230
ARITHMETIC.
IV. One who is pretty refldy in division, may, even in thelargest divisions, subtract each figure of the product as he pro-duces it, and write down only the remainders.
Example. 833)3104679(3727 J/j.
- 6030225 7591988
Reduction.
(17.) Reduction is the conversion of numbers from one nameto another, but still retaining the same value. If the reductionbe to a less name, it is commonly called reduction descending ;but if to a greater, reduction ascending.
Rule. Consider how many of the less name concerned makeone of the greater, and by that number multiply the given num-ber if the reduction be descending, but divide if ascending, andthe product or quotient will be the value in the other name."When there are names between the proposed and required ones,it is best to reduce the proposed to the next less or greater name,and this to the next less or greater again, and so on, till you havereduced it to the name required. When, in reduction descend-ing, the proposed is a compound number, you must add, or takein the small numbers in the name below the greatest, to the samenames as you proceed in the reduction. When, in reduction ascend-ing, you have any remainders after dividing, they will havethe samenames as their respective dividends, and may be placed after thelast quotient, according to the order of their names, the greatestlirst ; so shall the compound number thus formed be the answer.
(18.) The following tables are to be understood thus: thewords at the top are the names of all the numbers straight belowthem ; and all the numbers upon the same line, from right toleft, are of equal value : thus, 960 farthings, 240 pence, 20 shil-lings, and 1 pound are all equal to each other.
Of Money.
Farthings. Pence. Shillings.
4 1
4S 12 1
960 240 20
The full weight and value of our gold andbc-iow :
Gold. Value.
/. s. d.
A guinea . 1 1 0
Half-guinea. 0 10 6
Quarter-guinea . 0 3 3
Pound.
1
silver coin is as
Weight.divt. gr.3 91-
.2 16 |1 8 $
Silver.
A crown. 5
Half-crown. 2
Shilling . 1
Sixpence . 0
'1 lie value of gold is nearly M. an ounce, or 2d. a grain ; and
Value.x. d.0606
Weight.
dirt.
19931
S r -
l«i2122$
nearly il.
silver is nearly 5$. an ounce. Also any quantity of gold is to thesame weight of standard silver, in the proportion of 15 and 1-14th
to 1, or nearly 15 to 1.
Of Troy Weight.
Grains. Pennyweights. Ounces, Pound.
24 1
480 20 1
5760 240 12 1
Bv this weight are weighed jewels, gold, silver, corn, bread,and liquors. One grain of Troy weight is equal to one grain anda half of sound dry wheat.
Of Atothecaries Weight.
Grains.
20
60
Scruples.
1
3
Oram's.
1
Ounces.
Pound.
480
24
8
1
5760
288
96
12
1
This weight is so called, because the apothecaries use it in com-
pounding their medicines; but they buy and sell their drugs byavoirdupojse weight. Apothecaries is tnu same as troy weight,having only some different divisions.
Of
Avoirdupoise Wf.igiit.
O
O
g P
h-4
3
n
9 p
— £1
C
3
V
S' S'
16
I
ps
o u
256
16
1
7168
448
28 I
28672
1792
112 4
1
573440
35840
2240 80
20
By this weight are weighed all tilings of a coarse or drossy na-ture ; such as grocery auJ chandlers wares, and all metals exceptgold and silver.
oz. dwt. gr.
1 lb. Avoirdupoise makes 14 11 15$ Troy.
1 oa. 0 18 5‘-
I dr. 0 1 31
Of Long Measure,
<—*
•n
►a
CL
a
G
n
P
3-
o
a
12
1
36
3
l
198
161
% i
1
7920
660
220
40
63360
52S0
1700
320
An inch is supposed equal to three barley corns in length.
4 inch.—a hand.
6 feet, or 2 yards—a fathom.
3 miles—a league.
60 nautical or geographical miles—a degree, or 69 $ statutemiles nearly.
360 degrees, or 23000 miles nearly, are the circumference ofthe earth.
Inches.
9
36
Of Cloth Measure.
Quarters.
Nails.
1
4
16
3 qrs. = 1 ell Flemish.
4 qrs. 1-j. inch Scotch.
Of Square or Land Measure.
w to ' w «
~ ^ — o
Yard.
1
144
1296
39204
r
~~ 4
30$ 1
1568160
10890
1210 40
T
6272640
43300
484 160
4
n.
Of Wine Measure.
Pints.
O
o'
II lids.
. Tierc
y
B
n
*5’
3
Ton.
UJ
3
re
o
G
l
o
S3
8
5j
c
336
42 .
1
■a
504
63
1$ >
672
84
2 1 }
1
1008
126
3 2
n
1
2016
252
6 4
3“
2
1
231 cubit