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• 3. Allowing the net sum to be raised by a society to be $ 9700, and the allowance for collection to be 3 per cent., what is the gross amount to be assessed, and how much will be the cost of collection ?

Ans. Assessment, $ 10000 ; cost of collection, $ 300. 4. The taxable property in a certain district containing 450 polls is $ 756000. It is proposed to raise $ 18000 for building a union school-house. If the poll tax be limited to $ 1.50 a poll, and the cost of collecting be 3 per cent., what will be the required assessment on a dollar, and how much will be A's tax, who pays for 3 polls, and has property to the amount of $ 15600. Ans. Tax on $ 1, $.0236; A's tax, $ 372.66.

427. To apportion school expenses according to each pupil's attendance, or to make out rate bills.

Ex. 1. The expenses of a certain district school are $ 464, and the aggregate of attendance 9280 days. What is A's tax, who has sent pupils amounting to 157 days?

Since 9280 days' attendance cost $ 464.00 ; 9280 $ 0.05

$ 464, 1 day's attendance will cost

as many dollars as 464 contains $ 0.05 X 157 = $ 7.85. times 9280, and 157 days will cost

157 times as much as 1 day. Hence, The whole expenses of the school, less the public money, if any, divided by the number of daysattendance, will give the rate for each day's attendance.

The rate for each day, multiplied by the number of days of attendance of each patron's pupils, will give the amount of his rate bill.

OPERATION.

EXAMPLES.

2. If a district expends for a teacher's salary $ 500, for his board $ 150, for repairs of school-house $30; the public money being $ 350, and the whole number of days of attendance 5500, what is the rate per day, and what is A's bill, who sends 2 pupils 60 days each, and 1 pupil 30 days?

Ans. Rate per day, $ 0.06; A's bill, $ 9.00. 3. In a certain district the, teacher's wages amounted to $ 150, the fuel cost $ 18.50, the public money received was $ 63.50, and the number of days' attendance was 3000. What was A’s rate bill, whose pupils attended 121 days; and B’s, whose pupils attended 173 days?

GENERAL AVERAGE.

428. GENERAL AVERAGE signifies a contribution ratably made to a general loss by the three great mercantile interests, vessel, freight, and cargo, — when, on account of a common peril, one or more of these has been voluntarily sacrificed, in whole or in part, to effect the preservation of the rest.

Jettison is the term applied to the part of the vessel or cargo cast overboard, or otherwise sacrificed, to save the remainder.

429. Particular average means an average to which contribute only “some parts of the property when severed from the whole; as in the case of a boat-load saved from peril by a sacrifice, to which only the boat and its contents contribute.” Practically, it hardly needs to be discriminated from general average, since it is adjusted upon its contributory interest by the application of the same principles.

430. To constitute a valid claim to general average, there are three essentials, all of which must be present: 1. A common peril impending at the time ; 2. A voluntary and premeditated sacrifice of some property for the purpose of saving other property ; 3. The success of the endeavor. (Parsons on Mercantile Law.)

431. In adjusting a general average, the property sacrificed, as well as that saved, is regarded as contributory to the general loss. The entire value of the freight, however, is not contributory; } of its value in New York, and } of its value in other parts of the United States, being reserved for seamen's wages.

The goods, whether lost, injured, or saved, are valued at the price they would have brought in ready money on the vessel's arriving at her port of destination, unless the average is adjusted at the port of lading, when they are valued at the invoice price.

In compensating for the expenses incurred in repairing damages done to the vessel, only of the cost is allowed, as in general the new material is į better than the old.

432. To adjust the general average of losses at sea. Ex. 1. The ship America sailed on May 16, 1857, for New Orleans, with an assorted cargo. In consequence of a violent gale in the Gulf of Mexico, the captain was obliged to throw overboard a portion of the cargo, amounting in value to $ 4465.50, and the necessary repairs of the vessel cost $ 423. The contributory interests were as follows: vessel, $ 30000; gross freight, $ 6225; cargo shipped by R. S. Davis & Co., $3650; by Henry Mason, $ 6500; by G. T. Sampson, $ 2000; by J. Francis & Son, $ 550; by Morton Brothers, $ 5450 ; and by Sanborn & Carter, $ 8500. Of the cargo thrown overboard, there belonged to Henry Mason the value of $ 3000, and to Morton Brothers the remainder, $ 1465.50. The cost of detention in port in consequence 'of repairs was $ 116.50. How ought the loss to be apportioned among the contributory interests ?

OPERATION.

CONTRIBUTORY INTERESTS.

LOSS FOR GENERAL BENEFIT.

Vessel,

$ 30000 Thrown overboard, $ 4465.50 Cargo, 26650 Cost of detention,

116.50 Freight, less , 4150 Repairs, less

282.00 Entire contrib. int., $ 60800

Entire loss, $ 4854.00 $ 4864.00 · 60800 = .08, the loss per cent. $ 30000 X .08 = $ 2400, am't payable by vessel.

4150 x .08 332, am't payable by freight.
3650 x .08= 292, am't payable by R. S. Davis & Co.
6500 x .08 520, am't payable by Henry Mason.
2000 x .08 = 160, am't payable by G. T. Sampson.

550 x .08 44, am't papable by J. Francis & Son. 5450 x .08 436, am't payable by Morton Brothers. 8500 x .08 = 680, am't payable by Sanborn & Carter.

Proof, $ 4864, entire amount payable. $ 2400.00 – $ 398.50 = $ 2001.50, balance payable by vessel.

3000.00 - 520.00 2480.00, bal. rec'ble by H. Mason. 1465.50 — 436.00 1029.50, bal. rec'ble by Morton Bro's.

Since the vessel lost $ 116.50 + $ 282, $ 398.50, that amount is deducted in finding the net amount the vessel must contribute to the general loss. Henry Mason lost $ 520; the amount payable by him is therefore made so much less on that account; and Morton Brothers also, having lost $ 436, have the amount of their contribution lessened by that sum

=

Rule. — Multiply each contributory interest by the loss per cent., and the product will be its contribution to the general loss.

Ex. 2. The ship Hope, in her passage from Liverpool to New York, was crippled in a storm, in consequence of which the captain had $ 6500 worth of the cargo thrown overboard, and the necessary repairs of the vessel cost $ 1050. The charges for board of seamen, pilotage, and dockage amounted to $ 142. The contributory interests were: vessel, $ 31500 ; gross amount of freight, $ 4160; cargo shipped by Manning & Brother, $ 2145; by Anderson & Fisk, $ 1460; by Smidt & Huber, $ 960 ; by Greenwood, Laporte, & Co., $ 670; and by Allermann, Ritter, & Herr, $ 1000. In adjusting the general average in New York, the deduction made from the gross amount of freight on account of seamen's wages was one half. Required the several shares of the general loss.

EQUATION OF PAYMENTS.

433. EQUATION OF PAYMENTS is the process of finding the average or mean time when the payments of ral sums, due at different times, may all be made at one time, without loss either to the debtor or creditor.

434. A strictly accurate method of determining, by Arithmetic, the true average time for the payment of more than two sums, due at different times, it is believed, has not yet been discovered ; and, even when there are only two sums, the accurate method is the translation of an Algebraic Formula. The true equated time, however, may be readily found by Algebra.

Mercantile usage, however, gives its sanction to another method, and one which is not entirely correct, though, when the sums are small and the terms short, the variation from the exact truth is practically of no consequence. But this method, being far the most convenient of application, is adopted among business men.

Ex. 1.

6 x

435. To find the average or mean time of paying several debts due at different dates.

A owes B $ 19, $ 5 of which is to be paid in 6 months, $ 6 in 7 months, and $ 8 in 10 months. What is the average time of paying the whole ?

Ans. 8 months. OPERATION.

The interest of $ 5 for 6 5 X 6 30

months is the same as the inter7 42

est of $ 1 for 30 months; and of 8 x 10 80

$ 6 for 7 months, the same as of

$ 1 for 42 months; and of $ 8 for 19 19) 152 ( 8 months.

10 months, the same as of $ 1 for 1 5 2

80 months. Hence, the interest of

all the sums to the time of payment is the same as the interest of $1 for 30mo. +42mo.+ 80mo. 152 months. Now, if $ 1 require 152 months to gain a certain sum, $5+

$ 6+$8= $ 19 will require y of 152 months; and 152mo. 19=8 months, the average or mean time for the payment of the whole.

2. Purchased goods of Kendall & White at different times, and on various terms of credit, as by the statement annexed. What is the mean time of payment ? January 1, a bill amounting to $375.50 on 4 months. 20,

168.75 on 5 months. February 4,

386.25 on 4 months. March 11,

144.60 on 5 months. April 7.

386.90 on 3 months.

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OPERATION

Due May 1,

$ 37 5.50 June 20,

16 8.7 5 x 50 8 4 3 7.5 0 June 4,

38 6.2 5 x 34 131 3 2.5 0 6 Aug. 11, 1 4 4.6 0 X 102 1 4 7 4 9.20 July 7,

38 6.9 0 X 67 2 5 9 2 2.3 0 $ 1 4 6 2.0 0

6 2 2 4 1.5 0 days. 62241.50 1462.00 = 421831 days.

May 1+ 43 days = June 13, Ans. We first find the time when each of the bills will become due. Then, since it will shorten the operation and not change the result, we take the first time when any bill becomes due, instead of its date, for the point from which to compute the average time. Now, since May 1 is the period from which the average time is computed, no time will be reckoned on the first bill, but the time for the payment of the second bill extends 50 days beyond May 1, and we multiply its amount by 50. Proceeding in the same manner with the remaining

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