A R I T H 
tic; 2 pottles, i gallon; s gallons, i peck ; 4 pecks, 1 
bufhel; 5 pecks, i bufhel of water; 4 buthels, 1 comb; 
2 combs, 1 quarter; 4 quarters, 1 chaldron ; 5 quarters, 1 
tunorwey; 2 weys, 1 laft.' A veffel perfectly cylindri¬ 
cal, the internal diameter x8§ inches, and S inches deep, 
contains 2150-?- cubic inches, which is called the Winchef- 
ter bufhel, anil 21 5o|^-8=262f cubic inches in a gallon. 
Wine Measure. 28§ Cubic inches — 1 pint; 8 pints, 
z gallon; 42 gallons, iticrce; i^licrce, 1 hogfliead (hhd.); 
ij hogfliead, 1 puncheon; puncheon, 1 pipe or butt; 
2 pipes, 1 tun. A tun of 252 gallons, at 7 a 1 b. to the gal¬ 
lon, weighs 18901b. — i6cwt. 3 qrs. 141b. 31^ Gallons 
is a wine or vinegar barrel, and 236 gallons = 1 tun of 
i'weet oil. 
Ale Measure. 35^ Cubic inches = 1 pint; 8 pints, 
1 gallon; 8 gallons, 1 firkin; 2 firkins, 1 kilderkin; 2 kil¬ 
derkins, 1 barrel; i| barrel, 1 hogfliead. 
Beer Measure. 35^ Cubic inches — 1 pint; 8 pints, 
j gallon; 9 gallons, 1 firkin; 2 firkins, 1 kilderkin; 2 kil¬ 
derkins, 1 barrel; i£ barrel, 1 hogfliead ; 2 hoglheads, 1 
butt. This diftinftion, or difference, between the ale and 
beer meafure, is ufed only in London; but in all other 
places in England, the following table of beer and ale, 
whether ftrong or final], is to be obferved according to a 
flatute of excife made in the year 1689. 
Ale and Beer Measure in the Country. 35P Cu¬ 
bic inches = 1 pint; 8 pints, 1 gallon; 8| gallons, 1 fir¬ 
kin; 2 firkins, 1 kilderkin; 2 kilderkins, 1 barrel; 1 a bar¬ 
rel, 1 hogfliead. 
OfNuMBER, 12 Single—1 dozen ; 12 dozen, 1 grofs; 
12 grofs, 1 great grofs; 5 fcore, 1 fliort hundred ; 6 lcore, 
z long hundred; 24 fheets of paper, x quire; 20 quires, 1 
ream; 5 dozen (kins of parchment, 1 roll; no fheets in a 
book, 1 hundred. 
Bread. A peck loaf weighs, 171b. ooz. idwt. Alialf 
peck, 8lb. itoz. A quartern, 4H3. 50Z. 8dwts. 
Hay. 56 Pounds of old, or 6olb. new, hay, make a 
trufs; 36 tru fifes — 1 load. 
The Customary Weight of Goods. A firkin of 
butter is 561b. A firkin of foap, 641b. A barrel of pot 
allies, 2001b. A barrel of anchovies, 301b. A barrel of 
candles, i2olb. A barrel of foap, 2561b. A barrel of 
butter, 2241b. A fother of lead, igicwt. A ftone of 
Iron, 141b. A ftone of butcher’s meat in London, Sib- 
A gallon of train oil, 7&lb. A faggot of fteel, i2olb. A 
ltone of glafs, 51b. A (team of glafs is twenty-four ftone, 
or i2olb. 
Of Time. 60 Seconds — 1 minnte; 60 minutes, 1 
hour; 24 hours, 1 day ; 7 days, 1 week ; 4 weeks, 1 month ; 
13 months 1 day and fix hours, or 52 weeks 1 day and 6 
hours, or 365 days 6 hours — 1 year, for three years toge¬ 
ther ; 366 days — z year, for every fourth or leap year. 
Every 4th hundred year to contain 365 days only, accor¬ 
ding to the new ftyle, or civil and Gregorian account of 
time. 
COMPOUND ADDITION 
Is finding the furn of feveral numbers of different de¬ 
nominations. 
Rule. Place all numbers of the fame denomination 
under each other, and under them draw a line. Begin at 
the loweft denomination, and add up all the figures in that 
row, as in finiple addition; find how many units of the 
next fuperior denomination are contained in this fum; fet 
down the remainder or overplus under the added row, and 
carry the units to the figures of the next fuperior denomi¬ 
nation, whofe fum you muff find and proceed with as be¬ 
fore : and fo on of the reft. In the laft or higheft deno¬ 
mination add them up as integers, whofe fum fet down, 
which, together with the feveral remainders, will exprefs 
the fum required. The method of Proof the fame as in 
Simple Addition. 
The reafon of this rule is evident from what has been 
before faid : for, in Compound Addition, as 1 in the pence 
is equal to 4 in the farthings, j.in the fhillings to 12 in the 
M E T I C. , i6y 
pence, and fo on; therefore, cairying as dire fled, is only 
providing a method of placing the money ariling f rom each 
column properly in the fcale of denominations; and this 
reafoning will hold good in the addition of compound num¬ 
bers of any denomination whatever. 
Money. 
Ex. 2. 
Ex 
• 3 • 
1. s. d. 
Ex. r. 173 13 5 
Troy Weight. Apothecaries Wright. 
lbs. oz dvvt.grs. ■ 
' ft 5 
5 9 g'- 
87 n 7-1 
54 8 13 7 
76 7 
5 2 '7 
75 is 74 
1 38 5 17 19 
8710 
7 112. 
2 5 17 8* 
69 10 15 23 
38 5 
3016 
10 10 104 
147 9 19 12 
99 11 
7 2 19 
2 5 7 
85 7 5 16 
37 <* 4 
4 1 1 i 
Sum 376 3 10 
496 6 12 5 
679 4 
S 1 2 
202 10 5 
Proof 376 3 10 
Ex. 4. 
Ex. 5. 
Ex 
. 6. 
Rd. Sq. Mca. Avoirdupoife Weight. 
Ale&Bcer Mcafurt 
wa yd.ft. in. qrs. Tons.ewt. qr. lb. oz.drs. 
Hhds.b. k. 
g. c.in. 
1549 6 8 135 14 761 
16 1 25 13 15 
43 1 1 
14 247 
84 1 3 97 5 49 
*9 3 2 7 9 1 3 
74 <4 0 
11 3 i 
124 5 1 139 13 967 
14 0 I9 II I4 
9 1 1 
16 134 
!<> 4 7 37 7 89 
122 8 I 2 I 2 
36 z 0 
8 65 
37 2 5 126 12 376 
8 3 16 15 14 
821 1 
15 184 
673 0 0 105 3 2245 
12 0 15 0 4 
249 O O 
15 104 
SUBTRACTION 
Is the taking a lefs number (called the fubducend) from a 
greater called the minuend) in order to find a third number, 
called the remainder or difference. Its lign or charafter is 
—, called minus. 
Rule. Place the minuend, or greater number, upper- 
moft, and the fubducend under, fo that units may Hand 
under units, tens under tens, &c. Begin at the place of 
units, and take eacli lower figure from that which ftands 
over it, fetting the remainder under them below the line ; 
and all thefe remainders will be the required difference. 
When the lower figure 
Ex. From 8903562 minuend is greater than that 
Take 5831875 fubducend which ftands over it, 
Rem. 3071687 conceive ten to be bor- 
--—. rowed or added to the 
Proo f 8903502 uppermoft figure, and 
take the lower from the 
fum, fet down the remainder, and carry one to be added 
to the next lower figure, with whicli proceed as before. 
To prove fubtraftion, add the remainder to the fubdu¬ 
cend, and, if the fum be equal to the minuend, the work 
is right. 
The method of borrowing ten, according to the rule, 
will be explained by conftdering, that, when we add this 
ten to the minuend, we likevvife add one to the next place 
of the fubducend, which diminifhes the correfponding 
place of the minuend accordingly ; and therefore this is 
only taking from one place and adding as much to another, 
fo that the total is not altered. And the ten, which is 
added, is the value of an unit in the next higher place by 
the nature of notation. The reafon of the proof is evi¬ 
dent ; fince the difference of two numbers added to the 
lefs muft be always equal to tiie greater. 
Compound Subtraction, teacheth to find the dif¬ 
ference of any two numbers of different denominations. 
Rule. Place the given numbers fo that, the greater may 
be uppermoft, and that thofe of the fame denomination 
may Hand direftly under each other, and draw a line un¬ 
der them. Begin at the low-eft denomination, and take 
the lower number from the upper one, and fet down the 
difference or remainder underneath. Do the fame with 
the next denomination, and fo on to the laft, which muft 
be fubtradted as whole numbers. When the lower num¬ 
ber in any denomination happens to be the greater, add as 
many to the upper number as m^kes one of the next high¬ 
er 
