j^5 A R I T H 
Ex. 3. Three perfons, viz. X, Y, and Z, made a joint 
flock of 214I. of which X put 111 67!. Y 92I. and Z 55^* 
now upon adjufting their accounts they found that they 
had loll 16I. is. what was each perfon’s (hare thereof? 
Fir ft 16I. is. = 321s. the whole lofs. 
1. s. d. I. s. d. 
{ 67 : 100 6—5 o 6 X’s"j 
92 : 138 0=6 18 o Y’s V lofs. 
55 : 82 6 —4 2 6 Z 'sJ 
Proof 16 1 o 
The Double Rule of Fellowship determines how 
much gain or lofs is due to every partner concerned ; by 
having tiie whole gain or lofs, and the particular ftocks, 
and their time of continuance, given. 
Rule. Multiply every man’s ftock by the time it is em¬ 
ployed; then, by the Rule of Three, fay, As the fum of 
thefe products is to the whole gain or lofs, fo is each of 
thefe products to each man’s gain or lofs. 
Ex. 1. Three men, A, B, and C, enter into partnerfliip, 
A puts in 85I. for 6 months, B 72I. for 5 months, and C 
45I. for 4 months; they gain 35I. what is each man’s fliare 
r 
85k X 6m. 2 
=510 
produCt of A’s 
ftock and time 
Thus <! 
72X5 2 
=360 
do. 
of B’s 
do. 
1 
45 X 4 2 
12180 
do. 
of C’s 
do. 
105° 
fum 1 
of all the 
products. 
r 
cio : 
: 17I. 
A’s fliare 
As 1050 
: 35 J 
360 : 
: 12 
B’s fliare 
Or 30 
: 1 1 
180 
: 6 
C’s fliare 
Proof 
35 
the whole 
: gain. 
Ex. 2. Three perfons, A, B, and C, enter into partner- 
fhip, their common ftock being 4663I. 15s. whereof A put 
in 1653I. 15s. for 4 months; B 1417k 10s. for 7 months ; 
and C 1592I. 10s. for 9 months; they lofe 140k what is 
each perfon’s fliare thereof? 
1 . s. Crowns 
Fil'd: 1653 15=6613, 1110116615X4=26460"] prod, of each 
Alfo 1417 10=5670, alfo 5670X7=39690 > perfon’s ftock 
And 1592 10=6370, and 6370 x 9 =57330 J and tune. 
Sum of the products 123480 
Having the whole ftock, each man’s gain or lofs, and 
time, given, to find each perfon’s ftock. Multiply each 
man’s gain or lofs, by all the other’s time ; then fay, As 
the fum of thefe products is to the whole ftock, fo is each 
of thefe particular products to each man’s particular ftock, 
viz. Three perfons, A, B, and C, enter into partnerlhip, 
their common ftock being 3822I. A’s money was in 3 
months, and his gain was 52I. B’s money was in 5 months, 
and his gain was 78k and C’s money was in feven months, 
and his gain was 104k required each man’s ftock ? 
52X 5X 7=1820 product of A”s gain by B’s and C’s time 
78X3X7=t638 do. of B’s gain by A’s and C’s time 
104X3X5=1560 do. of C’s gain by A’s and B’s time 
5018 fum of the products. Therefore, 
1. 1. s. d. 
As 5018 : 3822 C 1820 : 1386 4 4^ A’s ftock 
Or 2509 : 1911 :: 8 1638 : 1247 11 115-97 B’s ftock 
Or 193 : 147 :: (,1560 : 1188 3 844 ? C ’s ftock 
Proof . 3822 o o 
LOSS and GAIN, 
Is a rule that difeovers what is gained or loft in the buy¬ 
ing or felling of goods, and inftrutts the merchant or trader 
to raife or lower the price of his goods in fuch proportion, 
that neither his gain may be fo exorbitant as to injure his 
cuftomer, nor his lofs fo great as to impoverilli himfelf. 
When the quantity of goods, prime coft. and propofed gain 
3 
M E T I C. 
or lofs, are given, by the Rule of Three DireCt, fay, As 
the quantity of goods is to the prime coft (the gain being 
added, or the lofs fubtraCted), fo is any part of the faid 
goods to the price they muft be fold for. When the pro¬ 
pofed gain or lofs is at fo much per cent. As 100k is to 
100k (-{- the gain, or — the lofs), fo is the prime coft to 
tire felling price. 
Ex. 1. An innkeeper bought a tun of wine which coft 
him 71k 8s. at how much per gallon muft he fell it to gain 
21k by the whole ? 
Firft 71 1 . 8s. +21=921. 8s. =i848s. the whole muft be 
fold for. 
As 252 galls. : 1848s. :: 1 gall. : 7s. 4d. the anfwer. 
Ex. 2. Bought 1 cvvt. of hops for 4k 12s. how much 
muft 1 fell them for to lofc 12 percent. 
As 100 : 88:: 4k 12s. : 4k os. 1 id. 2^qrs. the anfwer. 
BAR TER, 
Is the exchanging one commodity for another, fo that 
neither party may fuftain any lofs thereby. Toafcertain 
this, find the value of that commodity whole quanti¬ 
ty and rate is given, then find, by the Rule of Three, 
what quantity of the other commodity, at its propofed 
rate, may be bought for the fame money; and fo much 
of the latter commodity muft be given for the former. 
When one commodity is advanced above the ready-money 
price, find the advanced price of the other commodity in 
the fame proportion ; thus, by the Rule of Three Direct, 
fay, As the ready-money price of the one is to its advanced 
price, fo is the ready-money price of the other to its ad¬ 
vanced price. Then the quantity of the latter commodity 
may be found either from the ready-money or advanced 
prices. When the commodities to be exchanged are of 
unequal value, the defeCt is fupplied by money or fame 
other commodity equivalent in value. In a fimilar man¬ 
ner, all fuch queftions as do not fall underthefe directions 
are eafily folved by a little confideration of their nature. 
Ex. 1. How many hundred-weight of hops, at is.6d. per 
pound, may be had in barter fbr 116 bufhels of wheat at 
7s. per bulhel ? 
Firft 116 x 7=812s. value of the wheat=i624 fixpences. 
Then, as 3 fixpences : 1 lb. :: 1624 fixp. : 54151b. which 
is equal to 4 cwt. 3 qrs. 9|lb. the anfwer. 
Ex. 2. A wine-merchant, C, has port-wine worth 5s. 
6d. per gallon ready money, but in barter he will have 
6s. 3d. D has 572 bufliels of malt worth 4s. per bulhel 
ready money; how many gallons of wine muft D receive 
for his malt, and how muft he rate it per bulhel to equal 
the barter ? 
As 5s. 6d. : 6s. 5d.:: 4s. : 4s. 8d. the advanced price of 
one bulhel of malt. 
As 1 bulhel : 4s. :: 572 bufliels : 2288s. the real value 
of D’s malt. 
Again, as 5s. 6d. : 1 gall. :: 2288s. : 416 gallons of wine 
D muft receive. 
Or thus by the advanced price to find the quantity of wine. 
As 1 gall : 4s. 8d. 572 gall. : 2669s. 4d. the advanced 
price of D’s malt. 
As 6s. 5d. : 1 gall. :: 2669s. 4d. : 416 gallons of wine 
as above. 
Ex. 3. Two merchants have various kinds of goods to 
'barter; A has 735 yards of Indian lilk, at 8s. 6d. per yard 
ready money, and in barter 10s. alfo 532 canes at 3s. a- 
piece ready money, and in barter 3s. 4c!. alfo 16 pieces of 
muflin at 4k the piece ready money, and in barter at 41.10s. 
B has fcarlet cloth at ;h per yard ready money ; glafs ma¬ 
nufacture at is. Sd. ffer lb. ready money, and a finer fort 
at 2s. 4d. How many yards of cloth, and pounds of each 
kind of glafs, (of each a like number, i. e. yards of cloth 
and pounds of each glafs,) muft B give to A advancing 
his goods proportionally alfo in barter ? 1. s. d. 
A’s Indian filk 735 yds. at 8s. 6d. per yd. is 312 7 6 
Canes, 532 at 3s. a-piece is - - 79 16 o 
Muflin, 16 pieces at 4k per piece 64 o o 
The fum is 45^ 3 6 
B’s 
