By the present tariff, most duties of the United States are ad valorem, but some duties are specific, and some articles are charged both a spe cific and an ad valorem duty. The duty is reckoned on the actual cost at the place of purchase or manufacture, increased by all charges for transportation previous to final shipment.

Seaport towns, where customs are collected, are called ports of entry. The offices in which they are collected are called custom-houses; and the officer who superintends the collection of duties and other business of the custom-house is called collector of the port.

A vessel is entered at a port by lodging at the custom-house a manifest or statement of its cargo, and also a list of passengers, if it have any, these papers verified by the oath of the master. The clearance from its port of departure and papers proving its nationality must also be deposited before it is permitted to discharge its cargo.

A vessel is cleared from a port by lodging at the custom-house a manifest of its outward cargo, verified by oath, and agreeing with the ship. pers' manifests of parts of cargo. All government charges must be paid also, and everything connected with the discharging of the inward cargo settled, after which a "general clearance" is issued, and the vessel is at liberty to leave the port, having received its papers of nationality again. The illegal introduction of goods into a country otherwise than through the regular ports of entry is called smuggling.

544. All merchandise imported from foreign ports or places.must be consigned in the manifest, invoice, or bill of lading, to some person or firm at the port of importation, by whom it must be duly entered-either for immediate consumption or for warehouse

Merchandise not intended for immediate consumption may be deposited in U. S. Bonded Warehouses, and remain there not longer than three years, the owner being at liberty to withdraw it at any time upon pay. ment of the duties and charges for storage.

In custom-house business the long ton, cwt., and qr. are used. Foreign money is reduced by the table given in Art. 530, unless the invoice is accompanied by a consular certificate stating that a different rate of exchange is ruling at the time the invoice is made out.

545. The Quantities considered are: 1. The Cost of the goods, or the Quantity; 2. The Duty; 3. The Rate; 4. The Allowances.

NOTE.-Duties may be treated under three cases, as other applications of Percentage; but as the second and third cases are merely theoretical, they are not given here.

CASE I.

546. Given, the base and rate, to find the duty.

1. What is the specific duty on 75 drums of figs, each weighing 57 lb., tare 21 lb. to the cwt. at $11 a cwt.?

Rule I.-For ad valorem duties, multiply the cost of the goods by the rate of duty.

Rule II. For specific duties, deduct first the allowances, and compute the duty on the remainder.

NOTE. In reckoning duties, whole dollars, pounds, gallons, etc., are used as the base, fractions less than

being rejected and more than

being reckoned as 1. Duties are payable in gold.

WRITTEN EXERCISES.

2. I received from Havre an invoice of 50 dozen bottles of champagne, costing $12.50 per dozen; what is the duty at $6 a dozen, breakage 5% ? Ans. $288.

3. H. B. Claflin & Co. received an invoice of Brussels laces costing 2800 francs in Brussels, charges 101.56 francs; what was the duty at 30%? Ans. $168.

4. What is the duty at 20% ad valorem on 350 boxes of Naples oranges, invoiced at 20 lire per box, charges 475 lire, commission 2% ? Ans. $295.80.

5. What is the duty on 25 hhd. of sugar, each weighing 5cwt. 1 qr. 3 lb., tare 21 lb. per hhd., duty $14 per cwt., and 35 hhd. of molasses, 120 gal. each, duty 5¢ a gallon? Ans. $368/75.

SUPPLEMENTARY PROBLEMS.

To be omitted unless otherwise directed.

6. Sharpless Brothers imported from London 10 cases of woolen goods, net weight 1350 lb., value £756 15 s., commission 2%; what did the goods cost in store, duty 50¢ per lb. and also an ad valorem duty of 35 % ? Ans. $5771.04.

7. Chas. Ford & Son, linen merchants, Belfast, shipped to John Ford & Co., April 2, 1876, 40 pcs. Ducks, marked W. R., No. 14, containing 2063 yd. @7 d.; commission 2%; ship charges 5 s.; what will be the duty at 35 %? Ans. $107.45.

SUPPLEMENTARY PROBLEMS.

To be omitted unless otherwise directed.

8 An invoice of 75 Drums Caustic Soda, shipped per S. S. Germania for New York, by the undersigned on acc't and risk of Messrs. Smith & Bro.

What was the cost of this invoice, including duty, when delivered to Messrs. Smith & Bro. ? Ans. $1994.25 gold.

9. Invoice of Mdse., purchased, paid for in London, and shipped by David Taylor & Sons, per steamer Ohio to Philadelphia, for % and risk of Messrs. Snow, Gilbert & Co.

NOTE. The 8th and 9th problems are taken from actual custom-house transactions, and indicate the exact forms used. In problem 8, the letters at the left are the trade mark on the drums; indicates numbers of the drums from 1 up to 75; gross weight is 421 cwt. 3 qr. 3 lb., tare, 14 cwt. 3 qr. 23 lb.; net weight is 406 cwt. 3 qr. 8 lb. or 45564 lb., at 13s. 3d. per cwt.; from which a discount of 2 per cent. must be subtracted, giving the amount paid, and adding a commission of 21⁄2 per cent,we have the cost up to shipmeut, which must be reduced to United States currency, reckoning $4.8665 = £1. The duty being specific is, however, reckoned only on the weight. In the 9th example, having deducted discount and added price of case and the commission, and reduced the amount of the invoice to United States money. 45 per cent. of the nearest exact number of dollars will be the duty.

3. What is the relation of 12 to 3? Of 16 to 4? Of 18 to 6? Of 20 to 5? Of 24 to 6? Of 30 to 5?

4. What is the relation of 3 to 6? Of 4 to 12? Of 6 to 24? Of to 35? Of 8 to 57? Of 9 to 62?

5. The measure of the relation of two numbers is called their ratio 6. What is the ratio of 12 to 4?

Ans. The ratio of 12 to 4 is three. 7. What is the ratio of 18 to 9? Of 25 to 5? Of 48 to 8? C€£3 to 7? Of 64 to 4? Of 70 to 10? Of 80 to 8 ? 8. What is the ratio of 3 to 6 ?

9. What is the ratio of 4 to 12? Of 3 to 18? Of 5 to 30 Of 9 to 108? Of 11 to 132? Of 12 to 144?

10. What is the ratio of to? Of to? Of to ? Of.5 to .25? Of.2 to .04? Of .03 to .12?

11. The ratio of two numbers may be expressed by writing the colon between them; thus 8: 4 denotes the ratio of 8 to 4.

12. Required the value of 12:6; of 28 :7; of 42 : 6 ; of 24 : 12 ; of 12:24.

13. How does the ratio of 8 to 4 compare with the ratio of 12 to 6? Ans. They are equal.

14. What number has the same ratio to 12 that 18 has to 6? 15. What number has the same ratio to 20 that 40 has to 10? 16. The ratio of 9 to 36 is the same as the ratio of 15 to what number?

17. 25 is to 5 as 40 to what number? 24 is to 12 as 15 is to what number?

18. When we express the ratio of two numbers equal to the ratio of two other numbers, as, 24 is to 4 as 36 is to 6, we have a proportion. 19. What proportion can we derive from the two ratios 40 to 8 and 60 to 12?

20. How many numbers do we have in a proportion? How many ratios? Are the ratios equal or unequal?

21. The equality of two ratios may be expressed by writing the symbol between them; thus 8: 4 12: 6.

22. Write the proportion 16 is to 8 as 24 is to 12; also 15 is to 45 as 18 is to 54.

SECTION IX.

RATIO AND PROPORTION.

RATIO.

547. Ratio is the measure of the relation of two simila quantities; thus, the ratio of 8 to 4 is 2.

548. The Symbol of ratio is the colon (:); thus, 8: 4 signifies the ratio of 8 to 4. Ratio is also expressed by writing the numbers in the form of a fraction; thus, &.

549. The Terms of a ratio are the two numbers compared, called respectively the antecedent and the consequent. 550. The Antecedent is the number compared with the consequent; thus, in the ratio 8:4, 8 is the antecedent.

551. The Consequent is the number with which the antecedent is compared; thus, in 8: 4, 4 is the consequent. 552. A Ratio is found by dividing the antecedent by the consequent; thus, in 8: 4, the ratio is, or 2.

553. A Simple Ratio is the ratio of two numbers, as 6:3. A Compound Ratio is the product of two or more simple ratios; as (3: 4)x (5: 6), or × 8.

554. A Compound Ratio is usually expressed by writing the simple ratios one under another; thus, J3:4) 15:65

555. Ratio exists only between similar quantities, and is always an abstract number.

NOTES.-1. The symbol of ratio (:) is supposed to be a modification of the symbol of division.

2 Ratio is usually defined as the relation of two numbers. This is indefinite, for the ratio is the measure of the relation.

3. A few authors divide the second term by the first, calling it the French Method. The method and name are both founded in error; nearly all the French mathematicians, like the German, English, etc., divide the first term by the second.

PRINCIPLES.

1. The ratio equals the quotient of the antecedent divided by the consequent.