are in continued proportion. Thus, 3, 9, and 27, are in continued proportion, because 3: 9: =9: 27.

Since the equality of two ratios constitutes a proportion, we can easily decide whether any four numbers be in proportion, by bringing the fractions expressing the two ratios to a common denominator; for then, if the numbers be proportionals, the numerators also will be equal to one another.

Take the numbers 4, 2, 6, 3; if we make the consequents the numerators, the fraction expressing the ratio of the two first in the series is 2, and that expressing the ratio of the two last is. These fractions, when reduced to a common denominator, become 14 and 12; and this equality of the two fractions expressing the two ratios, proves that the four numbers are proportionals; for, if the four numbers were not in proportion, the fraction expressing the first ratio not being equal to the fraction expressing the second ratio, the numerator of the one would not be equal to the numerator of the other, when reduced to a common denominator.

Again, let us take the same numbers, 4, 2, 6, 3, and make the antecedents the numerators of the fractions expressing the ratios: thus, and. These fractions when reduced to a common denominator, are 12 and 12, which, being equal, prove the four numbers to be proportionals.

We see, therefore, whether we make the antecedents or consequents the numerators of the fractions expressing the ratios, that in both cases the equality of the ratios proves a proportion among the four numbers; and in both cases the numerators are precisely the same; for in the first case the fractions are 14 and 12, and in the second, 2 and, and these numerators, in both cases, are