2. If 25lb. at Boston be 22lb. at Nuremburg; 88lb. at Nuremburg, 92lb. at Hamburgh; 46lb. at Hamburgh, 49lb. at Lyons; how many pounds at Boston are equal to 98lb. at Lyons? Ans. 1001b. 3. If 6 braces at Leghorn make 3 ells English; 5 ells English, 9 braces at Venice; how many braces at Leghorn will make 45 braces at Venice? Ans. 50 braces.*

FELLOWSHIP.

Fellowship is a general rule, by which merchants, &c. trading in company, with a joint stock, determine each person's particular share of the gain or loss In proportion to his share in the joint stock.

By this rule a bankrupt's estate may be divided among his creditors; as also legacies adjusted, when there is a deficiency of assets or effects.

SINGLE FELLOWSHIP.

Single Fellowship is when different stocks are employed for any certain equal time.

*Barter is the exchanging of one commodity for another, and directs traders so to proportion their goods, that neither party may sustain loss.

Loss and Gain is a rule, that discovers what is got or lost in the buying or selling of goods; and instructs merchants and traders to raise or lower the price of their goods, so as to gain or lose a certain sum per cent. &c.

Questions in these rules are performed by the rule of Three. Vol. I.

RULE.*

As the whole stock is to the whole gain or loss, so is each man's particular stock to his particular share of the gain or loss.

METHOD OF PROOF.

Add all the shares together, and the sum will be equal to the gain or loss, when the question is right.

EXAMPLES.

1. Two persons trade together; A put into stock Si30 and B g220, and they gained g500; what is each person's share thereof

130 220

350 : 500 :: 130:

500

35,0)6500,0(185'71

35

300

280

200

175

250

245

50

35

15

* That the gain or loss, in this rule, is in proportion to their stocks is evident: for, as the times the stocks are in trade are equal, if I put in of the whole stock, I ought to have of the whole gain; if my part of the whole stock be, my share of the

2. A and B have gained by trading §182. A put into stock g3O0 and B g4O0; what is each person's share of the profit I Ans. A g78 and B §104. 3. Divide gl20 between three persons, so that their shares shall be to each other as 1, 2, and 3 respectively.

Ans. 820, 340, and $60. 4. Three persons make a joint stock. A put in 185 66, B g98 50, and C g76'85; they trade and gain §222; what is each person's share of the gain?

Ans. A gl*4 17810, B sg0 57-243, and C 847 2538774. 8104173810

5. Three merchants A, B, and C freight a ship with 340

whole gain or loss ought to be also.

And generally, if I put

in of the stock, I ought to have part of the whole gain or loss; that is, the same ratio, that the whole stock has to the whole gain or loss, must each person's particular stock have to his particular gain or loss. To efirg

tuns of wine; A loaded 110 tuns, B 97, and C the rest. In a storm the seamen were obliged to throw 85 tuns overboard; how much must each sustain of the loss?

Ans. A %7%, B 24A, and C 33|.

6. A ship worth 8860 being entirely lost, of which belonged to A, to B, and the rest to C; what loss wiil each sustain, supposing 8500 of her to be insured?

Ans. A 8+5, B 890, and C 8225. 7. A bankrupt is indebted to A 8~77 33, to B 8305 17, to C 8152, and to D 8105. His estate is worth only 8677 50; how must it be divided?

Ans. A 8223 812580, B 8246,28615

C 8122 6C|4|», and D 884736665

8. A and B, venturing equal sums of money, clear by joint trade 8154. By agreement A was to have 8 per cent, because he spent his time in the execution of the project, and B was to have only 5 per cent.; what was A allowed for his trouble? Ans. 835 55 11

DOUBLE FELLOWSHIP.

Double Fellowship is when different or equal stocks are employed for different times.

RULE.*

Multiply each man's stock into the time of its continuance, then say,

As the total sum of all the products is to the whole gain or loss,

So is each man's particular product to his particular share of the gain or loss,

EXAMPLES.

1. A and B hold a piece of ground in common, for which they are to pay 836. A put in 23 oxen for 27 days, and B 21 oxen for 35 days; what part of the rent ought each man to pay -?

* Mr. Malcom, Mr. Wahd, and several other authors have given an analytical investigation of this rule; but the mo6t gen

eral and elegant method perhaps is that> which Dr. HUTTON has given in his Arithmetic, namely,

When the times are equal, the shares of the gain or loss are evidently as the stocks, as in Single Fellowship; and when the stocks are equal, the shares are as the times; wherefore, when neither are equal, the shares must be as their products.