moving the goods and actually weighing the boxes or casks in which they are contained.

On liquors in casks, customary tare is sometimes allowed on the supposition that the cask is not full, or what is called its actual wants; and then an allowance of 5 per cent for leakage.

A tare of 10 per cent is allowed on porter, ale, and beer, in bottles, on account of breakage, and 5 per cent on all other liquors in bottles. At the custom house, bottles of the common size are estimated to contain 23 gallons the dozen. For tables of Tare and Duty; see Ogden on the Tariff of 1842.

EXAMPLES.

1. What is the net weight of 25 hogsheads of sugar, the gross weight being 66cut. 3qr. 14lb.; tare 117b. per hogshead?

2. If the tare be 4lb. per hundred, what will be the tare on 67. 2cwt. 3qr. 14lb.?

Tare for 67. or 120cwt. = 480lb.

3. What will be the cost of 3 hogsheads of tobacco at $9,47 per cut. net, the gross weight and tare being of

4. At 21 cents per lb., what will be the cost of 5hhd. of coffee,

the tare and gross weight being as follows:

5. What is the net weight of 18hhd. of tobacco, each weighing gross 8cwt. 3qr. 14lb.; tare 167b. to the cwt.?

6. In 47. 3cwt. 3qr. gross, tare 2016. to the cwt., what is the net weight?

7. What is the net weight and value of 80 kegs of figs, gross weight 7T. 11cwt. 3qr., tare 12lb. per cwt., at $2,31 per cwt.

8. A merchant bought 19cwt. 1qr. 24lb. gross of tobacco in leaf, at $24,28 per cwt.; and 12cwt. 3qr. 19lb. gross in rolls, at $28,56 per cwt.; the tare of the former was 1497b., and of the latter 491b.: what did the tobacco cost him net?

9. A grocer bought 171hhd. of sugar, each 10cut. 1qr. 14lb., draft 716. per cwt., tare 4lb. per cwt. What is the value at

$7,50 per cwt. net?

10. In 29 parcels, each weighing 3cwt. 3qr. 14lb. gross, draft 8lb. per cwt., tare 4/b. per cwt. how much net weight, and what is the value at $7,50 per cwt. net?

11. A merchant bought 7 hogsheads of molasses, each weighing 4cwt. 3qr. 14lb. gross, draft 7lb. per cwt., tare 8b. per hogshead, and damage in the whole 99376.: what is the value at $8,45 per cwt. net?

12. The net value of a hogshead of Barbadoes sugar was $22,50; the custom and fees $12,49, freight $5,11, factorage $1,31; the gross weight was 11cwt. 1gr. 15lb., tare 113. per cwt.: what was the sugar rated at per cwt. net, in the bill of parcels ?

13. In 7hhd. of sugar, each weighing 3cwt. 2qr. 14lb. gross, tare 21lb. per cwt., what is the value at $6,25 per cwt.?

14. I have imported 87 jars of Lucca oil, each containing 47 gallons: what did the freight come to at $1,19 per cut. net, reckoning 1/b. in 117b. for tare, and 9lb. of oil to the gallon?

15. A grocer bought 5hhd. of sugar, each weighing 13cwt. 1gr. 12lb., at 7 cents a pound; the draft was 11lb. per cwt., and the tare 5 per cent: what was the cost of the net weight?

16. A wholesale merchant receives 450 bags of coffee, each weighing 76 pounds; the tare was 8 per cent, and the invoice price 10 cents per pound. He sold it at an advance of 331 per cent what was his whole gain, and what his selling price? 17. A merchant imported 176 pieces of broadcloth, each piece measuring 461yd., at $3,25 a yard: what will be the duty at 30 per cent ?

18. What is the duty on 54T. 13cwt. 3qr. 20lb. of iron, invoiced at $45 a ton, and the duty 333 per cent ?

19. What is the ad valorem duty, at 25 per cent, on 3hhd. of molasses, at 35 cents a gallon, an allowance of 2 per cent being made for leakage?

20. If I import 50 chests of tea, each weighing 140 pounds, invoiced at 60 cents a pound, a deduction of 10lb. per cwt. being made for tare: what were the governmental duties, at 40 per cent ad valorem ?

21. What will be the duty on 225 bags of coffee, each weighing gross 160lb., invoiced at 6 cents per lb.; 2 per cent being the legal rate of tare, and 20 per cent the duty?

22. What duty must be paid on 275 dozen bottles of claret, estimated to contain 23 gallons per dozen, 5 per cent being allowed for breakage, and the duty being 35 cents per gallon?

23. A merchant imports 175 cases of indigo, each case weighing 1966. gross: 15 per cent is the customary rate of tare, and the duty 5 cents per lb. What duty must he pay on the whole?

24. What is the tare and duty on 75 casks of Epsom salts, each weighing gross 2cwt. 2qr. 24lb., and invoiced at 17 cents per lb., the customary tare being 11 per cent, and the rate of duty 20 per cent?

EQUATION OF PAYMENTS.

264. EQUATION OF PAYMENTS is a process of finding the average time of payment of several sums due at different times, so that no interest shall be gained or lost.*

1. B owes Mr. Jones $57: $16 is to be paid in 6 months; $18 in 7 months; and $24 in 10 months: what is the average time of payment so that no interest shall be gained or lost?

OPERATION.
$15 × 6
$18 X

= 90 7 = 126

=

57)456(8
456

$24 × 10 240

57

ANALYSIS. The interest of $15 for 6 months, is the same as the interest of $1 for 90 months: the interest of $18 for 7 months is the same as the interest of $1 for 126 months; and the interest of $24 for 10 months is the same as the interest of $1 for 240 months; hence, the sum of these products, 466, is the number of months it would take $1 to produce the required interests. Now, the sum of the payments, $57, will produce the same interest in one fifty-seventh part of the time; that is, in 8 months: hence, to find the average time of payment:

Multiply each payment by the time before it becomes due, and divide the sum of the products by the sum of the payments: the quotient will be the average time.

EXAMPLES.

1. A merchant owes $1200, of which $200 is to be paid in 4 months, $400 in 10 months, and the remainder in 16 months: if he pays the whole at once, at what time must he make the payment?

264. What is equation of payments? How do you find the average time of payment?

* The mean time of payment is sometimes found by first finding the present value of each payment; but the rule here given has the sanction of the best authorities in this country and England.

2. A owes B $2400; one-third is to be paid in 6 months, one-fourth in 8 months, and the remainder in 12 months: what is the mean time of payment?

3. A merchant has due him $4500; one-sixth is to be paid in 4 months, one-third in 6 months, and the rest in 12 months: what is the equated time for the payment of the whole?

4. A owes B $1200, of which $240 is to be paid in three months, $360 in five months, and the remainder in ten months: what is the average time of payment?

5. Mr. Swain bought goods to the amount of $3840, to be paid for as follows, viz.: one-fourth in cash, one-fourth in 6 months, one-fourth in 7 months, and the remainder in one year: what is the average time of payment?

6. A flour merchant bought at one time 150 barrels of flour, at $8 a barrel; 15 days afterwards he bought 176 barrels, at $8,50 a barrel; 25 days after that he bought 200 barrels, at $9 a barrel: how many days after the first purchase would be the equated time of payment?

7. A man bought a farm for $5000, for which he agreed to pay $1000 down, $1200 in 3 months, $800 in 8 months, $1500 in 10 months, and the remainder in one year: if he pays the whole at once, what would be the average time of payment?

NOTES.-1. In finding the equated time of payments for several sums, due at different times, any day may be assumed as the one from which we reckon.

2. If one of the payments is due on the day from which the equated time is reckoned, its corresponding product will be nothing, but the payment must still be added in finding the sum of the payments.

8. A person owes three notes: the first is for $200, payable July 1st; the second for $150, payable August 1st; and the third for $250, payable August 15th: what is the average time, reckoned from July 1st?

NOTES 1. May the equated time be reckoned from any day?

2. If one of the payments is due on the day from which the equated time is reckoned, what will be the value of the corresponding product?