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n
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X.
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111
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f
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»
•W
THE
PRIVATE INSTRUCTOR,
OR
MATHEMATICS SIMPLIFIEB. ^
COMPRISING EVERT THING NECESSARY IN ARITHMETIC, BOOK-
KEEPING, CONVEYANCING, MENSURATION, AND GVA6ING,
TO FORM AND COMPLETE THE MAN OF BUSINESS.
THE WHOLE UPON AN IMPROVED PLAN,
NOT ONLY ADAPTED TO PRIVATE INSTRUCTION, BITT ALSO TO
V
TBDB ITSSOB OF 8€«<N>L9.
"He that is ignorant of nnmbera la scarce half a man."
Cbamlxs XII, ov Swxssir.
BY JASON n. niAHAIV,
MATHlMATICIAlf, NSW ITALY, CHBSTSB GOUITTT, PSVlTStLVAVIA.
PRINTED FOR THE AUTHOR, BY SAMUEL KLING
1839.
C\A
I '■■ f
I
t
\
5
f . >^
9
Entered acoordiog to the act of Congress, in the year
1836, by Jason M. Mahan, in the clerk's oiBce of the
District Court of the Eastern District of Pennsylvania.
'7 ( a ^^ O
PREFACE.
The following work has been in contemplatioij for a
long time. Several years' experience as a teacher con-
firmed me in the opinion, that a work of this kind would
be serviceable, particularly to such as are to receive but a
small proportion of schooling. Its utility must be obvious
to every one who considers that the opportunity for im-
provement with many is limited ; and that many of the
treatises on Arithmetic, Mensuration, &c. are not alto-
^ gether calculated to give that instruction in so short a time
z as one intended for business ought to receive.
i- In order that the pupil may acquire a competent knowl-
O edge of the different branches, in as short a time and at as
litue expense as possible, I have carefully excluded all
irnelevant matter^ and have given only' what t deemed
necessary to prepare him for business. One of the most
'>difficult questions in each rule is wrought out at full
length, and by comparing these with the rules, which are
laid down in a plain and familiar manner, any person who
has the least knowledge of figures, or inclination to learn,
may understand them, either with or without the aid of a
teacher ; so that the work is not only adapted to private
instruction, but also to the use of sch^ls.
With these impressions, and hoping that the work may
be Qseful, it is now offered to the public, by
The public's most.humble servant,
JASON M. MAHAN.
New Italy, January 2, 1839.
t
I
COlfTKNTS.
CONTENTS.
Arithmetic.
Numeration, ^^^^
Addition of Integers, n
Multiplication of Integers 18
->luItipIication, 04
f^ong Division, ofj
Decimal Fractions, ^
Addition of Decimals, S
Subtraction of Decimals, S
federal Monev, t
Compound Addition, 59
J:;ompound Subtraction. 67
J^ompound Multiplication, 74
^ompound Division, 77
K^duction of Decimals, 78
practical Questions, 83
Single Rule of Three, 86
Double Rule of Three, 91
Practice, 93
Questions for exercise, 95 (
Interest, 100
B^bate or Discount, 111
Bank Discount, 113
Extensive Addition, 116
40S3 and Gain^ 118
larter, 120
fellowship, 124
Exchange, 128 1
Custom-house allowances, 140
UDited States Duties, 143
Vulgar Fractions, 145
Reduction of Vulgar Frac-
tions, j4g
Addition of Vulgar Frac-
tions, 255
Subtraction of Vulgar
Fractions, i^'y
Multiplication of Vulgar
Fractions, 153
Division of Vulgar Frac-
tions, 159
The Single Rule of Three
in Vulgar Fractions, 160
The Double Rule of Three
in Vulgar Fractions, 161
Contracted Multiplica-
tion of Decimals, 162
Contracted Division of
Decimals, jgg
Contracted Division, I64
Equation of Payments, 166
Alligation, . i^r
Single Position, \l\
Double Position, |^^
Arithmetical Progression l a^
Evolution,
Square Root,
Cube Root,
Duoedcimals,
PrQmi(sci|ous Qu
18^
-.Uoas, \^
6
BOOK-KEEPIKG.
Day-Book,
Alphabet,
Ledger A,
Balancing,
Ledger B,
coNTEirrs.
P.
201
211
212
217
217
Mercantile Forms.
Bills of Parcels, 218
Book Bill, 2i9
Dill of Lading, 219
Conveyancing.
Seaman's receipt, 222
Receipt in full of all de-
mands, 222
for rent, 222
for mone}'- receiv-
ed of a third per-
son, 222
for interest on a
bond, 222
Common negotiable Note 223
Promissory Note, 223
Note with security, 223
Accommodation Note to
Bank of U. States, 223
Forms and Directions for
transacting business at
the bank of Chester CO. 224
Note with Interest, 227
Judgment Note, 227
Notice from Landlord to
Tenant, 228
Proxy to vote for Direct-
ors of the Bank of the
U. States, 228
Assigni^ent of a bond or
bill, 229
Common Judgment Bond 229
Assignment of a Bond, 280
I
P.
For a Bond mislaid or lost 230
Indenture of an appren-
tice, 231
Assignment of an appren-
tice, 232
Lease of a Farm, 232
of a House, 233
Assignment of a Lease, 234
Agreement for sale of an
Estate, 235
building a House, 236
with a Clerk or
Workman, 237
Bill of Sale of Goods, 238
Letter of Attorney, 239
Letter of Attorney to re-
ceive debts, 241
Conditions of public ven-
due, 241
Sale of goods and chattels 242
Mortgage, 243
Deed, 244
Will, 247
Bond of Arbitration, 248
Award, 249
Petition for laying out a
Road,
Return,
Petition for review of a
Road,
Report,
Petition for vacating a
Road,
Report,
Petition for valsing lands 25|
Report,
Release from one to one,
of a Legacy, ^
to a Guardian, 2^
for money recciv- /.
ed on a purchase, 2^
250
250
251
251
252
252
0OKTKNT8*
Mensuration.
p.
Of the Square, 256
Of the Parallelogram, 257
Of the right-angled Tri-
angle, 258
uithe rrapezmiB, 260
Of regular Polygons, 261
Of the Circle, 263
Of the Oval or Ellipsis, 264
To measure the length of
standing Timber, 265
Board Measure, 266
Of a Cube, 269
J^ a Parallelopipedon, 269
Of a Cylinder, 270
Of a Cone, 270
Of a Globe or Sphere, 271
Ship's Tonnage, 272
Stone Measure, 273
To measure stone in a
Well, 274
Paying and Plastering, 275
Shingle or Roof Measure 276
To find the sid e of a square
piece of Timber, thatt
may be hewn or sawed
from a round piece, 276
Mechanics.
Of the Levor, 277
Of the Wheel and Axle, 279
Of the Screw, 279
Spboimo Gravity.
I^^e of specific gravities 281
p.
To find the specific gravi*
ty of a body, 282
To find th9 quantity of
two ingredients in a
given compound, 288
To ascertain whether
spirituous liquors be
above or below proof, 284
To find the pressure of
water against a sluice
or bank, 284
GuAGING*
To find the capacity
of an oblong or square
box, granary, &c. 285
Ota cylindrical or circu-
lar vessel, 286
of a circular vessel, wi-
der at one end than
the other, 287
pf a vessel whose bottom
IS hollowing, &c. 287
To find the content of a
Still or Boiler, 289
^f JjiS^aging, 290
Ut the ullage of Casks, 293
To ullage a standing
Cask, 294
QOLD CoiHAGE*
Table of Gold Coing, 296
To compute the fineness
of Gold Coin, aoQ
Miscellaneou* Questions, 301
, EXPLANATION
Of the characters made use of in this work.
es The sign of equality ; as 4 qrs. « 1 jard> signifies that
4 quarters are equal to one yard.
•— Minus, or less : the sign of subtraction ; as 8— 2='6, that
is, 8 lessened bj 2 is equal to 6.
+ Plus or more : the sign of addition ; as 4+3=7, that is,
4 added to 3 is equal to 7*
X Multiplied hy : the sign of multiplication; as 7x4=38,
that is, 7 multiplied bj 4 is equal to 28.
-f- Divided by: the sign of division; as 6-7-2=3, that is, 6
divided by 2 is equal to 3.
iW" Numbers placed like a fraction do also denote division;
the upper number being the dividend, and the lower the
divisor.
:: So is ; the sign of proportion ; as 3 : 6 :: 2 : 4, that is, as
3 is to 6 80 is 2 to 4.
8 — ^2+5=11, shows that the difference between 8 and 2
added to 5, is equal to 11.
8^.2+5=1, shows that the sum of 2 and 5 taken from 8, is
equal to 1.
y^ Prefixed to any number, signifies that the square root of
that number is required.
'^ Signifies that the cube root is required.
The letters composing the words " my big horse,'' will in
many places be substituted for figures. It will be easy to
conceive each letter a figure, thus :
My big horse
12 345 6789
^
■t
\
ARITHMETIC.
Arithmetic is that part of the mathematics which treats
of numbers, and teaches how to apply them to useful pur- '
poses. It has five principal rules, on which all its operations
depend," viz: Notation or Numeration^ Addition^ Subtract
tion. Multiplication and Division.
NUMERATION
Teaches the different value of figures by their different
places, and to read and write any sum or number with the
ten Arabic characters, called figures, or di^ts, viz : 1, 2, 3,
4, 5, 6, 7, 8, 9, 0.
All numbers may be expressed by these figures.
THE TABLE.
00
£ o ^ jll o ** 21
'g «:2'g BO §'5 »«g
en _•
^ 00
12345678 9, 123 millions, 456 thousand, 789-
1234567 8, 12 millions, 345 thousand, 678.
912345 6, 9 millions, 123 thousand, 456.
7 8 9 12 3, 789 thousand, 123.
4 5 6 7 8, 45 thousand, 678.
9 12 3, 9 thousand, 123.
4 5 6, four hundred and fifty -six*
7 8, seventy-eight. I
9, nine. I
The reading of numbers maj be greatly facilitated, by
dividing them into periods of three figures each; thus,
B
10 HUKEBATION.
123,4S6»789, reads one hundred and iwentj-ikree milGons,
four hundred and fifty-six thousand, seven hundred and
eighty-nine.
AppUcatum*
Write down in proper figures the following numbers:
Nine, s.
Fifty-six, -------- gh.
Eignt hundred and forty-ihree, . - - - nb^
Three hundred and five, ----- beg.
Six hundred and forty-one, ^ . - - - hinu
Nine hundred and forty-eight, . - - - gir.
Three hundred, - - . - - ^ - bee.
Three hundred and seventy-two, - - • - boy.
Nine thousand six hundred and seventy, - - - shoe..
E^ht thousand seven hundred and ninety, - - rose.
Nine thousand seven hundred and ten, - . - some.
Fifty-seven thousand seven hundred and ninety, - goose.
Nine hundred and sixty-two thousand, three hundred
and seventy -two, - - - - - shyboy..
I'lve hundred and seventy-seven milliona, nine hun-
dred thousand, five hundred and fifty-nine, gooseeggs..
Foriy-eight millions, four hundred and ninety-six thou-
sand, tiiree hundred and seventy -two, irishboy..
One million, two hundred and sixty-seven thousand,
eight hundred and ninety, - - - myhorse..
The following table» extending to nonillions, may sometimes
be useful :
Nonillions, Octillions, Septillions, SextiIlions,Quintillions»
628974, 587629, 719548, 327647, 591792,
Quadrillions, Trillions, Billions, Millions, Units.
614268. 438276, 951476, 679284, 151417.
NOTATION BY ROMAN LETTERS*
'»!• One» XI. Eleven.
n. Two* XII. Twelve.
III. Three* XIII. Thirteen*^
IV. Four. XIV. Fourteen*
V. Five. XV. Fifteen.
VL Six. XVI. Sixteen.
VII. Seven* XVII. Seventeen.
VIII. Eight. XVIII. Eighteen.
IX. Nine. XIX. Nineteen.
X. Ten. XX. Twenty.
XXX. TTiirty; CCCC. Four hundred.
XL. Forty. D. Five hundred.
L. Fifty. DC. Six hundred.
LX. Sixty. DCC. SeYen hundred.
IXX. Seventy. DCCC. Ei^t hundred.
IXXX. Eighty. DCCCC. Nine hundred.
XC. Ninety. M. One tfaeusand.
C. One hundred. MDCCCXXXV. One Ihougand eiriit
CC. Two hundred. hundred and tbir^
CCC. Three hundred. ty-five.
ADmnON OF nVTEGEBS.
Addition teaches to collect two or more numbers into one
total. sum.
HULE.
There must be a due regard had in placing {he figures one
under the other, that is, units under units, tens under ien8»
hundreds under hundreds, &c.; then begin at the right hand
column, and add up each column successively and set down
its amount; but if either of the amounts be ten or more, set
down only its right hand fi^e, and add the number expressed
by its left hand figure or ^^ures to the next column; and sa
continue to the last column, 'at which set down tiie total
amount.
Proof. — Perform the addition downwards; that is, begin at
the top and add the figures downwards— and if the sum total
be the same^ it is right.
JSxampIes*
2Ul 4123 135146
3212 8452 113884
1103 1215 106840
hi^
rose.
bigrye
87625
31784
198t
147
52
316
24tr8
6«78
32100'
315
«682154
1001
55344
22664*
78828
shoes robbery sorry
1000001
20012
500103
18704294
11264135
2171003
10012
5123100
39221815
288146
21001
87
146
390340
irisbboy
gooseegg
hishoe
Practical Questions.
1. A testator bequeathed to his widow 3640 dollars^ to his
eldest son 3100 dollars, to three other sons each 2550 dollars,
to his five daughters 1900 dollars each, to his executor 20D
dollars, and l^ft for charitable purposes 975 dollars. I desire
to know the amount of the several bequests.
Dollars.
3640 Bequeathed to the widow.
3100 " *' eldest son.
25501
2550 > Three other sons.
2550j
1900l
. 1900
1900 SFive daughters.
1900 1 ^
1900j
200 Executor.
975 Charitable purposes.
25065
2. A man bom in the year 1797-— when will he be 38 years
of age ? ' Ans. 1835.
2^ A man lent his friend, at different times, these several sums,
viz: 12 dollars, 91 dollars, 513 dollars, 9 dollars, 100 dollars,
69 dollars, and 721 dollars — How much did he lend in all?
Ans. 1515.
4.' Bought a parcel of goods, for which I paid 147 dollars;
for pacbi^, 3 dollars; carriage, 14 dollars— What do these
goods stand me in ? Ans. 164.
5. A. has due to him, on bond, 2159 dollars; on book ac-
counts, 641 dollars; in sundry notes and due biUfi, 550 dol-
lars, and in cash, 850 dollars. Required the amount due to
him in all. Ans. 4200.
ABDITIOK. 18
6. A. of West Chester, owes to B. of Philadelphia, for
goods received in January, 112 dollars; for goods received in
April, 396 dollars; for goods received in July, 841 dollars;
for goods received in October, 176 dollars, I desire to know
He amount of the whole bill. Ans. d25.
7. A gentleman left his elder daughter 1200 dollars more
than the younger^ and her fortune was 6000 dollars— What
was the elder's fortune, and what did the falher leave them^
Ans. Elder's, 7200; father left them, 13200.
8. Thomas has 25 apples, James double that number, and
William as many as bom—How many have they all ?
Ans. 150.
9. An agent having been out with bills, brings home an
account that A. paid him seven dollars, B. ninetjr-one dollars,
C. sixty-four dollars, B. 79 dollars, £. twenty-six dollars, F.
ninety-nine dollars, G. two hundred and forty dollars, and
H. one hundred and eighty-nine dollars. I desire to know
the whole amount. Ans. 795.
10. There are two numbers, the least whereof is 96; their
difference 144— *W"hat is the greater number and sum of
both? Ans. 240 greater; 336 sum.
11. A farmer raised in one season three hundred bushels of
wheat, two hundred and sixty-five of rye, seven hundred and
twenty-eight of oats, three hundred and eighty-seven of com,
one hundred and twenty-four of buckwheat, and one hundred
and ninety-six of barley— How many bushels had he alto-
gether? Ans. 2000.
12. Purchased 11 yards of clolh for seventy dollars, 15 yards
of linen for nine dollars, 25 yards of silk for forty-seven dol-
lars, 100 yards of muslin for thirteen dollars, 20 yards of
cassinet for twenty-five dollars, and other goods to ttie amount
of one hundred and sixty -four dollars— What is the amount of
the whole ? Ans. 328.
18. If I buy, at one time, ^elve acres of land for 312
dollars; at another, five acres for 800 dollars; at a third,
seven acres for 210 dollars; at a fourth, nine acres for 198
dollars; at a fifth, six acres for 72 dollars; at a sixth, twelve
Acres for 836 dollars ; and expend for building, 4728 dollars
—How many acres have I, what is the cost of the land alone,
also the cost including the building ?
Ans. 49 acres ; 1422 cost of the land alone ; 7
6150 cost including the building. 5 J
-J
14
StJBTRAOTlOK«
14. A geBflemaiL had a senrice of pkte> which consisted of
d^teen dishes, weighing 10 pounds; forty plates, weighii^
23 pounds; three dozen spoons, weighing seven pounds; fiye
sidts and five pepper boxes, weighing 4 pounds; knives and
forks, weighing 5 pounds; threelarge cups, a tankard and a
mug, wei^ng 10 pounds ; a tea kettle, weighing 7 pounds ;
together with several other small articles, weighing 12 pounds.
I aesire to know the weight of the whole* Ans. 78.
SlTBTRACnOir OF IXTEGERS.
SuBTRAOTioK teaches to take a less number from a greater^
tuid shows the remainder or difference.
Rule.
Place the smaller quantity under the largep-^units under
units, tens under tens, &c.— as in addition ; then begin at th^
right hand figures, and if the under figure be less than the
tipper, take the difference and set it down; take each differ-*
«nce successively, but if any of the under figures be greater
than the upper, then take it from ten, and add the upp^r figure
to this difference, observing to add one to the next under
figure; and thus proceed to the end.
jProo/;— Add the remainder and less line together, and (if
right) the sum will be the same as the greater number.
From 764973
Take 143651
Exampk».
^276549
13762715
4917637943
4162791574
Rem. 622328
34513834
754836369
froof, 764973
75762915
147623
48276519
KfoOOOOO
9715843
4917627943
aooooooo
19999999
Application*
1. A horse in his harness is worth one hundred and forty
dollars; out of it, one hundred and fifteen dollars. I desire
to know how much the horse is worth more than the hameii*
StJBTRAOTXOV. S5
Dolls.
140 Value of the horse and harness.
115 Yahie of the horse akme.
25 Value <^ the harness alone*
115 Value of the horse.
25 Value of the harness.
90 Ans. The horse worth more than die httrness.
2. A man bom in the year 1797, what is his age in the
year 1837? ^ Ans. 40 yeani. ^
3. Wliat is the difference in the ages of a man bom in
1793, and another bom in 1823 ? Ans. 90 years.
4. A gentleman dying, left 5864 dollars between two daugh-
ters: the youngest was to have 2932 doUareh— What was the
elder's share P Ans. 23932.
6. The mariner's compass was invented about the year
1302— -How long has it been invented, counting to the year
1837? Ans. 533 years.
7. If a man have two thousand seven hundred and forty-
one acres of land, and sell one thousand nine hundred and
ninety-nine acres — how many acres has he left? Ans. 748.
8. If a man have, in cash, six thousand seven hundred and
twenty-five dollars, and pay sundry debts amounting to two
thousand two hundred and ninety-four dollars-— How much,
has he left? Ans. 4481 dollars.
9. Bought forty-five barrels of flour for two hundred and
seventy dollars, and sold twenty-one barrels for one hundred
and forty-seven dollars— How many barrels have I left, and
how much do they stand me in?
Ans. 24 barrels, and stand me in 128 dollars.
10. A's annual income is six hundred and twenty-five dol-
lars, and B's four hundred and seventy dollars— How much
is A's more than B's ? Ans. 155 dollars.
11. A. travels westward one thousand eight hundred and
thirty miles; B. sets out from the same place, and follows in
the same direction one thousand seven nundred and ninety-
seven mile&-*How many miles are they anart? Ans. 88.
12. Sold goods for seven hundred ana twenty-^even dol-
lars, which cost me eight hundred and fourteen doUarfr— How
many dollars did I lose by the sale? AikB,87.
16 ADDITION AND SUBTRACTION.
13. What is the difference between nine thousand, and nine
hundred? Ans. 8100.
14. America was discovered in the year 1492, by Christo-
pher Columbus ; and American Independence was declared
m 1776. I wish to know the number of years between these
two events. Ans. 284.
15. A vintner bought 31 pipes of brandy, containing 3746
gallons ; and sold 19 pipes, containing 2294 gallons — How
many pipes and gallons were left ? Ans. 12 pipes, 1452 gals.
16. It is said that on the 19th day of June, 1835, a tor-
nado passed near Gravel Hill, Warren county. New Jersey,
which prostrated all the apple trees, in an orchard containing
three hundred trees, except four or five. I desire to know
how many there were prostrated. Ans. 295 or 296.
ADDITION AND SUBTRACTIOJr.
1. A tradesman, happening to fail in business, called all
his creditors together, and found he owed to A. 75 dollars, to
B. 140 dollars, to C. 64 dollars, to D. 95 dollars, to E. 72
dollars, to F. 27 dollars, to G* 55 dollars, and to H. 92 dol-
lars. His creditors found the value of his stock to be two
hundred dollars; recoverable book debts, 112 dollars; besides
money on hand, 134 dollars. I desire to know whether they
were gainers or losers, and how much?
Dolls. Dolls.
Value of stock, 200
Book debts, 112
Money, 134
446
Owing to A.
75
ToB.
140
ToC.
64
ToD.
95
ToE.
79
To P.
37
ToG.
55
ToH.
92
Whole am't of debt, 620
Am't of his effects, 446
Creditors lose, 174 Answer,
ADDITIOV AND SUBTRACTION. 17
2. A man setting out on a journey of 976 milea, travels the
first daj 52 miles ; the second, 50 miles; the third, 61 miles.;
the fourth, 49 miles; the fifth, 56 miles; the sixth, seventh,
eij^thy ninth and tenth dajs, each, 55 milea^-^ew far is he
from his journey's end ? Ans. 433 miles.
3. A merchant, at his outsetting in trade, owed 1200 dol-
lars: he had in cash, 600 dollars; good debts, 1150 dollars:
he cleared the first year, by commerce, 1000 dollars— What
is the neat balance at the twelve months' end ?
Ans. 1550 dollars.
4. A farmer has 5 granaries of wheat, containing 576
bushels : one contains 104 bushels ; anodier, 79 bushels ; a
tiiird, 85 bushels; a fourth, 159 bushels-— How many bushels
does the fifth contain ? Ans. 149.
5. Sent a servant to market to purchase vegetables : he laid
out for radishes, 12 cents ; for onicms, 9 cents ; for asparagus,
16 cents'; for potatoes, 14 cents, and for lettuce, 19 cents-
How much change should he return, 90 cents being the amount
he took with him ? Ans. 20 cents.
6. A farm of one hundred acres is divided, as follows, viz :
12 acres of wheat, 5 of rye, 17 of corn, 16 of oats, 1 of po-
tatoes, 16 of ^88, 12 of barley, 1 of flax; the orchard, gar-
den and buil^ngs, occupy 16 acres; the remainder is wood-
land—How much is there of it ? Ans. 4 acres.
7. Bought of A. 1000 bushels oats; of B. twice as much:
of which were sold to C. 500 bushels; to D. twice as much,
and to E« as much as to them both— How much have I on
hand? Ans. None.
8. A gentleman, having a farm of one hundred and ten
acres> purchased one adjoining, containing one hundred and
fifty-seven acres ; which at his decease he bequeathed to his
Ihree son»— to Thomas, seventy-five acres ; to Edmund, ninety-
eight acres, and the remainder to Gilbert— How many acrea
fell to Gilbert's share ? Ans. 94,
MULTIFLICATIOir OF INTEGERS.
Multiplication is the multiplying of any two numbers toge-
ther, and compendiously performs the office of many additions.
To this rule belong tiiree principal members, viz:
1. The multiplicand, or number to be multiplied;
2. The multi|dier, or number to multiply by;
8. The product, or number produced by multiplying*
Rule.
Set down the multiplicand, place the multiplier under it»
and draw a line under tiiem. Tftien besin with the right hand
figure, and witii it multijdy the unit figure in the multipli-
cand; set down its product; proceed in this way with each
figure ; but if eitiier of the products be ten or more, set down
only the number expressed by its right hand figure, and add
the number exjH'essed by its left hand figure or figures to the
product of the next figure ; and so continue to the last, where
the whole product must be set down. The multiplicand and
multiplier are called factors.
P'^oof. — ^Multiplication may be proved by inverting the fac-
tors. There is however a more compendious, but less accu-
rate mode, that is, by casting out the nines from the multi-
plicand and multiplier, the remainders put on each side of a
cross ; multiply the figures on each side together, cast the
nines from the product, and put the overplus at top; then cast
out the nines from the product of the multiplication, and
place its remainder at the bottom of the cross ; if it be the
same as the top, tiie work is supposed to be right* But the
former mode is the surest.
MULTIPLICATION TABLE.
Twice
3 times |
4 times
5 times
6 times |
7 times
)
1 are
2
1 are
3
*1 are
4
1 are
1 5
1 are
6
1 are 7
2
4
2
6
2
8
2
10
2
12
2 14
3
6
3
9
3
12
3
15
3
18
3 21
4
8
4
12
4
16
4
20
4
24
4 28
5
10
5
15
5
20
5
25
5
30
5 35
6
12
6
18
6
24
6
30
6
36
6 42
7
14
7
21
7
28
7
35
7
42
7 49
8
16
8
24
8
82
8
40
8
48
8 56
9
18
9
27
9
86
9
45
9
54
9 63
10
20
10
30
10
40
10
50
10
60
10 70
11
22
11
33
11
44
11
55
11
66
U 77
12
24
12
86
12
48
12
60
12
72
12 84
MULTIPUOATIOtf*
19
MdtipKeaiim TaUe^Ckmtinued.
|B times
9 times
10 times
11 times
12 times 1
1 lare
8
1 are
9
1 are
10
lare
11
1 are
19
h
10
2
18
2
90
2
22
2
24
8
24
3
37
3
80
8
83
8
36
4
33
4
36
4
40
4
44
4
48
5
40
5
45
5
60
5
55
5
60
6
48
6
54
6
60
6
66
6
72
7
56
7
63
7
70
7
71
7
84
8
64
8
72
8
80
8
88
8
96
9
72
9
81
9
90
9
99
9
108
10
80
10
90
10
100
10
110
10
120
11
8811
99
11
110
11
121
11
132
12
9612
106
12
120
12
132
12
144
I. Multiply 97627354 by 9-
Thus, 97637354
9
878646186
Explanation^ — ^Here I say 9 times 4 are 36 : I put down
6 and carry 3; saying 9 times 5 are 45, and 8^ that I carried,
make 48: I put down 8 and carry 4; then I say 9 times 3
are 27, and 4, that I carried, make 31 : I put down 1 and
carry 3; I tiien say 9 times 7 are 63, and 3, that I carried^
are 66; I put down 6 and carry 6; then I say 9 times 2
are 18, and 6, that I carried, are 24: I put down 4 and carry
12; tiien I say 9 times 6 are 54, and 2, that I carried, make
56: I put down 6 and carry 5; then I say 9 times 7 are 63»
and 5, that I carried, make 68: I put down 8 and carry 6; I
then say 9 times 9 are 81, and 6, that I carried^ male 87:
and here I set down the full product.
2. Multiply 123422 by 12.
Thus, 123423
12
1481064
Proofs by the cross, and explanation :
v^'
I commeace witii the right hand figure of tiie multiplicand,
ud say 9 and 2 are 4» and 4 are 8, and 8 are 11. 1 cast ft
20
MULTIPLICATION-.
from this, and 2 arc left, which I add to the two remaining
fibres, which makes five. I set down this on the left hand
of the cross ; then I add together the figures in the multiplier,
and find they amount to only 3. I put this down on the r^ht
hand of the cross. I then multiply these two figures together,
Aaying 3 times 5 are 15. I cast 9 from this, and 6 are left :
I put this down at the top of the cross. Then I add the
figures of the product, thus^-*-! say 4 and 6 are 10; I cast 9
from this, and 1 is left. I then say 1 and 1 are 2, and 8 are
10 : here I cast away 9 again, and 1 is left. I then say 1 and
4 are 5, and 1 are 6, which is the same as the top figure-— the
work is, therefore, presumed to be right.
41232314
2
Examples.
71536714
3
15976273845
4
82464628
319567843
5
214610142
719629735
6
63905095380
51483726791
7
9762971543
8
71479627951
9
8271468974
10
7627915435
11
271541793
12
7154276
12
When the multiplier is more than 12, and less than 20,
multiply by the unit figure of the multiplier, adding to the
product the back figure to that jou multiplied.
981573214 271876297 3715427143
13 14 15
12760451782
7962971485
16
719782154
17
5143715471
Id
MULTIPUCATIOK.
21
When there are several figures in the multiplier, there must
be as many products as figures in the maltiplie]>— observing
to place the first figure of every product under the figure vou
muldply by. Add the several products together, and tueir
sum will be the total product.
L Multiply 4917678291 by 547964.
Thus, 4917678291 Multiplicand.
547964 MultipUer.
19670713164
29506069746
44259104619
34423748037
19670713164
34588391455
2604710667049524 Product
2. Multiply 25362 by
3.
13. Product,
5127 by 19.
71526 by 25.
194 by 47.
5372 by 75.
958 by 93.
15927 by 104.
795 by 195.
67 by 241.
1005 by 376.
957 by 579.
2007 by 1008.
99999 by 9999,
When ciphers occur between the significant figures in the mul-
tiplier, they may be omitted in the operation ; but great care must
be taken that the next figure must be as many fimires farther
to the left hand, that is, under the figure you multiply by.
1. Multiply 400908 by 60008.
Thus, 400908 Multiplicand.
60008 Multiplier.
3207264
2405448
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
«c
c«
t«
c<
<c
cr
it
€€
t€
CI
29706.
97413.
1788150.
9118.
402900.
89094.
1656408.
155025.
16147.
377880.
554103.
2023056.
999890001.
24057687264 Product.
22
MutnniioATioir.
2. Mtdtiplj 51438 bj 906. Fro^ct. 105941«8.
8.
4.
5.
a
7.
8.
9.
10.
11.
12.
€€
t4
«C
t(
U
€€
6147 by 5007-
52764 bj 1006.
1375 by 3005.
317405 by 2104.
87196 by 10005.
157928 by 9003.
7184276 by 104.
51439 by 2009.
218743 by 7003.
30778029.
53080584.
4131875.
457420120.
872145980.
316329784.
747164704.
103340951.
1531857229.
969768694.
1597642 by 607.
When there are ciphers at the end of the multiplicand or
multiplier, they may be omitted in tiie operation. Multiply
by the rest of the figures, and set down the right hand of the
total product as many ciphers as were omitted.
1. Multiply 39400 by 672000.
Thus, 39400 Multiplicand.
672000 Multiplier.
M.
788
2758
2364
• ^ —
26476800000
% Maliiplj 9400 bj 130.
3.
A.
5.
6.
7.
8.
9.
M
(C
•C
CC
M
18000 by 4500.
4100 by 1530.
810 by 98000.
5400 by 6500.
21500 by 7200.
70500 by 460.
Product.
Product,
1322000.
58500000.
6273000.
80380000.
35100000.
154800000.
83430000.
1960000.
49000 by 40.
When the multiplier is the exact product of two factors in the
multiplication table, then multiply by one of those factors ; and
Ihat product, multiplied by the other factor,wUl give the answer.
. 1. Multiply 4793 by 42.
Thus, 4798
7 X 6 «s 43.
88551
6
901306 Product
Producti
, 93492.
«
131691.
<c
18288.
<c
346969.
«c
166144.
«
17244.
«
59640.
cc
24068.
(C
148446.
re
126784.
«
1S66936.
<c
774252.
<«
33759.
<f
S19744.
xviTonjcATioir* S3
% Mollify 6194 bj 18.
3. " 6271 by 21.
4. " 762 by 24.
6. « 9147 by 27.
6. " 5292 by 82.
7. ** 479 by 36.
8. « 1420 by ^
9. *• 547 by 44.
10. " 2749 by 54.
11. «• 1981 by 64.
12. " 21763 by 72.
13. " 7169 by 168. .
14. " 279 by 121.
15. *' 1526 by 144.
^ppKeaiion.
1. What sam must be divided among 12 mm, so ibat each
man may receiye 27 dollars ?
Dels.
27
12
324 Answen
2. A tradesman gave to his daughter, as a marriage portioD»
a scrutoire, in which were 12 drawers; in each drawer were
4 divisions ; in each division were 10 purses ; in each pnrse
SO dollars— How much had she to her tortune ?
12 Drawers.
4
^■^ •
48 Divisions.
10
480 Purses.
SO
24000 Dollars.
8. What will 97 cords of wood come to at S dollars per
cord. Ans. 135 dolls.
4. What is the product of 6742 multiplied by 241 ?
Ans. 1624892.
94 * JIBDITION, SUBTRACTION AND MULTIPLICATIOXJ
& Suppose 25 men were concerned in the payment of a
debt> ana each man paid 547 dollars—How much was the
debt ? Ans. 13675 dolls.
6. Admit an orchard consisting of 41 trees one way, and
37 the other — ^How many trees in said orchard ? Ans. 1517,
7. Bought 16 bales of linen ; in each bale 43 pieces ; in
each piece 19 yards — ^How many pieces and yards were
therein ? Ans. 688 pieces ; 13072 yard^.
8. A quantity of rails was hauled at 96 loads ; each load
104 rails— How many were there ? Ans. 9984.
AIXDinOir, SUBTRACTION AND MUIiTTPUE-
CATION.
1. The less of two numbers is 45; their difference 16. If
28 times 98 be subtracted from the product, how many are
left?
45 Less number. 98
16 Difference. 28
61 Greater number. 784
45 Less number. 196
305 2744
244
2745 Product.
2744 Product of 28 times 98.
1 Answer.
2. In an army, consisting of 84 squadrons of horse, each
131 men; and 112 battalions, each 798 men — How many
effective soldiers, supposing that in 5 hospitals there are 380
sick? Ans. 100000.
3. A gentleman, at his decease, left his widow 3000 dollars.
He bequeathed 405 dollars to each of his four nephews; 375
dollars to each of his fiv^ nieces ; to 7 poor families 75 dollars
each ; and to his executor 305 dollars. Now, on the sale of
his effects, the amount received was found insuflScient to an-
swer these legacies, by 100 dollars— What sum must he have
been possessed of at the time of his death ? Ans. 7225 dolls.
DmSIOX OF IXTEGERfii
toivisroN teaches to find how often one number id contained
in another, or to divide any number into i(irhat parts you choose.
It consists of four parts, viz :
1st, The dividend, or number to be divided ;
2d, The divisor, or number to divide by;
3d, The quotient, or number sought ;
4th, The remainder^ if any, which must be less than the
divisor.
SHOUT DIVISION.
SfioRT Division is that in which the divisor doeB^ not ex*
Ceed 12.
Fitkd how often the first figure or figures contains the divi-
sor, under which place the result 2 the remainder (if any)
conceive to be prefixed to the next figure. Find how often
these contain the divisor, and so proceed.
Proo/*rf— Multiply the divi«or and quotient together, adding
the remainder, if any; and the product will be the same aa
the dividend.
JExumpIes^
Divisor, 2)24862 3)712194 4)61278940
Quotient, 12431
2
237398
3
Proof, 24862 712194
5)7129714 6)3213645
1531973S
4
61278940
7)9827931
8)8271984 9)71589743 10)19762754
11)21796871 13)32719654 12)71962715
^F"*"*"
If any two numbers, being multiplied t<^ther, are exactly,
equal to the divisor, then, by diTidW the dividend by one oi
»kd numbers, and that quotient by ^e other number, it wiU
526 DIVISION.
gave the quotient required. But as it sometimes happens that
&ere 13 a remainder to each of the quotients, and neither of
them the true one, therefore, to find the true remainder, mul*
-dply the first divisor bj the last remainder ; to that product
aod the first remainder, which will give the true one*
I. Diride 9337 bj 108.
Here 12 X 9 = 108
Then, 9)9327
12)1036 + 3
86+4
Here is 3 for the first remainder, and 4 for the second ;
then say 9 times 4 are 36, and 3 are 39, the true remainder.
% Divide 9438 bj 24. Quotient, 393, Remainder, 6.
3. " 617 by 32. " 19, " 9.
4. " 7948 by 42. " 189, « 10.
5. " 19762 by 56. " 352, ** 50.
6. " 21958 by 60. " 865, •* 58.
• 7. " 9872 by 70. " 141, " 2.
8. " 719623 by 84. " 8566, " 79.
9. " 217167 by 110. " 1974, " 27.
10. " 718325 by 121. « 5936, « 69.
11. « 627196 by 144. « 4356, « 76.
LONG DIVISION.
Long division is that wherein the divisor exceeds 12.^
Rule.
For the first dividual take as many of the first figures of
the dividend as will contain the divisor : seek how often the
divisor is contained therein. Set the result down for the first
quotient figure ; multiply this fiigure into the'divisor ; subtract
the product from the dividual ; annex the next figure of the
dividend to this remainder, wMch will be the secon4 dividual
^-Hmd so proceed until all the figurea are used*
Pro(/-r-As ia Short Division.
EsNumples.
1- Divide 6197348 by 191.
Thus, 191)6197348(93446 Quotiettt,
573
467
3%
853
764
894
764
1308
1146
162 Remainder.
a. Divide 6471235*27 by 4792753, Quot 1390, Bern. 10189^}?.
3. •< 71826 by 964- " 74, •* 48Q.
4. « 2197163 by 7612- *' 288, " 4907.
5. « 574315 by 214a ^' 267, '* 799.
6. " 7162769 by 76. '* 94246, *' 78.
7. « 543795 by 987- ''^ 560, « 945.
8. •• , 6437 by 2003. '* 3, " 428,
9. « 9999 by 99. ** 101.
When there are one or more ciphers on the right of the
dirisor, omit them in the operatioin, separating fiHDm the right
of the dividend as many figures, vrhicn must be annexed to
the remainder-
1. Divide 76420000 by 9500.
Thus, 95,00)764200,00(8044 Quotient.
760
420
380
400
380
2000 Remainder.
28' DECIMAL FRACnONS.
2. Divide 742186 by 61000. Quotient 12, Remainder 10186-
2. « 9162 by 140. " 65, " &L
4. " 7436 by 570. " 13, " 26.
5. •' 98271 by 1600. " 61, " 671,
6. " 47219 by 45000. « , 1, " 2219.
nSpplication,
1. Sold 93 acres of land, for 2883 dollars — How many drf-
lars was It per acre ? Ans, 31.
Dolls.
93)2883(31 Answer.
279
93
93
2. Bought 19 cords of wood, for 57 dollars — What was it
per cord ? " Ans. 3 dolls.
3. How many barrels of flour can I buy for 594 dollars, at
6 dollars abarrel P Ans. 99.
.4. If 27 men have 648 dollars, what is it a piece ?
Ans. 24 dolls.
. 5. Sold a quantity of hay for 143 dollars, at 11 dollars per
ton : I desire to know how many tons there were ? Ans. 13L
6. If a, man spend 216 dollars in a year, what is it per
month P Ans. 18 dells^
7. A gentleman has a garden, containing 9600 square feet ;
the breadth is 80 feet — What is the length P Ans. 120 feet
8. What is the value of one thousand shinies, when 25
thousand are sold for 200 dollars P Ans. 8 doll&
9. A prize of 5184 dollars is to be divided equally amoi^
432 sailors — What is each man's share ? Ans. 12 dolls.
10. Divide 75 dollars equally between Tom, Dick and
Harry, and tell each one's share ? Ans. 25 doUsL
11. Sold 14 hundred weight of bacon, for 84 dollars : I de-
sire to know how much it was per hundred P Ans. 6 dolls*
DECIMAL FRACTIONS.
A DECIMAL FRACTION is a pact or parts of a unit, varies in
the same proportion, and is mimagea by the same method of
. DEGIBIAL 71U.CTIOVS. ' 29
foperatioii, ad a whole number : it is denoted by a point pre*
fixed to a figure or figures^ thus, .7, .78, .789. "Aie nrst figure
, denotes so many tenths of a unit ; the second, so many hnn-
^^ths of a unit ; the third, so many thousandths of a umt.
And as whole numbers, reckoned from ri^ht to left, increase -
in a tenfold proportion, so decimals, reckoned firom left to
right, decrease in a tenfold proportion : thus, «7 = ^even-
tenths ; .07 = seyen-hundredms ; .007 ^=^ seven-thousandths.
Ciphers annexed to decimals, neither increase nor decrease
their value : thus, .7000 and .7 are equal.
ADDITION OF DECIMALS,
Rule*
Place the numbers according to their value, viz : units un-
der units, tenths under tenths, &c. : then b^n at the right
hand, and add them up as in addition of integers* Be care-
ful to put the point in the sum total exactly iind^r those in
th^ example.
Acres. Dollars.
27.1 971.125
19.62 12.16
3.147 109.007
15.0274 16.1146
64.546 243.12
17.4 96.143
146.8404 1447.6695
iVb^6.— Cents are decimal parts of a dollar.
Application.
1. Borrowed at one time 574 dollars ; at another, sixty dol-
lars and ninety-seven ^ent^; at a third, eighty-seven cents.
What sum did I borrow in all ?
Dolls.
. 574.
60.97
.87
635.84 Answen
9L Add S74| 03.T41» 64.104, 54814. toe^tii^r, and tell the
ftmoUnt Ans. 2M.6364»
30 3S0IMAL PRAOTIOvMS.
SUBTRACHON OF DECIMAI^.
Place fee numbers as in addition^ with the less under the
greater* Begin at the right hand, and subtract as in integers ;
and set the point in flie remainder directly under those in the
example.
Examples,
Dolls* Yards. Acres.
From 513.49 126.4974 576.159
Take 27.16 17.143 31.27843
486.33 109.3544 544.88057
1. From 70.41 take 16.4®, and tell what is left.
Ans. 53.99.
2. Borrowed twt) hundred dollars, and paid one hundred
ignd eighty-seven dollars and sixty-four cents— How much do
1 yet owe ? Ans. 12.36 dolls,
3. Deposited in bank one thousand dollars; and having
drawn checks to the amount of six hundred and twenty dol-
lars and sevaity-'four cents— I demand what sum I have in
bank. Ans. 379.26 dolls.
MULTIPLICATION OF DECIMALS.
Rule.
Place the bgij9t$, and multiply them as in whole numbers ;
and from the product towards the right ha»d cut off as many
places for deeanate as there are in both factors together ; but
if there should not be so mitny places m the product^ supply
the defect with ciphers to tiie kit hand.
Exionfies,
1. Miiiii^yfiA82a714275 by .i28&
Thus, 54328.716275
4235
271643581379
16298614SS25
108657432550
5482S716275
69Q0.5O6459O639 Prodttct
BEOTHAX. T&ACTtOnB.
^
3. MttH'j 89.6785 bj 93.6 ProdH, 9673.7661
3.
4.
&
6.
7.
8.
9.
10.
it
t<
H
K
<«
((
etc
<«
.S1789 by
.785898 by
by
by
by
by
by
.7
.32
1.47
.07
2.31
.0005
.4182
105.4876
.12
.11
.3
.1436
.0024
by 00004.
.181145548
82.84ST5006ffi
.064
.0352
•441
!oi0052
.005544
.00000002
DIVISION OF DECIMALS.
Division of decimals is also worked as whole numbers : tho
only difficulty is in valuing the quotient, which is done by the
following
Rule.
When the dividend has not as many decimal places as the
divisor, or will not contain it, annex ciphers to supply the
defect ; then divide as in integers. The first figure in the
quotient will be of the same value with that figure of the divi-
dend which answers or stands over the place of units in the
diviftor : the quotieikt will also have so many decimal pl&ceft
as Uie dividend has more than the divisor.
Examples.
1, Divide 71623.5127169 by 2315.4169.
Thus, 2315.4169)71623.5127169(30.933
69462 507
Quotient.
2161.00571
2083 87521
77 130506
m 462507
76679999
6946^507
.7217492 ftemainder.
Here the ten's igure in the dividend stands over the unit's
figure of ^e divisor; therefore the first figure of the qub^ien)'
is a ten's figure, or the quotient may be valued by the latter
^art of the rule, vis \ there ate seven decimal figured in th^
3B DECIMAL FR/LOTIOirS.
dividend, and four in the divisor ; there are then three more
decimal figures in the dividend than the divisor, and therefore
there must be three decimal figures in the quotient*
^he last figure of the remainder is of the same value with
the last figure of the dividend.
2. Divide 42.1615 by 12.04.
Thus, 12.04)42.1615(3.50it Quotient.
3612
6041
6020
2150
1204
9460
8428
•001032
Herei in tiie third place, the dividual did not coiltain the
divisor, and a cipher was annexed, as was also the case in the
fourth place. When cases of this kind occur, the ciphers
annexea must be counted with those contained in the dividend,
and the quotient valued accordingly.
5. Divide 71.429 by 1.716. Quot. 41.625, Rem. XK)05
4. " 8.2533 by 6.71
6. " 28 by 112.
6. " 5 by .5
7. " .5 by 5.
8. « 25 by .5
9. •' 5 by .25
10. " .412335 by 539
When numbers are to be divided by 10, 100, 1000, 10000,
&c., it is performed by placing the separating point in the
dividend so many places towutis the left hand as there are
cijdiers in the divisor.
Thus, 6791 -^ 10 »^ 679.1 5443 -»- 100 «t 54.48
•746.31 -h 1000 «- 9.74091 11ri48»3 ^ 10000 - 1.71489
1.23
.25
.1
.1
50
20
.000765.
lUBIHJCTION.
REDUCTION teaches to reduce money, weights, measures,
&c., from one denomination to another, without changing the
value. When greater names are to be brought to less, it is
called Reduction descendine ; but when less names are to be
brought into greater, it is cdled Reduction ascending.
Rule*
When greater names are to be brought to less, multiply by
as many of the less as make one of the greater denomination,
adding into the product the numbers of the less, if any. But
-when less names are to be brought into greater, divide by as
many of the less as make one of the greater denomination.
s WEIGHTS AND MEASURES.
The following act, it is presumed, will not be amiss in this
place.
AN ACT
To fix the Standards and Denominations of Measures and
Weights in the Commonwealth of Pennsylvania.
Section 1. Be it enacted by the Senate and House of R«r
presentatives of the Commonwealth of Pennsylvania, in (xene-
ral Assembly met, and it is hereby enacted by the authoritv
of the same. That the standard unit of all measures of length
liiall be the yard, to conform to that in use in this Common-
wealth at the date of the Declaration of Independence, the
positive standard to be obtained as hereinafter described ; and
that one-third of said yard shall be one foot^ and that one-
twelfth of said foot shall be one inch.
Section % The standard of liquid measure shall be the
gsdlon, to contain two hundred and thirty-one cubic inches,
of the standard aforesaid, and no more ; and that the standard
of dry measure shall be the bushel, to contain two thousand
ooe hundred and fifty cubic inches and forty-two-hundredtha
of a cubic inch, of the standard aforesaid, and no more.
Sef^ion 3. The standard weight shall be a pound, to be
computed upon the Troy pound of the mmt of the Uiuted
States, referkd to in the act of Congresftof ike ^^^^^1^ rf
May, one thousand eight hundred and twenty-eight,, to ^^^^
34 rbduotipkJ
the Troy pound of this CommoBwealik shall be equal to the
Troy pound of the mint aforesaid ; and the avoirdupois pound
of this Commonwealth shall be greater than the Troy pound
aforesaid, in the proportion of seven thousand to five thousand
seven hundred and sixty.
Section 4. It shall be the duty of the Governor of this Com-
monwealth, to procure, within three y^ars from the date (rif
the passage of this act, a standard yard, to constitute the posi^
tive standard of lengtli in this Commonwealth; said standard
to be equal in length, at the temperature of melting ice, to the
distance between the eleventh and forty-seventh inches on a
certain brass scale of eighty -two inches in length, procured
for the survey of the coast of the United States, and now de-
posited in the Wat Department : the material of said standard
to be brass, and me divisions upon it to be inches and parts
of an inch, of the brass scale aforesaid.
Section 5. It shall be the duty of the Governor, to procure,
within three years after the passage of this act, for the use of
this Commonwealth, a standard gallon and bushel, to conform
to the provision of section second of this act : the material of
said standard to be of cast brass.
Section 0. It shall be the duty of the Governor of this Com-
monwealth, to procure, within three years after the passage
of this act, a duly authenticated copy of the Troy pound of
the mint of the United States, to constitute the positive stand-
ard of weight of this Commonwealth : the material of said
standard to be brass.
Section 7. It shall be the duty of the Governor of this Com-
monwealth, to have the positive standards of measures of
length and capacity, and of weight, provided by the foregoing
sections, inclosed in suitable cases, and deposited in the office
of the Secretary of the Commonwealtii, to be by him there
carefully preserved.
Section 8. It shall be lawful for the Governor of this Com-
monwealth, when he shall deem it expedient, to have tested
the conformilj of said positive standards of measure and
weight to the foregoing provisions of this act, or to the natural
invariable standards hereinafter provided ; and if Congress
shall, at any time hereafter, establish standards of weight and
measure, the standards aforesaid shall be tnkde to cwifovtA
thereto*
SBCtion 9* It shall be ihe duly of the Qovemor, to pttmde»
\^ithhi three years after Ihe passage of this act, for each of the
counties of mis Commonwealth, at the charge of the counties
respectively, positive standards of measures of length, of ca-
pacity, and of weight, of the several denominations in com-
mon use, or such of them as may be necessary for the accu-
rate and convenient adjustment of weights and measures;
said standards to be of approved construction, carefully com-
pared with the State standards aforesaid, and madB of the
same material: and, having caused the same to be duly
stamped, to have them delivered to the Commissioners of the
counties respectively, to be used as standards for the adjusting
of weights and measures, and for no other purpose.
Section 10. It shall be the duty of the Commissioners of
the respective counties, at least once in every ten years, and
oftener if they have reason to believe it necessary, to cause
the standards of the respective county to be examined and
tried, and, if necessary, to be corrected or renewed, according
to the standards of the Comnionwealth, heretofore referred to.
Section 11. It shall be the duty of the Governor, within
ten years after the passage of this act, to cause the positive
standards, herein described, to be referred to natural invaria-
ble standards, and to deposit, in the office of the Secretary
of the Commonwealth, the authentic certificates of such refe-
rence, with the apparatus t>y which it was made : the length
of the standard yard to be compared with that of the pencra-
lum vibrating seconds, at a certain and defined Spot in the
Indep^sdence square, in the city of Philadelphia, or in some
unalienable public property, at an ascertained and conveni^t
temperature and pressure — all the circumstances of the ooin-
parison to be stated ; the standard of weight to be compared
with that of one hundred standard cubic inches of water, at ita
maximum density, and at a convenient atmospheric pressure^
Section 12. The denomination of linear measure of this^
Commonwea^lth, whereof the yard as heretofore provided is the
standard unit, with the relations thereof, shall be as follows &
Twelve inches make one foot;
Three feet make one yard ;
Five and a half yards make one rod, pole or perch j
Fwty pdds make one furlong;
fiig^t j&uioiigB mskke one miu»
M ■ HEDUCTIOV'
Section 13« The denominations of superficial measure of
this Commonwealth, whereof the square of the linear jard, as
heretofore provided, is the standard unit, with the' relations
to said standard and to each other, shall be —
Thirty and one-fourth square yards make one pole or perch »
Forty square poles make one rood ;
Four square roods make one acre ;
Six hundred and forty acres make one square mile*
Section 14. The denominations of liquid measure of this
Commonwealth, whereof the gallon, as heretofore provided, is
the standard unit, with the relations to said unit and to each
other, shall be—
Four gills make one pint ;
Two pints make one quart ;
Four quarts make one gallon ;
Thirty -one and a half eallons make one barrel ;
Two barrels make one hogshead ;
Two hogsheads make one pipe ;
Two pipes make one tun.
Section 15. The denominations of dry measure of this Com-
monwealth, whereof the bushel, as heretofore provided, is the
standard unit, with the relations to said standard and to eadi
other, shall be —
Four pecks make one bushel ;
And the minor divisions of the peck shall be its aliquot parts :
Provided, That the form of the dry measure shall be conical ;
-fliat tiie diameter of the circle of the top of the measure shall
he not less than one-twentieth greater than the diameter of
the bottom of the measure, and the height not more than nine-
twelfths the diameter of the bottom.
Section 16. The denominations of weight of this Common-
vealth, whereof the Troy pound, as heretofore provided, is
the standard unit, with the relations thereof to the said stand-
wd and to each other, shall be —
Twenty -fou;r grains make one pennyweight;
Twenty pennyweights make one ounce ;
Twelve ounces msS^e one pound.
Section 17- The denominations of weight of this Common^
vealth, whereof the poundayoirdupoisi as heretofore proyided^
RSDUCTIOy.
37
is the standard unit, with the relations to said pound and to
each other, shall be —
Sixteen drams make one ounce ;
Sixteen ounces make one pound i
Twenty-five pounds make one quarter ;
Four quarters make one hundred ;
Twenty hundred make one ton.
WILLIAM PATTERSON,
Speaker of the House of Representatives*
JACOB KERN,
Speaker of the Senate.
Approved — The fifteenth day of April, Anno Domini,
eighteen hundred and thirty -four.
GEO: WOLF.
LONG MEASURE.
Long measure is used for measuring lengths or distances—*
the denominations, degree, league, mile, furlong, pole, fathom,
yard, foot, hand, and ];&ch.
4 Inches - - equal
12 Inches
3 Feet
6 Feet
5*5 Yards -^
40 Poles or 220 yards,
8 Furlongs or 1760 yds. "
3 Miles - -
60 Geographic, or>
(t
it
ft
c<
C(
s«
<(
1
1
1
1
1
1
1
1
hand,* marked h.
ft.
fm.
foot
yard,
fathom*
pole,
furlong,
mile,
league,*
69.5 Statute miles
360 Degrees -
fur*
m.
1.
deg.
1 degree,
the circumference of
the earth.
Distances are also measured by a four pole chain, yis:
7.92 Inches equal 1 link, marked 1.
100 Links " 1 chain, « ch.
80 Chains " 1 mile, " oi.
* Hand, is a term used in measuring the height of homes ; fathom^ the
cTfpth of water ; and a league, distance at aea.
98 BJH^VOTXOK.
Tlie American mile - - equids 5380 feet.
5328 "
5566 «
7920 "
26400 "
21120 "
French, "
Italian,
Scotch,
German,
Dutch, Spanish or Polish,
»
Indian mile, about three American.
1. Required the earth's circumference in inches.
Degrees.
360
69.5
1800
mm
2160
25020.0 Miles.
8
200160 Furlongs,
220
40032
40032
44035200 Yards.
3
132105600 Feet.
12
1585267200 Inches.
% In 56231427800 inches, how many miles ?
12)56231427800
3)4685952316 + 8
11)1561984105 + 1
220
r 11
1.
0)14199855,5
8)7099927 + 15, and 15 X 11 « 165
887490 + 7
Whence <he answer is, 887490 miles^ 7 furlongs, 165 yards,
1 foot, 8 inches*
HfiOUCTlOK*
>3. Reduce 546 miles to inches* Ana*
4> In 3 miles, how. many chains P Ans.
5* In 165 yards, how many poles? Ans»
6* Reduce 149 miles to furlongs. Ans.
7. Bring 571 furltonga to yards. Ans.
8. In 64 poles, how many yards P Ans.
9* Reduce 17 miles 6 furl'gs to furlongs. Ans.
d45e4»ediaches.
240 chains.
30 poles.
1192 furl's.
125620 yards.
352 yards.
142 furl's.
LAND MEASURE, OR SQUARE MEASURE.
Land (or square) Measure is used for finding the contents
of land and other surfaces, and has respect to length and
breadth. The denotninations are, mile, acre, rood, square
perch, square yard, square foot, and square inch.
144 Square inches - - equal 1 square fdot, ft.
9 Square feet
30.25 Square yards
40 Square perches
4 Roods, or 160 square perches,
640 Acres - - - -
10 Square chains
6400 Square chains
1. In 47 acres, 2 toods, 17 perches, how many perches P
A* R. Jr.
47 2 17
4
1 square yard, yd.
1 square perch, P.
1 rood, R.
1 acre, A.
1 mile, M.
1 acre.
1 mile.
190
40
7617
2, One square mile is called a section of land— How many
perches are there in 4 sections ?
4 Sections.
640
2560 Acres.
4
10240 Roods.
40
409600 Perches:
'
40 ftEDUCTIOK«
3. In 74fi2 perches, how many acres?
Ans. 46 A., 2 R., 22 P.
4. A tract of land contains 11740 perches— required the.
content in acres. Ans. 73 A., 1 R., 20 P.
5. In 51 A. 2 R. 39 P., how many perches ? Ans. 8279.
LIQUID MEASURE,
Liquid measure is used for beer, cider, wine, &c. [See
section fourteenth of the preceding act of Assembly.]
1. Reduce 7 hhds. 15 galls. 3 qts. of wine to gills.
Hhds. Galls. Qts. o
7 15 3
63
456
4
1821'
2
V
3654
4
-
14616
Answer.
3.
In 20048 gills, how many hogsheads ?
Gills.
4)20048
2)5012
4)2506 .
63-
■ 7)626 + 2
9)89 + 3
9 +8and7 X8 + 3=* 59.
Whence the answer is 9 hhds. 59 galls. 2 quarts^
3. In 16 barrels of beer, how many pints ? Ans. 4082.
4< Reduce 18 hhds. 1 barrel of wine, to gills^ Ans. 37296*
^KDUOTIOM. 41
5. How many gallons in 38 biuTels of l>eer P Ans. 883.
6. Bring 12 hhds. 1 barrel, to pints. Ana. 6800.
7. Reduce 19 bhds. 1 barrel, 1 gal. 1 ptl^to gills.
Ans. 39348.
DRY MEASURE.
This measure is used for dry goods. The Winchester
bushel is of a cylindrical form, 18.5 inches in diameter and 8
inches deep, and contains 2150*4252 cubical inches ; that de-
scribed in section 15th of the preceding act of Assembly, is
the frustrum of a cone, the top diameter of which is 15.902607
inches, the bottom diameter 15.14534 inches, and height
11.359005 inches. Grain, salt, &c,, are measured by level or
struck measure ; charcoal, lime, roots, fruit, oysters, &c,, by
heaped measure, which is about three -sixteenths more ^an
level measure. The bushel contains 2553,62 cubical inches.
The dimensions of a half bushel measure, of a similar shape
to the Pennsylvania bushel, is, top diameter, 12.6219 inches,
the bottom, 12.02086 inches, and height, 9.01564 inches.
2 Pints equal 1 quart, qt.
8 Quarts ** 1 peck, p.
4 Pecks •* 1 bushel, bu.
1. Reduce 91 bu. 2 ps. 7 qts., to pints.
Bu. P. Qts.
91 2 T
4
366
8
2935
5870 Answer."
2. Rodace 12 bushels, 2 pecks» to pecks^ Am. SO*
8. Reduce 16 bushels, 1 peck, 2 quarts, to (piarU.
Ans. 522.
4. BriBg 15 bushels, 2 peck«, 3 qmartg, 1 piirt, to pin^
5. In 421 pecks, how many bu»h«i«? An*. 106 ta. 1 p.
. . P
4S RKDVCTIOK.
6. In 3105 quarts, how many bushels ? Ans. 97 bu. 1 qt«
7. In 541 pints^ how many bushels ?
■ Ans. 8 bu. 1 p. 6 qts. 1 pt,
TROY WEIGHT.
This weight is used for weighing jewels, gold, silver, and
liquors : the denominations are, pounds, ounces, pennyweights
and grains. [See sixteenth section of the preceding act of
Assembly.
1. In 123 lbs. 6 oz. 12 dwts. 16 grains of gold, how many
grains?
lbs, oz. dwts. grs.
123 6 12 16
12
1482
20
29652
24
118624
59304
711664 Answer.
2. Reduce 12 lbs. 4 oz., to ounces, k Ans. 148*
3. Reduce 5 lbs. 2 oz. 16 dwts., to pennyweights. Ans. 1256.
4. Reduce 17 lbs. 6 oz. 4 dwts. 12 grs., to grains. Ans. 10(^908.
5. Bring 9764 grains to pounds.
Ans, 1 lb. 8 oz. 6 dwts. 20 grs.
6. Bring 12547 grains to pounds.
Ans. 2 lbs. 2 oz. 2 dwts. 19 grs«
AVOIRDUPOIS WEIGHT.
By this weight are weighed things of a coarse drossy na-
ture, and all metals, except silver and gold. The deiiomination&
are, ton,, hundred we^t, quarter, pound, ounce, and dram.
16 Drams (dr.) equal 1 ounce, - - - oz.
16 Ounces " 1 pound, - - - lb.
25 Pounds " 1 quarter of a hundred, qr.
4. Quarters " 1 hundred, - - C. -
20 Hundred " l^on,1 . « - T.
* nxDVOTioir. 43
Examplta.
1. In 16 T. 4 C. 3 qrs. 19 lbs. 11 oz. 15 drs., how BOtany
drams ?
T. C. qr. lbs. oz. drs.
16 4 3 19 11 15
20
824
4
1299
25
6514
2598
32494
16
194975
32494
519915
16
3119505
519915
■? \
irt»«
8318655 Answer.
2. Reduce 12 T. 3 C, to hundred weights. Ans. 243»
3. Reduce 5 T. 2 C. 2 qrs., to quarters. Ans. 410.
4. Reduce 10 C. 3 qrs. 12 lbs., to pounds. Ans. 1087.
5. In 5 tons, how many pounds, ounces, and drams ?
Ans. 10000 lbs. ; 160000 oz. ; 2560000 drs.
6. Reduce 51004 drams to ounces. Ans. 3187 oz. 12 drs*
7. Bring 16430 ounces to pounds. Ans. 1026 lbs. 14 oz.
8. Reduce 12915 ounces to hundred weights.
Ans. 8 C. 7 lbs. 3 oz.
9. Bring 2240 pounds to tons. Ans. 1 T. 2<J. 1 qr. 1j5 lbs.
10. In 1232000 drams, how many tons ?
Ans. 2 T. 8C. 12lbs*« 0*;
44 R&OVOTIOV*
JVb^c— In some parts of Pennsylvania, twenty-eight pound*
yet pass for a quarter, as is also the case in some other States z
m such locations the following table should be used —
16 Drams - equal 1 ounce.
16 Ounces - " 1 pound.
28 Pounds - '' 1 quarter of a hundred.
4 Quarters - "1 hundred weight.
20 Hundred weight. " 1 ton.
1. In 16 T. 5 cwt. 3 qrs. 7 lbs. 11 oz. 15 drs., how many
drams ? Ans. 9341887.
2. In 12 T. 3 cwt., how many pounds? Ans. 27216.
3. In 1 cwt. 2 qrs. 12 lbs., how many pounds ? Ans. 180.
4. Bring 3 qrs. 7 lbs. 15 oz. 1 dr. to drams. Ans. 23537.
5. Reduce 5 tons to drams. Ans. 2867200.
6. Reduce 52036 drams to hundreds.
Ans. 1 cwt. 3 qrs. 7 lbs. 4oz. 4 drs.
7. Reduce 16032 ounces to hundreds.
Ans. 8 cwt. 3 qrs. 22 lbs*
8. Bring 12345678 drams to tons.
Ans. 21 T;. 10 cwt. 2 qrs. 9 lb. 4oz. 14 drs.
9. In 784765 ounces, how many tons ?
Ans. 21 T. 17 cwt. 8 qrs. 19 lbs. 18 oz»
THINGS BOUGHT AND SOLD BT THE TALE :
12 Particulars or things equal 1 dozen, - doz.
19 Dozen - - '^1 common gross, gro.
12 Common gross - " 1 great gross, - g. gro.
580 Particulars - - " 1 score, - - see.
1* In 95 gross, how many dozen ? Ans. 1140»
2. In 16 great gross, how many dozen ? Ans. 2804.
3. In 11 great gross of eggs, how many score ?
Ans. 79 sc. 4 eggs.
APOTHECARIES^ WEIGHT.
Apothecaries- mix their medicines by this weight, but buy
and sell by avoirdupois weight. The denoninatiims are*
pMind. ounce, dimm, scruple, and grain*
XBDVOTIOir.
* ■
120 Grains (gr.) equal 1 scruple, 3.
3 Scruples " 1 dram, 3«
8 Drams '* 1 ounce, 5.
12 Ounces ** 1 pound, lb.
Examples.
1, In 12 pounds, 1 ounce, 2 drams, 1 scruple, JL6 grains,
how many grains ?
lbs. 5. 5- ^* ^'
12 1 2 1 16
12
145
8
1162
3
3487
20
69756 Answer.
tk In 3 drams, 1 scruple, 2 grains, how manj grains ?
Ans. 202.
3. In 1 pound, 1 ouBce, 1 dram, 1 scruple, 1 grain, how
many grains ? ^ Ans. 6321.
4. Reduce 27152 grains to pounds.
Ans. 4 lbs. 8 ^. 45.13. 12 srs.
5. Bring 11520 grains to pounds. Ans. 2 lbs.
6. Reduce 714 scruples to pounds. Ans. 2 lb. 5 §• 6 5*
7« In 20000 grains, how many pounds.
Ans. 3 lbs* 5 ^. 55. 1 3*
CLOTH MEASURE.
By this measure, cloths, tapes, or whatever is bought of
sold by the yard, are measured. The denominatians are^
>fard, quarter, nail and inch.
2^ Inches' (in.) equal 1 nail, - - na.
4 Nails ** 1 quarter of a ya^i qr.
4 Qoartoil '* % jwi^ « » y4>
»
46 BEDUCTIOK.
Examples,
1. In 5 yards, 3 quarters, 1 nail, 1.75 inches, how many
inches P \
Yds. qr. na. in.
5 8 1 1.75 i
4 '
23
4
93
2.25
640
186
186
211.00 ^ 211 inches. Ans.
2. Reduce 215 quarters to yards. Ans. 53 yds. 3 qrs*
3. Reduce 191 nails to quarters. Ans. 47 qrs. 3 nas-
4. In 16 yards, 2 qrs. 1 nail, how many nails ? Ans. 265.
5. In 30 yards, how many quarters and nails ?
Ans. 120 qrs. ; 480 nails-
6. Bring 30 nails to quarters. Ans. 7 qrs. 2 nails.
7. Reduce 154 nails to yards. Ans. 9 yds. 2 qrs. 2 nas.
8. Bring 900 inches to yards. Ans. 25 yards.
9. Bring 108 inches to yards. Ans. 3 yards.
CUBIC, OR SOLID MEASURE.
The solid content of that which comprises length, breadth
and thickness, is ascertained by this measure. The denomi-
nations are, ton, perch, cord, bushel, yard, foot, and inch.
1728 Cubic inches (c. in.) equal 1 cubic foot, c. ft.
46656 Cubic in. or 27 c. ft. ** 1 cubic yard, c.yd.
2150.42 C. in. or 1.24446 c. ft. ';" 1 bushel of st. meas. bu.
2553.624 Cubic in. or 1.4778 c. ft. " 1 bu. of heap'd measure.
128 Cubic feet - - " Icord, - - cd*
24.76 Cubic feet - - •* 1 perch, - ph.
40 Ft.of8q.(saw'd)timber,dr> ^ . q^
60 Feetof round timber, *k $ ^^^^ - - ^^
p
t
**
RSDUOTIOH* 47
1. In 500 cubic feet, how many inches, yards, bushels of
struck measure, also of heaped measure, cords, perches, tons
of iiound, also of square timber ?
C. ft. C. ft. Bu. Cft.
500 1.34446)500.00000(401 -97154 Struck measure,
1728 497 784
864000 Inches. 221600
124446
.97154
C. ft. C. ft. Bu. C.ft.
r 3)500 1.4778)500.0000(338 .5036 HeapM meas.
27^ 443 34
I. 9)166 + 2
56660
18 Yds. 14 ft. 44 334
12 3260
118224
.5036
C. ft Cords. C. ft C. ft. P. ft.
128)500( 3 116 24.75)500.00(20 5
384 4950
116 * 5.00
C.ft. C.ft.
4,0)50,0 5,0)50,0
12.5 Tons square timber. 10 Tons of round timber.
2. In 9 cubic feet, 1 cubic inch, how many inches ?
Ans. 15553.
3* In 12 cords, 6 feet, how many feet ? Ans. 1542.
4* Reduce 96 cubic feet to perches. Ans. 3 phs. 21*75 c. ft.
6* Bring 9 bushels of struck measure to inches.
Ans. 19353.7a
41 ftftOVOTlOK.
6* Reduce 3 cubic yards to bushels, struck measure.
Ans. 65 ba. 190*7 c* m4^
7. In 6 cords, 101 feet, how many feet ? Ans. 869*9f
Paper.
The sizes of Paper are designated bj post, foolscap, me^
dium, super-'royal, imperial, elephant, atlas, and antiquarian*
The denominations are, bale, bundle, ream, quire and sheet*
24 Sheets (sh.) - - equal 1 quire, qr.
20 Quires, or 472 sheets, " 1 ream, re.
2 Reams . - *< 1 bundle, bun.
5 bundles, or 10 reams, " 1 bale, ba.
The two outside quires of a ream'of paper contain only 20
sheets : these are broken or defective, and are termed casiie^
Excmiples.
1. In one ream of paper, how many sheets ?
IC*
1
20
20
24
480
The two outside quires want 8 sheets of being fulL
472 Answer.
2* In 16492 sheets of paper, how many r^juns ?
Sh. R. qr. sh.
472)16492(34 18 12
1416
2332
1888
24)444(18^12
24
204
192
ItB^UOTIOir.
40
[ Hete, after dividing bj 473, there are 444 sheets remain-
1 *' iBg, which must be reduced to quires.
Mflk^'tf? K^u^^ 12 bundles, 1 ream, 15 quires, 11 sheets, to sheets.
JP-aA 'JK Bun. re. qr. sb.
■■r^ 12 1 15 11
r 1 -
25
472
71
30
50
175
100
11800
371
371
12171 Answer.
4. In 1 bale, 2 bundles, 1 ream, 5 quires, 12 sheets, how
many sheets ? Ans. 7212*
5* In 146 reams, how many sheets ? Ans. 68912-
Time.
By this table is taught the computation of time,
nominations are, year, month, week, and day.
60 Seconds (sec.) - - equal 1 minute.
60 Minutes
24 Hours - - -
7 Days ...
4 Weeks - - -
13 Months, 1 day, 6 hours,
12 Calendar months (c. m.)
52 Weeks, 1 day, 6 hours,
865 Days, 6 hours, -
100 Years
Names of the calendar months :
((
i€
t€
(C
((
<i
it
(C
Thede
M.
. H.
D.
. W.
1 hour, -
1 day, -
1 week, -
1 lunar month, L. M.
1 year, - - jr*
I year.
1 year.
1 year.
1 century, - Cent-
1. January, having 31 days.
2. February, " 28
8. March, •• 31
4. April, " 30
6. May, " 31
(C
(t
«
((
7. July, having 31 days*
8. August,
9. September,
10. October,
11. November,
9 e* Jundi
44
30
1% Decembor*
31
30 «
31 *«
80 "
81 ••
fiO , R£9VCTIOJf*
Tlie leofftli of a year is computed to be 365 days, 6
hours, nearly ; hence a common year consists of 365 day
and every fourth is called a leap year, of 366 — the seco
month, February, having 29 days assigned it. The num]
of days assigned each month, may perhaps be the better rec
lected by the following : —
The fourth, eleventh, ninth and sixth,
Have thirty days to each affixed ;
And every other thirty-one.
Except the second month alone.
Which has but twenty-eight in fine.
Till leap year gives it twenty-nine.
Or,
Thirty days hath September,
April, June and November ;
Each of the rest has thirty-one.
Except February alone,
To which we twenty-eight assign —
But leap year gives it twenty-nine.
When the year will divide by four, and have no remainder,
it is leap year ; but if any remain it is so many years after
Feap year. ^
Examples.
1. Reduce 1837 years to seconds.
Years.
1837
365.25
9185
3674
9185
11022
5511
670964.25 Days.
24
268385700
134192850 ,
16103142.00 Hours.
60^
966188520 Minutes.
60
67971311200 Seconds* Ans\ver«
RBDUCTXOlf* 51
2. In 27 weeks, how man j days ? Ans. 18^.
3. In 19 lunar months, haw many weeks? Ans. 76.
4* In 62 hours, how many minutes ? Ans. 3720.
.9(. Change 163 seconds to minutes. Ans. 2 min. 43 sec.
(J. Bring 12 days to seconds. Ans. 1036800.
7* Reduce 91 years to weeks. Ans 4748.25.
8. In 7 years, now many weeks, days, and hours ?
Ans. 365.25 weeks ; 2556.75 days ; 61362 hour&. '
MOTION, OR CIRCLE MEASURE.
This measure is used by astronomers, navigators, &c. The
denominations are, revolution or circle, sign, degree, minute,
and second.
60 Seconds (") - equal 1 minute, - '.
60 Minutes - - "1 degree, - ^.
SO Degrees - - "1 sign, - - sig.
12 Signs, or 360 degrees ** 1 revolution or circle.
The latitude and longitude of any place is reckoned in de-
grees and minutes : thus, New Italy is situated in lat. 39° 59*
north of the equator, and longitude 75° 51' west from London,
or 43' west from, Philadelphia.
JExamples*
1. In 2 signs, 6 degrees, 41 minutes, 40 seconds, how
many seconds P
Sig. °
2 6 41 40
30
66
60
4001
60
240100 Answer.
2. How many degrees in 41 signs ? Ans. 1230*
3. Change 1 revolution to minutes. Ans. 21600.
4. In 160000 seconds, how many signs ?
Ans. 1 sig. 14° 26' 40 '.
6* Bring 3 signs td minutes^ . -^^^ 5400.
68 RBDVCTIOir.
6. Reduee 14680 seconds to degrees. Ans. 4*^ 4' 40"«
?• Id 13 degrees, 12 minutes, how many seconds ?
Ans. 47520,
;^
Application.
1. How many lockets, each to weigh 12 penny weights, will
8 pounds, 1 ounce, 4 pennyweights of ^old, ma!ke ?
lb. oz. dwt.
3 14
12
87
20
12)744
62 Answer.
% How many plates, each to weigh 6 ounces, will 36
pounds, 6 ounces of silver, make ? Ans. 73.
3. In 17 bags of coffee, each 72 pounds, how many hundred
weight? Ans. 12 C. 24 lb.
4. In 25 pounds of drugs, how many parcels, each con-
taining 20 drafns P Ans. 120.
5. Required the circumference of the earth in inches.
Ans. 1585267200-
6. Required the number of revolutions a wheel, 9 ft. 2
inches in circumference, will make, in running 75 miles.
Ans. 43200.
7. In 5 bales of cloth, each 16 pieces, and each piece 21
yards, how many nails ? Ans. 26880.
8. A tract of land, containing 216716 square perches, is
to have one plantation, containing 114 acres, 3 roods, 4
perches, taken from it, and the remainder to be divided into
11 plantations. Query— the number of acres in each ?
Ans. 112 A. 2 R. 32 P.
9. How many pint bottles may be filled with a cask of
wine containing 45 gallons P Ans. 360*
10. How many bags, each to contain 3 bushels, may h%
filled from a granary of wheat containing 100 cnbical feet ?
Ans* 26 bags» 2 bu. «4435 c. ft«
REDUCTIOH. 53
11. How many hours, minutes, and seconds, are therein
any leap year ? Ans. 8784 H. ; 527040 M. ; 31622400 S.
12. Reduce 12398400 seconds to weeks.
Ans. 20 W. 3D. 12 H.
13. How many seconds are there in a complete revolution
of any planet ? Ans. 1296000 sec,
14- How many steps, of 2 feet 10 inches each, must a per-
son take in walking from New Italy to Harrisburg, the dis-
tance being 55 miles ? Ans. 102494 steps, and 4 inches over.
15. How many yards from New Italy to Lancaster, tli6
distance being 19 miles P Ans. 33440.
16. How many inches is a horse in height, which measures
18 hands, 1 inch ? Ans. 73.
17. In 75 yards, 3 quarters, 1 nail, how many inches ?
Ans. 1213.
18. Reduce 124.446 cubical feet to bushels. Ans. 100.
19. How many hours are in there in a week ? Ans. 168.
20. Bring 5874 feet to poles. Ans. 356.
ENGLISH MONEY.
*The denominations are, pound, shilling, pence and farthing*
4 Farthings (qr.) equal 1 penny, d.
12 Pence ^ . " 1 shilling, s.
20 Shillings - '< 1 pound, £.
1. In %£. 138. 4|d.» how many farthings?
£. s. d.
3 13 4^
20
3523 Answer.
!8* In 12jfi. 68. 9d., how many pence ? Ans. 296L
S. Reduce 3560 farthings to pounds. Ans. 3^. 14s. 2d.
4. Bring 17643 farthings to pounds. Ans. 18^ 78. 6Jd.
S6 REDUCTION.
To find the Valtce of French Gold Coins.
Rule.
Reduce the weight of the coin to grains, then divide bj 27.5
— the quotient will be the answer in dollars and decimal parts.
Required the value of a French pistole, the weight whereof
is 4 pennyweights, 4 grains.
Dwt. gr.
4 4
24
— &
27-S)100.0(3.6368 + Answer.
825
1750
1650
1000
825
1750
1650
1000
825
175
To find the Value of either United States, Chreai Britain or
Portugal Gold.
Rule.
Reduce the weight of the coin to grains, then diyide bj 2T
—the quotient will be the answer in dollars and decimal parts.
1. Required the value of an Eagle, the weight whereof i»
,11 pennyweights, 6 grains.
Dwt. gr.
11 6
24
50
27)270(10 Antwcr.
27
B.EDUOTIQV* 57
Q. Required the value of an EngUsh Gumea^ ^ weight
whereof is 6 pennyweights, 6 grains.
Dwt. grs*
5 6
24
— 8
97)126(4.667 nearly.
108
180
162
180
162
180
189
3. Required the value of a Johannes, the weight whereof
Ia 18 pennyweights,
Dwt.
18
24
72
36
— 8
27)432(16 Answer.
27
162
162
4. Reqjuired the value of a quarter Eagle, the weight
whereof is 2 pennyweights, 19.5 grains. Answer 82^.
5. Required the vaWe of a Sovereign, or pound sterlings
the weight whereof is 5 pennyweights. Ana. 84.444.
£
The denominations are, eagle, dollar, dime, cent, and mill*
10 Mills (m.) - equqtt 1 cent, - ct.
10 Cents - * " 1 dime, - di.
10 Dimes, or 100 cents, " 1 dollar, g or doL
10 Dollars - v " 1 eagle, - E,
tii reading federal money, and keeping accounts, eagles
and dimes are not named : eagles are read tens, &c., of dol-
lars, anji dimes tens of cents. '■ Federal money, by one writings
is expressed in every denomination, thus, 5493 cents ; and
5 eagles, 4 dollars, and 93 cents, are expressive of the same
value; therefore, properly speaking, there is no reduction of
federal money, the decimal form making the dollar. The
money unit is properly adapted to practical purposes, and has
been sanctioned by a law of the United States.
In this work, dollars will be considered whole numbers,
and cents and mills decimal parts, of a dollar; thus, 12 dpi -
lars, 32 cents, and 7 mills, will be expressed, gl2.327 — mills
belonging to the third number at the right hand of the deci-
mal point*
If the number of cents be less than ten, write the figure
expressing the number, and prefix a (iipher before it — that is^
between the figure and the decimal point ; thus, for 8 cents,
write .08 dollars. If there be no cents, and the number of
mills be less than 10, prefix two ciphers, between the figure
expressing th^ number a.nd the decimal point; thus, for 7
mills, write .007 dollars.
JExamptes*
1. 12 Dollars, 19 cents, 5 mills^ iequal 212.195
2. 7 Dollars, 16 cents, 4 mills, " 7.164
3. 6 Dollars, . 5 cents, - ^ *« 6,05
4. 17 Dollars, 6 mills, - - *' 17.006
5. JO Dollars, 2 miUs, - - *' 10.002
ft. 26 D<?llars, 9 pents, 3 mills, " 26.093
7. 19 Dollars, 1 cent, 2 mills, " 19.012
8. 21 Dollars, 9 cents, 4 mills, " 21.094
9. 37 Dollars, 12 cents, - - " 37.12
10. 14 Dollars, 2 mills, - - " 14.002
11. 2 Dollars, 1 mill, - - •' 2.001
12. 9 Dollars, 5 mills - - '^ ^-OOS
13. 7 iBagles, 6 dollars; 1 mill, - equal 876.001
14. 1 Eagle, 5 cents, ^ mills, " 10.053
15. 5. Eagles, 3 mills, - - " 50.008
The money of the United States is more simple and easy
to reckon than' that of anj other country, as it increases in a
tenfold proportion from right to left.
COMPOUND Al>DITId]$.
Comp6und addition is the adding of several numbers oi*
quantities, of divers denominations, into one sum total* — as,
yards, feet, inched ; tons, hundreds, quarters, &c.
Rule*
Place tke sum or number so that each denomination Stand
under that of the same name. Add the first row or denomi-
nation together, as in integers ; then divide the sum by as
lUany of the same denomination as makes one of the next
(greater, setting down the remainder, if any, under the row
iadded, and carry the quotient to the next superior denomina-
tion—continuing the same to the last, which add as in addi**
lion of integers.
Examples*
•
£ 9. d.
■ £ 8. d.
£
s.
d.
5 12 6
9 11 2
7
5
3
#•2 3
7 16 3
2
11
S
6 14 1
4 11
6
3
7
7 19 4
9 17 6
4
17
6
6 2 3
8 7 2
9
15
4
be me g bs mb y be mb m
A. has owing to him, on bond, 2§ pounds, 12 shillings and
4 pence ; in bills and notes^ 76 pounds, 19 shillings and 6
pence : required the amount. Aus. mey J. mm 8. me d.
iVo^6.— The. use of pounds, shillings and pence, in the
United States, has nearly become obsolete ; it is, therefore,
presumed that but very few examples of the kind will be
requisite in this work*
00 QOMPOVNI) ADBITIOK*
LONG MEASURE.
Examples.
M. F. P. Yds. ft. in. Deg. G.m. fur.
3 31 6 19 16 20 7
I
7 26 7 2 8 52 54 6
71 18 647 3 17 1
4 2 37 5 7 11 12 19 5
51 12 21 10 214
yh m i by e s rh gb o
Applieaiion*
1, A. set out on a journey : he travelled the first day 25
miles, 3 furlongs, 6 poles ; the second day, 31 miles, 6 fur-
longs, 27 poles, 5 yards ; the third, 34 miles, 29 poles, 5
yards — How many miles did he travel in three days I
M. fur. P. yds.
25 3 6
31 6 27 5
34 29 5
91 a 23 4.5
Here 4.5 yards is equal to 4 yards, 1 foot, 6 inches ; con-
sequently the answer is, 91 miles, 2 furlongs 23 poles, 4
yards, 1 foot, 6 inches.
2. If fi;om Philadelphia to the Black Horse, be 42 miles, 5
furlongs, t27 poles ; from thence to the Rising Sun. 4 miles,
7 furlongs, 31 poles ; from thence to Lancaster, r4 fciles 7
furlongs, 31 poles ;^ from thence to Harrisburg, 35 miles,
7 furlongs, 10 poles— How far is it from Philadelphia ta
Harrisburg ? Ans. 98 miles, 4 fiir. 19 p..
LAND,
OR SQUARE MEASURE.
Examples,
A.
R. P.
A. R. P.
A. R.
P.
12
1 19
6 1 27
21 1
29
6
2 7
3 3 16
16 2
15
7
3 28
18 5
7 1
89
19
2 26
9 1 34
18 3
27
5
3 29
12 2 22
22 2
20
gy
ift ys
by b yi
ro e
me
.COMPOUKD AD01TIOlf« 61
1. Admit a man has a field of wheat, containing 12 acres,
S7 perches ; two fields of com, each containiiig 10 acres, 3
roods, 17 perches ; one of rye, containing 16 acres, 2 roods,
3 perches ; 41 acres, 27 perches, of pasture 5 orchard and
woodland, 25 acres, 1 rood, and 26 perches— What quantity
does he hold in all ?
12 O 37
10 3 17
10 3 17
16 2 3
41 27
25 1 26
inmo e o Ans.
2. IF one field contain 16 acres, 3 roods, 16 parches ;
another, 25 acres, 1 roT)d, 27 perches; a third, 27 acres, 3
roods, 36 perches ; and a fourth, 29 acres, 3 roods, 1 perch-
How much in all ? Ans* mee acres.
LIQUID MEASURE,
Examples.
Tf*. hhd. gal. Gal. (Jt. pt. Gal. qt. pt. ^1.
4127 511 5213
2247 B21 2dil
11 11 731 9112
63 54 421 11 ^13
7229 631 7301
yy b iy bm mm bo y e y
Application.
1. Bought 5 casks of wine, guaging as follows, viz: 94
gallonss 2 t[uarts, 1 pint ; 100 galloris, 3 quarts ,* 79 gallons,
2 quarts, 1 pint; 105 gallons, 1 pintj and 129 gallons, 1 pint
*— How much do they all contain ? Ans. 509 gal. 1 qt.
2. Sold 4 casks of cider, 3 of which contained each lOl
gallons, 2 quarts, and the fourth 19 gallons more than eitheir
•f the other three. ' Afls. 425 gallons*
■^
62 eoupouND At3timoiSn
DRY MEASURE.
Bxampka.
Bu. P. qt Bu- P. qt. Bti- P- qf,
31 1 a 17 1 6 12 1 7
18 1 12 6 41 2 1
3527 2784 19 15
41 3 6 16 1 7 12 2 7
12 1§ 525 47 34
13 31 411 11 11
16 1 4 19 3 6 17 2 6
' •m ' lU ' »-" ■
mhs J y meb b y mhy b o
Application.
1. Admit a man has 5 granaries, 3 of which contain 101
bushels, 3 pecks, 4 quarts, each, and the other two, 107
bushels, 1 peck, 3 quarts— «How much do they all (contain ?
B. P. qts.
101 3 4
101 3 4
101 8 4
107 1 8
imy b o Ans.
2. A farmer sold 3 loads of wheat, the first containing 41
bushels ; the second, 40 bushels, 3 pecks, 2 quarts ; and the
third, 38 bushels, ^ pecks, 6 quarts — required the whole
amount. Ans. 120 bu. 2 ps.
3. Add 29 bushels, 1 peck, 2 quarts ; 47 bushels, 2 pecks ;
16 bushels, 1 peck, 6 quar.ts; 38 bushels, 2 pecks; 118
bushels, 1 peck, and 100 bushels, together, and tell the
amount. Ans. 350 bushels.
TROY WEIGHT.
Examples.
lb.
oz.
dwt.
gT'
lb. oz. dwt. gr.
lb.
oz. dwt. gr»
27
9
16
31
4 1 9 16
41
1 13 14
19
6
13
16
3 5 13 21
43
2 11 2a
16
11
11
13
6 7 6 4
15
10 2 16
13
&
9
5
2 11 14 16
31
9 10 30
47
4
2
11
17 10 12 9
12
7 15 14
SI
10
17
19
12 9 3 17
42
4 5 1
^29
9
14
m.
14 10 12 14
26
1 12 19
ySr
~r
"h-
m«
hm r vam m
yeb
m mj mm
JtppHtation,
I. Bought 3 pair of buckles, Weighing 6 ounces, 14 benny-
weights ; 4 dishes, weighing 10 ounces, 1 pennyweight, 16
grains, dach ; 2 dozen spoons, weighing 1 pound, 10 ounces,
18 pennyweights, 12 grains; two cups, weighing 11 ounces,
16 pennyweights, 19 grains, each, with sundry other small
articles, weiring 3 pounds, 6 ounces, 11 pennyweights, 14
grains«^«<»I desire to know the weight of the whole.
lb. 02. dwt» gr,
6 12 . Buckles.
10 1 16^
10 1 16 f^^*^^*'
10 1 16j
1 10 18 12 Spoons.
11 16 19> p„^^
11 16 195 ^
3 6 11 14 Small articles.
I *■
liim i y r Answer.
% What is the sum of 18 pounds, 3 ounces, 8 penny-
vreights; 24 pounds, 3 ounces, 10 pennyweights, 21 grains;
Q8 pounds, li ounces, 21 grains; and 17 pounds, 1 ounce, 16
penn/weights, 14 grains ? Ans. 88 lbs. 7 oz. 16 dwts. 8 grs.
II
AVOIRDUPOIS WEIGHT.
JExamples,
T. C. qr. lb. T. C. qr.. lb. oz. C. qr. lb. oz. dr.
19 3 1 16 4 1 2 24 15 2 3 12 14 15
12 16 2 20 1 12 1 16 12 1 2 4 3 12
587 5 1 24 12 4 2 14 11 12 1 2 11 11
12 1 1 1 11 12 1 1 4 10 2 7 2 6
5 4 3 4 2 7 3 16 12 11 1 5 > 12
11 5 2 16 19 11 3 13 4 2 12 15 18
■h4 I' I life IHl^a. ^ In I .1 .J. I II !■ II *l| '. l !■ • II I I . . in'. -. 1 1 11 . 1
ro mo m h gm embbibeyer ^
AppHcatiofik
1. Suppose a tft^rchaiit bought 3 hogrfieaft of sugar, weigh-
ing ^ htmdtcd, 1 quarter, 20 pounds ; one hogshead of riee,
tireighipg 4 hundred^ 8 l^DarterSi }6 pounds ; 3 hogshead •£
tobacco, Weighing 6 hundred, S qu«rters, 34 poundtf^ efteh— '
Whftt weight has l)e to paj carriage for ?
c.
qr.
lb.
39
1
20
4
3
16
6
3
24
6
3
24
6
3
24
}
Sugars
Rice-
Tobacco*
gg m r
3. What is the weight of the above, contpttting 28 poundii^
to a quarter, of the odd poutids ? Ans. 55 cwt. 24 lbs.
3. Suppose a merchant bought 6 hogsheads of sugar, weigh'
ing as follows, viz : No. 1, 7 hundred, 3 quarters. Impounds }
No. 2, 12 hundred, 2 quarters, 5 pounds ; No. 3, 7 hundred,
2 quarters, 24 pounds ; No. 4, 8 hundred, 1 quarter, 17
pounds 5 Nos. 5 and 6, each 7 hundred, 2 quarters, 21 pounds
—•How much is the amount ? Ans. 52 C 4 lb.
4. What is the weight of the above, computing 28 pounds
to a quarter, of the odd pounds P Ans. 51 cwt 3 qrs. 20 lbs.
5* In 5 boxes of raisms, weighing as follows, viz: No.- 1,
1 quarter, 2l pounds.; No. 2, 2 quarters, 5 pounds j No. 3, 2
quarters, 12 pounds ; No. 4, 3 quarters, 1 pound ; and No. 5,
weighing 16 pounds more than No. I — What is the whole
weight ? Ans. 3 cwt. 1 lb.
6. What is the weight of the above, computing 28 pounds^
to a quarter, on the pounds P Ans. 2 C. 3 qrs. 20lbft#
^mm
APOTHtCAHIES' WEIGHT.
JSxamphs,
lb-- i 3 & gr- lb. I
1 11 7 2 19 23 11
12 3 3 1 9 19 8
2 2 5 6 27 7
19 2 2 1 14 14 10 6
21 811 7 1 512 11 5 412 17
6 431 9 12 151 12 152 10
in H, III ■■■■■ ■■■!
hb see i MSieaemjyjreioj
COMPOUND ADDITIOir* 06
1 • 1^ a druggist tHit several simples togeth&]>^lst, 3 ounces,
1 dram, 2 scruples ; 2d) 1 dram, 1 scruple, 14 grains ; 8d, 4
Frances, 7 drams, 2 scruples, 16 grains ; 4th, 3 ounces, 4 pen-
nyweights, 2 scruples, 10 grain*— How much do they all
weigh ?
ife- i 3 9 gi**
3 12
1 1 14
A 4 7 2 16
• 3 4 2 10
irMU
m e e e e
CLOTH MEASURE.
Examples.
Yds. qr.
nai
Yds. qr. na.
Yds* qr.
nai
14 1
2
547 2 S
1 1
1
13 2
1
164 2 1
2 3
1
61 1
3
14 1 3
5 1
3
42 2
1
142 3 2
1 2
3
16 3
2
140 1 1
5 2
1
19 1
1
11 2 3
2 1
1
25 2
3
25 3 2
4 3
3
16 1
1
4 2 1
6 2
2
mee e y ^egy e e be y b
1. Sold to A. 21 yards, 3 quarters, 1 nail, of cloth; to B.
twice as ttiuch; to C. 1 yard, 1 quarter, 1 nail, more than
Was sold to A. Required the quantity sold.
Yds- qr* na.
1 to A.
H to B.
21
8
21
3
21
3
21
3
1
1
\}u
c.
II !■ I ^ I I ^^l^'\ A.
rr y m
2. Bought 6 pieces of cloth— No. 1, contained 41 yards, \
quarter, 2 nails; No. 2, contained 33 yards, 2 quarters, j
6d CCMPOVHP APOITIOir.
nail ; No* 3, 39 yards, 2 quarters, 3 nails ; No. 4, 29 jardi.
S quarters, 3 nails ; Noe. 5 and 6, each 86 yards, 1 quarter,
2 nail*— What is the quantity ? Ans. 217 yds. 1 qr. 1 na.
S, Bought 7 pieces of linen*--No. 1, contained 12 yards, S
quarters, 8 nails ; No. 2, 9 yards, 1 quarter, 1 nail ; No. 3,
11 yards, 1 quarter, 2 nails ; No. 4, contained as much as No,
1 and No. 3, together ; No. 5, contained as much as No. 2 and
No. 4, together ; No. 6, contained as tnuch as No. 1 and No,
2 ; and No. 7, contained as much as No. 5 and 6. Required
the quantity bought. Ans. 169 yds|^2 qrs. 3 nails.
CUBIC, OR SOLID MEASURE.
Examples,
1. Bought 5 loads of bark, measuring as follows, viz: Ist,
116 feet; 2d, 1 cord, 2 feet; 8d, 99 feet; 4th, 1 cord, 12
feet; 5th, 120 feet; also, a stack, containing 45 CPrds, 86
feet— ^How much did I buy ?
ord.
eft.
116
First load.
I
2
Second load.
99
Third load.
1
12
Fourth load.
120
Fifth load.
45
26
Stack.
is mms Answer.
2. There are 7 pieces of square timber, 5 of them contain
18 feet, each; the other two, 40 feet, each. The number of
tons is required. Ans. 3.2 tons.
3. The cellar of a house contains 162 cubical yards ; that
of the kitchen, 79 cubical yards, 5 feet Required the con-^
tent of bothk Ans. 241 yds. 5 feet.
4. A man has a granary, containing 100 cubical feet ; ano-
ther, containing 109 feet, 1012 inches ; a thil-d, containing 88
feet, 441 inches, and a fourth, containing 9^ feet, 275 inches.
Required the solid content of the whole. Ans. 391 c. ft4
•OOiTPOtyND SUBTRACTIOlf, ffjf
TIME.
*s
Examples.
Yn
M.
W.
D.
Yr. M.W.D.
D.
H.
M.
Sec
12
1
8
2
6 5 3 6
17
23
50
27
7
2
1
5
1 13 1 a
6
19
12
54
1
9
2
4
3 12 5
16
12
11
16
17
6
2
6
5 12 3 1
14
6
17
24
9
5
1
5
3 14 6
5
I
3
7
16
12
2
4
15 8 2
7
9
16
a
9
3
2
7
2 11 2 6
. 15
1
4
16
oi
b
m
g
yi m y e
rb
e
gs
yh
JtppHcation,
From the 22d of March to the 4th of July, inclusiye, how
m&ny dajs ? Ans. 105 daj9«
MOTION.
OR CIRCLE MEASURE.
Examph
IS.
/ n
Sig. « ' "
5 27 46
•
1 27 50 12
3 39 27
2 19 35 45
5 16 54
4 17 31 52
6 9 21
5 15 2
I 17 46
5 16 19 41
4 39 24
2 17 34 51
2 55 47
4 29 45 24
ys yh yg yo a by io
COMPOUKD SUBTRACTIOJr.
CoKPOUND SUBTRACTION 18 the taking of a less sum op
quantity from a greater, of divers denominations.
Rule.
Subtract as in integers, only when any of Ae lower de^
nominations are greater than the upper, then subtract it from
as many of that denomination as ihake one of the next greater,
And add the upper nuihber to the remainder ; set down the re-
jwilt, and carry one to the next denomination — and so proceed^
Proof'^As in integers«
68 COMPOUND SUBTRACTIOK4
LONG MEASURE*
JExamplea.
Deg.G.M.fur. P* Vds.ft. in. Yds. ft in-
19 27 7 12 5 19 17 2
16 31 6 45 2 2 11 9 2 10
y gh e o y m me o y mm
Applications
1. From 4G miles, 6 furlongs, 19 poles, take 19 milled, 7
furlongs, 20 poles* ,
M. fur. P.
46 6 19
19 7-20
yK h bs Answer*
S. Tfwo persons set out from the same place, and travel the
same road : at the end of one week, A. has travelled 30i
miles, and B. 247 miles, 14 poles. I wish to know how far
they are apart. Ans. 53 miles, 7 fur. 26 P.
3. Admit a man set out upon a journey of 375 miles — ^how
ifar is he from his journey's end, when he has travelled 200
miles, 7 furlongs, 32 poles. Ans. 174 M. 8 P.
4. What is the difference between 7 miles, and 6 miles, 7
furlongs, 39 poles, 5 yards, 1 foot, 5 inches }
M. fur. P. yds. it. in.
7
6 7 89 5 1 5
^'
m Ans.
Here, because 5J- yards equal one pole, I borrow its equiva-
lent, 5 yards, 1 foot, 6 inches ; that is, 5 for the yards, 1 for
the feet, and 6 for th6 inches. I then say, 5 from 6 and 1 i«
left : I carry 1 and say, 1 from 1 and remains ; then 5 from
5 and remains ; then, as 52- yards => 1 pole, was borrowed,
I carry one to the poles, and say, 40 from 40 and is left,
&c.— consequently the difference is only one inch.
5. From 6# miles, 3 furlongs, 16 poles, take 59 miles, I
furlong, 29 poles, and tell what remains*
Ans, 1 M, 1 fur. 27 p«
6. What IS the difference between 100 miles, and 75 miles.
S furlongs, 20 poles ? Ans. 24 M, 4 fur. 20 P.
COMPOUND SUBTRACTION. 69
LAND, OR SQUARE MEASURE.
Examples^
A. R. P. A. R. P, A. R. P*
29327 16 11 439
12 1 39 15 2 2 1 3 10
17 1 28
1. A man purchased a tract of land, containing 406 acre*,
2 roods, 27 perches, and sold thereof 256 acres j 2 roods, 29
perches— What quantity has he left ?
A. R. P.
Bought 406 2 27
Sold 256 3 29
149 2 38 Ans.
2. A tract of land, containing 900 acres, is to be divided
among three persons, A. B. and C. : A. is to have 297 acres,
1 rood, 12 perches; B. 305 acres, 2 roods, 19 perches — What
is C.'s share? Ans. 297 A. 9 perches.
3. From a tract of land, containing 100 acres, was sold
two lots, each 5 acres, 21 perches — ^How many acres were
left ? Ans, 89 A. 2 R. 88 P,
LIQUID MEASURE.
Examples,
T.hhd.gal. T.hhd.gal. Hhd. gal. qt. pt.
5324 62 41 20 25 30
4 1 62 3 3 52 16 41 3 1
1 1 25
1. Bought 4 casks of cider, containing 126 gallons, of
which 96 gallons, 3 quarts, were sold — ^How much have I
left ? Ans. 29 gals. 1 qt.
2. A cask of wine, containing 110 gallons, having 51 gal-
lons, 1 qt. drawn from it— How much is left ?
Ans. 53 gals. 3 qts.
72 COMPOUND SUBTRACTIOX,
1. Bought 4 pieces of cloth, containing 31 jards each ; of
which were sold 3 pieces, and 21 yards, 1 quarter, 2 nails, of
the other — How many yards are left ?
Ans. 9 yds. 2 qrs. 2 nas.
2. From two pieces of cloth, each 25 yards, 2 quarters, 2
nails, having cut 26 yards, 1 quarter— How many yards ar©
left ? Ans. 25 yards.
CUBIC, OR SOLID MEASURE.
«
Uapamples.
C. ft. c. in. C yd. c. ft.
12 1470 91 16
3 1720 81 21
8 1478 9 22
TIME.
Examples,
Yr. M. W. D. D. H. M. sec.
12 1 2 5 14 19 43 51
3 7 16 10 20 1 59
8 7 6
1. Jacob, by contract, was to serve Laban 14 years, for his
two daughters ; and, when he had accomplished 11 years, H
months, 11 weeks, 11 days — ^the remaining time is required.
Yr. M. W. , D.
14
11 11 11 11
1 11 3 3 Ans.
Here I begin at the days, and, as I cannot take 11 from 7,
I borrow 2 weeks, and say, 11 from 14 and 3 are left. I then,
carry 2 to 11, which make 13 ; and, as I cannot take 13 from
4, I must borrow as many as will make 13 or more^— and
find that less than 4 months will not answer. I then say, 13
from 16 and 3 are left. I carry 4 to 11, are 15, borrow 2 yearg
and say» 15 from 26 and 11 are left; carry 2 to 11> are 13»
and 18 from 14 and 1 ia left.
Note 1.P— The interval of time, according to the calendar*
between two given dates, may be obtained thus : place the
COMPOUKD StrATKACTlOKi 73
ItftSB under the larger ; if the lower number of days be greater
than the upper, tsie the lower number of days from as many-
days as are in the month of the lower number, and add the
upper number of days to this remainder : then subtract and
carry its in other cases.
Note 2. — ^Old Style was changed to New in 1752, except in
Russia, where the old style is still in use. When one of the
dates is in old style, and the other in the new, eleven days
must be taken from the difference for any date before 1800 ;
or 12 days for any time between 1800 and 1900.
2. The compiler of this book was born on the twenty -ninth
day of September, 1797— How old was he on the 15th day
of July, 1685? .
Y. M. D.
1885 7 15
1797 9 29
;1;
37 9 16 Answer.
As I cannot take 29 from 15, I examine the*month in the
lower number, and find it contains 30 days. I therefore take
529 from 30, and 1 is left; which I add to 15, the upper num*
ber of days.
3. Thomas was born on the 17th of November, 1822 f Da-
Ti«, the 13th of May, 1831— What is the difference of their
ageSx and what the age of each on the 15th of July, 1835 ?
Ans. Difference 8 yrs. 5 mos. 26 ds. ;
Thomas' age, 12 yrs. 7 mos. 28 ds*
Davis' - 4 yrs. S mos. 3 ds.
4. The first permanent settlement in the United States,
was made (in Virginia) on the 10th of June, 1610, (old style)
—How many years since, reckoning up to the 15th of July,
1835 ? Ans. 225 years, 23 days.
5. America was discovered by Chiistopher Columbus, on
Ute 12th of October, 1492, (old style,) and the independence
trf the United States declared on the 4th of July, 1776. Re-
quired the space of time between those two events.
Ans. 283 ys* 8 mos. 13 ds.
ei A bond was riven on the 12th qf June, 1831, and paid
off the 4th of April, 1885^For what time must the interest
be reckoned hereon ? Ans. 3 yrs. 9 mos. 22 ds.
^ P
Ti COMPOUNB MU&TIPLIOATIOirr
MOTION, Or circle measure.
£xamples4
25 12 24 16 9 14 1,12 21 16
12 24 36 10 21 35 25 29 SB
■ I <■ aawHMUAb
12 48 48
When a planet has moved througli 11 signs, 11 degrees, 11
minutes, 11 seconds, of its orbit, how much is it short of a
complete revolution ? Ans. 18° 48' 49".
COMPOUND MULiTIPMCATIOJV.
Compound multiplication is the multiplying any given
sum or quantity, of divers denominations, by any proposed
number.
Rule*
Multiply tRe first denomination by the given number or
quantity, divide the product by as many of that as make one
of the next---setting down the remainder—and add the quo-
tient to the next superior, after it is multiplied; and so
proceed.
If the given quantity is above 12, multiply by any two
numbers which, multiplieft together, will make the same
number; 'but if no two numbers, multiplied together, will
make the exact number, then multiply the top line by as many
a$ is wanting, addjng it to the last product.
Proo/.— Double the multiplicand, and multiply by half the
multiplier
WEIGHTS AND MEASURES.
Examples^
M. fur. P. A. R. P. Gal. qt. pt
Multiply 5 3 19 1 3 29 17 2 1
by ,2 3 4
Product, me h br g b o oe y e
J
Hhd. gal. qt. Bu. P. qt. Bu. P. qt
Multiply 12 29 2 10 1 7 15 3 5
bj 5 6 7
Product, hy yra y hy b y mbs m b
lb. «z. dwt. lb. oz. dwt. gr. lb. oz. dwt.
Multiply 5 8 16 O 1 14 20 3 2 19
by 8 9 10
Product^ iy li r m b lub my by g me
C. <[r. lb. T. C. qr. lb. oz. dr.
Multiply 11 2 16 5 2 3 11 5 7
by 11 12
Product, myr m m hm mi ra mm m i
i 3 9 lb. I 5 9 lb. 3 5 9 gr.
Multiply 1 522612 5^61 18
. by 12 12 12
Prod't, ye i e be y i e lis s o m mh
Yds. qr. na. Yds. qr. na. Yds. qr. na.
Multiply 513 631 432
by 7 9 11
Product, br e m hm mm gb y y
1. Multiply I ton, 7 cwt 3 qrs. 12 lbs., by 27-
T. cwt. qr. lb.
Thus, 17 3 12
9x3«27
12 10 3 8
3
37 12 1 24
2. Multiply 3 yds. 1 qr. 1 na. by 16. Product, - 53 yards.
3. " 5M.2fur.7P. by 25. " 131 M. 6 fur. 15 P.'
4. '' 10 A. 1 R. 17 P. by 43. " 434 A. 3 R. 34 P.
7ft OOMPOVKO MULTIPJUIOATION.
6. MultipljB Gal. 2 qts. 1 pt. bj 66. Product* 437 gal. 1 qt.
6. *' 19 Bu. 2 P. 6 qta. bj 84. " 1653 bu. 3 P-
7. •' llb.5oz.l6dwt.byllO. " 163 lbs. 2 oz.
8. '* 5 Yds. 3 qrs. 2 nas. by 59.
Yds. qr. na.
5 3 2x3
8 x7 + 3«50
47
7
329
17
2
2
346 2 2
9. Multiply 2 yds. 3 qrs. 3 nas. by 118.
Product, 346 yds. 2 qrs. 2 nas.
10. •• 5 A. 2 R. 9 P. by 126. Product, 700 A. 14 P.
When the given quantity is greater than the product of any
two factors in the table — multiply continually by as many
tens, less one, as there are figures in the given quantity ; then
multiply the last product by the figure in the left of said
ciuantity, (if more than one,) into the multiplicand, and that
in the tens place into the first product, &c. Place the several
products as in addition, and their sum will be tiie answer.
Examples,
1. Multiply 5 pouadd, 1 shilling, 5 pence* by 457-
£. s. d.
5 1 5x7
10
50
14
2x5
10
607
1
8
4
9028
253
85
6
10
9
8
10
11
8317
7
5 Froduct>
COMPOUKD DITISIOV. 77
3. Multiply 1£. 4d. 3d. by 569. Product, 689d8. ISs. 3d.
3. " 2 yds. 1 qr, 1 na. by 4216. ". 9749 yds. 2 qrs.
COMPOUND DIVISION.
Compound divisiok is the dividing of several numbers, of
divers denominations.
Rule.
Divide the first denomination on the left hand ; and if any
remains, multiply them by as many of the next less as make
one of that ; which add to the next, and divide as before.
Proof, — ^By multiplication.
OF SHORT DIVISION.
Short division^ compound, is that wh^reia the divisor does
not exceed 12.
JSxamples^
iS 8. d, j8 s. d. £ s. d.
2)4 2 6 3)12 1 9 4)5 13 8
™ III I iiii y I iiaii . ■' ■' ■•
ymb ieo mrg
M. fur. P. M. fur. P. M. fur. P.
5)9 4 20 6)13 2 8 7)16 7 9
m my y m yr y bmy + g
Gal. qt. pt. Gal. qt. pt* Gal. qt. pt.
8)19 3 9)12 1 1 10)17 1 1
I I I .MMI^MMMMMM
ymm+h mmm m j m -{- ^
I
Bu. P. qt. Bu. P. qt. Bu. P. qt.
11)73 7 12)49 2 6 12)59 3 6
^^^_^i^^B^a^Hi a^BMBsMMi^aMMM mtmt^mmmm^mmm^mm
hyg iei+h ibo + m0
Yds. qr«na. Yds. qr. na. Yds. ^r. na.
8)19 1 2 10)15 1 12)27 2 3
t^l I > III Ill I I I ■ mAmA— .BMIBaM
f ni y4»h m y e + to y m e + ^^A
78 nzjyvonoK of x^ectimals*
OF LONG DIVISION-
Long division^ compound^ is that wh^^in the ditisor es**
ceeds 12.
1. Divide 543 miles^ 1 fuiiong, 8 pole9, by 17«
M. F. P.M- Fi P.
Th»9, 17)543 1 8(31 7 24
/
51
83
17
16
8
•
17)129(7
119
10
40
17)408(14
34
68
68
2. Ditide S0£. 10s. 2d, bj W. Quotient, 2£. iSs. 2(1-
8. " 501^. 103. 6d. by 19. " 26£.7s. lid,—
4. " 40 A. 2 R. SOP. by 21. " lA. 3R:30P.
5. " 78A. 3R.20P.by21. " 3A.3R—
6. '* 112 A. 1 R. 16 P* by 37- " 3 A. 6 P. nearly.
7. " 92 Gal. 3 qts. 1 pt. by 59. " 1 gal. 2 qts.—
«. '* 243 D. 13 H. 42 M. 12 sec. by 147.
Quotient^ 1 D. 15 H. 46 M.—
REDUCTIOX OF DECIMALS.
Reduction of decimals teaches Ito'w to reduce any given
vulvar fraction* or fractional part of" a day, hour, &c., to a
decimal, and ^e contrary.
-^o/&.iwmA Jimlgar fraction i% a part or parts of an integer, and
M.nated thus, ^, one-sinthi I, fiv9«8ijLih»4 The upper nnittbar
HkDVCTIOK OW DfidttALS. 79
b tailed the numei'ator, and shows thetpart or parts expressed
by the fractioil ; the lower number is called the denominator,
and denotes the number of such parts contained in a unit.
CASE I.
To reduce a Vulgar Fraction to a Decimal.
Annex as many ciphers as may be necessary to the numera-
tor of the fraction, and divide by the denominator : the quo-
tient will be the decimal required,
JSxamptes.
1. Reduce ^V ^o ^ decimal.
16)9.0000(.5625 Answer.
80
X 100
40
31
80
80
ft. Reduce |- to a decimal* i^/
8. Reduce ^ to a decimal*
4. Reduce | to la, decimaL
h. Reduce | to a decimal*
6. Reduce ^^ to a decimaL *•
7.* Reduce -f^ to a decimal.
8. Reduce •^V to k decunaL ^ •>
9. Reduce ^y to a decimal*
10. Reduce ^ to a decimaU ^ *-
CASE 11.
To re<tuce Weights y Measures ^ ifc» to a Decimal.
Rt^LS.
Set down the lowest name, to which annex as many ciphers
t& are necessary : divide by the next higW denomination :
place the parts given of the next superior denomination on
the left hand 6f the decimal thtts found \ a»d so proceed, till
you brin^ out the decimal parts of the high^t integer required*
uy still dividing b/ lAi« nest sUJ^erior denominati^ni
Ans^,
^
<c
.25
««
.75
c«
.625
cc
.0625
cc
43T5
it
.05
«
.4166&-'
«
.52941^
80 REDUOTIOX OF DECIMALS*
> Examples*
1. Reducfe 3 furlong, ?! poles, 2 yards, 2 feet, 3 inches,
to the decimal of a mile.
Inchei^
12)3.00
3)2.25
5.5)2.75(.5
275
Poles.
4,0)21.5
'i 8)3.5375000
'f
.4421875
2. Reduce 9 inches to the decimal of a foot. Ans. .75'
3. Reduce 1 foot, 6 inches, to the decimal of a yard.
Ans. .5*
4. Reduce 4 furlongs, 20 poles, to the decimal of a mile.
Ans. .5625.
5. Reduce 7 furlongs, 39 poles, 5 yards, 1 foot, 5 inches,
to the decimal of a mile. Ans. .9999842.+
6* Reduce 35 perches to the decimal of an acre.
Ans. .21875-
7. Reduce 1 rood, 12 perches, to the decimal of an acre.
Ans. .325.
8. Reduce 7 gallons to the decimal of a hogshead.
Ans. .111111.+
9. Reduce one cubical foot to the decimal of a bushel, struck
measure. Ans. .80356.+
10. Reduce 15 grains, Troy, to the decimal of a pound. '
Ans. .0026.+
11. Reduce 16 pennyweights, 9 grains, to the decimal of
an ounce. Ans. .8375.
12. Reduce 3 quarters, 24 pounds, to the decimal of a hun-
dred weight. Am. 99*
13. Reduce 6 ounces, 6 drams, 2 scruples^ 14 grains, to the
decimal of a pound. Ans. .571875.
14. Reduce 1 inch to the decimal of & y&rd.
And. 02777.+
DEDUCTION OF DECIMALS. 81
15. Reduce 3 quarters, 3 nails, 2 inches, to the decimal of
a yard. Ans. .993.+
16. Reduce 26 cubic feet to the decimal of a cubic yard.
Ans. .963, nearly.
CASE III. .
• To find tlie Value of any given Decimal Fraction.
Rule.
Multiply the given decimal by as many of the next lower
denomination as make one of tne higher, separating to the
right hand as many decimal figures as there are in the given
decimal.
Examples.
1. What is the value of .88125 of a pound Troy ?
lb.
.88125
12
10.57500 Ounces.
20
1 1 .500 Pennyweights.
24
12.0 Grains.
Ans. 10 ounces, 11 pennyweights, 12 grains.
2. What is the value of .95 of a mile ?
M.
.95
8
7.60 Furlongs*
40
2.4 Poles.
5.5
22.0 Yards. •
And. 7 furlongSi 2 poledi 2) y&rdd.
SQ mnj>vcrtos of SEciMAiiS*
3. What is the value of .17 of a jear ?
.17
365.25
85
84
85
102
51
62.0925 Days.
24
3700
1850
2.2200 Hours.
60
13.20 Minutes.
60
^■Mtfte
12.0 Seconds.
Ans. 62 days, 2 hours, 13 minutes, 12 seconds.
4. What is the value of .561 of a furlong ?
Ans. 22 ps. 2 yds. 1 ft. 3.12 inches.
5. W*hat is the value of .47 of a mile P
Ans. 3 fur. 80 p. 2 yds. 7.2 in.
6. What is the value of .521 of a degree ?
Ans. 86 m. 16 fur. 30 p. 2 yds. 7.2 in.
7. What is the value of .16 of an acre ? Ans. 25.6 ps.
8. What is the value of .29 of a perch ?
Ans. 8 sq. yds. 6 sq. ft. 113.72 sq. in.
D. What is the value of .93 of a bushel ?
Ans. 3 pecks, 5.76 quarts.
10. What is the value of .6875 of a bushel? Ans.2ps.6qts.
11. What is the value of .765 of a pound Troy ?
Ans. 9 oz. 3 dwts. 14.4 grs.
12. What is the value of .01 of an otince Troy ?
♦ Ans. 4.8 grs*
13» What i».the^ valu« 4>f .583 of d pound avoirdupois ?
Ans. 9 oz. 9.248 dt«
4MIACnCAt ^VKSTIOHS*
88
14. What
15. What
16. What
17. What
18. What
19. What
ts the raltte of ,79 of a hundred weight ?
Ans. 3 qrs. 4 Its.
is the value of .674 of a ton ?
Ans. 13 C. 1 qr. 23 Ib^
LS the value of .75 of a scruple ? Ans. 15 grs.
is the value of .67 of a great gross ?
Ans. 96 dozen, 5«78«
is the value of .875 of a yard ?
Ans. 8 qrs. 2 na».
is the value of .125 of a yard ? Ans. 2 nas«
20. How many yards, quarters and nails, are equal to
16.9375 yards? Ans. 16 yd?. 3 qrs. 3 naa.
21. What is the value of .49 of a day and .24 of an hour ?
Ans. 12 hours.
22. What is the value of tSG of an acre and .96 of a rood ?
Ans. 2 roods.
23. What is the value of «86 of a pole and .77 of a yard f
Ans. 1 pole.
24. What is the value of .72 of a nail and .72 of an inch ?
Ans. 1.04 nails«
25. What is the value of .8 of a quarter and .8 of a nail ?
Ans. 1 qr.
26. W^hat id the value of *75 of a yard and .76 of a foot ?
Ans. 1 yd.
27. What is the difference between .75 of a yard, and .75
of a foot ? Ans. 1 foot, 6 inches.
28. What is the difference between .7325 of a bushel, and
.5 of a peck ? Ans. 2 pecks, 3.44 quarts.
29. What is the difference between .875 of a pound avoir-
dupois, and .25 of an ounce i Ans. 13 oz, 12 drs.
30. What is the difference between .25 of a ton, and .25
of a hundred weight ? Ans. 4 C. 3 qrs.
81. What is the value of 5.75 yards ? Ans. 1 pole, 9 in.
PRACTICAL QUESTIONS.
It is essentially necessary that the learner should have ft
competent knowledge of decimals : to attain which, the fol-
lowing examples, in Multiplication and Division of Decimals*
are requisite. It will be recollected that cents, annexed to
dollars, are decimals of a dollar*
W PRACTXaAL QUESTIOXS*
1. What will 12 yards, 2 qrs. 1 nail of cloth come t3, at
4 dollars, 27 cents, per yard ?
[First reduce the quantity to decimals, then multiply by
the price.]
Thus, 4)1.00
4)2.25
12.5625
4.27 Price.
879375
251250
502500
53.641875
Ans. 53 dollars, 64 cents. +
2. What will 93 yards of linen come to, at 27 cents per
yard? Ans. g2.5.1l cts.
3. What will 71 yards of broad cloth come to, at 6 dollars,
59 cents, per yard ? Ans. 8467-89 cts.
4. What will 12 hundred of hay come to, at 12 dollars per
ton ? Ans. 87.20 cts.
5. What will 74 acres, 1 rood, 16 perches of land, amount
to, at 25 dollars per acre ? Ans. 1858 dolls. 75 cts.
6. What will 52 pounds of butter come to, at 12| cents
per pound ? Ans. 86*50 cts.
7. I demand the price of 4 J bushels of cloverseed, at
S3. 10 cts. per bushel. Ans. 13 dolls. 95 cts.
8. At 53 cents a bushel, what will 19 bushels of Indian
oorn come to ? Ans. 810.07 cts.
9. Calculate the amount of 8 acres, 2 roods, 17 perches of
land, at 25 dollars per acre ? Ans. 215.156 dolls.
10. What is the value of 7 gallons of wine, at 140 dollars
per hogshead ? ^ Ans. 15 dolls. 55 cts. 5 mills. +
11. What will a peck of potatoes come to, at 50 cents per
bushel ? Ans. 12|- cts.
12. What will one pound of silver come to, at 90 cents
per ounce ? Ans. 810.80 cts.
13. 1 demand the value of 13 barrels of corn, at two doU
lars, 96 cents, per barrel* Ans. 38 dolls* 48 ct«*
14. What is the value of 4 C. 3 qrs. 21 lbs. cf rice, at 3
cents per pound ? Ans. S14.88 cts.
15* If a kiln contains 876 bushels of lime, what %vill it
amount to at 11-J- cents per bushel ? Ans. S1C0.74 ct&.
16. What will a cheese, weighing 47 pounds, come to at
Bl- cents per pound ? Ans. 3 dolls. 5 els. 5 m.
17. What will 5 cords, 64 feet of black oak bark amount
to, at S5.40 cts. per cord ? Ans. 29 dolls. 70 cts*
18. What will 41 J- perches of mason work come to, at 48
cents a perch ? Ans. 19 dolls. 82 cts.
19. What will 963 pounds of pork come to, at S4.76 cts.
per 100 pounds ? Ans. 45 dolls. 74^ cts.
20. What will 312 days' work come to, at 40 cents per
day ? Ans. 124 dolls. 80 cts.
21. What will 105 shad come to, at 86.40 cts. per 100 ?
Ans. S6.72 cts.
22. Calculate the price of 765 pine shingles, at S10.50 cts.
per thousand. Ans. S8.03:| cts.
23. What is the value of 1 peck, 2 quails of cranberries,
^t 4 dollars per bushel ? Ans. 1 dollar, 50 cts.
24. New Italy, July 17th, 1835.
Mr. Elisha Buyers,
Bought of Samuel Sellers :
6^ Yards of blue broadcloth, at S5.12|- 8
31- " Cambric, - - at .72
9^ •* Black silk, - at .90
5J " Satin, - - at 1.12J-
7J- " Lace, - - ajt .621
51 •• Cassinet, - - at 1.0e|-
S60.00
25. Required the value of J- of a cord of wood, at S4.S0
ots. per cord. Ans. 83.75 ct».
* 26. At 810.80 cts. per pound, what is silver per ounce ?
Ans. 90 cts.
27. If 4 C. 3 qrs. 21 lbs. of rice sell for 814.88 cents,
what is it per pound ? Ans. 3 cts«
28. If 93 yards of linen sell for 25 dollars, 11 cents, what
is it.per yard ? *. Ans. 27 cts.
2®. Sold 7i yards of broadcloth for 842*60 cents, what
was it per yard ? Ans. 85.68 cts.
88 styais kule of THasa.
30. What is the value of 1 cwt. of hay, at 14 dollars per
ton ? Ang* 70 cts.
31. If 19 A. 3 R. 10 P. of land sell for 400 dollars, what
is it per acre ? Ans. S20.19 cts. nearly.
32. If 21^ pounds of butter sell for S4.25 cts., wliat is it
per pound ? Ans. 20 cts.
33. If a load of potatoes, containing 41 bushels, 3 pecks, sell
for 820.87^- cts., how much are they per bushel. Ans. 50 cts.
34. A kiln of lime, containing 744 bushels, sells for 96 dol-
lars, 72 cents, how much is it per bushel. Ans. 13 cts.
33. If 317 bushels, 1 peck of lime, be spread over 5 acres, 2
roods, 23. perches, how much is it per acre? Ans. 56 bus.
36. Sold 71 bushels, 3 pecks, 4 quarts, of buckwheat, for 50
dollars—- What was is it per bushel h Ans. 69 cts. 62 m.+
37. Bought 1980 cedar shingles for g23.76 cents, what wag
the price per thousand ? Ans. 12 dollars.
33. What is the value of one pound of coffee, at 12 dollars
per cwt. ? Ans. 12 cts.
39. Bought a Jag of coffee, containing 58 pounds, at 12
cents per pound ; another, containing 44 pounds, at 8 cts.
per pound : they were mixed, and sold at such a price as to
gain 83.76 cts- on the whole— What was the price this mix-
tare sold at per pound ?
56 X .12 =* 6.72 Dol.
44 X .08 = 3.52 And 1,00)14.00
100 Cost 10.24 Ans. 14 Cts. per lb.
Gain, 3.76
Sold for 14.00
40. What is the price of I sheet of paper, at 2 dolls. 36
cents per ream } Ans. 5 mills, or J- cent.
THE SIXGLE RULE OP THREE.
Th6 single rule of three teaches, by three numbere
given, to find a fourth, in such proportion to the third as the
second is to the first. /
RCLS FOR STATIKG.
Place th«t number for the third term, which is of the same
name with the answer. Then consider, from the nature of
8t)rOLS &UL£ OF THAB£« 87
the question, whether ihe answer is required to be greater or
less than this third term : if gi*eater, place the greater of the
other given numbers on the left, for the second term ; and the
less, on the left of this, for the first term. But if the answer
is required to be less than the third term, place the less num*
ber for the second term, and the greater for the first
Rule.
If the first and second terms be not of one denomination,
reduce both to the lowest in either, and the third to its lowest
denomination mentioned* Multiply the second and third
terms together, and divide the product by the first : the quo-
tient will be the answer to the question, in the same denomina-
tion you left the third term in.
, Proof, — Invert the question ; that is, place the answer for
the first term, the third term for the second, and the second
for the third. Multiply these second and third terms together,
and divide by the first | and, if right, the quotient will be the
same as the first term of the given question*
Note 1.— The pulse of a person in health beats seventy-five
times in a minute.
Note 2.— Sound moves at the rate of 1142 feet in a second,
Exojmples*
1. If a person sleep 2 hours per day, more than necessary,
for the terra of 10 years, how long does he deprive himself of
^e enjoyments of life, by unnecessary slumbering ?
D. yrs. H,
As 1 ; 10 :: 2
di>5.25
3652.5
2
24)7305.0(804 D. 9 H. Answer*
72
105
9
2. Bought 25 Ai 1 i^ood, 10 |)terches of latitd, at 87 doltar%
r acre : I demand the amounts Ans. 936 dolls. 56^ ct«.
88 SIN6t£ RULE Of THREfi.
3. If 4 pounds of cheese cost 47 cents, what will 9 pounds
cost? Ans. S1.05| cts.
4. What will 5J yards of muslin come to, at 12 cents per
yard ? Ans. 66 cts.
5. What will 96 yards of broadcloth come to, at 4.56^ cts.
per yard ? Ans. 438 dolls.
6. Required the value of 96 acres, 1 rood, 12 perches, at
17 dolls. 40 cts. per acre. Ans. 1676.055 dollars.
7. What is the value of 12 bushels, 3 pecks, 7 quarts of
wheat, at 99 J- cents per bushel.
Ans. 12 dolls. 90 cts. 4 mills, nearly.
8. What quantity of rice will S67.20 cts. buy, at 8 dollars
per C. ? Ans. 22 C. 1 qr. 15 lbs.
9. Bought 12 yards, 1 qr. 1 na. of cassinet, for 1 3 dollars,
what was it per yard ? Ans. 81.05| cts.+
10. When a bankrupt compounds with his creditors, at 65
cents in the dollar, what does that creditor lose to whom he
owes 1200 dollars ? Ans. 420 dollars.
11. What sum will pay for 16 pieces of cloth, each 19 yds.
1 qr. at 5 dollars per yard ? Ans. 1540 dollars.
12. If 1 C. 1 qr. 16 lbs. of iron, be worth 10 dollars, what
is it per ton ? Ans. 141 dolls. 84 cts. 4 mills, nearly.
13. What will 16 C. 3 qrs. 4 lbs. of tobacco come to, at
14 cts. per pound ? Ans. §235.06 ctS.
14. If 4674 shingles cost 87 dollars, 39 cents, 2 mills,
what price are they per thousand ? . Ans. 8 dolls.
15. What will 5943 cedar rails amount to, at 12 dollars
per hundred ? Ans. 8713.16 cts.
16. 5'^quired the price of 26 pounds, 10 ounces of loaf
sngar, at 14 dolls. 46 cts. per €. ?
Ans. 3 dollars, 85 cents, nearly.
17. If 1 J lbs. butter cost 13;^ cents, what is the price of 5^
pounds ? Ans. 46 cts. 3| m.
18. What will 19 bags of coffee, each containing 4I2- lbs.
oome to, at 11^ cents per pound ? Ans. 88.70625 dollars.
19» Sold 5^ yards of cambric, at the rate of two dollars for
3 yards, what is the amount ? Ans. S3.50 cts.
20* How many ringg, each weighing 4dwts. 13 grains, may
be made of 1 pound, 10 ounces, 14 pennyweights, 4 grains of
gcdd ? Ans. 100, nearly.
» 21 How many parcels, of 5 lb. 7 lb. 9 lb. and 10 lb., can I
haie out of 9 hogsheads of tobacco, each weighing neat 4 cwt-
I qr. 9 pounds ? Ans. 126.
SZNGLX RULE OF TH&KS^ 89^
22. How many steps of 2 ft. 9 in. will a man take in walk*
iag 5 miles, 1 furlong^ 26 poles, 2 yards, 2 feet, 3 inches ?
Ans. 9999.
23. If 4 C. 1 qr. of hay cost 3 dollars, what will 1 qr. 13
jMunds cost ? Ans. 26 cents, 8 mills. +
24. If a footman perform a journey in 4 days, when the
days are 12 hours long, how many days will it require of 16
hours long to perform the same journey ? Ans. 3 days.
25. If a staff, 6 feet long, cast a shade (on level ground) 9
feet-— What is the height of that steeple, whose shade at the
same time measures 100 yards ? Ans. 200 feet.
26. How long will it take 7 men to complete a piece of
work, which 5 men can do in 21 days ? Ans. 15 days*
27. How much in length, that is 9 inches lH*oad, will make
a square foot? Ans. 16 inches.
1^. If a pair of stockings cost 78 cents, how many dozen
pair can I buy for 468 dollars ? Ans. 50.
29. If my horse stands me in 13|^ cents per day keeping,
what will be the charge of 9 horses for 10 weeks ?
Ans. 85 dollars, 05 cts.
30. Borrowed of my friend, S49.50 cts. for 7 months, and
he hath occasion, another time, to borrow of me for 11 months
— ^How much must I lend him to requite his former kindness
to me ? • Aiis. £31.50 cts.
, 31* A merchant bought 37 pieces of stuff, which cost him
S416.25 cts. at 75 cents per yard : I demand how many yards
were in each piece. Ans. 1§.
32. If 27 men can build a. house in 100 days, how many
days will it take 180 men ? Ans. 15.
33. If the carriage of 3 cwt. 1 qr. for 20 miles, be one dol-
lar — How far may I have 4 T. 5 cwt. 1 qr. 9 lb. carried, for
the same money? Ans. 1340|- yards.
34. What is the half year's rent of 85 acres of land, at
S1.25 cts. per acre, per annum ? Ans. g53;12|^ cts.
35. If a man spend 7 cents per day for spirituous liquors
^^What will it amount to in 4 years ? Ans. S102.27 ets.
36. A. has 6 acres of pasture, ia which he has 5 head of
cattle ; B. has 3 acres adjoining, in which He has 4 head ; C
has 7 head, but no pasture : he succeeds in striking a bar-
gain with A. and B. to remove their line fence, and let all of
their cattle go together— and agrees to pay them 8 dollars for
G
90 SINGLE RCL£ Ot tfiRE£.
his share of the pasture. I desire to know how much of ihc
money falls to each man's share. •
6 5
3 4
— 7
9 Wholenumber of acres. —
16 Number of cattle pastured.
H. H. A. A.
As 16 : 5 : : 9 : 2.8125 For A's cattle.
As 16 : 4 : ; 9 : 2.25 For B's cattle.
As 16 : 7 : : 9 : 3*9375 For C's cattle, for which
he pays 8 dollars.
6 A. — ^2.8125 A. = 3.1875 A. for which A. is to receive pay*
3 A.— 2.25 A a= .75 A. for which B. is to receive pay.
A. A. dolls, gcts.m.
As 3.9375 : 3.1875 : : 8 : 6.47.6+ A's share. > .^
As 3.9375 : .75 : : 8 : 1.52.4 nearly, B's share. 5 ^°^'
37.' A gun being fired on one side of a river, an observer,
directly opposite, counts 12 pulsations at his wrist between
seeing the flash and hearing the report^-What was the breadth
of tlie river ? Ans. 2 M. 24 p. 2 yds. 1.2 ft
38. A gentleman hath an anijjial income of 1000 dollars ;
I desire to know how much he may spend daily, that at the
end of the year he may lay up S250, and give to the poor
monthly 25 dollars. Ans. 1 del. 23 cts. 3 mills.
39. A draper bought 15 packages of cloth, each package
containing 5 pieces, and each piece 31 yards; and paid at the
rate of 1000 dollars for every 10 packages. I desire to know
what the 15 packages stood him in. Ans. 1500 dolls,
40. What IS the cost of 1 yard, 3 quarters, 8 nails of vel-
vet, wlien a piece containing 15 yards, 1 quarter, 1 nail, cost
17 dollars, 20 cents ? Ans. 2 dolls. 17 cts. 6 m.+
41. If it take 290 Italian mulberry trees to plant one acre,
how many will it take to plant 8 acres, 2 roods, 17 perches ;
and what will be the cost, supposing the price to be 70 dolls, for
a hundred dozen trees ? Ans. 2496 trees ; cost, S145.60 cts.
42. What will 13 ounces of silk cost, if 4 pounds cost 22
dollars ? Ans. 4.46875 dollars.
43. Bought a pair of silver buckles, weighing 37 penny-
weights, 12 grains, at 1 dol. 12J cts. per ounce — ^What did
tiiey cost ? Ans. S2.109375 doUa.
J>OUBL£ RULE OF TBRES. 91
44. If tte report of a piece of ordnance be heard one
minute and forty seconds after the flash was observed— the
distance is required, Ans. 21 M. 1106 yds. 2 ft.
45. If 40 gallons of water, in one hour, fall into a cistern,
containing 256 gallons ; and, by a pipe in the cistern, 24 gal-
lons run out in an hour— in what time will it be filled.
Ans. 16 hours.
46. A person failing in trade, owes 1976 dollars, and the
inventory of his eflfects amounts to but 1079 dollars— How
much will this produce per dollar to his creditors ?
Ans. 54 cts. 6 mills.
47. If a man's annual income be g215.50 cts. and he ex-*
pend 59 cents per day, what tioes he save at the end of four
years ? . Ans. 1 cent.
48. A. can chop a cord of wood in two hours ; B. in three
hours, and C. in three hours and twenty minutes. I desire
to know how long it will take them all to chop a cord ?
Ans. 55|- M.
49. If I buy 10 acres, 1 rood, 29 perches of land for four
hundred dollars, and sell it again at 40 dollars per acre— do
I gain or lose, and how much ? Ans. 817.25 gain.
50. Sold 31 dozen, 4 pouUdB of candles, at the rate of 46
cents for 5 pounds : I desire to know how much they come to.
Ans. 34 dolls. 59 cts. 2 mills.
51. If 1| lb. of coffee cost 15^ cents, what will 4| pounds
come to ? Ans. 43 cts. 2 m.+
THE DOUBLE RUUB OF THREE,
Is so called, because it is composed of five given terms, to
find a sixth — ^three of which are a supposition, and two a
demand.
Rule.
Place that term which is of the same kind with the term
sought, for the third term. Complete a statement in the Sin-
gle Rule, as already taught, with this third term and each pair
of similar terms : reduce the third term to its lowest denom-
inatiou mentioned, and the similar terms to the lowest de-
nomination mentioned in either. Multiply the two quantities
in the first term together, and also the two quantities in the
second term together. It is then reduced to the Single Rule
I 82 JOOUBLE KUtE OF TRREIT^
of Three.. Multiply the second and third terms togefter, axu£
divide by the first— the quotient will be the answer.
Proof-'hA in tiie Single Rule of Three.
ExampUd,
1. If S6 acres of grass be mowed by 8 men in 6 days* hoir ^
many acres may 24 men mow in 2S days ?
Thus, 8 Men 24 Men
6 Days 38 Days
Acres..
48 : 912 : t 56
5472
4560
r 6)51072
484
1064 Acres. Answer.
In this 'question, the term sought is acres ; therefore, 5ff
acres must be the third term ; and, as 24 men will mow more
grass in 38 days than 8 men in 6 days, the 24 must be placed
for the second term, and the 8 for tn,e first.
2. If 24 pounds of bread be sufficient for 4 men, 24 days
—How many pounds will suffice 16 men, 12 days ?
Ans. 48 lbs.
8. If the carriage of 115 lb., 25 miles, be 21.50 cts.— how
far can I have 1200 pounds carried for 25 dollars ?
Ans. 39 M. 1637 yds.
4. If 10 men can accomplish a piece of work in 30 days,
working 12 hours per day, now long will it take 6 men, work-
ing 16 hours per day, to perform the same ? Ans. 13i days.
5. If 16 dollars pay 8 men for 5 days' work, how much
will pay 32 men for 24 days' work ? Ans. gd07*20 cts.
6. If 100 dollars, in 12 months, gain 5 dollars interest, what
principal will gain 12 dollars, 40 cents, in 7 months ?
Ans. 435.1438 dolls.
J>RACTieB.
93>
H. If Sliorses eat 8 bushels of oats in 16 days, how many
liorses will eat 40 bushels in 8 days ? An%. 20 horses.
8. If 8 men in 14 days build 2000 pannels of fence, how
many men must there be to build 1500 pannels in 4 days P
Ans. 21.
9. In a family, consisting of 7 persons, there are used 2
tjwt. of flour inS weeks, how much will suffice a family of 14
persons, 8 days ? Ans. 1 cwt. 2 qr. 2| lbs.
10. When 12 oxen graze down 16^ acres' iji 20 days, how
much of like pasture would suffice 24 such cattle for 100
days P Ans. 162| acres.
11. If 12 persons receive 4.625 dollars for 1 day's labor,
how much should 4 persons have for 10^ days' work P
Ans. 16.1875 dolls.
12. What money, at 8| per cent, per annum, will clear 77
dollars in 1 year and 3 months? Ans. 1760 dolls.
PRACTICE.
Practice is a short method of finding the value of any
quantity of goods, at a ^ven price^ pel' yard, pound, dozen,
&c. All questions in this rule are performed by takii^ ali-
quot, or even parts, by which means many tedious reductions
are avoided-— uie tables of which are as ^lows :
TABLES.
oz.dwt.gr,
1 «
14
1 6 16
1 10
2
2 8
^
4
6
1 ■
1
r
1
T
1
T
frg
T
1
i
ij
Peck. qt.
1
3
i[i
i)
cwt.qr.
2
2 2
4
5
10
R. P.
16
20
32
00
00
It g.
1
2
IT
1
T
i
iJ
3
mt
qr4 na* in.
S
4
2
'6
1 Q
2
tm^m
94
PRACTICE.
Rule.
Multiply the price by the integers of the quantity, and take
parts of the price for the rest.
Examples.
1. 53 pounds, 10 ounces, 16 pennyweights, 13 grains, at
S5.76 cts. per pound.
D.cts,
5.76
53
oz.
6
i
4
1
7
dwt.
10
1
5
I
1
i
gr-
12
1
1
A
1728
2880
288
192
24
12
24
12
1
Value of 6 ounces.
4 ounces.
10 pennyweights.
5 do.
1 do.
12 grains.
1 do.
(C
((
tc
ft
((
((
310.477 Answer.
In this question I say, 6 ounces are 4 of a pound, and 4
ounces are ^^ of a pound ; for both of which, parts are to be
taken of S5.76 cents, because they are both parts of a pound,
and 85.76 cts. is the price of d, pound. Then I say, 10 pen-
nyweights are ^ of 4 ounces : this part must be taken into
192, the value of 4 ounces. I then say, 5 pennyweights are
i of 10 pennyweights: this part must be taken into 24, the
value of 10 pennyweights. I then say, 1 pennyweight is } of
5 pennyweights : tliis part must be taken into 12, the value of
6 pennyweights. I then say, 12 grains are i a pennyweight :
this must be taken into 24, the value of 1 penny weight. Then
I say, 1 grain is -^j of 12 grains : 1 take this into 12 grains^
Add the product of the integer to the quotients produced by
the parts, and the sum, 310 dollars, 47 cents, 7 mills, is the
answer,
2. 16 lb. ^oz. 16 dwts. 4 grs. at 29 cts. per pound. S cts. m,
Ans.4.78 +
8. 6 lb. 2 oz. 11 dwts. 17 gri. at 41 cts^ " 2.13.8+
4. 3 lb. 1 oz. 12 dwts* m grt* at 64 cts* *^ 1.36,6+
r
(QUESTIONS FOR EXEROISbT 95
5. 17 lb* 2 oz. 19 dwts, 16 grs. at 59 cents g ctd.m.
|>erlb. Ans.l0.17,6.+
6. 34 lb, 1 oz. 11 dwts. 5 grs. at gl.l6 per lb. 39.59.+
7. 5 C. 3 qrs. 6 lb. at 12 dollars, per ton. 3.48.6-
8. 7 C. 1 qr. 10 lb. at 84.80 cts. per. C. 35.28.
9. 16 C. 1 qr. 15 lb. at S4.12i cts. per C. 67-65.
TO. 1 A. 2 R. 12 p. at g25.60 cts. per acre. 40.32.
11.5 Yds. 1 qr. 2 nas. 2 in. at 86.84 cts. per yard. 37.14J
12. 4 Bu. 2 P. 7 qts. at 81-28 cts,. per bushel. 6.04
13. Bought 19 C. 3 qrs. 24 lbs. of iron, at 99 dolls. 99
cts. per ton : required the amount. Ans. 99 dolls. 94 cts.
14. If a yard of cloth cost g4.91 cts., what is the value of
69 yds. 2 qrs. 2 nails ? Ans. 341.85875 dolls.
15. What is the value of 12 Bu. 2 P. 1 qt. of oats, at 39s
cents per bushel ? Ans. 84.95 cts. nearly.
16. If land be rated at 42 dollars per acre, what is the
value of a plantation containing 243 A. 3 R. 10 P.?
^ Ans. 810240.125 cts.
17. If corn sell for 52 ceM per bushel, what must I pay
for 16 bushels, 3 quarts ? Ans. 8.36875 dolls.
QUESTIONS FOR EXERCISE
In the preceding Rules*
1. Five auditors, in a public office, receive 70 dollars a
quarter, for which they attend 7 times during that period ;
but if one or more be absent at any timej then the absent
persons' shares are divided among those who attend. A. and
B. never miss attendance on these occasions; but C. and D.
are absent four times, viz : the first, third, fifth and seventh
days of meeting. E. is absent three times, viz: the second,
fourth and sixth days. When payment becomes due, I wish
to know what each is to receive.
Ds. ds. 8 8
As 7 : 1 : : 70 : 10 The Wages for each day^s attendance.
Aud.Aud. 8 8
As 5 : 1 : : 10 : 2 Each auditor's wages for one day.
C. and D. were each absent four days, when each of the
Oth^r thret wer^ in attendance j therefore^ their wages for the
46 4lVB8TlOirS FOR SXEftOISC.
time of their absence (which are 16 dollars) must be equally
divided between A. B. and £•
Aud.Aud. S Sets.
Aa 3 : 1 ; : 16 : 5«d3} Coming to A. B. and E« each*
£. Was absent three days, when each of the others were ia
attendance; therefore, his wa^es for these three days, which i»
six dollars, must be equally divided between A. B. C. and D.
Aud. Aud. % % cts;
As 4 : 1 ; : 6 : 1.50 •Coming to A. B.C. and D. each.
A's wages for the term, viz : 7 days, at 2 dollars
per dav, S14*00cts«
Share of C's and D's wages, - . . 5.33|
Share of E's wages, 1.50
A. receives 20«83j
B's wages for tlie tenn, viz : "J^ays, at 2 dollars
per day, ' w " S14.00ct8#
Share of C's and D's wages, - - - - 5.33^
Share of E's wages, 1.50
B. received 20.83|
C's wages, viz : 3 days, at two dollars per day, 86.00 cts.
Share of E's wages, 1.50
C. received 7.50
D's wages, viz : 3 days, at two dollars per day, S6.00 cts*
Share of E's wages, 1.50
D. received £7.50
E's wages, viz : 4 days, at two dollars per day, S8.00 cts*
Share of C's and D's wages, • . - 5*33^
E. received 13^
2. The Spectator mentions a club of fat people, whose
number was only 15, and yet weighed three tons : what was
the weight of each person, on an average. Ans. 4 cwt.
3. What quantity of lining, 3 qrs. of a yard wide, will it
take to line 7i yards of cloth, li yards wide?
, Ans. 15 yards.
4. What quantity of stutf, that is 3 qrs. of a yard wide*
will line 17 yardd of ailki that i« 6 qrft. wide ? Ans. 34 yds.
<IQSSTI0HS FOR SXEltOXSE* 8T
5* I demand the amount of 90 cords, 21 feet of bark, at 7
dollars, 50 cents per cord. Ans. 376 dolls. 23 cta»
^. If 5 men can make 240 pair of shoes in 80 days, how
many men can make 1200 pair in 75 days ? Ans. 10 men,
7. If 3 men can do 18 rods of ditching in 6 days, hov
many rods may be done by 24 men in 8 days ? Ans. 192.
8. The breadth of a river is required — at one side of which,
A* firing a gun, B. directly opposite, at the other, counts 6
pulsations at his wrist, between seeing the flash and hearing
the report. Ans. 1 mile, 67.2 yards.
9. Bought 104 bushels, 3 pecks of potatoes, at 31| cents
per bushel, what do they amount to ? Ans^S32.734375.
10. The earth's orbit, or track, which it describes round
the sun in 365 days, 6 hours, is computed, by astronomers, to
be about 596900000 miles— How far, then, per minute, must
we \^ carried through the firmament by this wonderful motion i
• Ans. 1134 miles, 7 furlongs. +
11. What will a yard of cloth cost, when 4 pieces, each
containing 21 yards, cost 504 dollars ? Ans. 6 dolls.
12. Bought a granary of wheat, containing 100 solid feet,
at the rate of one dollar per bushel : I wish to know the cost
■of it. Ans. 80 dolls. 35 cts. 6 mu
13. Bought 4 sections of land, for four thousand dollai^-*-
How much do I pay per acre ? Ans. S1.56I cts,
. 14. Sold 4 sections of land, at S1.93I cts. per acre — How
much does it amount to ? Ans. 4960 dollars.
15. Laid out 500 dollars in hats, at 2 dolls. 50 cts. a piece
—How many do I receive ? Ans. 200.
16. A. and B. depart from the same place, at the same
time. A. travels due west, at the rate of 30 miles per day.
B. travels due east, at the rate of 25 miles per day. A. rs
<letained, by indisposition, 4 days ; and B. alter having pro-
<5eeded on his journey 40 miles, returns for some articles of
wearing apparel ; remains at home one day, and undertakes
his joi^rney anew. I wish to know how far they are apart at
the end of ten days ; also, how far would they be apart if
they had both been travelling due east or west ?
Ans. 325 miles ; E. or W. 35 miles.
17- Laid out 300 dollars for wheat and rye : the value of
the wheat was 250 dollars, and the quantity of rye 100
bushels ; also, for every & bu^els of wheat there were 2 of
98 QUESTIONS FOR EXERCISE.
rye-— How many bushels of wheat were there, and what wa»
the value of a bushel of each ?
Ans. 250 bushels of wheat, at 1 dollar ; rye, 50 cts.
18. Bought a quantity of cloth, at the rate of 812.80 cts.
for every j3 yards ; of which, a certain part was sold at the
rate of g25.25 cts. for every 5 yards, and gained thereby as
much as 105 yards cost — How many yards were sold ?
Ans. 571 yds. 3 qrs. 2 nas,+
19. Bought 5 pipes of wine, containing 120i, 126?, 125,
127J and 128i gallons : the price of the two first was gl.50
cts. per gallon, and the three last, gl.75 cts. per gallon. I
wisli to know the amount. Ans. gl037.31i cts.
20. If 12 men in 4 days mow 72 acres of grass, how many
acres will 2 men mow in one day ? Ans. 3.
21. Bought 574 bushels of lime, at 11 dolls. 875 cts. per
hundred bushels — How much does it amount to P ^
Ans. S68.1625-
22. Sold 535 bushels of lime for 12.5 cts. per bushel — How
much does it amount to ? Ans. S66.875 cts.
23. A farmer, having sown 12 bushels, found that it pro-
duced 150 bushels the first year : now, supposing he sows 20
bushels of grain, each year, for 16 years successively, what
will be his whole increase at the expiration of the last year ?
Ans. 4000 bushels.
24. If li pounds of pork sell for 6i cents, what is the
value of 6i pounds? Ans. 26 cts. 04 m.+
25. What will 59 pounds of cheese come to, at 7i cents
per pound ? Ans. 84.5^1 cts.
26. What is the value of 1 yard, 1 quarter, 1 nail, H
inches of broad cloth, at the rate of 85.97? cts. for li yards P
Ans. 86.44 cts. nearly.
27. If eggs sell at 6i cts. per dozen, how much is that for
one hundred eggs ? ^ Ans. 53 cts.+
28. If a basket of sweet potatoes,* containing 3 pecks, sell
for 431 cents, how much is that per bushel P Ans. 58^ cts.
29. What must I pay for 1674 bricks, at 85.40 cts. per
thousand P Ans. 89*04 cts. nearly.
30. Paid one cent a piece for 2548 cedar shingles ; twenty
oents per hundred for carriage, and 70 cents per thousand for
jointings— iHow much do they stand me in P
Ans. 832.36 cta» nearly*
QUESTIONS FOR EXERCISE- 99
31* If the pasturing of 5 head of cattle, 5 weeks, be S6*23
^ents, how much will the pasturing of 117 head come to, in 4
weeks? Ans. 117 dollars.
32. What is tobacco an ounce, when 5 cwt. 3 qrs. 7 lbs* 4
oz. 8 dr. sell for §93. 16^ cents ? Ans. 1 cent.
33. What will 1$ pecks of the Siberian crab apple come
to, at 181 cents per quart ? Ans. S2.25 cts%
34. At S 1.57a cts. per barrel, what is cider per gallon ?
Ans. 5 cts.
35. A horse and cow can eat a certain stack of haj in 21
days ; the cow can eat the same quantity in 70 days — How
long would it take the horse alone ? Ans. 80 days,
36. W^hat will 27 Cwt. 3 qrs. 1 lb. of buckwheat flour
Come to, when 4k cwt. sell for 15 dollars ?
Ans. S92.53J cts.
37. If a barrel of mackerel, containing 175, cost six dol-
lars ; how much is the cost of half a dozen ?
Ans. 2O5 cents. +
38. Suppose an innkeeper buys one barrel of brandy at two
dollars per gallon, and afterwards retails it out at 12j cents
per gill — ^I demand what it Sold for, (allowing a waste of one
gfU per gallon) ; and what he gained thereon.
Ans. Sold for S122.06i cts. }
Gained, 859.061 cts. 3
39. If I borrow of my friend 11 dollars on the first of Au-
gust, and pay him again on the first of October ; and ke have
occasion to borrow 20 dollars of me on the first of November
■^When will the payment be due ?
Ans. The 5th of December.
40. A person bequeathed to his widow 1000 dollars ; to
each of his five children 800 dollars ; he had been 37i years
in trade, and had cleared (at an average) 80 dollars a year-*
What had he to begin with ? Ans. glMMX).
41. An oil -man bought 9 C. 1 qr. 20 pounds of oil—
How many gallons were there ; allowing 7i lbs. to a gallon ?
Ans. 126.
42. How many yards of cloth, at S4-25 cts. per yard, can
I have for 16 C. 2 qr. 14 lb. of wool, at 85 cents pei*
pound? . Ans. 137. +
43. What is the value of 12 barrels of soap, at 6? cents per
pound ; each barrel containing 248 pounds ? Ans. 2186,00*
100 iirrEREST*
44. An usurer put out 75 dollars, for 12 months ; and re-
ceived for principal and inter.e8t S79.50 cts.— I demand at
what rate per cent, he received interest. Ans. 6 per cent.
45. Bought 50 yards of cloth, for five times as many dol-
lars, and sold them again for six times as many : but if the
cloth had cost me as much as I sold it for, what should I have
sold it for to gain after the same rate ? Ans. 360 dollars.
INTEREST.
Interest is a premium allowed in the landing or forbear-
ance of a sum of money, according to a certain rate per cent,
agreed on for a determined space of time, which by law is
generally limited to 6 per cent, per annum.
The principal is the money lent, for which interest is to be
received.
Rate, or ratio, is the sum per cent, per annum agreed on.
The amount is the sum of principal and interest.
It is evident that the rate per cent, expressed decimally is
the ratio ; thus 6 per cent. = .06 the ratio ; 6i per cent.
=» .065 the ratio.
Interest is also applied to Commission, Brokerage, purcha-
sing Stock, and Insurance.
^ Rule.
Multiply the principal by the ratio, and point off as many
figures m the product as there are decimals in both factors,
for the int(Brest for one year, commission, brokerage, insu-
rance, &c.
For more years than one: multiply the interest of one
year by the number of years given in the question, and the
product will be the answer.
For months, take the aliquot parts of a year ; or for months
and days, for the months take the aliquot parts of a year, and
for the days, the aliquot parts of 30*44. Or reduce the months
and days to the decimal of a year, which multiply by the in-
terest of one year ; the product will be the answer.
When the rate is six per cent., for months, multiply the
principal by half the number of months, and remove the deci-
»«1 point two figures to the left hand.
iirrEREST* 101
To find the interest of any sum for months, weeks or days,
at any ratio.
Multiply the principal by the ratio, and that product by the
number of months, weeks or days given : and divide this pro-
duct by the months, weeks or days in a year for the answer.
Or, as the months, weeks or days in a yeaf are to the number
given, 80 is the interest of one year, to the interest required.
' Examples.
1. Wljat is the interest of 56 dollars for one year, at 6 per
[ cent, per annum?
56 principal.
.06 ratio.
3.36 interest. Ans.
2. Required the amount of a bond of S934.76, for four
years, at 7 per cent.
S 934.76 principal.
^07 ratio.
65.4332 interest of one year.
4 number of years.
261.7328 interest for four years.
934.76 principal.
1196.4928 amount. Answer.
3. Required the interest of £49.29 cts. for 3 years, 6 ma.
and 22.83 days, at 6 per cent.
S49.29 principal.
.06 ratio.
M.
6
k
da.
32.83
i
2.9574 interest for one year.
3
8.8722 int. for 3 years.
1.4787 for 6 months.
1848375 for 22.83 days.
10.5357375 Answer.
4* Required the amount of a bond of 604 dollars, for 10
months, at six per cent, per annum.
604 principal.
5 half the number of months.
30.20 interest.
604 / principal.
634.20 amount*
5. What is the interest of 108 dollars, for 11 months, at 7
per cent. ?
S
108 prindipal.
.07 ratio.
7.56
11 the months given.
Months in a year 12)83.16 ^
6.93 Answer.
6. What is the interest of 700 dollars, for 2 weeks, at 6
per cent. ?
S700 principal.
.06 ratio.
42.00
2 the weeks given,
Number of weeks in a year, 52.17857)84.00000(1.609. Ans.
52.17857
31821430
31307142
51428800
46960713
4468087
7. Required the interest oi £365^25 cts., for 75 days, at 5
^r cent*
tNTERESr. 103
S365.25 principal.
.05 ratio.
18.2625
75 given number of days.
II I II ■
913125
1278375
The days in a year, 365.25)1369.6875(83.75. Answer.
109575
273937
255675
182625
182625
8* Bought goods for a friend, to the amount of S537.42, at
1 J per cent commission ; required my demand.
8537.42
.015 ratio.
268710
53742
8.0613 Answer.
9. What is the interest of 8456.27 cts. for 5 years, at 6
per cent. ? Ans. 136.881 dolls.
10. Required the amount of 8127.40. for 3 years 12 days,
at 7 per cent. Ans. 8154.447.
11. Calculate the interest due on a bond of 5764 dollars,
for 16 months, at 55 per cent. Ans. 8422.69^.
12. My correspondent writes me word, that he has bought
goods to the amount of 1112 dollars, on my account, what
does his, commission come to, at 3$ per cent. ?
Ans. 838.92.
13. What is the interest of 1000 dollars, for 16 years, 7
months and 30 days, at 6^ per cent, per annum ?
Ans. 8999.92*8.
14. What is the interest of 135 dollars, for 10 days, at 5
per cerit. ? Ans. I85 cents, nearly.
15. Required the interest on a bond for 1000 dollars, gWn
104 INTEREST.
the 11th day of March, 1830, and taken up the first day of
August, 1835, at 6 percent* per annum.
Ans. 2323.45 dolls, nearly.
16. What is the amount of 400 dollars, for 4 years, 5
months and 12 days, at 5 per cent. ? Ans. g488.99 +
17. What will g4264.71 amount to in 10 years, at 4? per
oent. per annum ? Ans. S6183.8295*
18. What is the interest of one dollar, for 61 days, at 6
per cent. ? Ans. 1 cent.
19. What is the amount of one dollar, for 1461 days, at 6
per cent, per annum ? Ans. 21.24.
20. Required the value of a fifty dollar bank note, that is
5 per cent, below par. Ans. S47.50 cts.
21. Required the amount of a note of hand for 11 dollars
for two months, at 6 per cent. Ans. SI 1.11 cts.
22. What is the interest of 130 dollars for 100 days, at 6
per cent. ? Ans. 82.13$ cts.
23. What is the interest of 500 dollars for 81 months, at
04 per cent. ? An* £23.691 +
24. Required the value of 81750, United States Bank
stock, at 125 per cent. Ans. 82187.50 cts.
25. What is the amount of 1691 dollars for one day, at 7i
per cent, per annum. ? Ans. 81691.347.
26. An uncle left, by will, to his niece, 1500 dollars ; at
the time of her marriage, there were 5 years interest due on
the legacy, at 5i per cent, per annum — What sum must her
^ecutor pay ? Ans. 81893.75 cts.
27. Required the interest of 899^99 cts. for 366 days, at
6 per cent. Ans. S0;01 cts.
28. W^hat is the interest of 125 dollars, for one year, ^
months and 12 days, at 6 per cent per annum ?
Ans. 89.62 cts.
29. If I allow my factor 2| per cent, for commissibn, what
vmj he demand on the laying out of 976 dollars, 28 cents ?
Ans. 826.841 cts.
30. If a broker is employed to buy a quantity of goods, to
tiie value of 652 dollars, what is thebrokage at H per cent.?
Ans. 88.15 cts.
81. When a broker sells goods to the amount of 1008 dol-
fera, what mjiy he demand for brokage, if he is allowed 90
cents per cent.? Ans. 89<C72.
INTEREST. 105
S2« What is the purchase of 9748 dollars, bask stock, at
108* per cent. ? C 'A^^s. 810600.95 cts.
33. What is the interest of 950 dollars, for 20 weeks, at
6 per cent.? Ans. S21.848.
.34. What is the amount of 50 dollars, for 16 years and 8
months, M 6 per cent, per annum ? Ans. S100.00
35. What is the amount of 100 dollars, for 20 years, at 5
per cent, per annum? Ans. S200.00.
On computing interest on notes, fyc.
We have no special acts of Assembly on this subject.-—
Chief Justice M'Kean, in 1785, fixed upon the following rule
for calculating interest, [see 1st Dallas, p. 124] viz. That the
interest of the money paid in before the time, be deducted
from the interest of the whole sum due at the time appointed
hj the instrument for making the payment.
Examples*
1. A note, dated January 1st, 1835, was given for 160 dol-
lars, payable in one year, with 6 per cent, interest ; and on
Ae first of July following, was paid 100 dollars — What
balance remains due on said note, January 1st, 1836 ?
The note, S160.00
One year's interest, 9.60
Whole sum due at the time appointed for the
payment, - - - - - - 169.60
l^ly 1st, 1835, By cash, - - glOO.OO? ino nn
Jan. 1st, 1836, By int. of SIOO.OO, 3.005
Balance due Jan. 1st, 1836, 266.60
!J, A. received of B. his note for 400 dollars, dated July
«t, 1834, payable in 15 months, with six per cent, interest!;
and January 1st, 1835, A. received of B. 300 dollars, which
A. credited on said note — What sum must B. pay to A. on
the first of October, 1835 ? Ans. 8116.50 cts.
SL A note, dated January 1st, 1835, was given for 8160.00,
on demand, bearing interest at six per cent. \ and on the first
of July following, was paid 100 dollars — What balance re-
mains due on said note, January 1st, 1836 ?
H
106 tHTBItSST*
The note, -*-•-" gieOiOd
Interest of ftlGO for 6 months, to July 1st, 1895, 4<80
amM
Amount of the note at the payment, - - 164.80
Deduct the payment made, . . - 100.00
Balance of the note after the first payment, 64.80
Interest of 864.80 cts. for 6 mos. to Jan. 1st, 1836, 1.944
S66.74.4
4. A note, dated July 1st, 1834, ^vas given for 400 dollars,
on demand, bearing interest at six per cent. ; and on January
1st, 1835, was endorsed a payment of gSOO.OO : I demand
how much remained due on said note on the first of October^
1835 ? Ans. 8117.04.
When partial payments are endorsed before the note be-
comes due, this rule is applicable ; but in all other cases. Hie
resort must be made to the rule of court for the district where
the business is transacted. QSee the difference in the first
and third, also in the second and fourth examples : the balance
due on the fourth, being 8117.04 cts. in consequence of the
note being on demand and due at the time the first payment
was made ; and the balance due on the second, only 8116.50*
in consequence of the note not being due at the time the first
payment was made.^
Rule of Courts for computing Interest.
If it be one year or more from the time interest commene-
ed to the first payment, add the interest for the time to the
principal, deduct the payment from this amount: if there be
after payments made, add the interest on the balance due,
up to the next payment to the said balance ; deduct the pay-
ment from the amount as before, and so proceed from one
payment to another, mntil all the payments are absorbed, pro-
tided the time between one payment and another be one yea»
or more. But if any payment be made before one year,5
interest hath accrued, compute the interest on the principal
sum due on the obligation for one year, add it to the principal^
and compute the interest on the sum paid from Ihe time it
was paid up to the end of the year; add it to the sum paid.
tirrx&BST. 107
afti dedmet fhai sam from ihe principal tnd interest added as
before*
If any tiajments be made of a less sum than the interest
arisen' attne time of such payments, no interest is to be com-
pmted, but only (m ike principal sum for any period*
Hxampks.
1. A bond, dated January Ist, 1832, was given for 500 dol-
lars, at 6 per cent, interest, on which were endorsed three
equal annual payments, of gl87.05^ cts. each. I wish to
know if any tmng remains unpaid.
8
500 PrincipaL
.6 Ratio.
80.00 Interest the first year.
500
5da00 Amount
187.055 First payment
842.945 Balance after first payment
.06
20.57670 Interest on balance.
842.945
863.5217
187*055 Second payment
176.4667 Balance after second payment.
.06
10.588002 Interest on balance.
176.4667
187.055
187.055 Third payment
0.00 Ans. The full amount is paid.
2. A bond dated April 1st, 1881, was given for £266.50 cts.
at 6 per cent interesty and tiiere were payments endorsed
106 iirrERSsT.
upon it as follows, viz ; first payment, 850 October 1st, 1881 ?
second payment, 8100 January Ist, 1833; third payment,
S150 April 1st, 1835* I demand how much remains due on
said bond the first day of January 1836 P Ans. g9.16 cts^
3. A bond was given on the first of January, 1835, for
fS1200, and there were payments endorsed upon it as follows,
viz : first payment 600 dollars, July 1st, 1835; second pay-
ment, October 1st, 1835, of 400 dollars; required the balance
due on the 1st of January, 1836, interest at 6 per cent, per
annum. * Ahs. 248 dollars.
4, A note was given on the 10th of June, 1835^ for 56 dol-
lars 50 cents, and 25 dollars paid thereon on the 25th of
September following : I demand the sum due on the 25th of
December, 1835, at which time the note was taken up and
paid off— interest at 7 per cent, per annum. Ans. S33.20I.
CASE II.
To find the principal, when rate per cent., time and amount
are given.
Rule.
As the amount of glOO, at the rate and time given.
Is to the amount, (or sum given,)
So is SlOO,
To the principal required.
Or, add 100 to the product of the time and rate per cent*
for a divisor ; and annex two ciphers to- the amount, for a di-
vidend ; the quotient from thence arising will be the principal,
^r present worth.)
^ote — If the time be not years, reduce it to the decimal
part of a year, or years and decimal parts.
Examples.
1. What sum at interest for 11 years, will amount to
S453.18 cts. at 6 per cent, interest ?
glOO
.06
6.00
11^
66 interest of SlOO for 11 years.
+100
166 amount of glOO for 11 yearst
INTEREST. ' 109
As 166 : 458.18 :: 100
100
g
166)4531800(273 Ans.
332
1211
1162
498
498
Or thns by rule 2.
6 rate per cent. S453.18
11 time. 100
S
66 166)4531800(273 Ans.
100 332
166 cUvisoi!. 1211
1162
498
498
2. What principal, at interest for 2 years, at 5 per cent,
will amount to 253 dollars ? Ans. g230.
3. What sum, being put to interest for 5 years, at 7 per
cent will amount to g275.40 cts. ? Ans. 8204.
4. What principal at interest will amount to 811048.89i
cts. in one year and nine months, at 6 per cent. P
Ans. 9999 dollars.
5. What sum at interest for 16 years, at 4 per cent, inter-
est, will amount to g656 ? Ans. 8400.
6. A man at his decease bequeathed a certain sum to his
son, whose age then was 17 years and 3 months, to be put at
interest at 6 per cent, until he should arrive at the age af 21
years, which his guardian then found to be 8815.85 cts.— I
Wish to know how much wa* bequeathed by his father.
Ans. 8666.
110 nrniBXST.
CASE III.
To find the rate per cent, when Hie principal, time and
amoant are ^ven*
Rule.
Deduct the principal from the amount, and the remainder
will be the interest for the whole time : then saj.
As the product of the time and principal
Is to glOO,
So is the interest for the whole lime
To the rate per cent.
Hxamples*
1. At what rate per cent, will 674 dollars amount to
2754^ cts. in 2 ^ears ?
8674 principal. 8754.88 amount.
2 years. 674 principal.
1348 product. 80.88 interest,
S 8 8 cts.
As 1848 ; 100 :: 80.88
100
1348)8088.00(6. Ans.
ouoo
% At what rate per cent, will 666 dollar^, amount to
8815.8S cts. in 3 years and 9 months ? Ans. 6»
3. At what rate per cent, will 400 dollars amount to 8656
in 16 years ? Ans. 4.
4. At what rate per cent, will 9999 dollars amount to
£11048.89^ cents, in 1 year and 9 months ? Ans. 6.
5. At what rate per cent, will 204 dollars amount to
8275.40 in 5 years ? Ans. 7.
6.^ At what rate per cent, will 81*50 cts. amount to 82.10
cts. in 8 years ? Ans. 5u j
7. At what rate per cent, nill 8273 amount to 8458.18 in I
11 years ? Ana^ 6.
CASE IV.
To find the timei ^en the rate per cent* principal and
MQountare pveUi
&9BAtK OR Dl900UJiT* l^It
Rule*
Aft the interest of the principal for one year, at the given
rate per cent.
Is to the whole interest.
So is one year.
To tiie time required.
Ob*, divide the whole interest by that of the principal &r
one year, and the quotient will be the time required*
Examples,
1. In what time will 347 dollars amount to S419.67, at 6
per cent, per annum P
£419^ amount. S S yr>
347.00 principal. As 20.82 : 72.87 : : 1
1
72.87 whole interest*
2082)72.87(3.5 » 8i years
0347 6246 Ans.
6
10410
«D.82 interest for 1 year. 10410
2. In what time will 674 dollars amount to 8754j83, at 9
per cent, per annum ? Ans. 2 years.
3. In what time will 666 dollars amount to S815.85, at
per cent, per annum ? Ans. 3 years, 9 mo.
4. In wnat time will 400 dollars amount to 656 dollars, at
4 per cent, per annum ? Ans. 16 years*
5. In what time will 9909 dollars amount to gl 1048.89},
et 6 per cent, per annum ? Ans. 1 year, 9 mo.
6. In what time will 204 dollars amount to S275.40, at 7
per cent, per annum ? Ans. 5 years.
7* In what time will 273 dollars amount to 2453.18, at 6
per cent, per annum ? Ans. 11 years*
REBATE OR DISCOUNT.
BsBATE OR Discount, is an abatement for the paytnent of
money before it^ becomes due, by accepting sucn a sum as
Would, if placed at interest, atnount to the whole debt 4t th9
l^e payable* This sum is call^ the present worthy
113 ftVBATl! OR DlSOOtJlfT«
Rule.
Antiex two ciphers to the amount or given debt for a diti*
dend ; add 100 to the product of the rate per cent, and time
for a divisor, and the quotient arising from thence will be the
present worth : or work by rule 1st, case 2d, Interest.
Or, add 100 to the product of the rate per cent, and time,
&r a divisor; and the continued product of the amount, rate
and time, for a dividend ; the quotient will be the discount*
iVb^e— The time must be computed in years.
Examplee*
1. What sum must I pay for a note of S218.22i cts« ^ue 3
months hence, discount at 6 per cent. P
S
101.5)21822.5(215 Ans.
6 rate per cent. 2030
•25 time in decimal parts of a year.
1522
1.50 1015
100
5075
101.5 divisor. 5075
iVb/c— When there are cents in the given debt, instead of
annexing two ciphers, consider the cents placed instead
thereof.
2. What is the discount on a note for 242 dollars, due two
years hence, at 5 per cent, discount ?
5 rate per cent. £242 amount.
2 years. 5 rate per cent*
10 1210
100 2
110 divisor. 110)2420
S 22 discount.
3. What is the present worth and discount of 100 dollars,
for one year and six months, at 6 per cent. ?
Ans. Present worth, S91.7481 ; discount, 88.256ft.
4. What is the present worth of 574 dollars, one half paya*
We in one months and the othei* half in one year ?
Ans. 2556.82.7.
BANK DISOOUMT. 118
5. Bought a quantity of goods for 305 dollars, at a credit
-of 5 months, and sold the same immediately for 300 dollars
cash— How much do I gain bj the sale, allowing discount at
6 per cent. ? Ans. g2.44 cts.
6. How much ready money should I receive for a note of
93 dollars, due 17 months hence, at 5 per cent, discount ?
Ans. g85.914.
7. What is the discount on a note of 10 dollars, due in 8
months* discount at 8 per cent* ? Ans. 19 cents, 6 m.
BANK DISCOUJTT.
It is customary at banks to allow three days of grace ;
therefore, when a note is discounted at bank for 60 days,
(that is, payable 60 days after date,) the discount is computed
nius :—
For 1 day on which the note is discounted;
60 days which it has to run after that day ; and
3 days of grace.
For 64 days in all ; as Rowlett, formerly accountant in
the Bank of North America, says in the introduction (page 9)
to his celebrated Tables of Discount and Interest : " It is
usual with the banks to reckon days inclusively upon all notes^
thus the day on which a note is discounted and the day on
which it becomes due, are both calculated upon.''
Bank discount is 6 per cent, per annum ; reckoning, when
for days, the year as twelve months of thirty days each,
equal to exactly 1 per cent, for 60 days. It is then either
computed by multiplying the principal, or given sum in dol-
lars, by the number of days which the note has to run after
the day 6n which it is discounted, that day and the three •
dajp-s of grace, and dividing by- 6 for the answer in mills : or,
which is shorter, by counting off (when those days together
amount to 64) two decimal figures, in the sum of the princi-
pal, from the right to the left, which will then stand in dol-
tars and cents for the discount of the 60 days, and by adding
the 15th part for the 4 days. The discount being computed
da the whole sum^ a second excess arises, which is deducted^
114 BANK DISaOtTNT*
and the balance only advanced to. the holder ; thus intepest it
charged on the part deducted, as well as on the part advanc-
ed* In large sums such excess amounts to something con-
nderable.
1. What is the discount on 600 dollars, for 60 days ?
S
600
64 time, including the days of grace and first day »
2400
3600
Or, 6.00
6)38400 Add the 15th part 0.40
6.40.0 Answer. S6.40 Ans*
2. B borrowed of the Westchester bank, 1000 dollars, for
00 days ; required the amount he must receive.
S
1000
64 time, including the days of ^ace and
-'— - Tday on which discounted.
6)64000
10.666 or 10| discount.
1000 10.00
10.67 The 15th part, 67
$^909.33 sum he must receive. glO.67
iVb^c— *In case it be not convenient to pay off the note at
tte proper time, a new note must be presented on the daj of
discount, immediately preceding the expiration of the time^
and the same discount paid as before.
1. A man borrowed of bank 1200 dollars for 30 days, and it
not being convenient to pay the money at the proper time, he
renewed his note for anomer 30 day&— Required the sum he
has to pay more by renewing his notei than if he had tskei^
the money ©ut for 60 day* *t first-
BANK DispoTTirr* 115'
81200 * laO© 12.00 for64 days
add^ 12.80 34 off, 6.00 for 30 days
discount vrhAn drawn ■ •
for 30 days. 4800 6.80
8600
6)40800
6.80 disc'nt when drawn for 30 days*
2^
13.60 discount for 2 thirty days.
12.86 discount for 60 days.
So that he has .80 cents more to pay by drawing
his note twice for 30 days, than if he had drawn it for
60 days at first.
8. What are the proceeds of a note for 1000 dollars*—
Ai 3 months, or 90 days ?
Days, 64 =^ 10.67 glOOO.OO
30 » 5.00
^ 15.67
8984.33
At 4 months, or 120 days.
Days, 64 -= 10.67 81000.00
60 = 10.00
20.67
94
124
979.33
At 116 days — (to bring it due npon the same weekly dis-
count-day, 17 weeks from that on which it is first discount*
ed, and make the discount an even sum.)
Days. 8
116 1000
4
120 -• 20
8980
4. If I borrpw 600 dollars at bank for SO days, &d at the
exjnration of that time get it r^ewed forSOdays longer^
what is the disoount thereon i Ans* 85.664
116 EXTENSITB ASDITIOKSU
EXTEXsivi: ADinnoifiS.
The following method of adding together large sums will
be found very convenient, and may be practised with advan-*
tage in banks and other large monied establishments ; and
more particularly when the accountant is subject to frequent
interruptions : because, if any error be made in summing
up any particular column, it has no dependence on any other
eoluma, and may be detected without interfering with it.
Rule.
*
Add each column by itself, and place the respective aggre-
gates in such manner that units may stand under units, tens
under tens, hundreds under hundreds, &c. Then, by adding
together these aggregates, you have the whole sum.
Note, — It makes no difference whether we begin at the
right hand, left hand, or middle column.
«
Examples*
8 51.94 g 19.20
123.12 12.50
12.41 13.27
54.70 14.61
355.16 714.32
4271.13 16.12
715.78 71.54
43.82 1.12
769.51 1654.23
27.69 16.22
5.43 124.17
13-97 14.74
5126.43 ' 6.30
49 = sum of first column. 34
66 = sum of second column. ^
54 = sum of third column. 54
41 = sum of fourth col. 22
21 = sum <rf fifth col. 14
9 = sum of sixth col« 1
Hm^
211^71^ — sum total. 23678.34
BXTftirSXte ADDITIONS. 117
The use qf the preceding method of addition in bank accounts. '
Am^t of notes. Discounts for 60 days. Proceeds of notes.
1500
gl6.00
gl484.00
1800
19.20
1780.80
1248
13.31
123469
900
9.60
890.40
20O
2.13
197.87
500
5.33
494.67
1200
12.80
1187.20
100
1.07
98.93
250
2.67
247.33
3000
32.00
2968.00
450
4.80
445.20
750
8.00
742.00
ISO
1.60
148.40
600
6.40
593.60
800
8.53
791.47
700
7.47
692.53
400
4.27
395.73
300
3.20
296.80
550
5.87
45
544.13
8
45
29
68
83^
81
87
85
7
7
134
78
6
15398 notes.
164.25 discounts.
■
15233.75 proceeds
164.25 discounts
Amount of proceeds and discounts, » 15398.00
N. B. Discount charged on each for 64 dajs> as explained
on page 113.
'By the nature of the aboye account, it is evident that the
nixnmnt of the notes must be equal to the discounts and pro-
ceeds. If any error has arisen, it may perhaps be discover*
€d by going over obq rank of the figures.
118 LOSS AHD OAIir.
liOSS AND GAIN.
Loss AND Gain is a rule that discovers lyhat is gained or
lost in the buying or selling of goods ; and* instructs us to
rise or fall in the price, so as to gain or lose so much per cent*
or otherwise*
Rule.
Work by the Rule of Three or Practice, as {he nature of
the case may require.
Examples*
1. If for ready money 1 could buy cloth at 5 dollars per
yard, and sell the same on three months credit, at 6 dollars
per yard, what would be my gain per cent. ?
SlOO As 101.50 : 6 : : 100
6 100
3 I i I 600 101.50)600.00(5.91.1
150 int. of 8100 for 3 mo. 50750 5.00.0
100.
92500 .91.1 gwn
101 .50 am't of glOO, 3 mo. 91350 per yd.
8^88 ^ 11500
As 5 : 100 : : .911 10150
100 '
13500
5)91100 10150
18.22 gain per cent* 3350
Kote. — ^When goods are bought or sold on credit, the pres-
ent worth of their value must be found, in order to find the
true gain or loss.
2. If 296 yards of broadcloth be sold for 81184, at 25 per
cent, profit, what was the prime cost per yard ? Ans. 83.20.
3. Bought 51 yards of cloth at 83.23 per yard, and ' sold
file same for 8200 : required the gain per yard ?
Ans. 69 cts.+
4. If one dozen hats cost 50 dollars, how must I sell them
singly to gain 20 per cent. Ans. 5 dollars.
5. If 90 yards of silk sell for 8100, how must I sell it ptr
yard, to gain 12i per cent. Ans. 81*25.
6. Bought broadcloth for 3 dollars per yard, and sold it
agtdtt at att advance of S5 per cent'.— What was thut pei
yard ? Ans. 83.75.
7. Paid J8175 for a ton of steel — What is the profit or loss
on the sale thereof at 10 cents per pound, computing 2S
pounds for a quarter of a hundred weight ?
Ans. 825 profit.
8. If a yard of cambric cost 80 cents, and I sell it a^ain
for 95 cents— What do I gain per cent. ? Ans. isf.
9. Bought a cask of oil, containing 77 gallons, for 91 ctft.
per gallon; but, by accident, 28 gallons leaked out — How
must I sell the remainder, per gallon, so as to sustain no loss ?
Ans. 81.43.
10. If I buy 431 pounds of wool, at 34 cents per pound,
and sell it for- 144 dollars : do I gain or lose, and how much ?
Ans, I lose 82.54.
11. Bought a barrel of vinegar, for 83.931, and retail it
out at 25 cents per gallon— What do I gain per cent., allow-
ing no waste in the measure ? Ans. 100.
12. Bought a watch for 15 dollars, and sold the same im-
mediately for 821, at 10 months' credit: required the gain
per cent, in ready money, and what is the gain per cent, per
annum.? Ans. gain in ready money, 33^ per cent. ; > ,
per annum, 48 per cent. J
13. A vintner bought 63 gallons of wine, at 81.10 per gal-
lon, and sold it again for 45 cents per quart : I demand what
he gained in the whole, and what he gained per cent. ?
Ans. whole gain, 844.10 ; gain per cent. 863.63. .
14. If by selling cotton yarn at 18 cents per pound, there
is 2 cents per pound loss, what is the loss per cent. ?
Ans. 10 per cent.
15. Sold goods on a credit of 9 months, for 160 dollars,
which cost me 8150 cash : do I gain er lose by this transao-
tion, and how much ? Ans. I gam, in ready money, 83.11*
16. Bought 4 pieces of broadcloth, each piece containing
12 yards, at the rate of 47 dollars for every 12 yards: do
I gain or lose by selling the same at the rate of 819. for every
5 yards ? . Ans. I lose 85.60 cts.
17. Bought cloth for 81.90 per yard, which I find, on ex-
amination, to be of an inferior quality to what I expected,
and I must losd 20 per cfent. by it— What will I then sell It
for per yard ? Ans. 81.58J.
120 BARTER.
18. If I buy 147 ponnds of tea> at one dollar per pounds
and sell 98 pounds of it at 80 cents per pound, and the re-
mainder at gl.lO per pound: do I gain or lose, and how
much? Ans. I lose S14.70.
19. If I buy 1 cwt. 2 qrs. of tobacco, for £22.50 cts. and
«ell the same for 14^ cents per pound : whether do I gain or
lose P Ans. I lose 75 cents.
20. Bought 20 pieces of cloth, at 10 dollars per piece, and
afterwards sold 9 of them at 12 dollars per piece, and 6 at 8
dollars per piece : at what price must I sell the remainder to
gain gl6.00 on the whole ?. Ans. S12.00 per piece.
21. Sold 1 cwt. 2 qrs. 10 lbs. of hops, for g9.60, at the rate
of 20 per cent, profit — What would have been the gain per
cent, if I had sold them for g5.50 cts. per hundred weight ?
Ans. 10.
22. Bought 250 yards of cloth, for £510.00; retailed the
aame at g2.50 per yard— What is the profit in the whole, and
how much per cent. ?
Ans. whole gain, 8115.00; gain per cent. 822*568.
23. Cloth bought at g2.50 per yard, and sold at 3 dollars
,per yard — What is gained per cent. ? Ans. 20 per cent.
24. If a barrel of mackerel, containing 175, cost S5.50—
What is gained by retailing them at 5 cents a piece ?*
Ans. 83.25.
25. If Is herring cost Is cents, what is gained by selling
one hundred for li cents a piece ? Ans. 50 cts*
BARTER,
Is the exchanging of one commodity for another, according
to the prices agreed upon between the parties trading.
Rule 1st.— -Find the value of that commodity whose quan-
tity and price is given ; then find what quantity of the other,
to be received in exchange, at the price it is rated at, will
amount to the same value.
2d.— When the quantities of two commodities are giyen,
and the rate of selling them — ^in case there be a difference m
the valtle, and some other commodity is to be given to make
w this difference — find the value of the two given commodi-
ties f}eparately ; deduct the less from the greater ; then will
BARTER.
121
€bg^ dtSbrence be the value of the third commodity, which
divide by its price per pound, yard, &c. for Ihe quantity.
3d. — When one has goods at a certain price, ready money,
but, in bartering, advances it to something miore, find what
the other ought to rate his goods at, in projportion to that ad-
vance, and then proceed by rule 1st.
Examples, *
1. What quantity of rye flour, at 22.S0 per C, must be
given for 5 C. of wheat flour, at g4 per C. ?
C
5
4
20 Value of the wheat flour*
C.
And 2.50)20.00(8 of rye flour. Answer.
20.00
2. A has 15 pieces of cloth, each piece containing 32 yards,
at 82.40 per yard, for whijch B. is to give him 145 barrels of
wheat flour, at g6.00 per barrel, and the remainder in pork,
at 5 cents per pound— How many pounds of pork must A.
receive ?
Pieces. Barrels.
15 145
32 6
30
45
870 Value of the flour*
480
2.40
192
1152.00 Value of the cloth,
870.00 Value of the flour.
•05)282.00 Value of the pork.
S640 Answer.
122 BARTS8.
3. A* has 240 pounds of wool, worth 36 cents per pound,'
ready money, but in barter will have 44 cents per pound;
B. has cheese, worth 9 cents per pound, which he raises in
proportion to A's wool— what is the barter price of B's wool,
and how much cheese must he giro to A. for his 240 pounds
of wool ?
cts. cts. cts.
As 86 : 9 : : 44
9
36)396(11 Ans. The barter price of B's cheese.
36
36
36
lbs.
240
.44
960
960
11)105.60 Value of A's wool,
960 lbs« of cheese coming to A. Ans«
4* How many pounds of sugar, at 11 cents per pounds
must be given for 132 pounds of tobacco^ at 17 cents pear
pound ? Ans. 204 Iba.
5. A. has silk at SI .50 per yard, which he barters to B. for
150 yards of broadcloth, at 22.00 per yard— How mu<^
silk must B. receive ? Ans. 200 yds^
6. A. gives B. 10 bushels of clover seed, at g3.50 pesr
bushel, for 50 bushels of rye— How much per bushel does tbft
rye stand him in ? Ans. 70 cts,
7* A. has beeswa:!^, at 25 cents per pound, ready money,
but in barter will have 30 cents per pound ; B. has cnocolat^
at 15 cents per pound, ready money— What price must thie
chocolate be in barter, and how much chocolate must be bar^
tered for 75 pounds of beeswax ?
Ans. the chocolate in barter, 18 cts. per lb. and 125 >
lbs. of chocolate must be gitei^ foi: 75 U)t* of l)eeswax« 5 ,
Barter. 12^
8. B. has coffee, which he .barters with C. at 6 cents per
^und more than it cost him, against tea, which stands C. in
70 cents per pound, but puts it to 81.00. I demand how
much the coffee did cost at first. Ans. 14 cents.
9. Two merchants barter : A. has 9 C of tobacco, at 18
cents per pound, and B. has 40 yards of broadcloth, at 5 dol-
lars per yard : which of them must receive money, and how
much ? Ans. B. must receive S38-
10. A merchant has 500 yards of muslin, at 12 cents pef
yard, which he barters for silk> at 81.50 per yard — How many
yards must he receive ? Ans. 40.
11. If A. hath cotton at 15 cents per yard, how much must
he give A. for 165 pounds of candles, at 10 cents per pound ?
Ans. 110 lbs,
12. C. has nutmegs, worth 80 cents per pounds ready
money, but in barter will have 81.00 per pound; and D. has
rice, worth 4 cents per pound, ready money — How much
must D. rate his rice at per pound, that his profit may be
equivalent with C's ? Ans. 5 cents*
13. A. and B. barter : A. has 160 pounds of tallow, at 10
cents per pound, for which B. gives him 810.00 in roady
money, and the rest in candles, at 122 cents per pound : I
desire to ktiow how many pounds of candles B. gives A. be-
side the money. Ans. 48 pounds.
14. C. andD. barter: C. has 21 pounds of pepper, at 7
cents per pound; D. has ginger, at lOh cents pci* pound— ^
How much ginger must he deliver in barter for the pepper ?
Ans. 14 pounds.
15. A. has 15 C. of cheese, at 10 cents per pound ; B. has
7 pieces of muslin, at 82.40 per piece, and 14 pieces of Irish
«loth, at 89.00 per piece-: I desire to know who must receive
the difference, and how much ? Ans. A. must receive 87.20.
16. A. has 1000 bushels of lime, at 12 cents per bushel,
ready money, which he barters with B. at 15 cents per bushel,
taking wheat at 81.30 per bushel, which i| worth but 81 '00
^^How many bushels of wheat will pay for the lime ? who
gets the best bargain ? how much on the whole, and what per
cent* }j Ans. 115 bu. 1 P. 4 qts. + wheat; B. gains?
84.4615 on the whole, and 5 per cent. >
FELLOWSHIP.
Fellowship is a rule which enables merchants and others^
trading in partnership, to determine each person's particular
share of the gain, in proportion to each one's share of the
stock and time of its continuance in trade,
Bj this rule, legacies may be adjusted, when there is &
deficiency of assets or effects ; as also, a bankrupt's estate^
may be divided among his creditors.
CASE I.
When the several stocks in company are considered with-
out regard to time, or continue an equal space of time.
Rule 1.
As the whole debt or amount of stock.
Is to any partner's share in stock.
So is the whole gain or loss
To the same partner's share or dividend.
Rule 2«
Find the gain or loss per dollar, by dividing the whole gain
or loss by the whole stock ;
Then, multiply the gain or loss per dollar, by each part-
ner's stock respectively ; and the product is the prc^rtional
gain or loss required.
Proof, — Add all the shares together, and the sum will be
equal to th*e given gain or loss ; but the surest way is, to say.
As the whole gain or loss, is to each partner's share of the
gain or loss, so is the whole stock, to hia share in stock.
Examples.
1. A. B. and C. join their stocks in trade: the amount of
their stock is S3672, and are in proportion as 1, 2 and 3, arc
to one another ; and the amount of their gain is equal to GH
stock-— What is each man's stock and gain ?
1
2
3
As 6 : 1 : : 3672 : 612 =» A's stock.
6:2:: 3672 : 1224 = B's stock.
6:3:: 3672 : 1836 => C's stock, and whole gain*
Fellowship. 125
As 3672 : 612 : : 1836 : 306 = A^s gain.
3672 : 1224 : : 1836 : 612 = B>s gain,
3672 : 1836 : : 1836 : 918 = C's gain.
12. Two merchants trade together : A. put into stock gl20,
^nd B. S160 : they gained 860 — What is each person's share
thereof? Ans. A's gain, 825.714; B's, S34.286.
3. A. and B. having gained by merchandize 8500; A. put
in 81274, and B. 8726 — I demand each of their shares of the
profit. Ans. A.'s 8318.50; B.'s 8181.50.
4. Three butchers pay among them 850 for a grass inclo-
sure, into which they put 200 cows ; whereof A. had 50, B,
70, and C. 80-^How much had each to pay ?
Ans. A. 812.50; B. 817.50; C 820.00.
5- Three persons, B., C. and D., join in company; B.'8
«tock was 600 dollars, C's 700 dollars, and D.'s 1100 dolls.
and they gained 600 dolls. — What is each partner's particular
share of the gain ?
• Ans. B. 81S0; C. 8175; D. 8275.
6. A bankrupt is indebted to A. 2000 dollars ; to B. 1500
dollars ; to C. 2500 dollars, and to D. 3000 dollars ; and his
effects are found to amount to only 4500 dolls. — I demand
what sum each creditor must receive, and how much it will
be on the dollar. Ans. A. must receive 81000 ; B. 8750;
C. 81250; D. 81500;— on the dollar, 50 cts.
7- A man bequeathed his estate to his three sons, in the
following manner, viz. To the eldest, 480 dollars, to the
second, 440 dolls, and to the third 360 dolls. ; but when his
debts were paid, there were but 960 dolls, left — what is each
one's share of the estate ?
Ans. Eldest, 8360 ; second, 8330 ; third, 8270.
8. Af, B. and C. freight a ship from Paris for Philadelphia,'
with 200 tuns of wine, of which A. had 40 ; B. 100, and C.
60 ; the mariners, meeting with a storm at sea, were con-
strained, for the safety of their lives, to cast 50 tuns over-
board — I wish to know now many of the 50 tuns each particu-
lar merchant has lost, according to the rate of his adventure.
Ans. A. 10 ; B. 25, and C. 15.
9. A^father left his estate of 2400 dolld. among 3 sons, in
Buch manner that for every 3 dolls, that A. gets, B. shall have
4 dolls, and C. 5 dolls.-^How is the estate to be divided ?
Ans. A.'8 share^ 2600; B.'&,8800; C.% 81000.
126 tZLLOvrsKtp.
10. A merchant being deceased, it is found he owes to A.
400 dolls. ; to B. 480 dolls., and to C. 530 dolls, though he
left but 1200 dolls, behind him — I demand how much each is
to have in proportion to his debts.
Ans. A. S342.8571 ; B. S411.4286; C. 8445.7143-
11. A man dying, left an estate worth 6000 dolls, which is
to be divided as follows, viz. the widow to have one-third,
and the remainder to be divided among 4 sons and 7 daugh-
ters ; the sons taking two shares to the daughters' one— what
sum will each receive ? Ans. The widow, S2000 ; each
of the sons, g533.33^ ; each of the daughters, S266.66f .
CASE II.
Wlien the respective stocks in company continue an nn^
equal space of time.
Rule 1.
Multiply each partner's stock by the time It wartn trade ;
Then, As the sum of the products,
Is to each particular product ;
So is the whole gain or loss,
To each partner's share of the gain or loss.
Rule 2.
Find the gain or loss per dollar, by dividing the whole
gain or loss by the sum of the products of the stock and time;
Sien multiply the gain or loss per dollar by each product, for
each partner's share of the gain or loss.
Examples.
1. Three merchants join in company for 12 months; D-
puts in 400 dolls., and at five months' end took out 100
dolls., and at the end of 7 months took out 200 dolls, and at
11 months' end put in 400 dolls. ; E. puts in at first 600
dolls., and at the end of 3 months puts in 8100 more ; at the
end of 9 months he took out 500 dolls., but puts in 200 dolls.
at the end of 10 months, and withdraws. 100 dolls, at the end
of 11 months ; F. puts in at first 1000 dolls., and at the end
of six months took out 500 dolls., at the end of 7 months puts
in 100 dolls., but takes out 400 dolls, at the end of 10 months ;
at the end of 12 months they gained 560 dolls.— I desire t«
know eaik man's share of the gain«
VELLOWSHZF* 137
B. at firdt puts in 2400 for 12 inonth8,«400xl2«4800
He then takes out 100 for 7 months, =100 X 7= 700
4100
He also takes out 800 for S months>»200x 5»1000
3100
He puts in 400 for 1 month, » 400 X 1= 400
D>8 product, 8500
E. at first puts in 600 for 12 months, =600 x 12=7200
He also puts in 100 for 9 months, =100 x 9>= 900
«100
He takes out 500 for 8 month8,=S00x 3=1500
6600
He puts in 200 for 2 months, =200 X 2= 400
7000
He takes out 100 for 1 month, = lOOx 1= 100
E's product, 6900
V. at first puts in 1000 for 12 mo's,= 1000x12= 12000
He takes out 500 for 6 mo's,= 50Ox 6= 3000
9000
He puts in 100 for 5 mo's,= 100 X 5« 560
9500
He takes out 400 for 8 ino'9,= 400 X S-* 800
F's product, 8700
1>'8 product, 3500
E's product, 6900
F's product, 8700
As 19100 : 3500 : : 560 : 102.6178 D's shar*,
" 19100 ; 6900 :: 560 : 202.3087 E's share,
" 19100 ; 8700 : : 560 : 255.0785 F's share,
Sk» A. and B. enter into partnership ; A. puts in 90 dolls*
1
138 SXOHAirdti.
for 6 iXMmthB, and B. 130 dolls, for 4 months, and they gain<!d
85 dolls. — What is each man's share of the gain ?
Ans. A's 845 ; B's 840.
3» A., B. and C. hold a piece of ground in common, for
which they are to pay 65 dolls. ; A. puts in 40 oxen for lOO
day«; B. 64 oxen for 120 days, and C. 90 oxen for 80 day&—
What is each man to pay of said rent ?
Ans. A. 813*771 ; B. 826.441 ; C. 824.788L
4. B. commenced trade January 1st, with a capital of 800
dolls* and meeting with success in business, took in C. as a
partner, with 4 capital of 1200 dolls, on the first of May
following ; two months after that, they admit D. as a third,
partner, who brought sufficient stock in to entitle him to share
equal profits the first of the following year with his partners;
at which time they found they had gained 600 dolls. — ^Re-
quired D's stock, and each man's share, including his stock
and gain. Ans. D's stock, 81600; B's share, 81000;
C's, 81400, and D's, 81800.
5. A, and B. enter into partnership ; A. puts in 120 dolls,
for 9 months, and B.200 dolls, for 6 months ; A's share of the
gain was 27 doUs^— What was gained in all P Ans. 857.
£!X€HAirGC2.
By fixoHANGE is meant the giving of the money,'weight or
measure of one country, for the lijce value in money, bills,
weight or measure of another country.
Kir, in Exchange, is a supposed equality between the
money of one country and that of another ; the course of ex-
change is frequently above or below par ; for bills of exchange
are a kind of commodity which rise and fall in price, ac-
ceding as there is greater or less demand for them.
Agio is a term used to signify the difference in some coun-
tries between bank and current money.
Exchange may be computed by tne legal or intrinsic
value of the coins, when remittances are made in bash;
but as they are generally made between distant places, by
bills of exchange, and most frequently pass for more or lesd
than the intrinsic values of the sums for which they are drawn^
the rate of exchange must then be taken into the account*
exchange* 129
England*
In England accounts are kept in pounds, shillings, pence
lind farthings.
The par of exchange between the United States and
England, is 84.44 for one pound sterling,.or 40 dollars for 9
pounds sterling; therefore, to reduce federal money to ster-
ling, (or English) : *
Rule.
Multiply the dollars by 9, and divide by 40, for the answer
in pounds sterling; or.
As 40 dollars,
Is to the federal money given,
So is 9 pounds
To the sterling required.
Or, multiply the federal money in cents by 27, and divide
by SO, for the answer in pence*
To reduce Sterling to Federal Money*
Rule.
Multiply the pounds by 40, and divide by 9, for the answer
in dollars ; or,
As 9 pounds sterling.
Is to the sterling given.
So is 40 dollars, *
To the federal money required.
Or, reduce the sterling money to sixpences, annex two
ciphers, and divide by 9, for the answer in cents ; or, reduce
the sterling money to pence, annex two ciphers, and divide by
64, for the answer in cents.
EiCamples.
1. I demand the sterling that will discharge a bill of ex-
change for 2800.
As 40 : 800 : : 9 : 180 Answer.
% A. of Philadelphia, drew a bill of exchange upon B. of*
London, for 1260 pounds sterling— What id the value of this
bill in federal money, exchange at par ?
jg jg R 8
As 9 : 1260 M 4Q \ 5600 Answer*
1
180 EXCHANGE*
3. I demand the sterling that will discharge a bill of ei^'*
cbange for S1760, exchange at par. Ans. 396 poundd^
4. B. in New -York, drew a bill of exchange upon a mer-
chant in London, for 531 pounds sterling — How much fede-
ral money will discharge the draft, exchange at par ?
Ans. 82360.
5« K. of Baltimore, received of R. of. London, a quantity
of goods, valued in the invoice at 361dB. 178. 4|d. sterling ;
required their value in federal money. Ans. ^1608.30.+
Note 1.— When the bill of exchange is above par, multiply
Hie sum of the bill by the amount of one pound or dollar, at
flie given rate per cent.
Note 2.— When the bill of exchange is below par, find one
year's interest of the given sum, which must be deducted
therefrom ; the remainder will be the value required.
6. What is the value of a bill of exchange for S603, at 3
.per cent- below par.
603 X .03 == 18.09
Then, 8603—818.09 = 8584.91 Answer.
7. What is the amount or value of a bill of exchange for
8S1234, at 5 per cent, above par ?
1234 X 1.05 = 81295.70 Answer.
8. G. in New-York, owes P. in London, 400 pounds ster-
Ifng, to discharge which, he purchases a bill at 5 per cent,
helow par— How many dollars must he give for it, and how
much will he save by the bill ?
Ans, 81688.881- paid, and 888.88f saved.
A TABLE,
Showing the value, in dollars and cents, of the principal
foreign coins and currencies throughout the world,
France.
Names of coins. Value.
A Livre, tournois, - - - g0.185
Franc, ... - 0.1873125
Five franc piece, - - - 0.9365625
Louis d'or, . . * 4.44
Spain.
A Real plate, - - - 0.10
RealteUon, « - * 0.053135
£XORANGfi«
131
A Piastre of exchange, - a
Ducat of exchange.
Doubloon of exchange,
PoRTUGAI.
Silver,
A Crusado of 400 reas, not stamped.
Do. of 480, stamped in 1643, -
Half Crusado, or 12 vintin piece, -
Five Vintin piece, -
Two and a half Vintin piece.
Gold.
A Double Johannes, - ^ .
Single do.
Half do. - - -
Quarter do. - - -
Eighth do. - - -
Testoon, - • , «
Moidore, - - - -
Half Moidore, - - -
Quarter Moidore, - - •
Holland*
A Ducatoon, ...
Ducat, - - - ,
Pound" Flemish, - - •
Rix Dollar, - -
Florin, - - - -
Shilling, - • ^ -
Stiver, - - - -
Groat, - - _ -
80.80
1.10
820
A Pound Flemish,
.Rix dollar, -
Shilling Flemish,
Mark Banco,
Shilling Lub.,
A Ruble,
Politin,
Polpolitin, -
HAMBUROt
Russia.
.50
.60
.30
.125
.0625
32.00
16.00
8.00
4.00
2.00
1.00
6.00
3.00
1.50
8.00
2.00
2.40
1.00
.40
.12
.02
m
2.50
1.00
.125
.3331
sms
.75
.375
4875
183 £X0HAK<}9«
Leghorn*
AGeroni, * - - . gl.gQ
Testoon, - - - . ,3q
Chevalet, * - - - .04
Lire, - . . . *20
Venice.
A Ducat of exchange, (imaginary,) - .9305
China.
A Tale, - . . . 1.4S
Mace, . - - . .143
Candareeil, - ^ . .0148
Algiers, Tripoli and Tunis.
A Pistole, - - - * 3.00
Zequin, - - - . 2-25
Chequin, - - - * .75
Rial, - . . . 425
Turkey.
A Piaster, . - - . ^2614
Para, - . . . .0065
Spanish West Indies.
A Peso, - - - . 1.00
Real, - - - . .125
A comparison of the American foot, of 13 inches, with that of
other countries.
Feet.
Great Britain and its dependencies, ^ 1.
Riga, - - * - - 1.83
Mantua., - u . . 1.5683
Bologna, - - . - 1.2037
Venice, .... 1.1609
•lunn, . - - . 1.0613
Lejden, - - . . 1.0324
Copenhagen, - - - ^ * .9641
Bremen, - . - . . .963
Dantzic, - *. . . .9433
Frankfort,, (on the Main,) - - .948
Amsterdam, - . - - - . .941
Antwerp, - .- .. - .9456
France, - • • - .92
Strasburgh, • . - . ,919
EXCHANGE. |^
Tlte conformity of the Weights of the principal trading cities
of fJurope, with those of the United States.
Weight of the United States,
lbs. lbs. 02.
100 of Geneva, - - equal to 123 Q
100 of Amsterdam, Paris, Bordeaux, - 109 9
100 of Hamburg, - - - 107 5
100 of Antwerp, , - - 103 12
100 of Seville, Cadiz, &c. - - 103 7
100 of Spain, - - - - 97
100 of England, Scotland, Ireland, &c. 100
100 of Portugal, - - - 95 4
100 of Lyons, (France,) - - 94 3
100 of Toulouse, - - - 92 6
100 of Marseilles, - - - 88 11
100 of Leghorn, • • - 75 8
100 of Genoa, - - - 73
100 of Venice, - - - 65 11
100 of Naples, - - ^ 64 10
A TABLE OF DIFFERENT MONIES,
With explanatory remarks^
France.
12 Deniers - - equal 1 sol.
20 Sols - - " 1 livre.
6 Livres equal (1 ecu, or) 1 crown.
Spain.
There are two sorts of money in Spain ; the one is called
vellon, and the other, plate money.
The vellon is to the plate money, as 17 to 32.
Accounts are kept in reals and maravedies vellon, by the
dealers and commissioners of excise.
Some bankers, merchants and remitters, keep their accounts
in old plate, or money of exchange.
Denominations of vellon money.
4 Maravedies vellon equal 1 quai-to.
84 Quartos or 34 maravedies vel.** 1 real vellon.
15 Reals vellon, or 510 do. " 1 peso or current dollar.
90 Do. do. or 680 do. " 1 silver or hard dollar.
16 Qaartos, or 64 do. " 1 real plate.
134 SXCBAKGAi
Denominations of plate money *
84 Maravedies of plate, equal 1 real plate.
8 Reals of plate, - "1 piaster of exchange*
10 Reals of plate, - " 1 dollar.
11 Reals of plate, - "1 ducat of exchange.
S2 Reals of plate, - "> 1 doubloon of exchange.
Portugal.
In Portugal, accounts are kept in millreas and reas.
The millrea is an imaginary piece, and is equal to one
thousand reas.
For the real monies of Portugal, see table, page 131.
4
Holland.
In Holland, accounts are kept in guilders, stivers and pen-
nhigs. The denominations are—
8 Pennings - - 6qual 1 groat.
2 Groats - - - « i stiver.
6 Stivers, or 12 groats " 1 shilling.
20 Stivers - - . « i florin or guilder.
2k Florins, - - «« i rix dollar.
6 Florins, or 20 shillings, '' 1 £ Flemish.
5 Guilder3 - - « 1 ducat.
Hamburg and Lubeck
Keep account in different ways, viz ;
Lubishy or of Lubech
12 Deniera equal 1 shilling, Lub.
16 Shillings " 1 mark, do.
Flemish, a fictitious currency.
12 Groats or Den. - equal 1 shilling Flemish.
20 Shillings - . « 1 jg do,
6 Deniers Lub. - equal 1 groat Flemish.
2 Groats Flemish - " 1 shilling Lub.
6 Shillings Lub. - " 1 shilling Flemish.
120 Shillings do. * *' \ £ do
1 £ Flemish - * " 2J Rix dollars. '
Their Banco money is better thaju tiieir current
EXCHANGE. 13g
. * The exchange between the United States and Hamburg, is
S3J cents per mark banco, or one dollar for every rix
dollar of 3 marks banco.
Russia.
In Petersburg, accounts are kept in rubles and copecs.
The denomination^ are :
3 copecs - - equal 1 altine.
10 copecs, - - 1 grivena.
25 copecs, - - 1 polpolitin.
2 polpolitins, - - 1 politin.
2 politins, - - 1 ruble.
2 rubles, - - 1 ducat.
Genoa, Leghorn. Florenge and Corsica.
*
Accounts are kept in St. George's Bank in pezzoes or pi-
astres, soldi and denari.
12 denari equal 1 soldi*
20 soldi - 1 pezzo, piastre or dollar*
This is the money of exchange.
Out of the bank, accounts are generally kept in lire, soldi,
and denari, divided as before,
The lire or livre of Genoa is only ^ value of the exchange
money ; that of Leghorn ia equal in value only | of the ex-
change.
12 denari - equal 1 soldi.
20 denari, - - 1 lire.
4 denari, - - 1 chevalet.
30 denari, - - 1 testoon.
6 testoons, - - 1 geroni.
Venice,
There is a public depository of the merchants' money call-
ed tlie bank of Venice, where bills of exchange and foreigji
business are done. The funds of the bank were fixed at
6,000,000 ducats.
The denominations are :
5J- soldi - equal 1 gross.
24 gro9i> 2 " ^ ducat*
136 EXCHANGE.
For the sake of ease in calculation, merchants and bankers
Kbep their accounts in ducats, sols, and deniers d'or.
12 deniers d'or - equal 1 sol.
20 sols - - - 1 ducat.
This money is imaginary ; 100 ducats of which are equal
to 120 ducats, current money : the difference is called agio.
China.
In the empire of China they reckon by tales, mace, canda-
reens and caxas. The denominations are :
10 caxas - - equal 1 candareen.
10 candareens, - - 1 mace.
10 mace, - - - 1 tale,
Barbary.
The denominations are :
10 aspers - equal 1 rial.
2 rials, - - 1 double.
4 doubles, - - 1 dollar.
24 medins, - - 1 chequin«
32 chequins or 80 aspers, 1 dollar*
180 aspers, , - - 1 sequin.
15 doubles or 300 aspers, 1 pistole*
Turkey.
The denominations are :
3 aspers, - - equal 1 para.
40 paras or 120 aspers, ' - 1 piaster.
English West Indies.
Accounts are kept here in pounds, shillings and pence*
One pound is equal to 3 dolls, federal money.
Spanish West Indies.
Accounts are kept here in dollars and reals ; or in pesos or
dollars, reals, and maravedies. Their peso or dollar is equiv^
fllent to a dollar, federal money«
34 maravedies • equal 1 real.
8 reals, - - - 1 peso or dollar.
Rule.
The various operations, in the exchan^ng of monies, are
performed by the single rule of three or practice.
^0^^— The par of exchange between the United States and
othor countries may be ascertained by the table, pages 130 to
133.
EXCHAXGE. jgiy
Examples,
•
1. A merchant in Paris is iildebted to a merchant in Phil
adelphia 5642 livres, 15 sols, 7 deniers-What is the amoui
m tederal money ; exchange at par?
Livre. Livres. Sols. Den.
As 1 ; 5642 15 7 ::
20 20
S
.185
20 112855
12 12
240 1854267
.185
6771335
10834136
1354267
240)250539.395(1043.914 Answer.
240
1053
960
939
720
2193
2160
339 . '
240
995
960
35
2. Reduce 625 reals, 20 maravedies, vellon, to reals of
plate or exchange, also to federal money.
• «
K
23Q EXCHANGB^
• • •
R. M.
As 32 : 625 2(f :: IT
34
2520
1875
21270
17
148890
21270
r 4)361590
32^
IP
I 8)90397.5
R. Mar.
34)11299.6875(332 11.G875 plate money. Ans.
102
• R. R. Marv. S
109 As 1 : 382 11.6875 :: 10
102 34 34
79 34 1389
68 996
11 34)1129.9.6875(33.23437 federal value.
102
109
102
79
G8^
116
102
148
130
127
102
255
238
17
EXCHANGE* 139
A'ofe— -A more concise way of reducing vellon to plate
jnonej, is to reduce the vellon to maravedies, and divide bj
64 ; th-e quotient will be the reals plate.
R. M.
Thus, G25 20
34
2520
1875
r 8)21270
i 8)2658.75
S32.34375
84
137500
103125
11.G375
Kencc 332 reals 11.0375 maravctlics, as before.
3. A. of LisboTi, dravrs on B. of Nevr York, for 1947 mill-
reas, 400 reas — How much federal money will discharge this
bill ; exchange at Si. 24 per millrca.^ Ans. S2414.776.
4. What is the value of 47 crusados in federarmoney?
Anr,. S2S.50.
5. Reduce 19 moid ores to dollars. Ans. §114.
6. A merchant in Rotterdam remits £327, 5 shillings, IO5
groots, Flemish, to be paid in Baltimore — ^how much federal
money will discharge this bill^ exchange at par?
Ans. S785.505.
7- A. of New York, receives from B, of Anisterdam, an
invoice of ^oods,, amounting to 15120 florins, 12 stivers, 6
pennings — How much federal money must be remitted to
discharge the bill, at 40 cents per florin ?
Ans, S6048.24J cts.
To reduce current money (0 bank,
Rule.
As 100 with the agio added. Is to 100, So is the given «uin
in current money, To the bank money required.
n
140 CUSTOM-HOUSE ALLOWANCES.
#
Examples,
8. What will 988 guilders, current money, amount to ifl
bank money, the agio being at 4 per cent. ? Ans. 950.
To reduce hank mo7iey to current money.
Rule.
As 100 Is to 100 with the agio added ; So is the bank
money given, To the current money required.
Examples,
9. What is the amount, in current money, of 1900 guilders,
bank money, the agio being at 3 J per cent. ? Ans. 19662-
10. B. in Boston, dr^vs on H. of Hamburg, for 1254 marks
banco, 3 shills. 7 deniers ; and receives at the rate of one dol-
lar for every three marks — What is the value in federal
money ? Ans. S418.07a nearly.
11. In 465 rubles of Russia, l\ow much federal money?
Ans. 8348.75.
12. In 196 pezzos, 5 soldi, 6 denari, (Genoa,) how much
federal money ? Ans. S196.272.
13. Bought a bill of exchange on Venice, amounting to
81212.07 — What is the amount in Venetian ducats of ex-
change, at 8.9305 per ducat ? Ans. 1302 ducats, 12 sols.+
14. In 674 tales of China, how many dollars, federal
money ? Ans. 8997.52,
15. What sum, in federal money, will pay a bill of 500
chequins at Tunis ? Ans. 8375-
16. What sum, sterling, will pay a bill in Constantinople,
of 3400 piastres ? Ans, 199^. 19s. 5d,
17. Sold goods in Jamaica, for 604 pounds, 6 shillings and
8 pence — What is the amount in federal money ?
Ans. 1813 dolls.
18. A merchant of Vera Cruz, .exported goqds to Philadel-
phia, which, when disposei^Lpf, ^mounted to 8943,20 — What
is the value thereof in Spanish West India currency }
Ans.. 943 pesos, 1 rial, 20 mara.
CUSTOM-HOUSE ALIiOWAJiTCES.
Allowances are made in the weight of goods, at the custom-
houses of the United States, for tare and draft or scalage.—
Tare is the weight of the box, barrel, bag, hogshead, cask, &c.
CUSTOM-HOUSE ALLOWANCES. 141
vKich •ontains the goods ; and is either the real or actual tare,
or computed at so much per cent, at so much per box, &c.
Draft or scalage is an allowance of 5 per cent., computed
on the whole gross weight of the goods, (tea and sugar ex-
cepted.) There is a deduction to be made on sugar, for draft
or scalage of 2 pounds on every barrel, 4 pounds on every
Havana box, 4 pounds on every tierce, and 7 pounds on every
hogshead. No draft is allowed on tea.
Gross weight is the whole weight of the goods, together
with that which contains them.
Netit weight is the weight of the goods alone, after aM al-
lowances have been deducted. . , •
CASE I.
To find the neat weight of the goods, when the real or
actual tare is allowed, with allowance for draft or scalage.
Rule.
When the scalage is i per cent, divide the whole gross
weight by 200, the quotient will be the scalage. '
When the scalage is rated per hogshead, box, &c., multiply
the scalage of one by the number of hogsheads, boxes, &c. :
the product wilj be the scalage of the whole.
Add the scalage and tare together, and subtract their sum
from the whole gross weight*— the remainder will be the neat.
Examples,
1. What is the neat weight and value of 5 casks of raisins,
weighing as follows : — No. 1 , gross 79 lbs tare 7 lbs. ; No. 2,
gross 81 lbs. tare 10 lbs. *, No. 3, gross 95 lbs. tare 12 lbs. ;
No. 4. gross 67 lbs. tare 6 lbs. ; No. 5, gross 93 lbs. tare
12 lbs — scalage i per cent, and price 13 cents per pound ?
lbs. lbs. lbs.
79 7 415
81 10 49
95 12 .
67 6 366 Neatans.
93 12 .13
3,00)4,15 Gross. 47 Tare. 1098
— 2 Scalage. 366
2 lbs« scalage^
49 847.58 Value. _
142 dUSTOM-ftOUSE ALLOWANClSs.
2. What is the neat weight and value of 6 boxes t)f Ha-»
vana sugar, weighing 200 pounds each ; tare, in the whole,
200 pounds; scalage, 4 pounds per box — ^at 11 cents per
pound ? Ans. neat &Sf6 lbs. ; value S 107-36.
3. Sold 4 casks of indigo, weighing, gross, 15 G. 1 qr. 15
lbs. ; tare, 40 pounds per cask; scalage, i per cent.— -What
is the neat weight and value at S2.25 per pound ?
Ans. neat 13 C. 2 qr. 22.3 lbs. ; Value, S3087.672.
CASE II.
When th? tai^e is at so much per cent, with allowance far
draft or scalage.
Rule.
l^'ind the scalage as before, which deduct from the gross
weight; multiply .the remainder by the tare per cent.; divide
the product by 100 : this quotient will be the whole tare.
Deduct the tare from what remained after the scalage was
deducted, and the remainder will be the neat*
Examples.
1. What is the neat weight of 7 bags of coffee, weighing
840 pounds gross, allowance 3 per cent, for tare, and 5 per
cent for scalage? and what is the value of the neat weight, at
17 cents per pound .^
lbs.
2,00)840
4 Scalage.
lbs.
840
4
lbs.
886
25 Tare*
836
3
811 Neat.
17
25.08 Tare*
5677
811
gl37.87 Ans.
2. What is the neat weight of 9 boxes of Havana sugar,
each weighing 400 pounds, allowance ij- per cent, for tare,
scalage 4 pounds per box? and what is the value of the neat
weight, at 89.40 per 100 lbs.?
Ans. neat 3475 lbs. ; valuej 8326*65*
USlTfiD STATES DUTIES. , 143
N
S. What is the neat weight and value of 3 boxes of figs,
Weighing 25 pounds each, with allowance of 4 per cent, tare,
and I per cent, salvage, at 11 cents per pound?
Ans. neat 71 lbs. ; value, S7.81.
CASE III.
When the tare is so much per barrel, box, chest, &c., either
with or without tlie allowance for draft or scalage.
Rule.
If any allowance be made for draft or scalage, cast and
deduct it as before directed.
Multiply the number of barrels, boxes, chests, &c., by the
tare of one ; subtract this product from what remained after
t^e scalage was deducted ; but when no scalage is allowed,
deduct the tare from, the whole gross weight : the remainder
will be the neat weight.
Examples*
1. What is the neat weight and value of twenty chests of
hjson tea, weighing 1500 pounds grpss, tare 24 pounds per
chest, at 50 cents per pound?
lbs.
20 1500
24 .480
480 Tare. 1020 Neat.
50
' 8510.00 Value.
2. What is the n6at weight a;;id value of 9 casks of raisins,
Weighing 720 pounds gross, tare 12 pounds per cask, allowing
2- per cent, scalage, at 6 cents per pound?
Ans. neat 608 lbs. ; value, g36.48.
3. What is the neat weight of 5 chests of tea, each weighing
gross 75 lbs., tare 5 lbs. per chest? and Kow much is the
value of the neat weight, at 60 cents per pound?
Ans. neat 350 lbs. ; value S20O*
UNITED STATES DUTIES*
Goods, wares and merchandise, imported into the Uniteft
144 UNITED STATES DUTIES*
liundred, gallon, &c. The ad valorem rates of duty are com-
puted by adding 20 per cent, to the actual cost of the goods,
if imported from the Cape of Good Hope, or any place be-
yond it ; and 10 per cent, if imported from any other place
or country.
Case I.
To find the amount of duty for any amount of goods, warea
or merchandize, when the rate per centum ad valorem is
given.
Rule. •
To the sum reduced to federal money, add 20- per cent., if
imported from or beyond the Cape of Good Hope ; or 10 per
cent, if imported from any other place or country ; multiply
this amount by the given rate per cent, ajid divide by 100, for
the duty required.
Examples.
1. What is the duty on an invoice of cloth imported from
London, which cost 873 pounds sterling, at 40 per cent, ad
valorem?
£ £ S '
As 9 : 873 :j 40
40 •
9)34920
10)3880 actual cost in federal money
388 10 per cent, added.
4268
40
81707.20 duty required.
2. What will be the duty on an invoice of raisins, imported
from Spain, which cost 320 piasters, at 30 per cent, ad va-
lorem? Ans. 884.48 cts.
8. What will be the duty on an invoice of silk goods, im-
ported from India, which cost 2000 rupees of 50 cents each,
at .20 per cent ad valorem? Ans. g240.
. Case XL
To find the duty on any amount of goods, wares or mer-
chandize, at any given rate per gallon, pound, &£<
vulgar fractioxs. 145
Rule.
Multiply the number of gallons, pounds. Sic. hx the given
rate per gallon, pound, &c. and the product ^vill be the duty
required.
Examples.
1. What vriW be the duty on 300 chests of tea, imported
direct froiu China, in a vessel of the United States, weighing
gross 22500 lbs. tare 20 lbs. per chest, at 40 cents per pound?
lb.
300 22500 gross.
20 6000 tare.
6000 lbs. tare: 16500 neat.
40
S6600.00 Answer.
2. What will be the duty on 30 pipes of French brandy,
containing 3780 gallons, at 50 cents per gallon.^
, Ans. gl890.
3. What will be the duty on 675 gallons of wine, imported
from France, at 48 cents per gallon? Ans. S824.
VUL.GAR FRACTIONS.
A Vulgar Fraction is apart or parts of a whole number,
and is written thus, j, one-fourth ; -J , one-sixth ; ^, four-
sevenths.
The figure above the line is called the numerator, and the
under figure the denominator, which shows liow many parts
the integer is divided into ; and tlie numerator shows how
many of those parts are meant by the fraction.
There are four sorts of vulgar fractions ; proper, improper,
compound and mixed, viz. —
1. A proper fraction is when the numerator is less than the
denominator, as ?, |, y\, -^-^j, &c.
2. An improper fraction is when the numerator is equal to
or greater than the denominator, as |, |, y , ^p, &c.
3. A compound fraction is the fraction of a fraction, and
known by the word of; as i of g^ off of -f of 4, &c.
4. A mixed number or fraction is composed of a whole
kimnber and a fraction ; as li, 3f , 61 , 12^, 15^, &c.
14G VULGAR FRACTIONS.
^^otc — Any v/hole number may be made an imprcper frac*
tioii, by chawing a line under it, and putting unity or 1. for a
c!euominator ; as 7 may be expi:essed fraction -wise, thus, -J,
and 15 tlius, \^, &:c.
9
REDUCTION OF VULGAR FRACTIONS
Is the bringing of them out of one form into another, in
order to prepare them for the operation of addition, sub-
traction, multiplication, division, &lc.
Case I.
To reduce a vulir^r fraction to its lowest terms.
Rule.
1st. Divide the greater term by the less, till nothing be
left; the last divisor will be the common measure, by which
divide both terms for the fraction required: Or,
2d, Which is often the shortest way, take the aliquot parts
of both terms continually, till in their lowest terms*
Examples.
h Reduce |^ to its lowest terms.
66)84(1 r66 = ll
60 6J— — '
— (.84 = 14 Answer*
18;66(S
54
12)18(1
12
6)12(2
12
2. Reduce -y^y^Q- to its lowest terms.
3. Reduce -}^^|- to its lowest terms.
4. Reduce -^^^ to its lowest terms.
5. Reduce |g^ to its lowest terms.
6. Reduce f ^J. to its lowest terms.
7. Reduce ||^| to its lov/est terms.
8. Reduce ^fij^ to its lowest terms.
Case II.
Ans.
4'r
i.
?•
2
T-
3
X»
233
2j7r*
2
1-
7
10<J*
vuLctAa yaAcrioxS/ 147^
Rule.
Multiply the whole number by the denominator of the frac-
tion, and to the product add the numerator of the fractioili
Under which write the denominator.
Examples*
1. Reduce 41 ^f to its equivalent imnroner fraction*
41 '4-
47
299
164 '
1939 1
y The fraction sought.
47J
2. Reduce 4.i to its equivalent improper fraction. Ans. |#
5. Reduce 12| to its equivalent improper fraction. ** ^-g-^*
4. Reduce 19 J- to its equivalent improper fraction. *' ^-i-^.
5« Reduce 41y.to its equivalent improper fraction. ** ^Y*
6. Reduce 75i to.its equivalent improper fraction. ** ^^i,
7. Reduce lO^^J to its equivalent improper fraction. " '^nnr •
8. Reduce 5-J4 to its equivalent improper fraction. *• \y «
Case III.
To reduce a whole number to an equivalent fraction, that
shall have a given denominator.
Rule.
Multiply the whole number by the given denominator 5
place the said denominator under the product, and it will
form the fraction required.
Note, — All fractions represent a division of the numerator
by the denominator. Thus, ^-^ denotes 12 to be divided by
4, and = 3 ; and -J denotes 4 to be divided by 5, and = •^.
Examples^
1. Reduce 12 to a jfraction whose denominator shall be 5.
12 X 5 ss 60, and *y^ the answer.
2. Reduce 16 to a fraction whose denomiuator shall be 7.
Ans. 1^^
8« Reduce 19 to a fraction whose denominator shall be 9.
148 VULGAR I^RACTIGNS*
4. Reduce 21 to «l fraction whose denominatoi* shall be 10-
Ans. \V-
5. Reduce 85 to a fraction whose denominator shall be 6.
Ans. 2|o.
6. Reduce 14 to a fraction whose denominator shall be 3.
Ans. ^^2.
7. Reduce 63 to a fraction whose denominator shall be 12.
Ans. ^2^-
8. Reduce 9 to a fraction whose denominator shall be 41.
Ans. \Y.
Case IV.
To reduce an improper fraction to its equivalent whole, or
mixed number.
Rule.
Divide the numerator bj the denominator— the quotient
will be the whole number ; and if there be a remainder, it
will be the numerator to the given denominator.
Examples.
1. Reduce W^^ to its equivalent whole, or i?iixed number.
163j5184(3H|i
489
294
. 163
131
163
2. Reduce '^^^ to its equivalent w^hole, or mixed number.
Ans. 53-j^2'
3. Reduce ^^V ^^ ^^^ proper terms. " 5jV
4. Reduce ^^ to its proper terms. " 12.
6. Reduce ^\^ to its proper terms. " 16y.
6. Reduce -J-f- to its proper terms. " ly\.
7. Reduce U id its proper terms. . '* 7jV.
8. Reduce ^l'* to its proper terms. " 44|-
Case V.
To reduce a {Compound fraction to a single one*
Rule.
Multiply all the numerators together, for a new numerator^
and all the denominators, for a new denominator*
VULGAR FRACTIONS. 149
If any pjwt of the compound fraction be a whole or mixed
number, it must be reduced to an improper fraction.
Like figures in the numerators and denominators may be
expunged, and frequently others be contracted by taking their
aliquot parts.
Examples,
1. Reduce k of f of S of J- of f , to a single fraction.
1x2x3x4x5 = 120 1
= - Ans.
2x3x4x5x6 = 720 6
Or,
^ of f of J of ^ of -J = \l^ = |.
Or having like figures expunged, thus :
1 2' 3' 4' 5' 1
- of - of - of - of - = -
2' 3' 4' 5' 6 6
2. Reduce ^ of 5 of 7 to a single fraction.
A of .1 nf X =3 -7 =3 1 1
8. Reduce 3 of ^ of f to a single fraction. Ans. |.
4. Reduce f of J of 7 to a single fraction. " Y=i'
5. Reduce | of |- of -f- to a single fraction. " J4. ,
6. Reduce f of J^ of |- to a single fraction. " /y.
7. Reduce -^-^ of |f of m to a single fraction. " ■}.
8. Reduce f of y^j of |-| of gf -^-i. to a singb fraction. |.
Case VI. ,
To reduce fractions to a common denominator.
Rule.
Multiply each numerator into all the denominators, except
its own, for a new numerator ; and all the denominators for a
common denominator.
Examples,
1. Reduce |, -f, f and |- to equivalent fractions, having a
common denominator.
1 X5x7x6=a 210, the new numerator for k
3x4x7x6 = 504, do*
3
T
4x4x5x6= 480, do. ^
5x4x5x7 = VOO, do. f
4x5x7x6= 840, the Common denominator.
Therefore the nev/ equivalent fractions are f J^, Iff, |U
' 700
and^*'^
150 VULGAR FRACTIDXS.
2. Reduce y> h 'i ^^^ f » ^^ Iractlons having a common
denominator. Ans. |-|J-, -JJ^, a^^ and |f^.
S» ReJuce J, -f and -Jf, to fractions having a common de-
nominator. Ans. -jVa* 1V2 ^^^d /^^g^
4. Reduce -J, 5 and ~-ff, to fractions having a common de-
nominator. Ans. l^-^-, l^^ and -^-JS*
5. Reduce -J-, ^, i and -j, to fractions having a common de-
nominator. Ans. -JIf, fO-°-, 1-^5 and -ff 4^
Case YII.
To reduce anj given fractions to others, which shall liave
the least common denominator possible.
Ret down all the denominators in a horizontal line ; find a
divisor that v»-iil divide more than one of them ; set down the
quotients, and bring into a line with them the numbers which
this divisor will not measure. If more than one of these can
lie divided bj anv divisor again, proceed as before ; and take
fhe continued product of the divisors, and i\\Q numbers in
this line, v»'hicn will be the common denominator.
Divide the common denominator bj the denominator of
each fraction, and multiply the quotient by the numerator of
fhe fraction, and the product will be the numerator of the
fraction required*
Examples.
1. Redi^ce f , -J, J- and ^J, to fractions having the least possi-
ble common denominator.
S)3, 5, 6, 8
2)1, 5, 2, 8
1, 5, 1, 4
3x2x1x5x1x4= 120, the least csmmon cl.eaominator,
3)120 5)120
40 . .24
2 4
80 1st nurarrator. 96 2d numerator.
VULGAR FRACTIONS. 151
6)120 8)120
20 15
1 5
20 3cl numerator. 75 4tii r.uni crater.
I survey inj given numbers, and find 3 vriil divide two of
tHem, viz: 3 and 6, whicli I divide by 3, bringing into a line
with the quotients the numbers which 3 v/ill not measure, I
view the numbers in the second line, and find 2 will measure
2 and 8 ; and these I divide by 2, and in the third line get 1,
5, 1 and 4. I multiply ^ti^o numbers in the said line, and the
divisors 3 and 2, continually together, for iA\c r^.ruircd com-
mon denominator, and find it J 20, which I divide bv i\\Q dc-
nominator of each fraction, and multiply the quotients by the
numerator of each fraction respectively — and find the equiva-
lenc iractions, "]"2o'» t^o*' "3*20^ anci "rg^.
2. Reduce li, S, -J- J, and |, to fractions havino; the least
common denominator. Ans. f J, ^-^, ^% and .^o.
3. Reduce |-, \-, £-J, and ^^'u^ ^-^ fractions having the least
common denominator. Ans. -Jg-^-, •^^g'^^, Y^i ^^^ TeV*
4. Reduce -J, -J, |, and -^^y to fractions havinp; the least
common denominator. Ans. -^^ J|, l-\ and |4«
5. Reduce |, -J-, -j^g. and ^V» '^^ fractions having the least
common denominator. Ans. ^^2 , ttV' tt^ ^"^ Ty2-
6. Reduce f, |-, -^^ and \l-, Id fractions having the least
common denojninator. Ans. -i^^, |f§, \^ and -||-J.
7. Reduce f , |-, |- and -^, to fractions having the least
common denominotor, Ans. ^W» tVo f |V ^^^^ ill'-
8. Reduce |, -J-, gV ^^^ "8^r» ^^ fractions having the least
common denominator. Ans. f f , /i-, -g\ and -g^j.
Case VIII.
To reduce fractions of one denomination to the fraction
of another, but greater, retaining the same value.
• Rule.
Reduce the given fraction to a compound, one, by com-
paring it with all the denominations between it and that de-
nomination which you would reduce it to ; then reduce that
compound fraction to a single one by case 5th.
152. VULGAR FRACTIOXS,
Examples*
1. Reduce f of a grain to the fraction of a pound troy.
6 of -,-1- of ^V of tV = 4:of 2^ ^ ^T2o Answer.
From what has been remarked, it is very easj to conceive
^ of a grain to be f of -2V of 2V of tV of a pound, which re-
duced to a single fraction, is -^2"^ of a pound.
2. Reduce d of a cent to the fraction of a dollar.
Ans. ^^. ■
8. Reduce 4 of a foot to the fraction of a yard. Ans. i.
4. Reduce d- of a yard to the fraction of a perch.
Ans. -jlj-.
5. Reduce f of an ounce 1 the fraction of a pound avoir-
dupois. Ans. -if-g-*
(i. Reduce 1 of a peck to the fraction of a bushel.
Ans* -g-.
7. What part of a yard is I of an inch? Ans. yV
8. What part of a day is 4- of an hour? Ans. -^V*
Case IX.
To reduce a fraction of one denomination to the fraction of
another, but less, retaining the same value.
Rule.
Multiply the numerator of the given fraction by that num-
ber which one of the higher contains of the lower, for a new
numerator to the denominator of tlie given fraction.
Exdmples.
1. Reduce ^^Vo of a pound troy to the fraction of a grain.
_!l vl2v20v24 5760 34 A„o
2. Reduce ^^ of a dollar to the fraction of a cent.
Ans.* h»
3. What part of a foot is f of.a yard? Ans. |.
4. What part of a yard is y^ of a perch? Ans* j.
5. What part of an ounce is y|-g- of a pound avoirdupois?
Ans. f .
6. Reduce ^ of a bushel to the fraction of a peck.
Ans. 5^.
7. Reduce y^ of a yard to the fraction of a foot.
Ans. 5^*
8. Reduce ^V of a day to the fraction of an hour.
Ans. k* •
VUXOAR FB.ACTIONS* 1^
Case X.
To reduce the value or quantity of a fraction to the known
parts of an integer, as of weiglit, measure, coin, &c.
Rule.
Multiply the numerator by the parts in the next lower de-
nomination, and divide by the denominator ; if there be a
remainder, multiply it by the next lower denomination, and
divide by the denominator as before, and so on, as far as
necessary ; place the quotients after each other in their regu-
lar order, for the required answer.
In examples of federal money it is oifly necessary to annex
ciphers to the numerator, and divide by the denominator.
Examples.
1. What is the value of ^J- of a mile?
1x8 =8
And 7)8
1 fur. ^ per. 3 yds. 2 it- 0^ in. Answer.
2. What is the value of f of a pound? Ans. 13s. 4d.
3. What is the value of f of a yard? Ans. 2 ft. 6f in.
4. Reduce f of a pound troy to its proper value.
Ans. 8oz.
5. Reduce f of a yard to its proper value.
Ans. 3 qr. If na.
6. Reduce |^ of an acre to its proper value.
Ans. 2 R. 20 P-
7- What is the value of | of a dollar?
Ans, 12 cts. 5 mills.
8. What is the value of | of a dollar? Ans. 25 cts.
9. What is the value of -J- of a dollar? Ans. 20 ct«.
10. Reduce -J of a dollar to its proper value.
Ans. 33^ cts.
11. What is the value of -^ of a dollar? Ans. ll^cts.
12. What is the value of f of a dollar? Ans. 57| cts.
13. What is the value of f |^ of a dollar? Ans. 65f cts,
14. Reduce \-^ of a dollar to its proper value.
Ans. 95 cts.
15. AVhat is the value of |- of a moidore? Ans. 5 dolls.
16. What is the value of | of an eagle? Ans. 83.33|.
17. What is the value of -^^ of a day? Ans. 4 h. 48 min.
L
154 VULGAR rRAOTIONS.^
18. Reduce ^ of a year to its proper value.
Ans. 73 d. 1 h. 12 mittr
19. What is the value of | of 3 days? Ans. 2 d. 6 h.
20. What is the value of | of a ton? Ans. 5 C.
Case XL
To reduce any given value, or; quantity, to the fraction of
any greater denomination of the same kind.
Rule.
Reduce the given quantity to its lowest term mentioned,,
for a numerator, then reduce the whole number into the same
name for a denominator ; this fraction, reduced to its lowest
terms, will be the fraction required.
Note — If a fraction be given, multiply both parts 6y the
denominator thereof, and to the numerator add the numera-
tor of the given fraction.
Examples.
1. Reduce 1 fur. 5 p. 3 yds. 2 ft. Oy in. to the fraction of
a mile.
Fur. P. yds. ft. in. Mile,
1 5 3 2 9f 1
40 8
45 8
5j 4a
228 320
22i 5i
250i 1600
3 160
753i 1760
12 3
9051 5280
7 12
63360 numerator, 63360
7
443520 €lenoininator«
es36#):^yi^ 5= 4" Answer.
VVhQk^ FRACTION 8. 155
3. Reduce 13s. 4d. to the fraction of a pound. And. |.
3. Reduce 2 ft. 6f- in. to the fraction of a yard. Ans. ^.
4. Reduce 8 ounces to the fraction of a pound Troy.
Ans. |.
5. Reduce 3 qrs. If na. to the fraction of a yard. Ans.f.
6. Reduce 2 H* 20 perches, to the fraction of an acre.
Ans. |.
7. Reduce 12 cts. 5 mills to the fraction of a dollar.
Ans. |.
8. Reduce 20 cts. to the fraction of a dollar. Ans. j.
9. Reduce 30 cts. to the fraction of a dollar. Ans. -j\.
10. Reduce 33| cts. to the fraction of a dollar. Ans. },
11. Reduce 11^ cts. to the fraction of a dollar. Ans. -J.
12. Reduce 57y cts. to the fraction of a dollar. Ans. f .
13* What part of a dollar is 65f cents ? Ans. f^.
14. What part of a dollar is 95 cents? Ans. -J^J.
15. What part of a moidore is 5 dollars? Ans. ^'
16. What part of an eagle is S3.33^? Ans, |.
17. What part of a day is 4 H. 48 min. ? Ans. i.
18. What part of a year is 73 D. 1 H. 12 min. ? Ans. |.
19. What part of a ton is 5 hundred? Ans. ?.
ADDITION OF VULGAR FRACTIONS.
Rule.
Prepare the fractions, by reducing the compound ones to
single ; the mixed numbers to improper fractions : then re-
duce each of the fractions to a common denominator ; add the
numerators together, and place the sum over the common
denominator. If it be an improper fraction, reduce it to its
equivalent whole or mixed number : if there be any whole
numbers, they may be added to the sum of the fractions.
Examples*
1- Add J of I of f of ^, 7f, I md 5 together.
i of f of -J- of "^ss -^^ ass J, value of the compound frac.
7f «3 V» '^^^ mixed number reduced to an improper
fraction.
156 VULGAR FRACTIONS.
Then, it V &i^A l» the given fractions, prepared*
1x3x4= 12 *= the numerator for i.
33 X 4 X 4 «= 368 = the numerator for V«
8x4x3= 36 = the numerator for |.
416 = the sum of the numerator.
4x3x4= 48= the common denominator.
48)416(8f sum of the fractional part.
384
32 2
48 3
And 8f
5 = the whole number.
131 Sum. Answer,
2. Add f , f and f , together. Ans. i^/^.
3. Add'i, i and -/y, together. '' 1.
4. Add, 6, 4 and | of f , together. " lOJ.
5. Add 5J-, 4i and 3-]-, together. " 13i*j.
6. Add 16|, i of f and 7-^, together. " 24.
7. Add 4|, 5^ and 2|-, together. " 11J|.
,8. Add i of a week to I of a day. Ans. 2 D. 12 H.
9. Add } of a dollar to i of a dollar. Ans. 70 cts.
10. Add i of a pound Troj to i of an ounce.
Ans. 6 oz. 10 dwts.
11. Add i of a yard to J of a foot. Ans. 2 feet.
12. Add f of a day, J of an hour and 48 minutes, together.
Ans. 11 H. 9 min.
13. Add jV ^^ ^ bushel, J of a peck and 26 quarts, to-
gether. Ans. 1 bushel.
14. Add I of a yard, | of a foot and -^V of a mile, together.
Ans. 770 yds. 1 ft, 4i inches,
15. Add f of a week, i of a day and i an hour, together.
Ans. 5 D. U H.
16. Add f of a mile to f of a yard. Ans. 1174 yards.
17. If a merchamt own it^ of a ship, valued at 5000 dol-
lars, and buys another person's share of her, which is |J,
what part belongs to him, and what is it worth ?
Ans. II, worth 4200 dollars.
I
VULGAR FRACTIONS* 157
18. Add ^5^ of an eagle to ^ of a dollar. Ans. 1 dollar.
19. What is the sum. of | of four dollars, | of two dollars
and f of one dollar ? Ans. 2 dolls«
20. Add I of 3 pecks to f of 2 bushels.
Ans. 1 bu, 2 P. a§ qts.
21. What is the sum of f of a moidore, f of an eagle and
;r of a dollar ? Ans. S8.25.
22. What is the sum of ^ of a dollar and |- of a moidore?
• Ans. 1 dollar.
23. What is the sum of i of a day, | of an hour and | of
a week? Ans. 2 D. 20 H. 45 M.
SUBTRACTION OF VULGAR FRACTIONS.
Rule,
Prepare the fractions as in addition ; subtract the numerator
of the less from the numerator of the greater; place the
common denominator under this difference— so is this hew
fraction the difference of the given fractions.
In subtracting mixed numbers, reduce the fractional parts
only to a common denominator ; place the less quantity under
the greater, and the difference of the numerators will be a
numerator to be placed over the common denominator*— and
the difference of the whole numbers will be a whole number ;
but if the numerator of the fraction in the lower quantity be
^eater than the numerator of the fraction in the upper quan-
tity, then take the lower numerator from its denominator, and
add the numerator of the fraction in the upper quantity ta
the remainder ; set it down and carry one to the integer of
the lower number.
Examples.
1. From 9 T^ take 6 J|.
2)14 22
. 7 11 And 2 X 7 X' 11 =. 154, common multiple.
And 154 -^ 14 X 5 => 55
154 -^ 22 X 17 -> 119
em
'3^ — 2^ Anitwer,
158 VULOAR FRAOTIOirStf
2. From 6| take 4|. Ang. 2J.
3. From 14^^ take 12J. "' I14.
4. From | subtract i. " J,*
5. From 19 take } of 17. ' " 13|.
6. From 75 take 47f 1 ^ " 27f
7. From f of -^ subtract 4 of ^. •* ^^
8. From i a dollar take i of a cent. Anu, 49f cts.
9. From i of a mile take -^ of a league. Ans. 88 yds*
10. From f- of a week take ^f J^^ of a year. Ans. 1 day.
11. From -jij- of a day take ? of an hour. Ans. 51 min.
12. From 4 weeks take 21| days. Ans. 6f days.
13. From ? of a yard take I of a foot. Ans. 3 inches.
14. From -J- an eagle take -J a dollar. Ans. S4.50.
15. From J of a pound Troy take 2 ounces. Ans. 1 oz.
16. From J a bushel take 5 a peck. Ans. 12 quarts.
17. From yV ^f ^^ ^^^^ ^^^ t of an hour. Ans. 12 min,
18. From h an acre take i of a rood. Ans. 1 R. 30 P.
19. Borrowed 40 dollars, paid -J- of 110 dollars — What re-
mains? Ans. 18 dollars.
19. Take i a moldore from 5 an eagle. Ans. 2 dolls.
MULTIPLICATION OF VULGAR FRACTIONS.
• Rule.
If a mixed number be given, reduce it to an improper frac-
jdon, orif a whole number, put it to a fractional form, by
writing 1 for the denominator. Compound fractions, in the
operation, may retain their original form.
Multiply the numerators together for a new numerator, and
the denominators for a new denominator — ^which reduce to
their proper terms for the answer required.
Where.several fractions are to be multiplied, if the numera-
tor of one fraction be equal to the denominator of another^
their equal numerators and denominators may be omitted.
Examples.
1. Multiply i of I of ^ by i of 6f .
• 6| = V
Then, i, of i' of ^^' X J of »|, - ff = f Ans.
«. Multiply i, *f i by i of \i. Ans. ^.
YUJLGAIL TItACTIONS* 159
3. Multiplj 3i by ^. Ans. •/;•
4. Multiply 62J by ^, " 4^
5* Multiply 61 by 5|. " 33^|.
6. "Wliat is the product of f of 9, multiplied by i of If.
Ans. 2.
7- What is the continued product of |, 1|, |, Ss and
3 o Ans ^-^
8. Multiply 7h by i of f . Ans. 2I.
9. Multiply 6i by i of 6. • Ans. 9^.
10. Multiply 100 by i of | of | of ^ of f of f of | of
4 of yV' '^'^s. 10,
11. What is the continued product of 3J, 2J, |, ^ and 1|?
Ans 2^-^
. 12. Multiply 6f by 2|. Ans. isf.
13. Multiply 41 by f of 4. Ans. 109^.
DIVISION OF VULGAR FRACTIONS.
Rule.
Prepare the fractions, if necessary, as in multiplication ;
then multiply the denominator of the divisor by the numera^
tor of the dividend for a numerator ; and the numerator of
the divisor by the denomiiiator of the. dividend for a denomi-
nator.
Examples,
1. Divide i by 6f .
5i. Divide i of4by|of|.
i of |-)i of 1(1^ = 1^ Answer.
Or J by reducing the compound fractions to sijigle ones.
Thus, ^ of f == ^ '
^ of 1 = ^. -^yMU =* l^V as before.
3. Divide 4 by ?. Ans. 16^
4. Divide 27i by i oJi27. Ans. 2j\.
5. Divide I by i. Ans. li.
6. Divide 9 J by 6. Ans. 1^.
7. Divide 4J by ^ of 4. Ans. 6i.
8. Divide ]- of 4 by 4^, . Ans. A.
Oi Divide ^ by ^. Ans. Sj.
160 VULGAR FIlAOTIO]fS»
10- Divide J of 6 bj f of f of 8^. Ana. 1.
11. Divide 6| bj 4- ^»«' ^iV
12. Divide 620i bj 206^ Ans. 8.
Note, — When the denominator ©f the .divisor and of the
dividend are equal, the quotient maj be found by common
division, viz* bj dividing the numerator of the dividend by
the numerator of the divisor : or this rule maj be rendered
more general, bj reducing the fraction to a common denomi-
nator, and dividing^ as before, rejecting the common denomi-
nator entirely.
As, if 5 were to be divided by i ; 4 is equal to f , and %
divided by 1 is 2, the quotient required.
13. Divide ^ by i-
^ and I reduced to a common denominator, ia ^ and^*
and 15-7-14 = 1^ Answer.
14. Divide f by f . Ans. 3.
15. Divide \^ by -5^.* Ans. 5.
16. Divide f by J, Ans. f .
17. Divide \i by ^j. Ans. 1|^.
THE SINGLE RULE OF THREE IN VULGAR
FRACTIONS.
Rule.
Prepare the given terms, if necessary, by reduction, and
dtate tnem as in whole nufkibers ; multiply the second and
third terms together, and divide that product ,by the first
term: Or,
Multiply the denominator of the first and the numerators
of the second and third terms continually together, for a nu-
merator; and. the numerator of the first, and denominators of
the second and third termss for a denominator.
Examples^
1. If 5^ pounds of butter cost 6^ cents,, what cost.Sf
pounds P
5J«V 68i«'|* 2f.-y
lb. lb, cts*
As y : y :: 'I* : «|H' -2^ cts. Answer.
V0LGAR JRACTIONS. . 161
2. If -f^lb. •£ sugar cost 9 cts. what cost 151 lbs.?
Ans. gl.52|.
S. When 2 ounces of silver cost Sl-94«, what is thevalu*
of ^ of an ounce? Ans. 32}^^ cts.
4. Sold 48} bushels of com for g23.20 — How much was
it per bushel f Ans. 48 cts.
5. what will 91 pounds of tobacco come to, when 3J
pounds sell for 63| cents ? Ans. S 1.751.
6. Bought 5i yards of silk, at the rate of 7 jards for ^
dollars — How much does it amount to ? Ans. 84.95/^.
7. What will 7i pounds of bees-wax come to, at 27j| cts,
per pound ? Ans. g2.00.
8. If 16 men finish a piece of work in 28J days, the time
is required in which 12 men should do it. Ans. 37^ days.
9. What quantity of stuff that is J yd. wide, will line 7i
yards of cloth, 1} yards wide? Ans. 15 yards.
10. How many yards of cloth, at 6 dollars per yard, must
be given for 221- yards, at 4i dollars per yard. Ans. 16|^ yds.
11. A. lends to B. 12* dollars for 3^ months — What sum
should B. lend to A. for ^ month, to requite his kindness?
Ans. 81f dollars.
THE DOUBLE RULE OF THREE IN VULGAR
FRACTIONS.
Rule.
Prepare the terms, when necessary ; then state and work
them agreeably to the directions given in whole numbers : or
invert the dividing terms, and multiply the upper figures
continually for the numerator, and those below for the de-
nominator, of the fractional answer.
Hxamples*
1. Two brothers at school compute the expenses of Hieir
boarding, tuition, &c. for ^ of a year to be 80f dollars-— How
much will the education of 3 sons for 2i years cost their
father at that rate ?
If J®- !*• Ih^
f yr. }yr. i ^
ix|x|x|x*** « *W* =■ 6811 dolls. Answer.
163 CONTRACTED MULTIPLICATION OF DECIMALS. •
2. If a footman perform a journey of 294 irfiles in 9-f days
of 12| hours long — How long will it take him to travel 76|-
miles when the days are 10| hours long ?
Ans. 2 D. 9 H. 46J M.
3. When 12 persons use 1} pounds of tea p^r month, how
much should a family of 8 persons provide for a year ?
Ans. 9 lbs.
4. If 5 persons drink 7j gallons of beer in a week, what
quantity will serve 8 persons 22J weeks? Ans. 280y gals.
5. If 70 dollars in -J^ of a year gain 1-| dollars interest, in
what time will 100'- dollars gain G^^ir dollars ?
^ Ans. 12mpnths.
COSTTRACTED MUL.TIPI.ICATIOX OP
DECIMALS.
Rule.
Place the units place of the multiplier under that place of
the multiplicand that is intended to be kept in the product ;
then invert the order of all the other figures, that is, write
them all the contrary way ; then in multiplying, begin at the
figure in the multiplicand, which stands over the figure you
are then muhiplying wiA, and set down the first figure of
each particular product directly one under the other, and
have a due regard to the increase arising from the figures on
tlie right hand of that figure you begin to multiply at in the
multiplicand*
Note — That in multiplying, the figure left out every time
next the right hand in the multiplicand, if the product be 5
©r upwards, to 15, carry 1 : if 15, or upwards, to 25, carry 2i
and if 25, or upwards, to 85, carry 3, &c.
Examples.
1> Multiply 296.14364 by 12.71584^ and let there be only
4 plftGeci'of decimals in &e prodi^ct*
CONTRACTED DIVISION OF DBCIMAlS. 163
296.14364
48517.21
29614864
5922873
2073005
29614
14807
2369
118
3765.7150
^. Multiply 743.56815 by 52.647, and let there be only 8
peaces of decimals in the product. Ans. 39146.632.
3. Multiply 17.14 by 62.197, reserving only the integers
in the product. Ans. 1066.
4. Multiply .7164 by 12.1, reserving 3 places of decimals
in the product. Ans. 8.668.
5. Multiply 1.0034 by 799.99, reserving only 2 places of
decimals in the product. Ans. 802.72.
CONTRACTED DIVISION OF DECIMALS.
Rule.
Find what place of integers or decimals the first figure of
the quotient Will possess, and consider how many quotient
• figures will serve the present purpose ; then take* the same
number of the left hand of the divisor, and as many of the
dividend as will contain them, (less than ten times,) rejecting
the rest ; then, instead of bringing figures down from the
dividend, separate one from the right of the divisor as often
ad necessary, till the whole be exhausted, remembering to
carry from the right hand figures of the divisor, as in con-
tracted multiplication.
When there are not so many figures in the divisor, divide
as usual, till there be as many of the quotient figures found
as the divisor is short of the intended quotient; then use the
contraction.
Examples*
V Divide 642.27541 by 8.671265, and let thcr^ be only
fettr placei of^decimalt in the quotient.
164 COXTAAOTED DIVISION*
3.671265)642.27541(174.9466 Ana.
3671265 '
2751489
2569886
181603
146851
34752
33041
1711
1468
243
220
23
22
2. Divide 2508.928065051 by 184.8207, so as to have 4
places of decimals in the quotient. Ans. 13.5749L
8. Divide 43.538163 by 4.6827035, and let there be t
places of decimals in the quotient. Ans. 9.2976552.
4. Divide 1254.46403 by 46.205175, and let there be 4
places of decimals in the quotient. Ans. 27.1498.
• 5. Divide 3765.715 by 296.14364, and let there be 5 places
of decimals in the quotient. * Ans. 12.71584.
6. Divide 39146.632 by 743.56815, and let there be three
places of decimals in the quotient. Ans. 52.647.
CONTRACTED DIVISION.
The following contracted method of dividing, being taken
notice of in few works that I have seen, I have chosen to de«
liver it by itself.
Rule.
Set down the sum a^ter the usual manner ; find the first
quotient figure, and multiply the divisor as usual, but instead
of setting down the product^ subtract the product of each re*
CONTRACTED DIVISION, 165
spectiYe figure, from the figure above, borrowing as many as
necessary, which must he carried to the product of the next
figure ; bring down the figures as necessary for a dividual,
and thus proceed to the end.
JSxamplea.
1. Divide 59148684 by 627812.
627812)59143684(94 quotient.
2640604
129356 remainder.
Explanation. — I find the first quotient figure is 9, and say
9 times 2 are 18, take 18 from 18 and is left; I set this
down under the 8, and carry 1 ; then 9 times 1 are 9, and 1
that I carry make 10 ; take 10 from 16 and 6 are left; I set
this down, and carry 1 ; then I say 9 times 8 are 72, and 1
that I carry make 73; take 73 from 73, and is left ; then 9
times 7 are 63, and 7 that I carry make 70; take 70 from
74, and 4 are left ; then 9 times 2 are 18, and 7 that I carry
are 25 ; take 25 from 31, and 6 are left; then 9 times 6 are
54, and 3 that I carry are 57; take 57 from 59 and 2 are left ;
J then bring down the next figure (4) for a new dividual, and
proceed in every respect as before.
2. Divide 7854 by 67.
67)7854(117 quotient.
115
484
15 remainder.
S. Divide 61427 by 121.
121)61427(507 quotient.
927
80 remainder.
4. Divide 7157264 by 28144.
23144)7157264(309 quotient.
214064
5768 remainder.
5. Divide 96215496 by 514217.
514217)96215496(187 quotient.
4479379
3656436
56917 remainder.
166 EQUATION OF PAYMENTS.
6. Divide 623917842 by 7219543.
7219543)623917842(86 quotient.
,46354402
3037144 remainder.
7. Divide 543 by 17. Quotient 31 ; rem. 16.
8. Divide 7259 by 72. Quotient 100 ; rem. 59,
EQUATIOX OF PAYMENTS.
CASE I.
To find the equated time for the payment of a sum of money
due at several different times.
Rule 1. Find the present worth of each payment, for its
respective time ; add all the present worths together, and
deduct the sum from the sum of the payments ; tnen divide
this remainder by the product of the sum of the present
worths and the ratio : the quotient will be the true equated
time.
Rule 2. Multiply each several payment by the time it has
to run : then divide the sum of the products by the sum of
the payments ; the quotient will be the equated time, nearly.
Examples,
1. A^owes B. S1800, whereof 8200 is to. be paid at 6
months, g400 at 9 months, and S1200 at 20 months — At what
time may the whole debt be paid together, rebate being made
at 6 per cent. ?
ot S( S( ft
As 103 : 200 ;: 100 : 194.174 present worth of the
first payment.
104.50 : 400 :: 100 : 382.775 " 2d paym't.
110 : 1200 :: 100 : 1090909 " 3d paym't.
8 1667.858 sum of present worths.
1800.000 sum of -the payments.
1667.858 sum of the present worths,
132.142 discount.
1667.858 sum of the present worths.
.06 ratio.
100.07148 divisor.
EQUATION OF PAYMENTS* 167
Ydrs
100.07148)132.14200 ( 1.32047
10001^148 12
32070520 3.84564
30021444 80
20490760 25.36920
20014296 True answer,
« 15 M. 25 da.
47646400
By rule 2. 40028592
200x 6 = 1200 76178080
400x 9 = 3600 70050036
1200x20 =- 24000
6128044
1800 ) 28800(16 montlis. Answer, nearly,
1800
10800
10800
Note, — Rule 2 is more compendious than rule 1, but can-
not be depended upon as sufficiently accurate.
2. D. owes E. gl200, which is to be paid as follows, viz.
2200 down ; S500 at the end of 10 months, and the rest at
the end of 20 months ; but they agreeing to have an equal
Eayment of the whole, the true equated time is required, re-
ate at 6 per cent.
Ans. By rule" 1, 12 mo. 75 days.
By rule 2, I2k months.
3. A merchant has owing to him g400 to be paid as follows,
yir.. 8100 at 3 months, 8100 at 4 months, -and the rest at 8
months ; but it is agreed to make one payment of the whole—
When will that time be, rebate at 6 per cent. ?
Ans. By rute 1, 5 mo. 21 da.+
By rule 2, 51 months.
4. G. owes H. 8800, of which 8500 are to be paid present,
and the rest at 8 months; but they agree to make one pay-
ment of the whole, and wish to know the time, rebate at 6
per cent. ? Ans. By rule 1, 2 mo. 28 da.
By rule 2, 3 mox^Jhs.
168 EQUATION OF PAYMENTS.
CASE 11.
When a sum of money is to be apportioned among several,
in such a manner that each one's share, placed at interest for
unequal terms, shall produce equal amounts.
• Rule.
Find the amount of SlOO, at the given rate per cent, for
the time each one's share is to remain at interest, and multi-
ply the continued product of these amounts by the whole sun^
tor a dividend.
Leave out one uf these amounts, and multiply the othera
continually together ; then leave out another of the amounts,
and multiply the remaining on'es continually together; and
thus proceed, leaving out one of the amounts each time, until
each of the amounts are respectively left out, and the remain-
ing oncn multiplied continually together; then multiply the
sum of these products by 100, for a divisor. The quotient
will be the equal amount of each one. The present worth of
this equal amount, for the time it remains at interest, will be
each one's share.
Examples,
1. A man at his decease left 872C0, to be divided among
his four sons, whose several ages were 14, 17, 18 and 20
years, in s^ch manner that their several portions, when they
respectively would arrive to the age of 21 years, should be
equal, reckoning interest at 6 per cent, during their minori-
ties — I desire to know the sum bequeathed to each.
gl06 amount of SlOO for one year.
118 " " three years.
124 " " four years,
142 " " seven years.
106x118x124x142x7200 =1585734220800 dividend*
106x118x124 = 1550992 here 142 is left out
106x118x142 = 1776136 " 124 is leftout.
106x124x142 = 1866448 ** 118 is leftout.
118x124x142 = 2077744 " 106 is left out.
7271320
100
727132000 divisor.
EquATioN OF payments! 169
7271320.00)15857342208.00(2180^.7 received by each
14542640 . [at the age of 21.
13147022
7271320
58757020
58170560
58646080
58170560
47552000
50899240
As 106 : 2180.807 :: 100 : 2057.365 bequeathed to him"
i [aged 20'year8.
118 : 2180.807 : : 100 : 1848.141 " "18 years. ^ g
124 : 2180.807 : : 100 : 1758.715 *' " 17 years.
142 : 2180.807 : : 100 : 1535.779 " •• 14 years.
7200.000 whole sum bequeathed.
2. Divide S400 into two such parts, that the amounts will
be equal, one being put to interest for one year, and the
other for two years, at 6 per cent.
Ans. 8205.54 and S194.496.
7^0 find the annual rent which any real property should
bring, so as to pay debt, interest and costs in 1 years*
Rule.
Multiply the given debt by .17913, the product will be the
annual rent which the property should rent for.
iVb/e.— If real property will rent for as much as will pay
the debt and costs, with interest, in seven years, it cannot
be legally condemned and sold for debt.
Examples.
1. What annual rent would be sufficient to pay the amount
of debt and costs, upon a property amount!^ in the whole to
2558.25$ cents, in seven years.
558.255X.17918 « lOO^+Answer.
M
170 BQUATIOir OF PATMEirrs*
1
PROor.
558^285 whole amount of debt and costs.
83.495 interest for one year.
591.750 amount due at the end of the first year.
100.000 rent received the first year.
491.750 balance due after receiving the first year's rent.
29.505 interest on this balance for one year.
521.255 amount due at the end of the second year.
100.000 rent received the second year.
421.255 balance due after receiving the 2d year's rent.
25.275 interest on this balance for one year.
446.530 amount due at the end of the third year.
100.000 rent received the third year.
346.530 balance due after receiving the 3d year's rent.
^•792 interest on this balance for one year.
367.322 amount due at the end of the fourth year.
100.000 rent received the fourth year.
267.322 balance due after receiving the 4th jear's rent
16.039 interest on this balance for one year.
283.361 amount due at the end of the fifth year.
100.000 rent received the fifth year.
183.361 balance due after receiving the fifth year's rent.
11.001 interest on this balance for one year,
194.362 amount due at the eYid of the sixth year.
100.000 rent received the sixth yearl
94.362 balance due after receiving the sixth year's rent.
5.638 interest on this balance for one year.
100.000 amount due at the end of the seventh year.
100.000 rent received the seventh year.
Hence it is evident that the debt^ interest and costs «re
*11 paid.
ALLl«ATieN. 171
H. A property which rented annually, for S860, was con-
demned bj a court of enquiry, for an amount of debt against
it of 22100 — Was the condemnation legal ?
S
2100 X. 17913 = 376.173 the sum it should rent for an-
[nually.
Now, because this sum exceeds £360, the condemnatioil
was legal.
8, What annual rent would be sufficient to pay the amount
of debt and costs, (upon a property) amounting in the whole
to S12000, with the interest, in seven years ?
Ans. 82149.56.
4. A property worth an annual rent of S300, has a debt of
S1500 against itr— Should it be condemned ?
S1500X-17913 = S268.69i.
Now, because, this is less than 2300, the property should
not be condemned.
5. Should a property worth an annual rent of S600, be
condemned for a debt of g3400 ?
3400 X .1791 3= 8609.042.
Now, because this sum is more than the annual rent, it
should be condemned.
AliLIGATION.
Alligation is a rule by which we adjust the prices and
dimples of compound quantities.
CASE I.
Whenjthe quantities and their prices are given, to find the
price of a part of the composition.
Rule.
As the sum of the several quantities.
Is to any part of the composition,
So is their total value,
To the value required.
Examples.
1. A merchant mixes 3 C. of Sugar^ at 88.25; 1 C. at
87.50; 5 C. at %8JQ0 ; and 2 C. at 86.50—1 desire to know
-what 10 C. of this composition is worth.
172 ALLIGATIOir.
C. 8
3x8.25 = 24,75
1x7.50= 7.50
5x8.00 = 40.00
2x6.50 = 13.00
11 85.25 total value.
CCS 58
As 11 : 10 :: 85.25 : 77.50 answer.
2. If 12 bushels of corn, at 50 cents per bushel ; 100 of
oats, at 30 cents; 16 of rye, at 60 cents; and 14 of buck-
wheat, at 55 cents, be mixed together, what will 22 bushels
of the mixture be worth ? Ans. 811.127, nearly.
3. A wine merchant mixes 6 gallons of wine, at SI. 00 peF
gallon, with 4 gallons at 81.05, 7 gallons at 81.40, and 5 gal-
lons at 81.50— what is a gallon of this mixture worth } •
Ans, 81.25.
CASE II.
When the prices of several simples are given,' to find how-
much of each must be taken to.make a compound at any pro-
posed price.
Rule. '
The prices or rates must all be of the same denomination.
Set down the prices, one under the otjier, and the mean rate
on the left hand of these. Join or link together the several
rate's, so that each rate which is less than the mean rate be
linked with some one that is greater, or with as many greater
as you choose ; and each of the greater with some one that i»
less," or as many less as you choose ; the diiference, or sum of
the differences, between each rate and the m6^ price,
placed opposite the respective rate with which it or they
are linked, will be the respective quantities required.
Note 1. — Different modes of linking will produce different
answers.
2. Any number of answers may be had, by dividing or
multiplying any set of differences, by any common divisor or
multiplier ; which is evident from the following example.
Examples,
. 1. A n^erchant would mix wines at 81.20, 81.50, 82, and
82.50 per gallon, so that the mixture should stand him in
S1.60 per gallon— -What quantity of each sort must he take^
•>
ALLIGATION.
173
L250-
r
120—
l^^i 2§t
L250-
at SI 20.
1 50.
2 00.
2 50.
at &1 20.
1 50.
2 00.
2 50.
70 or 7,
20 2,
30 3,
60 6,
20 or 2,
70 7,
60 6,
30 3,
2. How much rye, at 48 cents per bushel, barley at 36 cts
and oats at 24 cents, will make a mixture worth 30 cts. per
bushel? Ans. 1 at 48 cts. 1 at 36 cts, and 4 at 24 cts.
3. How much sugar at 4 cts. at 6 cts. and at 11 cts. per
lb, must be mixed together, so that the composition may be
worth 7 cts. per lb. ? Ans. Any weight of equal quantity.
4. It is required to mix several sorts of wine, at 75 cents,
Sl.OO and 81.25 per gallon, with water, that the mixture
may be worth 50 cents per gallon — How much of each sort
must the mixture consist of?
75
100
125—,
0—1—
50 or 1 at 75 cents.
50 1 100
50 1 125
25+50+75=150 3 of water.
(<
((
Case III. '
When the price of each simple is given, also the quantity
of one of them, and the mean rate of the whole compound,
to find the several quantities of the rest. '
Rule.
Place the several prices one under the other, and the mean
rate to the left hand, and take their diiference as in case 2 ;
then.
As the difference of the same name with the quantity given
Is to the rest of the differences, respectively,
So is the quantity given
. To the several quantities required.
Examples.
1. Twelve bushels of wheat at Sl.OO, with rye at 50 cts.,
barle^uat 40 cts. and oats at 25 cts. — What quantity of these
Baust be mixed with the wheat, to rate at 60 cts. per bushel ^
1
174 ALLIGATIOW.
flOO-
125.
50—
40
10 + 20 + 35 =* 65
40
40
40
As 65 : 40 : :. 12 : 7/^ of rje. ")
65 : 40 : : 12 : 7tt of barley. I Ans.
65 : 40 : : 12 : 7^ of oats. J
2. How much alloy, and how much gold, of 21 and 22
clirats fine, must be put to 30 ounces, of 20 carats fine, to-
bring it to 18 carats fine. Ans. 30 oz. of 21, 30 of 22,
and 15 oz. of alloy.
3. How much Malaga at gl.l2^ per gallon, sherry at gl.OO,
and white wine at 75 cts. must be mixed with 30 gallons of
canary at 87i cts., so that the mixture may stand in 93 J cts^
per gallon ? Ans. 10 gal. at 81.12J, 30 gal. at 81J0O, }
and 10 gal. at 75 cts. per gallon. J
Case IV.
When the particular rates of all the ingredients proposed
to be mixed, the sum of all their quantities, with the mean
rate of that sum being given, to find the particular quantities
of the mixture.
Rule.
Set down all the particular rates, with the mean rate as
before; find the differences, and add them all into asum;^
then,
As the sum of the differences
Is to the diffe|*ence opposite each rate.
So is the quantity to be compounded
To the required quantity of that price.
Examples^
1. Hiero, king of Syracuse, gave orders for a crown, to be
made entirely of pure gold ; but suspecting the workmen had
debased it, by mixing with it silver or copper, he recom-
mended the discovery of the fraud to the famous Archimedes,
and desired to know the exact quantity of alloy in the crown.
Archimedes, in order to detect the imposition procured two
other musses, the one of pure gold, and the other of silver or
copper, and each of the safae weight with the former ; and by
puttine^ach, sepai^tely, into a vessel full of water, theqiian-
titj of water expelled by them determined their specific
FOStTIOV* 175
bulks. Now, suppose the weight of each mass to have been
S lb. ; the weight of the water expelled bj the alloy, 23 oz. ;
bj the gold, 13 ounces, and by the crown, 16 ounces ; that is, *
tnat their specific bulks were as 23, 13 and 16 : then, what
were the quantities of gold and alloy in the crown ?
ri3_l 7 of gold? And the sum of these is 7+3 =10,
^^ ^23 — I 3 of dloy 5 which should have been but 6.
Whence by the rule,
oz. oz. lb. lb.
As 10 :7 ::5 :3i of gold> .
10 : 3 :: 5 : U of alloy S ^*^®^-
2. How many gallons of water must be mixed with wine,
at S1*00 per gallon, so as to fill a vessel of 100 gallons, that
may be afforded at 80 cents per gallon ? Ans. 20 gallons.
3. A grocer had 4 sorts of sugar, at 4 cents, 8 cents, 10
cents and 12 cents per lb. the worst would not sell, and the
best was too dear ; he therefore concluded to mix 90 pounds-—
What quantity of each must he take, so as to sell at 9 cents
per pound ?
Ans. 27 lbs. at 4, 9 at 8, 9 at 10 and 45 at 12 cts.
Or, 9 lbs. at 4 cts. 27 at 8, 45 at 10, and 9 at 12.
POSITION.
Position is a rule that by false or supposed numbers, taken
at adventure, and worked with according to the nature* of the
question, discovers the true number sought.
SINGLE POSITION
Teaches to resolve such questions as require only one sup-
posed number, by the following
Bulb.
Take any number, and perform exactly the same opera*
tions with it, as are described to be performed in the ques-
tion: then,
As the result of that operation.
Is to the given sum or number, *
So is the supposed number.
To the true number requirsd.
176 POSITIOK.
iVb/e— If the results of two or more supposed numbers be
in the same proportion as the supposed number ; or if, upon
working with two supposed numbers, and multiplying each
'of them by th« result of the other, the products be equal, then
the qViestion may be solved by. Single Position ; if otherwise,
it cannot.
Examples.
1. A gentleman, at his decease, left S3000 to be divided
amongst his three sons, whose several ages were 18, 19, and
20 years, in such a manner that their several portions, when
they would arrive to the age of 21 years, should be equal,
reckoning interest at 6 per cent, during their minorities, — I
desire to know the sum bequeathed to each.
Suppose SIOOO the sum received by each at the age of 21
years ; S106, 112 and 118, the respective amounts of
SlOO during the time the several bequests are at interest;,
then,
So Q Q
As 106 : 1000 :: 100 : 943.396 sum bequeathed to the eldest
112 : 1000 :: 100 : 892.857 " " second
118 : 1000 :: 100 : 847.458 " " youngest
according to this
2683.711 supposition.
C^ Q Q Q
As 2683.711 : 3000 :: 1000 : 1117.86, the sum received by
[each at the age of 21. Ans.
As 108 : 1117.86 :: 100 : 1054.58 bequeathed to the eldest.
112 : 1117.86 :: 100 : 998.09 " " second.
118 : 1117.86 :: 100 : 947.33 " " youngest.
3000.00 whole sum bequeathed,
according to the question.
2. A gentleman bought a ohaise, horse and harness, for 240
dollars ; the horse came to twice the price of the harness, and
the chaise came to the price of the horse and harness — What
did he pay for each }
Ans. Harness, 840; horse, 880; -chaise, 8120.
3. A., B. and C. bought a quantity of goods for 8420, and
agreed among themselves that C. should have a third part
t»0&ITION* ITT
more than A,, ^nd B. should have as much as them both — ^I
desire to know how much each must pay.
Ans. A. S90; B. S120, and C. 8210.
4. The yearly interest of a sum. of money at 6 per cent,
exceeds ^^^ of its principal by 840 — I wish to know the prin-
cipal. Answer, 84000.
5. A gentleman bought two pieces of cloth, containing to-
gether 60 yards ; the price of one of the piecefs was 83.00 per
yard, and of the other 85.00 per yard, and the value of each
piece was the same — How many yards were in eaoJi piece,
and what the total amount ? Ans. 87* yards in. one.
225 " in the other.
8225 total amount.
6. In an orchard of fruit trees, 5 of them bear apples, ?
pears, -} plums, 30 of them peaches, and 40 cherries — How
many trees does the orchard contain ? Ans. 1000.
7. What is the age of a person who says that if } of th^
years I have lived be multiplied by 4, and | of them be added
to the product, the sum will be 82? Ans. 41 years.
DOUBLE POSITION
r
Is by making use of two supposed numbers, and if both
prove false, (as it generally happens,) they are, with their
errors, to be thus ordered :
RutE 1. %
1. Place each error against its respective supposed number.
2. Multiply them cross ways.
' 3. If the errors be alike, that is, both too much or too little,
take their difference for a divisor, and the difference of the
product for a dividend ; but if unlike, take their sum for a
divisor, and the sum of the products for a dividend ; the quo-
tient will be the-answer.
JVote 1. — If be used for the first and 1 for the second
supposed number, the first of the errors, divided by their dif-
ference, will, (in many instances,) be the answer.
Note 2. — Multiply the difference of the supposed numbers by
the least error, and divide the product by the difference of
the errors, if like, or by the sum, if unlike ; the quotient is
178 FOSITtOK.
the correction of the number belonging toihe least error«
which error is to be added or subtracted according as that
number was too little or too great.
Examples.
1. A gentleman has two horses, worth S200: ke has also a
saddle, which, if put upon the first horse, makes his valtte
double that of the second ; and if put upon the second horse,
makes his value equal to the first — I wish to know the yalue
of each hprse, also the value of the saddle.
First— -Suppose 8110, for the value of the first horse.
Then will 90 be the value of the second horse.
180 the value of the first horse and saddle.
110 value of the first horse.
, 70 value of the saddle alone.
90 value of the second horse.
160 value of the second horse and sad-
dle, which, according to the ques-
tion, is equal to the first horse.
110 value of the first horse.
50 error too little.
Again — Suppose gl25 for the value of the first horse.
Then will 75 be the value of the second horse.
2
150 vdlue of the first horse.
125 value of the second horse.
25 value of the saddle.
75 value of the second horse.
100 value of the second horse and saddle,
which, according to the question, is
equal to the first horse.
125 value of the first horse.
25 error too much.
FOSITIOV* 179
<» Sttp. Errors.
»i 110^50=6250
135^25 = 2750
75 ) 9000(120 An8. Value of the first horse*
75 80 Value of the second horse,
~ 2
150
150 160 value of the first horse and saddle,
— 120 value of the first horse. *
—
40 value of the saddle.*
By Note 2.
125 one ofthe supposed numbers, 50 greater error.
110 the other. 25 less error.
15 difference. 75 sum of the errors.
25 least error.
75
80
75)375(5 correction belonging to the least error; which is tO
S75 be subtracted, because the number is too greats
Hence 125 — 5 == 120 value of the first horse, as before.
2. A man had 2 silver cups, weighing together 20 Bunces,
and having one cover for both, now if the cover be put on the
lesser cup, it will be half the weight of the greater cup ; and
»et it on the greater cup, it will be five times as heavy as the
lesser cup— What is the weight of each cup ; also of the
oover? Ans. Lesser cup, 4 ounces.
Greater cup, 16
Cover, 4
3. A young gentleman having asked his father how old he
was, received the following reply: 12 years ago my age was
in a four-fold ratio to yours ; but if we should both happen to
live 6 years hence, my age will be just double to yours.— I de-
are to know their several ages. Ans. 48 and 21 yearS.-
4* A gentleman caught a fish, whose head was 8 inches
long, the tail as long as the head and half the body, the body
was just the lengfli of the head and tail — ^What was the
length of the whole fish? Ans. 5 feet 4 inches.
180 , ARITHMETICAL PROCRESSIOK.
5- A. B. and C. discoursing of their ages, A. affirmi&d that
he was 22 years of age ; B. said his age was equal to that of
A. and half the age of C. ; and C. affirmed that he was as old
as both A. and B. — What was the age of each person?
Ans. A. 22, B. 66, and C. 88.
ARITHMETICAL. PROGRESSIOJfe
, Arithmetical Progression is a rank or series of numbers
which increase oi* decrease regularly, bj a common differ-
ence^ that is, by the continual adding or subtracting of an
equal number.
In arithmetical progression five things are to be observed,
viz.
1. The first term.
2. The common difference.
3. The last term.
4. The number of terms.
5. The sum of all the terms.
Any three of which being given, the rest may be found.
Note — When any even number of terms differ, by arith-
metical progression, the sum of the two extremes will be
equal to the sum of the two middle numbers, or any two
means equally distant from the extremes; as 3, 5, 7, 9, 11,
13; where 7+9, the two middle numbers, are'= 3+13,
the two extremes, and == 5+11, the two means = 161
When the number of terms are odd, the double of the
middle term will be equal to the two extremes, or of any two
means equally distant from the middle term ; as 1, 2, 3, 4, 5,
where the double of 3 = 5+1 = 2+4 = 6.
Case I.
The first term, common difference, and number of terms
given, to find the last term, and sum of all the terms.
Rule.
Subtract the common difference from the product of the
number of terms, multiplied by the common difference, tlie
remainder, added to the first term, gives the last term.
Multiply the sum of the two extremes, (the .firsjt and last
ARITHMETICAL PROGHESSIOlft. 181
terms) by the number of terms, and half the product will be
the sum of the series.
Examples.
1. Twenty-five persons bestowed charity to a poor man;
the first gave him 10 cents, the second 12, and so on in
arithmetical progression — What did the last person give, and
what sum did the man receive ?
25 number of terms.
2 common difference.
50
2 common difference.
48
10 first term.
58 last term, or last person gave,
10
68
25 number of terms.
2)1700
88.50 sum receiyed.
2. A. covenanted with B. to serve him 12 years, and to
have SIO the first year, and his wages to increase annually
g3, during the term — What had he the last year; what on an
average yearly, and what for the whole time ?
f S43 the lastyear.
Ans. < 26.50 annually.
L 318 the whole time.
Case II.
When the two extremes and number of terms are given, to
find the common difference.
• Rule.
Divide the difference of the extremes by the number of
terms less one, the quotient will be the common difference.
183 GEOMETRIOAL PROGRESSIOK.
Examples.
1. Admit a debt be discharged at 14 several payments, in
arithmetical progression, the first to be 820, the last Sd8—
What is tiie common difference, and what the whole debt ?
98
20
14 — ls= 13)78(6 common diSbrence.
78
98
20
118
14
2)1652
8826 whole debt.
GEOMETRICAL. PROGitESSIOX.
When a number of quantities increase by the same mul-
tiplier, or decrease by the same divisor, they form a Geome-
trical Series. . This common multiplier, or divisor, is called
the ratio. Thus 2, 4, 8, 16, 32, 64, &c. increase by the con-
tinual multiplication of 2 ; and 64, 32, 16, 8, 4, 2, decrease
continually by the division of 2, or multiplication of .5.
Rule.
Multiply the first term into such a power of the ratio as is
indicated by the number of terms less one, and the product
will be the last term.
Multiply the last term by the ratio, from the product sub-
tract the first term, and divide the remainder by the ratio less'
one ; the quotient will be the sum of the series.
Examples,
1. If a man were to engage to pay another 1 cent; for the
first month, 6 for the second, 36 for tne third, and so on, in a
six-fold ratio, for 12 months' service.— How much would his
wages amount to?
OEOMIETILICAL PK0ORE8SIO9. 188
12 3 4 indices.
6 36 216 1296 leading terms.
1296
1679616 eighth power.
216
362797056 11th power and last term.
6 ratio.
2176782336
1 first term.
6—1=5)2176782335
84353564.67 Answer.
2. A country gentlem'an wishing to buy some oxen, meets
with a person who had 20 ; he demanded the price of them,
and was answered £32 a-piece ; the gentleman offers him
830 a;piece, and he would buy all : the other teUs him it
could not be taken, but if he would give what the last ox
would come to, at 1 cent for the first, and doubling to the
last, he should have all, which he agreed to.-*— I wish to know
how much he paid for them. Ans. 85242.88.
3. A man agreed with his neighbour for a team of 5 horses;
and was to give 9 cents for the first horse, 9 times as much
for the •second, increasing the price of each horse in a nine-
old ratio— What was the price of the team ?
Ans. 8664.29.
4. If a man was to work 23 days for the following wages^
viz. at 1 mill for the first day's work, 3 for the second, 9 for
•the third, and so on, increasing each day's wages in a three-
fold proportion— Required the amount of his wages.
Ans. 847071589.413.
5. The first term of a decreasing geometrical series is 2048,
the ratio i, and the number of terms 12 — ^Required the sum
of the Series. Ans. 4QIQ^0
184 iNVOnTTiojr.
iNvoMrTiox,
OR THE METHOD OF RAISING POWERS.
A power is the product arising from multiplying any given
number into itself continually a certain number of times; thus,
4x4 = 4^ the 2d power or square of 4.
4x4x4 = 4^ the 3d power or cube of 4.
4x4x4x4=4^^ the fourth power of 4. &c.
The number denoting the power is called the index of that
power.
RULE.
Multiply the number, continually by itself, till the number
of multiplication be one less than the index of the power to
be found, the last product will be the power required.
Examples. ^
1. What is thie sixth power of 8 ?
8
8
64= 2d power,
8
512= 3d power,
8
4096 =4th power,
8
32768 =5 th power,
8
Ans. 38416.
Ans. 11236.
Ans. 912673.
Ans. 5.0625.
262144=6th power.
2. Required the 4th power of 14.
8. What is the square of 106 ?
4. What is the cube of 97?
5. Required the 4th power of 1.5.
6. A square chamber is 31 feet each way-— How manjr
square feet does it contain? Ans. 961.
7. In a plantation 160 perches square, how many square
perches? Ans. 25600.
From the foregoing examples, we d«em the doctrine of
raising powers -clear.
EVOLUTION. 185
EVOLUTIOir,
OR THE EXTRACTION OF ROOTS.
The root of any numbei' or power, is such a number, as,
being multiplied into itself a certain number of times, will
produce that number or power. Thus, 4 is the square root
of 16, because 4x4 = 16 ; and 3 is the cube root of 37, be-
cause 3x3x3 =27, and so on.
EXTRACTION OF THE SQUARE ROOT.
To extract the square root is to find out such a number, as,
being multiplied into itself, the product will be equal to that
number.
Rule.
First — ^Prepare the number for extraction, by pointing it off
from the units place, or decimal point, into periods of two
figures each ; and when the decimal doe^ not consist of an
even number of figures, annex a cipher.
Secondly — Seek the greatest square number that is con-
tained in the first point towards the left hand; place the
square number under the first point, and the root theregf as a
quotient figure ; subtract the square number from the first
point, and to the remainder bring down the ne^t point for a
dividend.
Thirdly— Double the root already found, and place it for a
divisor, on the left hand of the dividend, and find how often
it is contained in the dividend, exclusive of the place of units;
annex the result to the quotient, and also to the divisor ;
then multiply by the fi^re last put in the quotient, subtract
as in division, and bring down the next period for a new
dividend.
Fourthly — Double the ascertained root for a new divisor,
and repeat the process to the end.
JVb^»— -The root of a vulgar fraction is found by reducing
it to its lowest terms, and extracting the root of the numera-
tor for a new numerator^ and of the denominator for a new
N
166 EVOLUTION.
denominator; a mixt number may be reduced to an improper
fraction, and the root thereof extracted as before. If the
fraction be a surd, that is, a number where a root can never
be exactly found, reduce it to a decimal, and extract the
root from it.
The following rule, the same in substance with the fore-
going, may perhaps be more easily recollected :
First, to prepare the square, this do.
Point off the figures two by two ;
Beneath the last the square next less
Put, and its root in the quotient place ;
From the last period take the square.
Then the next lower period there
To the remainder must be brought ;
Be this a dividend : the quote
Doubled must the divisor be
To all but units place ; then see
How oft the greater holds the less,
That figure njust the quote express.
And the divisor units too.
Then as in plain division do,
Thus every period one by one
We manage, and the work is done.
Proof.
Square the root, adding in the remainder, (if any,X which
will equal the number given.
Examples,
1. What is the square root of 185511.1041?
1855il!l041(430.71 Answer.
16
83)255
249
8607)61110
60249
86141)86141
86141
EVOLUTION.
187
H, Required the square root of 10.
• •' «
10.00000000 ( 3,16228 Answer, nearly.
61)100
61
€26)3900
3756
6322)14400
12644
63242)175600
126484
632448)4911600
5059584
3. What is the square root of 299082436 ?
4. What is the square root of 49491225 ?
5. Required the square root of 41370624.
6. What is the square root of 11831 ?
7. Required the square root of 10759.58022089.
Ans. 103.7283.
8. Required the square root of 2.5?
9. How much is the square root of 257?
10. Required the square root of 99.99.
11. W:hat is the square root of if^-ii?
12. What is the square root of .00172 ?
Further use of the Square Root.
13. If 1024 trees be planted in a square orchard, how
many must be planted in a row each way ? Ans. 32.
14. Required the length of a side of a square acre of land.
Ans. 69 yards, 1 ft. 8i in.-f
iVbfc— The square of the longest side of a rigU angled
triangle is equal to the sum of the squares of the ot\ier two
sides ; and consequently the difference of the sq^iarea of tleie
longest and either of the other sides, is the square of the r^-*;
maining side.
Ans. 17294.
Ans. 7035.
Ans. 6432.
Ans. 109.
Ans. 1.58114.
Ans. 16.0312.
Ans. 9.9995.
Ans. -/y.
Ans. .0131148.
188
EVOLUTION.
15. A line of 100 feet in length extends from the top of a
wall to a point 80 feet from its base— What is the height of
the wall ?
c
©
CD
13
^•.
s
:3
^;
X''/
^
a
^v
^
N^
B
100x100
80x 80
Base, 80 feet. A
10000 square of AC.
6400 square of AB.
3600 square of BC.
x/3600 = 60 = BC. Answer.
16. A line of 365 yards in length, will exactly reach from
the top of a fort, known to be 27 yards high, to the opposite
bank of a river— The breadth of the river is required.
Ans. 364 yards.
17. Suppose a ladder 68 feet' long be so placed as to reach
a window 32 feet from the ground, on one side of the street,
and without moving it at the foot, will reach a window 60
feet high on the other side — What is the breadth of the street,
and wnat is the distance from one window to the other ?
D F
EVOLUTION. 189
68x68 = 4624 square of ED.
60x60 = 3600 square of AD.
1024 square of AE.
-v/1024 = 32 = AE.
68 X68 = 4624 square of EC.
32X32 = 1024 square of BC.
S600 square of EB.-
v/3600 = 60 = BE.
AE+EB^ AB.
32 + 60 = 92 breadth of the street. Ans.
DF =s Alj = 92, and BF = AD, consequently
CF = AD— BC = 28. ^
92x92=8464 square of DF.
28x28= 7S4 square of CF,
9$i48 square of DC.
and 5/9248 = 96.167 = DC, as required.
18. A castle wall there was, whose height was found,
To be an hundred feet from the top to the ground ;
Against the wall a ladder stood upright,
Of the same length the castle was in height ; \
A waggish youth did the ladder slide,
The bottom of it ten feet from the ^ide ;
Now I would know how far the top did fall,
By pulling out the laddef from the wall.
Ans. 6 inches +
Effects of Light and Heat.
The effects or degrees of light, heat and attraction are
Teciprocally proportional to the square of their distance from
the centre whence they propagated.
19. in a room where two men, A. and B. are sitting, there
is a fire, from which A. is two feet and B. is four feet dis-
tant; it is required to find how much hotter it is at A's feet
than at B's. Ans. A's is 4 times as hot as B's.
20. The distance between the earth and sun is account-
ed 95 millions of miles; I wish to know what distance frotii
the sun another body must be placed, so as to receive light
and heat double to that of the earth. Ans. 67175144 miles.
190 EV0LX7TI0N.
Velocities of heavy bodies falling.
The velocity of heavy bodies falling near the surface of
the earth, is 16 feet in the first second; and, As 16 feet are to
the given distance. So is the square of one second, or 1, To
the square of the seconds required.
21. In what time will a bullet, dropped from the top of a
steeple 324 feet high, come to the ground ?
ft. ft. sec. sec.
As 16 : 324 :: 1 ; 20| and ^/20J = 4i Ans.
22. A bullet dropped from the top of a' building, was found
to come to the ground in 2i seconds — Required its height.
sec. sec. ft. ft.
As 1 : 25X2i :: 16 : 100 Answer.
23. Ascending bodies are retarded in the same ratio that
descending bodies are accelerated ; therefore, if a ball dis-
charged from a gun, returns to the earth ia 10 seconds — How
high did it ascend P Ans. 400 feet.
EXTRACTION OF THE CUBE ROOT.
To extract the cube root, is to find out a iramber which be-
ing multiplied into itself, and then into that product, pro^
duceth the given number.
RtJLE.
1. Point every third figure of the cube number given, be-
ginning at the units place or decimal point, seek the greatest
cube of the left hand period or to the first point, and subtract it
therefrom; put the root in the quotient, and bring down the
figures in the next point tathe remainder for a dividend.
2. Square the root and multiply it by 3 for a defective di-
visor; see how often the said defective divisor is contained in
the said number, (the units and tens excepted) which place
in the quotient, and its square to the right of the said divisor,
•applying the place of tens with a cypher, if the square be
less than ten.
8. Complete the divisor, by adding thereto the product of
43ie last figure of the root by the rest, and by 30. Multiply
and subtract as in Division; bring down the next^ period, fur
liHiich find a divisor as before, aad so proceed with every pe<*
riod. .
EVOLUTION. IMI
Note. After the first, the defective divisors may be found
more concisely, thus : To the last complete divisor add the
number which completed it, with twice the square of the last
£a^re in the root : tiie sum will be the next defective divisor.
Examples.
1. What is the cube root of 676836152?
676836152(878
512
5 Defective divisor and square of 8=« 19249)164836
\ + 1680« complete divisor 20929)146503
Defective divisor and square of 7-2270764)18333152
4-90880» complete divisor 2291644)18333152
«. What is the cube root of 926859375 ? Ans. 975.
8. Wliat is the cube yoot of 2077552.576 ? Ans. 1276.
4. What is the cube root of .015252992? Ans. .248.
5. What is the cube root of 1371.74211248? An8.11.111,+ .
6. What is the cube root of 794022984? Ans. 926+
7. What is the cube root of 15.926972504? Ans. 2.516+
8. What is the cube root of 27054.036008? Ans. 30.02.
». What is the cube root of 36155.027576? Ans. 33.06+
10. What is the cube root of .001906624 ? Ans. .124.
11. What is the cube root of 33.230979637? Ans. 3.215+
12. What is the cubq root of 53157376? Ans. 376.
To extract the Cube Root of a Vulgar Fraction.
Rule.
Reduce the fraction to its lowest terms, then extract the
cube root of its numerator and denominator for a new numer-
iitor and denominator; bnt if the fraction be a surd, reduce it
to a decigi^, and then extract the root from it*
Examples.
13. What is the cube root of ||^? Ans. f.
14. What is the cube root of /^? Ans. |.
15. What is the cube root of ^V? '^^^* ^*
16. Wh^t is the cuhie root of }f ? Ana. |.
192 DUODECIMALS.
SURDS.
17. What is the cube root of |^? Ans. .822+
18. What is the cube root off? Ans. .829+
19. What is the cube root of I? Ans. .873+
20. What is the cube root of |? Ans. .736+
DUODECIMALS.
Duodecimals is a rule by which workmen and artificers
take the dimensions, and cast up the content of their work.
It is also used for finding the tonnage of ships, and the con-
tent of bales/cases, &c. The denominations are :
12 fourths "" make 1 third,
12 thirds 1 second,
12 seconds 1 inch, in.
12 inches 1 foot.
Rule.
Set the feet of the multiplier under die lowest nairfe of the
multiplicand, and in multiplying carry 1 for every 12; plac-
ing the results of the lowest name in the product, under its
multiplier, or.
Multiply by the feet and take parts for the inches, &c. *
Note. — Feet multiplied by feet give feet.
Feet multiplied by inches give inches.
Feet multiplied by seconds give seconds.
Inches multiplied by inches give seconds.
Inches multiplied by seconds give thirds.
Seconds multiplied by seconds give fourths*
Examples.
1. Hqw many square feet in a board 14 feet 7 inches long,
and 1 foot 5 inches broad P
ft. in. Or thus :
14 7 4in. U
15 1 U
14 7
Xl
6 11
14 7
14 7
4 10
1 2
4
7
on T 11
AnB, 20 7 11
PROMISCUOUS QUESTIONS. 193
2. Required the superficial contents of a walnut board, 11
feet 4 inches long, and 1 foot 6 inches broad. Ans. 17 ft.
3. What is the solid content of a load of wood, measuring
6 feet 6 inches in length, 3 feet 4 inches in width, and 3 feet
6 inches in height ? Ans.#75 ft. 10 in.
4. How many yards of yard wide paper ^\\\\ it take to
paper a ceiling 47 feet 6 inches long, by 25 feet 6 in. wide?
ft. in. ft. in. ft. in.
47 6 X 25 6 = 1211 3
ft. in. yds. ft.
Then 1211 3 — 9=134 5i Answer.
5. A mahogany board measures 16 feet 10 inches, by 3 feet
2 inches — What is its content? Ans. 53 ft. 3 in. 8".
PROMISCUOUS dUESTIOJfS.
1. There is a square pavement, containing 110889 square
stents, all of the same size— I demand the number contained '
in one of its sides. Ans. 333.
2. If 40 yards of broadcloth cost S240, what must it be
sold at per yard, to gain 20 per cent, by the whole ?
Ans. 87.20.
3. If 12 apples are worth 21 pears, and 3 pears cost one
cent, what is the price of 100 apples ? Ans. 58} cts.
4. A gentleman at his decease left 83000 to his 3 sons,
whose ages were as follows : A. 18 years, B. 19 and C. 20
years ; the guardian had directions to divide this sum in such
a manner that the share of each, bv being put to interest at 6
per cent, should be equal when they should respectively ar-
rive to the age of 21 years — I wish to know how much each
must receive at this age; also the sum bequeathed to. each.
f Each must receive 81117.86.
A J Bequeathed to A, 947.33.
Ans.< ,, ,, ^ 998.09.
L " " C, 1054.58.
5. A. and B. jointly purchase 300 acres of land for 8600»
each paying 8300: wheji they came to divide the land between
them, it was agreed upon, that A. should have his choice, and
the part he took was valued at 75 cents per acre more than
194 PROMISCUOUS qU£STtONS«
B's— I wish to know the price per acre of each one's land,
and the number of acres falling to each.
JRule for solving all questions of this nature.
1. Divide the sum paid by each, by the whole number of
acres, and add «the quotient to one half of the diiference in
the price per acre, and reserve the number.
2. Multiply the sum paid by each by the diflPerence in
the price per acre ; divide the product by the whole number
of acres, and deduct the quotient from the square of the
reserved number; then extract the square root of this re-
mainder, and add the root to the reserved number, and the
8um will be the value of A's land per acre.
3. Deduct the difference in the price per acre of their
land, from the value of A's land per acre, and the remainder
will be the value of B's land per acre.
4. Divide the sum paid by each by their respective prices
per acre, and the quotients will be the number of acres fall-
ing to them respectively.
iVo^e.— -This rule applies to all questions of the above na-
ture, whatever the articles piirchased may be, if the name of
the article or articles purchased be understood^ and used in-
stead of acre or acres.
300)300 2).75 diaference in price.
— — 300 sum paid by each.
1 .875 .75 difference in price
•375 —
300)225
1.375 reserved number. —
1.375 .75
}. 890^25 square of the reserved number*
f7d Acres.
800-^2.448 « 122.8 A.
1.140625(1.068 300-T-1.693 =« 177.2 B.
1 1.375 reserved number.
906)1406 2.443 Ans. Price of A's land.
1236 .75
2198)17025 1.693 price of B's land.
17024
l^ftOMISCUOUS qUESTI0N9« 199
6« Two drovers, A. and B. purchased 100 cattle between
them for g2400, each paying gl200; they divided ihem be-
tween them in such a way that A's stood him in 810 a head
more than B's — I wish to know what each of their cattle
stood them in per head, and how many fell to each.
^A's, 830.00 per head.
. ' J B's, 20.00 • "
Answer.^ A had 40 head.
B 60 "
7. A. B. and C. wrought 365 days between them, at the
following wages, viz, A. 50 cents, B. 60, and C. 70 cents per
day ; they each wrought such a length of time as to receive
the same wages,— I wish to know the amount of each one's
vvagea and the time he wrought.
fEafh received 871.635.
Answer J ^' wrought 148.27 days,
Answer.-jjj „ ^^^3^ ,,
LC. " 102.34 •*
JRule for solving all questions of this nature, whether the
number of persons be three or more*
1. Take the continued product of the wages and time for
a dividend.
3. Leave out the daily wages of one and multiply the wa^i
of the others continually together, aAd thus continue leavmg
out the wages of one and multiplying the others, until the
wages of each are respectively left out, and the others multi-
plied together, then add together these products for a divisor.
3. The quotient will be the amount of each one's wagea
foi'the time he wrought.
4. Divide this quotient by each ones daily wages, the quo-
iient will respectively be the time each wrought.
8. A person willing to distribute some money among some
indigent persons, wanted 20 cents to give them 20 ceats a
piece he therefore gave them 19 cents a piece and had 19
cents left— How many were there of thetn? Ans. 3d<
9. A sheep fold was robbed three successive nights; the
first night, half the sheep were stolen and half a sheep more;
the second, half the remainder and half a sheep more ; the
last night they took half that were left, and half a sheep more ;
by this time they were reduced to \%\ how many were therQ
at first? Ana, 103,
196 PROMISCUOUS QUESTIONS.
10. A can mow an acre of grass in 12 hours, B can mow
An acre in 8 hours — ^how long would it take both of them to
mow an acre?
H. H. A. A.
As 12 : 72 : : 1 : 6 would be mown by A in 72 hours.
8 : 72 : : 1 : 9 would be mown by B in 72 hours.
15 bj both of them in 72 hours.
A. A, H, H. M.
Then as 15 : 1 : ; 72 : 4 48 Answer.
11. A gentleman sold a horse for S 80. by which he clear-
ed as much per cent as ;tihe horse cost him. I wish to know
how much that was P Ans. S 52.47.
Fule far such ^uestion^.
Multiply the price sold\for, by 100, add 2500 to the pro-
duct, and extract the square root of the sum, then deduct 50
'from this root for the prime cost.
12. A toper finding a cask of brandy containing one hun-
dred gallons, filled a keg therefrom, and refilled the cask
with water; coming a -second and a third time, he did like-
wise ; after which the owner coming to try the proof, found
it half water ; query, how much did the toper's keg hold?
Ans. 20.63 gallons.
Huh for such questions*
Raise the qtiantity first in the cask to such a power that
the index may he one less than the kegs filled from it. Mul-
tiply this power by the quantity left in the cask ; take such a
root of this product as is indicated by the number of kegs §11-
c I, and deduct the root from the quantity first in the cask ;
the remainder will be the contents of the keg.
13. How much rye at 00 cents a bushel, must be given in
barter for 120 bushels of wheat, at S 1.00 per bushel ?
Ans. 200 bushels.^
14. A person having engaged to remove 800 C a certain
distance in 9 days; with 18 horses in 6 days he removed 456
CJ. — ^how many horses will be required to remove the remain-
tier, in the remaining 3 days? Ans.. 28 horse*.
15. If a board be 9 incnes broad, what leitgth wilt it re^
quire to measure 6 square feet ? Ans. 8 feetx
16. What money at 51 per cent will clear S 481.55 in S
years? Ans. S 980.J5u.
PROMISCUOUS qUKSTIONS. 197 ,
17. A man dying, left glOOOO to be divided amongst his
three sons, (whose ages were 19, 16 and 10 years respectiver
ly,) in such a manner that their several portions when they
became 21 years of age might be equal, reckoning interest
at 6 per cent, during their minorities — required the share of
each. * r 8 2660.235'
Ans. -{ 3396.916
i 3942,849
18. At what times of the day do the hour and minute hand*
of a watch form a continued straight line?
h. h. m. h. m. h. m.' h. m*
Ans. At 6, 7 5y\ 8 10 14, 9 16^, 10 21 ^V
h. m. h. m. h. m» h. m. h. m. h.
II 27t\- 32t\ 1 38^ 2 43fr 3 49^ and 4 ^^
19* If axoll of butter weighs in one scale 4 pounds, and
being changed into the other, weighs 6} pounds — ^what is the
true weight? Ans. 5 pounds.
Rule for such questions*
Extract the square root of the product of their respective
weights.
20. An Eagle is about an inch broad ; how many of them
laid edge to edge, would reach from New Italy to Harrisburg,
a distance of 55 miles? Ans. 3484800.
21.* Admitting the state debt to be 825000000, how long
would it take one man to count the money sufficient to pay it
in half dollars, allowing him to count 60 per minute, and to
be engaged 12 hours each day?
Ans. 1157 da. 4h. 13 m. 20 sec.
22. The distance from the market house in Harrisburg to
the Susquehanna bridge is 200 yards ; from thence down the
river bank to the Black Horse tavern 497 yards — I wish to
know the distance upon a straight line from the Black Horse
to the market house, admitting it to be a right angled triangle.
of which the given distance are the legs.
Ans. 535.73 yds. +
33. Suppose two drovers, A. and B., purchase 100 cattle
equally between them for i24O0s and divide the cattle in such
a way that one of A's and one of^B's are worth g 50—1 wish
to know how many fell to the lot of each, and how much p^
head ihey were valued at? Ans. A. 40, valued at 2 30*
B. 60, .. .. 20.
198 PROMISCUOUS QUESTIONS.
24. I demand the height of a wall, against the top of which
a ladder, 26 feet long, is so placed as to stand 10 feet from
thebdttom of the wall. Ans. 24 feet.
25. If the length of a building be 40 feet, and its breadth
30, what distance should it measure from corner to corner
diagonally? Ans. 50 feet.
26. Bought a quantity of goods, amounting to 826000, at
5 per cent, commission — what is my commission?
Ans. g 130.
27. A gentleman courted a young lady, and as their birth
days happened together, they agreed to make that their wed-
ding day. On the day of their marriage it happened that the
gentleman's age was to that of the lady's as 3 to 2. After
they had lived together 9 years, the gentleman observ^ed that
his age was then to hers as 4 to 3, and at their death the gen-
tleman's age was to the lady's as 8 to 7 — I demand their sev-
eral ages at the day of their marriage, and of their death.
Ans. 27 and 18 years were their respective ages
at marriage, and 72 and 63 at their death.
28. Sold 99 yards of cloth for S600, which was at 24 per
cent profit — What was the prime cost per yard?
Ans. S4.88I +
29. A may -pole there was, whose height I would know.
The sun shining clear, straight to work I did go ;
The length of the shadow upon level ground.
Just sixty five feet, when measured, I found;
A staft' I had there, just five feet in length.
The length of its shadow was four feet one tenth ;
Howhiffh was the may- pole, I gladly would know.
And it IS the thing you are desired to show.
Ans. 79.268 ft.+
80. If 8100 be divided amongst four persons, in the pro-
portion of -J, ^, -J, and -J-; required the share of each.
Ans. 8 35^, 26f^ 21j\ and 17|f
31. The Harrisburg Hotel and Red Lion tavern, (Harris-
burg,) are on the same side of Market street, at opposite cor-
ners of Market and Third streets: diiectly opposite the Red
Lion, is a dry goods store ; I wish to know how far it is from the
Harrfeburg hotel to the drj» goods store, admitting the breadtfi
of Market street to be 27 yards, and Third street 18 yards.
•Ans. 32.45 yds. nearly.
BOOK-KEEPING.
That method of book -keeping here treated upon, is called
Single Entry. Every person m, or intended for, business,
should by all means learn and understand it completely.
The Day Book and Ledger are the principal books of accounts;
the forms of which may be sufficiently comprehended by in-
specting the following specimens.
THE DAYBOOK.
In the day-book every person is written down debtor to
the things he has received from you on trust, and creditor by
the things which you receive from him. The dates are placed
in the middle of the page.
THE LEDGER.
This is the grand book of accounts : all the several debts
and credits of each particular person's accounts, which lie
scattered through different parts of the day-book, are here
collected together, into spaces allotted for them, and placed
in such an order as will show the whole state of the account
at 'once.
POSTING.
Your books being ruled in the proper form, commence with
the first person who stands Dr, or Cr. in the day-book, and
•write his name at the head of the entry, and the Contraction
Dr. or Cr. in the columns assigned them, according to the
following specimen ; then if the person be Dr., begin the entry
■with To; place the amount in the Dr. columns, and place the
xnonth and day in the same line with the article ; also place
the number of the page of the day-book in the column assign-
ed it. When the person is Cr., enter it in like manner, begin-
ning the entry with By^ placing the amount in the Cr. column.
200 BOOK-KEEPING.
and page of the day-book as before directed. Any account
that consists of more than one article, should be written To
or By Sundries, and the sura of the amounts in its proper
column. Lastly, turn to the alphabet, and under the proper
letter insert the name and number of the page of the ledger
in which the entry is made, leaving a proper space under each
person's name, to receive more accounts, if necessary. Do
the same with the next entry in the day-book', and so on till
all be finished, (excepting such as are marked "paid.")
When a name occurs for which an account is already open-
ed in the ledger, post the item or items to that account, un-
less the place assigned it is full; and then remove it to
another pa^e, writing at the bottom ** Transferred to," and at
the head of the page or subsequent entry, write "Brought
from," in each case placing the number of the page at the
end of the words, which must be understood to have no
reference to the day-book, but pertaining to the transfer only;
the amount of the columns must also be cast up and trans-
ferred into the respective columns assigned them, and oppo-
site the words " Brought from." When ledger A is filled,
transfer the unsettled accounts to ledger B ; and so on froia
ledger B to C, &c. as occasion may require.
' BOO&-KBBPING.— DjLT-BOOK.
su
NEW Italy, January 1, 1836. 1
Peter Fulton,^ I)r,
To 16 gallons Oporto Wine, at gl 25, 8 2 60
12 do. White do. at 1 40, 16 80
* 6 do* Lisbon do. at 1 00, 6 00
8-
D.
Jonathan Jenks,
To 2 pounds of Tea, at gl 25 per lb,
12 do. Sugar, at 10 cts.
12 do. Coffee, at 12r ets.
JDr.
2 50
1 20
1 50
18
Ralph Bentley,
To 16 lbs. of Hard Soap, at 10 cts.
12 lbs* Starch, at 6 cts.
Dr.
1 60
72
20
Matthew Twtght, ^ Cr»
Bj 650 bushels of Lime, at 12 dolls, per hundred.
<(
Sarah Feoman,
To 11 ibs. of Rice, at 5 cts.
6 do. Coffee, at 11 cts.
12 do. Brown Sugar, at 8 ^ts;
Dr.
55
66
96
23
Timothy Hedge, Dr.
To 17 yards of Tow Linen, St 20 cts. 3 40
25 do. Cotton Stripe, at 17 cts. 4 25
21 do. Coarse Flannel, at 30 cts. 6 30
24
Morris Davis,^ Cr.
By 25 bu, of dried Peaches, at g2 50, 37 50
20 do. ** Apples, at 875 cts. 17 50
25
C.
4200
S20
232
7800
17
1395
Peter Fulton,
Bj 24 bushels of Wheat, at gl 10,
O
Cr.
5500
2640
2»2
2
BOOK-KEEPIKCfr
NEW ITALY, January 25, 188ff.
Jonathan Jenks,
1 To 6 pounds of Coffee, at 13 cents,
10 do. Loaf Sugar,, at 15 cts.
27
Isaac Klingy
To 46 pounds of Ham, at 9 cents,
20 do. Flitch, at 7 cents
80
Susan EmherSy
To 14 yards of Cambric, at 50 cents,
3 do. Calico, at 28 cents.
c<
. Christian Cor mv all,
To 1 barrel of Vinegar,
February 1.
Matthew Twight,
To 12 bbls. of superfine Flour, at g6 25,
3 do. Rye' " at 3 25,
Valentine Vezey,
By 120 pounds of Tobacco, at 14 cts.
3
Martha Fullback,
To i pound of Tea,
8
Jason Sprouly
To I5 pounds of Indigo, at g2 80,
50 do. Logwood, at -5 cts.
80 do. Fustic, at 7 cts.
. 60 do. Nicaragua, at 20 cts.
Dr.
SO 78
1 50
Dr.
4 14
1 40
Dr.
7 00
84
Dr.
Dr.
75 00
9 75
D.
C,
22s
554
784
400
Cr.
Timothy Hedge, Cr.
By 6 cords of Hickory ^Vood, at S2 50, 15 00
4 do. Oak do. 1 75, 7 00
8475
1680
Dr.
Dr.
4 20
2 50
5 60
12 00
2200
30
2430
DAT-BOOK.
203
NEW ITALY, February 6, 1886. 3
Matthew Twight,
Bj an order on Charles Rakestraw, for
Cr.
«
Charles Rakestraw^ Br.
To Matthew Twight's order on him, for
<(
Joseph Quigley, Cr.
By a Rhode Island Cheese, weight 40 lbs.
at 12 cents per pound, S 4 80
12 bushels of Beaivs, at gl 25, 15 OOl
cc
William Ingles, Dr^
To 6 gallons of Brandy, at SI 50, 9 00
5 do. Madeira Wine, at 1 60, 8 00
2
Valentine Vezey,
To 5 gallons of Tar, at 27 cents,
1 do. Train Oil,
20 pounds of Sulphur, at 5 cts.
Dr.
1 35
75
1 00
8
Louisa Wirtf Dr.
To 10 yds. of Cambric Muslin, at 80 cts. 8 00
11 do. Coarse do. at 12 cts. 1 32
10
George Price,
To 5 pounds of Raisins, at 12 cents,
12 do. Candles, at 11 cts.
16 ounces of Blueing, at 20 cts.
Dr. i
. 60
1 32:
3 20
11
Charles BaJcestraiv, Dr.
To 43 reams of double Medium Paper, at
S4 25 per ream, 182 75
16 do. Super royal Paper, at 3 75, 60 00
I
^^tei
70
00
19
80
17
00
242
10
32
12
75
904
BOOK-KEEPING.
NEW ITALY, February 11, 1836.
Zachariah Andrews,
To 25 bushels of Potatoes, at 25 cts.
16 do. ^Turnips, at 18 cts.
Dr.
86 25
2 88
18
Davis Mahan, j)j,^
To 105 bushels of Wheat, at gl 05, 110 25
63 do. Buckwheat, at 60 cts. 37 80
((
Joseph Quigley^
To cash in part, -
Dr.
John Lemon,
4 To a set of China,
15 China Bowls,
— 15
Dr,
5 00
1 80
17
Matthew Twight,
To 50 bushels of \Vheat, at gl 05,
2U do. Rje, 50,
18
Dr.
52 50
10 75
Henry Gill,
To 14 yards of coarse Linen, at 20 cts.
6 do. fine do. 50 **
Df.
2 80
3 00
-24
Morris Davis, j)j.^
2 To 66 yards of Cambric Muslin, at 80 cents
26^ !_
6
Zephaniah Norcross, J)r,
To 1 C. 1 qr. 16 lb. of Iron, at g6 per C.
.27
Uriah Umstead, ^ Br.
To 26 cords of Oak Wood, at g2 50, 65 00
12 cords Hickory do. 3 25, 39 00
28 ZZZL
Timothy Hedge,
^ To cash in full,
Dr.
D. C.
913
14805
16
10400
805
00
80
6325*
580
5280
846
J
DAT-BOOK. 20{{
NEW ITALY, February 29, 1836. 5
WiUiam Ingles,
Bj 16 pounds of Butter, at 16 cts.
12 do. Lard, at 10 cts.
Cr,
82*56
1 20
March S.-
Hannah Old,
To 16 yards of Muslin, at 17 cents,
5 doz^n Eggs, at 9 cents.
Dr.
2 72
45
George Price,
By 19 bushels of potatoes, at 25 cents,
— 4
Cr.
Jason Sproul,
To 19 yards red Flannel, at 60 cents,
14 do. white do. 55 cts.
Dr.
11 40
7 70
William Ingles,
To 13 yards of Black Satin, at
— 8
Dr.
81 05
Davis Afahan, Cr.
By 1564 bushels of Lime, at 812 per 100 bushels,
10 —
Zephaniah Norcross, Dr.
To 12 yards of Silk, at 81, 12 00
5 do flowered Silk, at 81 05, 6 25
12
Hannah Old,
To 6 yards of Chintz, at 81 07,
5 do. black Satin, at 81 00,
Dr.
6 42
5 00
5
Davis Mahan,
To cash in full, -
15
Dr.
Hannah Old,
By Ca»h in full,
17
> ■! *
Cr.
B.C.
376
17
475
19
1365
18768
11
3963
1459
10
1725
43
206
BOOK-KEEPIKG.
NEW. ITALY, March 19, 1886,
Andrew Zug, Dr,
To 24 Comlj^s Spelling Books, at 20 cts. S4 80
3 quires Writing Paper, at 21 cts. ''"
6^
20
Charles RakestraWy
Bj a Bank Check for
Cr.
27
Ralph Bentley,
To li yards of Broadcloth, at 84 50,
IJ dozA Coat Buttons, at 32 cts.
Dr.
6 7&
48
D.
30
Henry Gill,
To 12 pounds of hard Soap, at 9 cts.
14 do. white do. at 14
12 do. Starch, at 7
13 do. Candles,^ at 12
Dr.
1 08
1 96
84
1 56
April 3.
Jonathan Jenks,
To 27 pounds of Cheese, at 9 cents,
— 5
Dr.
C,
543
000*00
7ii3
Isaac Kling, Cr.
21 Bj 164 bushels of Lime, at 812 per 100 bushels,
8 '
Louisa Wirtf
Bj cash in part.
Cr.
Sarah Yeoman,
To 2 pounds of Sugar, at 10 cents,
1 do. Coffee, 13 do*
3 do. . Candles, 12 do.
2 do. Starch, 7 do.
1 do. Raisins, 12 do.
11
Dr.
20
13
36
14
12
Zachariah Andrews,
4| By 64 pounds of Beef, at 5 cents,
16 do. Sausage, at 7 cent».
Cr.
3 20
1 1
I
544
243
1968
50O
95
432
{
DAY-BOOK.
207
NEW ITALY, April 15, 1836.
Christian Cornwall,
Bj cash in full.
Cr.
17
D.
Jonathan Jenks,
By a gray Horse,
15 pounds of Butter, at 15 cents.
Cr,
850 00
2 25
20
John Lemon,
To 13 yards of Tow Linen, at 25 cents,
12 do. Coarse Muslin, at 11 cts.
Uriah Umstead^
By cash in part, -
25
Susan Embers,
By cash in part, -
30
May 1.
:2
Jonathan Jenks,
By 1200 bushels of Lime, at 812,
-i 9
Isaac Kling,
By cash in part.
— 10
Morris Davis,
To 20 pounds of Cheese, at 11 cents,
16
John Lemon,
By cash in full.
17
Dr.
3 25;
1 32
Cr.
Cr.
Valentine Vezey, Dr.
To 4 yards of Broadcloth, at 83, 12 00
li dozen Coat Buttons, at 40 cents, 60
22 pounds of Rice, at 5 cents, 1 10
Cr.
Cr.
Dr.
Cr.
Andrew Zug, Dr.
To iCheese^ weight 45 pounds, at 9 ct3f
C.
400
5225
457
5000
500
1870
14400
2000
220
11
37
405
BOOK-KSEPlMG*
8
NEW ITALY, May 17, 1886.
Zachariah Andrews,
By 2 cords of Oak Wood, at g2.
Hauling. do.
•June 10
Susan EmberSt
Bj ^ pounds of Butter, at 14 cents.
Cash ia full,.
18
8
Henry Gill,
To 42 Mackerel, at 4 cents,
16 pounds of Candles, at 12 cents,
2 gallons Lamp Oil, at 60 cents,
3 quarts Tar, at 8 cents.
27
George Pricey
To 11 pounds of Coffee, at 16 c^nts,
2 do. Loaf Sugar, at 14 ctsv
5 do. Brown Sugar, at 9 cts,
July 1.
10
Lomsa Wirt,.
By 18 yards of Linfia, at 24 cents,
i 27
Andrew Zug,
By 16 yards coarse *Lme», at 20 cents,
4 do. fine do. at 45 cents^
•«— - August 1* *-«*-
Zephaniah Norcrosa,
B J 149 pounds of Baooa* Ai fi oenti*
Cr.
84 001
81
Cr.
84
2 00
D.
81
Dr.
1 68
1 92
1 20
24
Dr.
1 76
28
45
Thomas T. Mahan, Dr.
To 3 yardshlue Broadcloth, at 85 50, 16 50
2i do. brown Pollard, at 20 cts. 50
li do. Silk, at gl, 1 60
Cr.
Cr.
3 2011
1 80
Ck
284
M)4
249
1850
432
5ba
1341
DAT-BOOK.
909
NEW ITALY, August 5, 1836. 9
wr
Joseph Quigley,
To 1 hogshead Madeira Wine, 110 gallons,'
at SI 10 per gallon,
^ 8
^y^-^^^m^^—^-^i^mm^^^
Jason Sproul,
To 5 yards Scaiiet Cloth, at 84 50,
4 do. Velvet, at 1 03,
3 do, Cca-duroy, at 1 06,
20
William Ingles y
To 14 yards #f Calico, at 30 cts.
1 pair Men's Gloves,
27
Henry Gill,
By 14 yards of Muslin, at 15 cents,
15 do. Linen, at 40 cents.
September 1.
Ralph Bentlev,
By 191 pounds of Beef, at 5 centsr>
— 4 —
Fetef^ Fulton,
To 5 pounds of Candles, at 13 cenjts,
14 do. Coffee, at 12 cents.
12
Isaac Kling,
To 13 yards Irish Linen, at 75 cents,
12 do. Muslin, at 15 cents.
October 23.
Uriah Umstead,
By 450.bushels of Lime, at 12 cents,
•30
^rah Vteman,
To 5i. yards Calico, at 30 cents,
2 do. Cambric, at 60 cents,
Dr.
822 50
4 12
3 18
D.
121
C.
00
Dr.
4 20
50
Cr.
2 10
6 00
Cr.
2980
Dr.
60
1 08
Dr.
9 75
1 80
Cr.
Dr.
1 65<
1 20
8
ro
10
955
250
11
55
54 Qd
2SS
^
210
10
BOOK-KEEPING.
NEW ITALY, November 1, 1886.
2
"3
CO
-»
William Ingles, Cr*
Bj a cask of Wine, containing 15i gallons,
at SI per gallon, S15 50
Cash in lull, 16 09
Jonathan Jenks,
To 40 Sheep, at 82 40,
Dr.
Jason Sproul,
By cash in full.
17
Cr.
Andrew Zug,
By cash in full.
26
Cr.
Peter Fultqn,
By cash in full.
December 1.-
Cr.
Joseph Qt^igley,
By cash in full.
11
Cr.
-16
Zephaniah Noreross,
By cash in full,
-22
Cr.
Henry Crill^ ^
By cash in full.
Cr.
24
Daniel Cope^ Dr.
To 12 pounds of Raisins, at 11 cents, 1 32
3 do. Loaf Sugar, at 16 cents, 48
25
Cornelius ffalton.
To 12 pounds Candles, at 121 cents,
14 do* Sugar, at 10 cents.
Dr.
1 50
1 40
31
Sarah Yeoman,
By 15 yards of Linen, at 29 cents*
18 pouadjs BacoD» at 8 cents.
Cr.
4 35
1 62
D.
C.
31
59
9600
73t20
448
1810
11720
12i30
18
80
29a
69T
LCiDGER A.
THE ALPHABET.
A.
Zachariah Andrews,
4
B.
Ralph Bentlej,
1
C.
Christian Cornwall,
2
Morris Davis,
2
E.
Susan Embers,
2
F.
Peter Fulton,
1
1
G.
Henry Gill,
45
H.
Timothy Hedge,
2
I&J.
Jonathan Jenks,
William Ingles,
1
8
K.
Isaac Rling,
2
L.
John Lemon,
4
M.
Davis Mahan,
4
5
Zephaniah Norcross,
3
0.
Hannah Old,
P.
George Price,
4
Q.
Joseph Quigley,
3
R.
Charles Rakestraw,
3
S.
Jason Sproul,
3
T.
Matthew Twight,
1
U.
Uriah Umstead,
5
V.
Valentine Vezcy,
2
W.
Louisa Wirt,
' 4
Y.
Sarah Yeoman,
1
Z.
Andrew Zvi%,
5
212
1
BOOK-KEEPING.
LEDGER A.
1836.
Jan. 1,
" 25,
Sept. 4,
Dec. 1,
folio
1
1
9
10
PETER FULTON. i DR.
To sundries, g] 42 00
By 24 bushels of Wheat,
To sundries,
Bj cash in full.
2 50i
1836.
Jan. 8,
" 25,
April 3,
" 17,
May 7,
Nov. 4,
'mmp^
44 50
Cr.
826 40
18 10
44 50
1
2
6
7
7
10
1836.
Jan. 18,
March 27
Sept, 1,
1
6
9
JONATHAN JENKS.
To sundries.
To sundries.
To 27 pounds of Cheese,
By sundries.
By 1200 bushels of Lime,
To 40 Sheep,
Transferred to Ledger B,
1836.
Jan. 20,
Feb. 1,
" 6,
" 17,
1
2
3
4
RALPH BENTLEY.
To sundries,
To sundries.
By 191 pounds of Beef,
*mm^mmt^mm^m
5 20
2 28
2 43
96 00
105 91
2 32
7 23
9 55
52 25
144 00
196 25
1836.
Jan. 20,
April 9,
Oct. 30,
Pef, 31,
T 1.
1
6
9
10
MATTHEW TWIGHT.
By 650 bushels of Lime,
To sundries.
By order on Chas. Rakestraw
To sundries.
84 75
68 25
148 00
SARAH YEOMAN,
To sundries,
To sundries.
To sundries,
9^ sundries,
■•"»
9 55
9 55
78 00
70 00
143 00
2 17
95
2 85
5 9711
5 87
5 87
*
.BOOE*K££PINO.
LEDGER A.
313
1836.
Jan. 23,
Feb. 3,
Feb. 28,
foi.
1
2
4
1
4
7
2
6
7
9
1
2
7
8
2
7
2
3
7
TIMOTHY HEDGE.
To sundries,
By sundries,
To cash in full.
DRj
S13 95
8 05
CR.
22 00
22 00
22 00
1836.
Jan. 24,
Feb. 24,
May 10,
MORRIg' DAVIS.
By sundries, /
To 66 yards Cambric Muslin
To 20 pounds Cheese,
52 80
2 20
55 00
55 00
55 00
1836.
Jan. 27,
April 5,
May 9,
Sept. 12,
ISAAC KLING.
To sundries.
By 164 bushels Lime,
By cash in part.
To sundries.
Transferred to Ticdger B,
5 54
11 55
19 68
20 00
39 68
16 09
1836.
Jan. 30,
April 30,
June 10,
SUSAN EMBERS.
To sundries,
By cash in part.
By sundries in fall,
.7 84
•
5 00
2 84
4
7 84
784
1836. .
Jan. 30.
April 15,
CHRISTIAN CORNWALL,
To 1 barrel of Vinegar,
By cash in full.
4 00
.400
4 00
4 00
1836.
Feb. 2,
Feb. 7,
May 1,
VALENTINE VEZEY.
By 120 pounds Tobacco,
'Eo sundries.
To sundries in full.
3 10
13 70
16 80 1
16 80
16 80
2U
3
BOOE-KEEFING.
LEDGER A,
1836.' fol.
iFeb. 5, 2
March 4, 5
Aug. 8, 9
Nov. 17, 10
1836.
Feb. 6,
Feb. 11,
March 20
3
3
6
1836.
Feb. 6,
Feb. 13,
Aug. 5,
Dec. 11,
3
4
9
10
1836.
Feb. 6,
Feb. 29,
March 7,
Aug. 20,
Nov. 1,.
3
5
5
9
10
1836.
Feb. 26, 4
March 10 5
Aug, 1, 8
Dec. 16, 10
JASON SPROUL,
To sundries,
To sundries.
To sundries,
Bj cash in full.
CHARLES RAKESTRAW.
To Matthew Twight's order.
To sundries,
Bj a bank check.
Transferred to Ledger B.
JOSEPH QUIGLEY,
By sundries,
To cash in part,
To a hogshead Madeira wine.
By cash in full.
WILLIAM INGLES.
To sundries.
By sundries.
To 13 yards Black Satin,
To sundries,
Bv sundries.
ZEPHANIAH NORCROSS.
To 1 C. 1 qr. 16 lb. Iron,
To sundries.
By 149 pounds of Bacon,
By cash in full,
DR.
S24 30
19 10
29 80
73 20
70 00
242 75
312 75
16 00
121 00
137 00
17 00
13 65
4 70
35 S5
8 46
17 25
25 71
CH.
873 20
73 20
300 00
300 00
19 80
117 20
137 00
3 76
31 59
35 35
13 41
12 30
25 71
BOOK-KEEPING*
LEDGER A.
213
4
1836.
Feb. 8,
April 8,
July 10,
fol.
'3
6
8
3
5
8
1
4
6
8
4
5
5
4
7
7
4
6
LOUISA WIRT. .
To sundries.
By cash in part,
By 18 yards of Linen,
DR.
S9 32
CR.
85 00
4 32
9 32
9 32
1836.
Feb. 10,
March 3,
June 27,
GEORGE PRICE.
To sundries.
By 19 bushels Potatoes,
To sundries,
Transferred to Ledger B.
5 12
2 49
4 75
7 61
4 75
1836.
Feb. 11,
April 11,
Maj 17,
ZACHARIAH ANDREWS.
To sundries.
By sundries,
By sundries.
9 13
1
4 32
4 81
9 13
9 13
1836.
Feb. 13,
March 8,
March 15
DAVIS MAHAN.
To sundries,
By 1564 bushels of Lime,
To cash in full.
1
148 05
39 63
187 68
187 68
187 68
1836.
Feb. 15,
April 20,
May 16,
JOHN LEMON.
To sundries.
To sundries.
By cash in full.
6 80
4 57
11 37
11 37
11 37
1836.
Feb. 18,
March 30
HENRY GILL.
To sundries,
To sundries.
Transferred to folio 5,
5 80
5 44
11 24
1
2ie
5
BOOK-KEEPING.
LEDGER A.
June 18,
Aug. 27,
Dec. 22,
fol.
8
9
10
4
7
9
5
5
5
6
7
8
10
HEISJIY GILL.
Brought from folio 4,
To sundries.
By sundries.
By cash in full,
•
DR.
gll24
5 04
CR.
8 10
8 18
16 28
16 28
1836.
Feb. 27,
April 25,
Oct. 23,
URIAH UMSTEAD.
To sundries.
By cash in part.
By 450 bushels of Lime
104 00
50 00
54 00
104 00
104 09
1836.
March 2,
March 12
March 17
HANNAH OLD.
To sundries,
To sundries,
By cash in full
3 17
11 42
14 59
14 59
14 59
1836.
March 19
May 20
July 27
Nov. 26,
ANDREW ZUG.
To sundries
To a Cheese, weight 45 lbs.
By sundries,
By cash in full,
5 48
4 05
5 00
4 48
g9 48
89 48
BOOK-KEKPIVG.
217
BALANCING.
1836.
Dec. 31,
STOCK,
To Jonathan Jenks, due to him^
B J Isaac Kling, due to him
By Charles Rakestraw, due tome
By George Price, due to me
CR.
812 75
286
113 93 15 61
15 61
Balance due me,
898 32
When Ledger A is filled, (as was add before,) transfer the
amount of the unsettled accounts to another ledger, distin-
guished bj Ledger B, The alphabet may be made similar to
the alphabet for Ledger A.
The pages from whence the account is transferred should
be placed intbefalio column, in the same line with the entry,
as m the following specimen:
I.EDGCR B.
1886. 1 fol.
I 1
JONATHAN JENKS.
Brought from ledger A,
Cr.
8196 25
1836. 1 fol.
I 2
ISAAC KLING.
Brought from ledger A,
Dr. II Cr.
816 0911 839 68
1836. 1 fol.
I 3
CHAS. RAKESTRAW.
Brought from ledger A, W8312 75
II
Dr.
Cr.
300 00
1836. 1 fol.
4
GEORGE PRICE.
Brought from ledger A.
Dr.
87 61
Cr.
84 75
|CjF» Besides the foregoing, there are several other books
kept by most merchants ; as the Cash Book, Expense Book,
Invoice Book, &c. &c«
MERCANTILE FORMS.
BILLS OF PARCELS.
When goods are sold, it is customary for the seller to de-
liver to the buyer, a note of their contents and prices, with
a total of their value cast up; this m called a bill of parcels.
New Itdy, Jan. 1st, 1836.
Jason M. Mahan^
Bought of F. W^ Leopold,
12 yards superfine broad cloth, at g4 50 S54 00
3 do. blue muslin» 25 75
20 skeins sewing silk, 6 1 20
10 balls cotton thread. 4 40
836 35
UnionviUe, January 12th, 1836.
James Faxon,
Bought of Charles Postmaster,
20 pounds of chocolate, i
6 do. coifee,
34 do. sugar,
2^ do. hyson tea.
By 12 pounds butter, at 20ct8.
18 do lard, 12
go 20
16
11
1 20
84 00
96
3 74
2 70
Amount, gll 40
2 40
2 16
4 55
Balance, 6 84
Received payment in full,
ChARLBS P0STIIASTI&.
XEROANTILS FORMS* 219^
BOOK BILL.
I
A Book Bill is the copy of the account that one person hat
against another, and is made out from the book accounts, and
presented for settlement and payment.
1835. Rasselas Thomas, Dr.
-To Henry S. Faulks, & Co.
Jan. 6th, To 4 yards superfine cloth, at g4 25 817 00
May 14th, To 5 do. Irish linen, 85 4 25
July 23d, To 12 do. Russia sheeting, 40 4 80
Sept. 26th, To 30 pounds rice, 5 1 50
1836,
May 16th, Received payment in full
827 55
Henry S. Faulks.
BILL OF LADING.
Shipped in good order, by A. Boardman, on
the good ship Washington, A. Boardman,
master, now riding at anchor in the bay of
Funchal, and bound for Boston, to say,
C, D. No. 1 a 50 5 quarter casks of wine,
C. B. No. 1 a 4 4 pipes of wine.
Being marked and numbered as in the mar-
gin, and are to be delivered in the like good
order (dangers of the seas, fire and enemies
excepted) at the aforesaid port of Boston,
unto C. Denman or his assigns, he or they
paying freight for the said goods, with pri-
mage and average accustomed. In witness
whereof, the master of said ship hath affirmed
to three bills of lading, of this tenor and
date, the one of which being accomplished,
the other two to be void.
A. Boardman.
Ftmchal, July 10th, 1836.
330 MSROANTILB F0SV9.
Sales of sundry merchandize at Funchal, on account of C.
Denman, merchant, of Bpston ; bemg part of the cargo of
the ship Washington.
100 barrels of Beef, at 16 dolls.
150 barrels of Pork, at 20 dolls.
10000 feet of White Pine Boards, at 25 dolls.
S cts*
1600 00
3000 00
250 00
Expenses.
Boat hire,
Cooperage,
Commission at 5 per cent.
Nett sales,
Funchal, June 6th, 1836.
Errors excepted.
glO 00
5 50
242 50
4850 00
258 00
84592 00
A. BOARDMAN.
Invoice of wines shipped at Funchal, on board the ship Wash-
ington, by A. Boardman, master of said ship, on account
and risques of C. Denman, a native citizen of the United
States, resident at Boston, and consigned to him.
Marks.
CD.
JJTo. 1 a 50
C.B.No.la4
50 qr. casks of Wine, at 830,
4 pipes Wine, 120,
Expenses.
Commission at 2i per cent. 849 50
Boat hire for shipping Wine, 1 60
I 8 cts.
1500 00
480 00
Funchal, June 1st, 1836.
Errors excepted,
A. Boardman.
1680 00
51 10
2031 10
liERCAMTILE FORMS.
221
Disbursements of the ship Washington, A. B. master.
1836.
Maj 1
4
6
8
11
At Funchal.
To a Shipping Paper,
To Ballast,
To Block Maker's bill.
To Blacksmith's bill,
To Ship Chandler's bill.
To Butcher's bill.
*
g cts.
60
12 00
14 00
16 00
16 15
11 11
869 86
April 1
At Madeira.
To fresh Meat and Vegetables,
To one cask of Wine for ship's use,
g cts.
2 12
15 09
81812
1836.
May 11
G, I)unn, owner of skip Wash-
ington.
To disbursements of the ship
Washington, at Funchal,
To do. at Madeira,
Dr.
g69 86
18 12
Cr.
June 6
To wine, as per invoice.
To a bill of exchange for ^8100
sterling, drawn by E.F., mer-
chant, Funchal, on G. N., mer-
chant, London, at par.
By net sales of merchandize at
Funchal,
To balance due the owners of
said ship,
Funchal, June 6, 1836.
Errors excepted,
A. BoARDMAN, master.
2031 10
444 44
•
3028 48
4592 00
*
4592 00
4592 00
1836.
April 1
14
«/. Codline, mate of ship Wash-
ington.
To 1 qr. cask of Wine,
By two barrels Beef sold for gl6
per barrel.
To cash, to balance,
Dr.
30 00
300
Cr.
82 QQ
S32 00
S3»(iP
CONVEYANCING*
A Seaman's Receipt.
Received at !Boston, May 6th, 1836, of Aaron Boardmanr,
master of the ship Washington, fiftj dollars, in full for wa-
ges, and in full satisfaction for other demands against tBe
owners, master and officers of .said ship»
850 00 Jack Haltaro.
A Receipt in full of all demands.
Received, May 10th, 1836, of Henry Hogan, twenty scv-
fn dollars, sixty four cents, in full of all demands.
827 64 James Justice.
A Receipt for rent.
Received, June 2nd, 1836, of Timothy Hedge, one hun-
dred and fifteen dollars, in full for one year's rent, due the
first of April last.
8115 00 . Peter Takeall,
Another.
Received, October 4th, 1836, of Job Warner, the sum of
twenty seven dollars, in money, which, with twenty five dol-
lars and fifty cedts more, disbursed by the said Job Warner,
for repairs and taxes of the tenements he now occupies,
making in the whole fifty two dollars and fifty cents, the
«ame J>eingin full for a half year's rent, due the 1st of Octo-
ber, instant.
852 50 John Receiver.
For money received of a third person..
Received, November 8th, 1835, of Peter Amos, by the
hands of Francis Porter, the sum of Ten Dollars, Fiftj
Cents, on account.
810 50. Jesse Hughes.
For Interest due on a Bond*
Received, Jan. Ist, 1836, of James Brooks, the sum of
Thirty Dollars* in full for one yearns mterest of Five Hun*
r
convETAvoiiro- 333
>Ared Dollars, due to me tke th«nd daj of April last, on bond,
4)y the said James Brooks.
830 00. David West.
The form of a common Negotiable Note.
gSOO— Westchester, Jan. 4ih, 1836.
Sixty days after date, 1 promise to pay to the order of
John Bobb, Three Hundred Dollars, without defalcation.
Value Received.
James J.ohnson.
Promissory Note.
8400— New Italy, January 14th, 1836. '
Three months after- date I promise to pay to William
t](oald, or order, the sum of Four Hundred Dollars, for value
Jieceived. Witness my iiand the 9th of August, one thous-
and eight hundred and thirty-six.
John Porter.
(No witness is required.)
Note with Security.
B150—
We, or either of us, promise to pay William Mulberry,
^r order. One hundred and Fifty Dollai^, on the first day of
August, one thousand eight hundred and thirty six, with law-
full interest for the same, for value received. Witness our
hands this 1st day of December, one thousand eight hundred
and thirty six.
Samuel Rapf.
Henrt Love.
Yhe form of an Accommodaiion Note to he discounted at
the Bank of the Utiited States.
8300— New Italy, January Ist, 1886.
Sixty days after date I promise to pay to the order of Jacob
Paxson, Three Hundred Dollars, without defalcation. Val-
jue received.
Peter Martik.
Credit the drawer,
Jacob Paxson*
234 eQvr^rjk^90iV9.
Forms avo direotioks for TRANSAcrtifd busijixss at
THE Bank of Chester County.
Ibrm of an accommodation note,
8100— December 31, 1835-
Sixty days after date, I prontise to pay Davis Mahan or
order, at the Bank of Chester County, one Hundried Dollars
without defalcation, value receivedr
Amos Pricb.
Credit the drawer.
Davis Mahan.
iVb^e.— -The above note must be endorsed on the back by
Davis Mahan previoits to its being offered at Bank^ and u
^iscounted> will pass to the credit of AnuoB Price-
Fbrm of a Real or Business Note,
810G— December 31, 1835.
Sixty days after date, I promise to pay Davis Mahan, or
order, at the Bank of Chester County, one hundred dollars,
without defalcation, value received.
Amos Priced
Note, — The above note must be endorsed on the back bjr
Davis Mahan, previous to its being offered at Bank, and if
discounted, will pass to the credit of Davis, or to a subse-
quent endorser, bein^ the last.
Form of a Draft or inland Bill of Exchange.
810Q December 81, 1835.
At sight pay to the order of Davis Mahan, one hundred
dollars, and charge to account of
Yours respectively, Amos Price.
Jesse Watson,
Merchant, Philadelphia.
Another.
8100 December 31, 1835,
Five days afi;er sight, pay to the order of Davis Mahan,.
one hundred dollars, and charge to my account.
Yours respectfully, Amos Pbxcs»
Jesse Watson,
Merchant, Philadelphia^
CONYETANCIirG. 225
jYo/*.— Billg payable after date, er after sight, must be
presented for acceptance, and if after date, the acceptor
writes at the bottom of the Bill or across its face, the word,
•'accepted," and signs his name ; if after sight, the acceptor
must write at the bottom of the Bill, or on its face, thus,
"accepted, January 5, 1836, Jesse Watson." Such Bills must
always be endorsed by the payee, who in the foregoing cases
is Davis Mahan, and if discounted, will pass to the credit of
Davis, or of a subsequent endorser.
Eorra of a Power of Attornty to transfer Stock*
Know all men by these presents, that I, Elisha Harper, of
the township of Salisbury, in the county of Chester, and
■Statue of Pennsylvania, do hereby constitute and appoint
Amos Price my true and lawful Attorney for me and in my
name to sell, assign and transfer unto Davis Mahan ten
shares of my stock in the Bank of Chester county.
' Witness my hand and seal this 31st day of December,
one thousand eight hundred and thirty five.
Sealed and delivered >
in the presence of 3 Elisha Harper.
Peter Dale,
Samuel Frent.
Form of a Bill Single with Warrant of Attorney.
This Bill binds me, Amos Price, of the township of East
Marlborough, in the county of Chester, and State of Penn-
sylvania, to the Bank of Chester County, in said State, and
its assigns in the sum of two hundred dollars of lawful money
of the United States of America, conditioned for the payment
of one hundred dollars of lawful money aforesaid, { with law-
ful interest*) on the thirteenth day of March next ensuing.
And I do hereby authorise any Attorney of any Court of
Record of this State, or elsewhere, to appear for me, and after
one or more declarations filed for the above penalty, there-
upon to confess judgment or judgments for the saq^e, in
* If the^Note is to be diaeomited the words in brackets will
bd omitted.
S226 OOVTETAKCIMO*
faTor of the Bank of Chester Countj aforesaid, and its as*
signs, against me with costs of suit and release of errors.
Witness my hand and seal this thirty- first day of Decenl*
ber, in the year of our Lord, one thousand eight hundred and
thirty five.
Sealed and delivered >
in the presence of 5
Thomas Seal, Amos Price.'
Amos Davis.
Form of a Proxy.
I, Amos Price, of East Marlborough, in the county of Ches-
ter, do hereby authorise John Gill for me and in my name, to
vote for Directors of the Bank of Chester county, at the en-
suing election, as fully ai^ I could if personally present. '
Witness my hand and seal, February 1st, 1836.
Sealed and delivered ?
in the presence of J Amos Price.
Samuel Eachus,
William James.
Note — ^Proxies must be given and dated within 60 days of
the election.
Form of a Power of Attorney to receive Dividends.
I, Amos Davis, of the township of Charlestown, county of
• Chester, do hereby constitute and appoint James Henna my
attorney to. ask, demand and receive from the Bank of Ches-
ter county the dividends due |[or that may become due*^ to
me on my stock in said bank, and to give full and sufficient
discharges for the same.
Witness my hand and seal this 31dt day of August, on«
thousand eight hundred and thirty-five.
Scaled and delivered >
in the presence of 5 Aico^ Price.
Joseph Flowers,
# • John Mahan.
• The words in brackets may be inserted if the power is
intended to be perpetual ; otherwise they may be omitted.
OONVETANCINO.
227
Form of a Check,
December 31, 1835.
Bank of Chester county, pay to Amos Price or bearer, one
hundred dollars.
otiQQ Davis Maham.
Another.
December 36, 1835.
Bank of Chester county, pay to Amos Price or order, one
hundred dollars.
oiQo^ A Davis Mahah.
JSfote. — This check must be endorsed by Amos Price, or it
^11 not be paid.
Note with Interest.
I promise to pay to Samuel Jackson or order, the sum oi
Eighty Dollars, on demand, with interest till paid, for value
received. Witness my hand, this 7th day of July, one thou-
sand eight hundred aad thirty-six.
William Caub^
Judgment Note.
I promise to pay Matthias Long, or order, Nine Htindred
Dollars, on the first day of April, one thousand eight hundred
• and thirty six, with lawful interest for the same. For value
received. And further, I do hereby empower any attorney
' of the court of Common Pleas of Chester county, or any other
court of record of Pennsylvania, to confess judgment for thft
above sum and costs, with release of errors, &c. Witness
my hand and seal this 1st day of June, one thousand eight
hundred and thirty five.
Sealed and delivered 7
in the presence of > Jacob Watts-
John A. Moore,
Owen Johnson.
Note 1.— Promissory notes are assignable by endorsement ;
that is, any person to whom a note is given, may assign it to
a second person, by endorsing or writing his name on the
239 CONVETAKCINO.
back of it ; and the second may do the same, and so on from
the third to the fourth, &c.: this gives the last assignee a right
against all the antecedent parties.
Note ?♦ — A note may be assigned either before it become^
due or afterwards. When assigned before it is due, no cir-
cumstances existing between the antecedent parties will in
anj wise affect the assignee : when assigned after it is due,
the assignee receives the note subject to all the equitable
rights existing between the said parties.
Note 3. — A sealed note is not debarred by the statute of
limitation, and is paid in the settlement of a decedent's es-
tate in preference to a note without a seal. *
Notice from a Landlord to a Tenant.
SIR, — Being in possession of a certain house and lot of
ground, with the appurtenances, belonging to me, situate in
the township of Sadsbury, in the county of Chester, which
was demised to you by me, for the term of one year, which
said term will expire and terminate on the first day of Aprils
I hereby notify you that it is my desire to have again and re-
possess the said premises, and I do hereby demand and re-
quire you to leave the same.
Witness my hand this first day of January, one thousand
eight hundred and thirty-five.
John Rigg.
Mr. Isaac Bear.
8400. New Italy y October 17, 1835.
Sixty days after sight, pay to Lemuel Hastings, or
order, this my first bill of exchange for Four Hundred Dollars,
^[second, third and fourth, of the same tenor and date, not be-
ing paid,) for value received, without further advice from
Your humble servant,
Lewis Johns.
To James Piatt, Esq. Philadelphia.
JO^oxy to vote for Directors of the Bank of the United States
Know all men by these presents, that I, Samuel Dale, of
Chester county, have constituted, appointed, and do hereby
institute and appoint John Cope, of Philadelphia, to be mj
OONVETAKOIKO. ^29
true and lawful substitute and proxy for me, and in my name
to vote at any election for Directors of the Bank of the United
States, or any other question that may be put, at a stated or
special meeting of the stockholders of the said bank, as full
as I might or could do if present. Witness my hand this $rst
day of June, one thousand eight hundred and thirty-five.
Assignment of a Bond or Bill,
I do hereby assign and set over all my right, title, claim,
interest, property and demand whatsoever, in and to the
within bond, (or bill,) unto David Haines, for value received.
Witness my hand and seal, this first day of July one thousand
eight hundred and thirty -five.
John Crabb.
Note. — Assignments must be made under the hand and
seal of the assignor, and in the presence of two or more credi-
ble witnesses.
Common and Judgment Bond.
Know all men by these presents, That T, Henry Painter,
<if the township of Earl and county of Lancaster, State of
Pennsylvania, am held and firmly bound unto Benjamin
Linville of the t<?wnship of Salisbury, in the County and
State aforesaid, in the sum of two thousand dollars, lawful
money of Pennsylvania, to be paid to the said Benjamin
Linville, or to his certain attorney, executors, administrators
or assigns. To which payment well and truly to be made,
I bind myself, my heirs, executors and administrators, and
every of them, firmly, jointly, and severally by these pre-
»ents. Sealed with my seal ; dated the first day of April,
in the year of our Lord one thousand eight hundred and
thirty-five.
The condition of this obligation is such, that if the aboTe
bounden Henry Painter, his neirs, executors, administrators,
or any of them, shall and do well and truly pay, or cause to
be paid, unto the above named Benjamin Linville, or to his
certain attorney, executors, administrators or assigns, the
sum of one thousand dollars, like money as aforesaid, on or
before the first day of April next ensuing the date hereof,
with lawful interest^ without any fraud or further delay;
CONYETANCING.
then the above obligation to be void, or else to be and. remain
in full force and virtue.
[The above is the Common Bond ; and the Judgment Bond
will be completed by attaching to it the following i]
And further, I do hereby empower any attorney of th«
Court of Common Pleas of Lancaster county, or any other
Court of Record of Pennsylvania or elsewhere, to appear for
me, and after one or more declarations filed for the above
penalty, thereupon to confess judgment or judgments, as of
last, next, or any subsequent term, with stay of, execution
until the day of payment herein before contained, with re-
lease of errors, &c.
Sealed and delivered in the presence of
Assignment of a Bond,
FOR a valuable consideration, to me in hand paid by Hen-
ry Seymour, I do hereby a^ign and set over the within obli-
gation and all the moneys due thereon, unto the said Henry
Seymour, his heirs and assigns. And in case the same cannot
be recovered of Henry Painter, the obligor within named,
then I promise and agree to pay the amount hereof with all
charges thereupon accruing, unto the said Henry Seymour,
his heirs and assigns. Witness my hand and seal, this first
day of April, one thousand eight hundred and thirty five.
Benjamin Linville.
For a jBond mislaid or lost.
The condition of this obligation is such, that whereas Hen-
ry Painter, in and by a certain obligation, bearing date on or
about the first day of August, became bound unto Benjamin
Linville in the sum of Two Thousand Dollars, which said
bond is since lost or mislaid. And whereas the said Henry
Painter hath fully satisfied and paid the sum of One Thousand
Dollars, with its interest, due on the said obligation, the rei
eeipt whereof the said Benjamin Linville doth hereby a«l
OOHVETANCINO. 281
knowledge, and thereof, and from every part thereof, and all
actions, suits and demands concerning the same, doth acquit
and forever discharge the said Henry Painter, his heirs, ex-
ecutors and administrators, by these presents. If,* therefore,
the said Benjamin Linville, his heirs, executors and admin-
istrators shall and do deliver up the said obligation, when it
shall be found, to the said Henry Painter, his heirs, executors
and administrators, to be cancelled; and until the same
shall be so delivered up and cancelled, shall save, defend,
keep harmless, and indemnify the said Henry Painter, his
heirs, executors and administrators, and his and their goods
and chattels, lands and tenements, of and from the said obli-
gation, and of and from all actions, suits, payments, costs,
charges and damages, for or by reason thereof. Witness my
hand and seal, the third day of December, one thousand eight
hundred and thirty-five.
Benjamin Linville.
Sealed and delivered in presence of
Indenture of an Apprentice.
This Indenture witnesseth, that James Long, of the town-
ship of Lower Makefield, in the county of Bucks, son of
Francis Long, by and with the consent of his father, as tes-
tified by his signing as a witness hereunto, hath put himself,
and by these presents doth voluntarily, and of his own free
will and accord, put himself apprentice to Samuel Downs, of
the same place, Blacksmith, to learn his art, trade and mys-
tery, and after the manner of an apprentice to serve him from
the day of the date hereof, for and during the full end and
term of four years and two months, next ensuing. During
all which term the apprentice his said master faithfully shall
serve, his secrets keep, his lawful commands every where
gladly obey. He shall do no damage to his said master, nor
see it done by others, without letting, or~giving notice thereof
to his said master. He shall not waste his said master^
goods^ nor lend them unlawfully to any. With his ow|i
goods, nor the goods of others, without license from his saicl
master, he shall neither buy nor sell. He shall not absent
himself day nor night from his said master's service without
his leave ; nor haunt ale-houses, taverns or play-houses ; but
in all things behave himself as a faithful apprentice ought to
233 COVTETANCIKO.
do, during the said term. And the said master shall use the
utmost of his endeavors to teach or cause to be taught or in-
structed the said apprentice, in the trade or mystery of a
Blacksmith ; and procure for him sufl&cient meat, drink, ap-
parel, lodging and washing fitting for an apprentice, during
tlie said term of four years and two months, and give him
within the said term six months^ schooling, one-halt thereof
is to be in the last year of the said term ; and when he is free,
to give him two suits of clothing, one whereof is to be entirely
new. And for the performance of all and singular the cove-
nants and agreements aforesaid, the said parties bind them-
selves each unto the other, firmly, by these presents. In
witness whereof, the said parties have set their hands and
seals hereunto — Dated the first day of January, in the year of
our Lord one thousand eight hundred and thirty-six.
James Long.
Sealed and delivered in the
presence of !l^rancis Long.
Assignment of an Apprentice.
Know all men by these presents, that I, the within named
Samuel Downs, for divers good causes aud considerations,
have assigned and set over, and by these presents, as far as
I lawfully may or can do, assign and set over the within In-
denture, and the apprentice therein named, unto Isaac How,
his heirs and assigns. He and they performing all and sin-
gular tlie covenants therein contained on my part and behalf
to be done, kept and performed, and indemnifying me from
the same. Witness my hand and seal the second day of
August, one thousand eight hundred and thirty six.
Samuel Dowks.
Witness present.
Lease of a Farm.
This Indenture, made the first day of January, in the year
of our Lord one thousand eight hundred and thirty six, be-
tween Jacob Lamb, jr. of the townshijj of West Cam, in the
county of Chester, and state of Pennsylvania, yeoman, of the
one part, and Isaac Ward, of Sadsbury township, county and
«tate aforesaid, yeoman, of tlie other part, witnesseth, that
CONVEYANCING. 233
the said Jacob Lamb, jr. for and in consideration of the yearly
rent and covenants hereinafter mentioned and reserved on
the part and behalf of the said Jacob Lamb, jr. his heirs, ex-
ecutors and administrators, to be paid, kept, and performed j
hath demised, set and to farm, let, and by these presents doth
demise, set and to farm, let, unto the said Isaac Ward, his
heirs and assigns, all that certain messuage or tenement,
tract, piece or parcel of land, situate in the township of West
Cain, aforesaid, adjoining land of John Lawrence, Job Rapp,
Jonathan Watkins and others, and now in the tenure of Isaac
Lemon, containing one hundred and ten acres, together with
all and singular the buildings, improvements, and other the
premises hereby demised with the appurtenances; to have
and to hold the same unto the said Isaac Ward, his heirs and
assigns, from the first day of April next ensuing the date
hereof, for and during the term of five years, thence next en-
suing, and fully to be complete and ended ; yielding and pay-
ing for the same unto the said Jacob Lamb, jr. his heirs and
assigns, the yearly rent or sum of two hundred dollars, on
the first day of April in each and every year during the term
aforesaid : and at the expiration of the said term, or sooner, if
determined thereof, he the said Isaac Ward, his heirs and
assigns, shall and will quietly and peaceably surrender and
yield up the said demised premises, with the appurtenances,
tinto the said Jacob Lamb, jr. his heirs and assigns, in as
good order and repair as the same now are, reasonable wear,
tear and casualties which may happen by fire or otherwise,
only excepted. In witness whereof the parties have hereunto
interchangeably set their hands and seals, the day and year
above written,
Jacob Lamb, Jr.
Isaac Ward.
Sealed and delivered in presence of
r
Lease of a House.
Agreed the first day of March, in the year of our Lord
one thousand eight hundred and thirty-six, between How-
ard Pugh, of Newtown township, in the county of Bucks,
and state of Pennsylvania, yeoman, of the one part, and
James Parker, of the same place, stone mason, of the other
part^ as follows: The said Howard Pugh doth let unto the
Q
234 COKTETANCING.
said James Parker, his heirs and assigns, a certain lot of land,
whereon is erected a brick dwelling and stable, situate in the
township aforesaid, and now occupied by Henry Janney, ad-
joining land of John Plumly, for the term of one year from
the first day of April next, for the yearly rent of forty dol*
lars, to be paid in four equal quarterly payments, viz: on the
first days of July, October, January and April, which said
yearly rent the said James Parker doth hereby for himself,
his executors and administrators, covenant and agree to pay
unto the said Howard Pugh, his heirs, executors and assigns:
and atHhe expiration of the said term, or sooner, he, the said
James Parker, his heirs and assigns, shall and will quietly and
peaceably surrender and yield up the said demised premises,
with the appurtenances, unto the said Howard Pugh, his heirs
and assigns, in as good order and repair as the same now are;
reasonable wear, tear and casualties which may happen by
fire or otherwise, only excepted.
In witness whereof, we have hereunto set our hands and
seals the day and year above written,
James Parker,
Witness present, Howard Pugh.
Assignment of a Lease*
Know all men by these presents, That I, Philip Hathaway,
the lessee within named, for and in consideration of One
Hundred Dollars, to me in hand paid by William Mulberry,
at and before the ensealing and delivery hereof, the receipt
whereof I do hereby acknowledge, have granted, assigned,
and set over, and by these presents do grant, assign, and
set over, unto the said William Mulberry, his heirs and
assigns, the within indenture of lease, together with all and
singular the premises hereby demised, with the appurtenan-
ces, to haye and to hold the same unto the said William
Mulberry, his heirs and assigns, for the residue of the term
within mentioned, under the yearly rent and covenants with-
in reserved and contained on my part and behalf to be done,
kept, and performed.
Witness ray hand and seal the first day of January one
thousand eight hundred and thirty-six.
Philip Hathawat*
Sealed and delivered in presence of
t
OONTETANCINO. 235
Agreement for mle of an Estate.
Articles of agreement, indented, made, concluded, and
agreed upon, the second day of October, in the year of our
Lord one thousand eight hundred and thirty -five, between
John James, of the township of Warwick, in the county of
Bucks, and state of Pennsylvania, yeoman, of the one part,
and Alexander Harper, of the township and county aforesaid,
merchant, of the other part, as follows, to wit:
The said John James, for the consideration hereinafter
mentioned, doth for himself, his heirs, executors and admin-
istrators, covenant, promise, grant and agree to and with the
said Alexander Harper, his heirs and assigns, by these pres-
ents, that he the said John James, shall and will, on or before
the first day of April next ensuing the date hereof, at the
proper costs and charges of the said Joh^i James, his heirs
and assigns, by such deed or deeds of conveyance as he or
they, or his or their council, learned in law, shall advise, well ,
and sufficiently grant, convey and assure unto the said Alex-
ander Harper, his heirs and assigns, in fee simple, clear of
all incumbrances, all that plantation or farm, containing one
hundred and ten acres, in the township of Cranberry, in Ve-
nango county, adjoining lands of Bela Smith, and now in the
tenure of James SiVerty, together with all and singular the
buildings, improvements, and other the premises hereby de-
mised, with the appurtenances. In consideration whereof,
the said Alexander Harper, for himself, his heirs, executors
and administrators doth covenant, promise and agree fo and
with the said John James, his heirs and assigns, by these
presents, that he the said Alexander Harper, his heirs, ex-
ecutors and administrators, or some of them, shall and will
well and truly pay, or cause to be paid, unto the said John
James, his executors, administrators or assigns, the sum of
one thousand eight hundred dollars, in manner following, to
wit: six hundred dollars, part thereof, on the delivery of the
deed for the premises ; six hundred dollars more thereof, on
the first day of July, which will be in the year of our Lord
one thousand eight hundred and thirty-six, and six hundred
dollars on the first day of October then next ensuing.
And for the true performance of all and every the covenants
and agreements aforesaid, each of the said parties bindeth
himself, his heirs, executors and administrators, unto the
other, his executors, administrators and assigns, in the penal
236 OONVETANCINO.
gum of three thousand six hundred dollars, firmly by these
presents.
In witness whereof, the said parties to these presents have
hereunto set their hands and seals, bated the day and year
first above written.
John James^
Alexander Harper.
Sealed and delivered in the presence of
Agreement for building a House.
Articles of agreement, made and fully agreed upon the
second day April, in the year of our Lord one thousand eight
hundred and thirty-six, between James Cope, of Middletown
township, in the county of Bucks, and state of Pennsylvania,
yeoman, of the one part, and Jason Webb, of the township of
Tinicum, in the county and state aforesaid, carpenter, of the
other part, to wit: The said Jason Webb, for the considera-
tion hereafter mentioned, doth for himself, his executors and
administrators, covenant, promise and agree to and with the
said James Cope, his executors, administrators and assigns,
that he the said Jason Webb, shall and will, within the space
of Aye months next after the date hereof, in good and work-
manlike manner, and according to the best of his art and
skill, well and substantially erect, build, set up and finish
one house or messuage, in Middletown, Bucks county, of the
dimensions following: [here insert the dimensions] and com-
pose the same with such stone, brick, timber, and other ma-
terials as the said James Cope or his assigns shall find and
Provide for the same. In consideration whereof, the said
ames Cope doth for himself, his executors and administra-
tors, covenant and promise, to and with the said Jason Webb,
his executors, administrators and assigns, well and truly to
pay or cause to be paid, unto the said Jason Webb, his ex-
ecutors, administrators and assigns, the sum of one thousand
dollars, in manner following, to wit : five hundred dollars at
the beginning of said work ; two hundred and fifty dollars
more m three months, provided said house be at least one
half done, and the remaining two hundred and fifty dollars,
in full for the said work, when the same shall be complete! j
finished. And also, that the said James Cope, his executors*
CONVETANCIKO. 237
administrators or assigns, shall and will, at his and their
own proper expense, find and provide all the stone, brick,
tile, timber and other materials necessary for making and
■building of the said house. And for the true performance of
all and singular the covenants and agreements aforesaid, each
of the said parties bindeth himself, his heirs, executors and
administrators, unto the other, his executors, administrators
and assigns, in the penal sum of two thousand dollars firmly
by these presents. In witness whereof, we have hereunto set
our hands and ^eal« the day and year first above written,
James Cope,
Jason Webb.
Sealed and delivered in presence of
•Agreement with a Clerk or Workman.
It is agreed, this first day of January, in the year of our
Lord one thousand eight hundred and thirty- six, between
David Irwin and Job Young, both of the borough of West-
chester, and county of Chester, in manner following, to wit :
The said Job Young covenants and agrees faithfully, truly
and diligently to write [or work] for, and act as the clerk
[or journeyman] of him the said David Irwin, from the day
-of the date hereof, for and during the space of one whole
year, if so long both parties live, without absenting himself
from the same ; during which time he the said Job Young
will resort to the said David Irwin's office [or shop] in West-
chester, and there attend, and do and perform the clerkship
[or work] aforesaid, without revealing any of the secrets of
. the said David Irwin, his occupation or business. In con-
sideration of which service so to be performed, he the said
David Irwin covenants and agrees to allow and pay to the
«aid Job Young the sum of two hundred dollars, by four
equal quarterly payments, or oftener if required. Provided,
nevertheless, that when and as often as the said Job Young
hath not writing [or work] sufficient to keep the said Job
Young in employ, then and so often during such time, it shall
be lawful for the said Job Young to do any other business for
his own use and on his own account ; but if it should happen
that the -said Job Young fall sick, or shall be absent from the
•office [or shop] of the said David Irwin, when he has employ-
ment far him^ then «ttch absent tim^ shall be deductecli al^
238 OONVEYAKCINO. ;
lowed for and made up to the said David Irwin. And for tbe
true performance of all and singular the covenants and agree-
ments aforesaid, each of the said parties bindeth himself, his
heirs, executors and administrators, unto the other, his ex-
ecutors, administrators and assigns, in the penal sum of five
hundred dollars, firmly bj these presents.
In witness whereof we have hereunto set our hands and
seals the day and year above written ►
David iRwiWy
JOBT YOUNG.-
Sealed and delivered in presence of
Bill of Sale of Goods*
Know all men by these presents, That I, Allen Armstrongs
of the city of Philadelphia, state of Pennsylvania, merchant,
for and in consideration of the sum of eight hundred dollars,
to me in hand paid by Benjamin Davis, of the same place, at
and before the ensealing and delivery of these presents, the
receipt whereof is hereby acknowledged, have bargained,
sold and delivered, and by these presents do bargain, sell
and deliver unto the said Benjamin Davis, [here insert the
goods sold^ to have and to hold the said [goods'] unto the
said Benjamin Davis, his executors, administrators and as-
signs, to his and their own proper use, benefit and behoof
for ever. And I, the said Allen Armstrong, my heirs, ex-
ecutors and administrators, the said baigained premises unto
the said Be^yamin Davis, his executors, administrators and
assigns, from and against all person and persons whomsoever
shall and will warrant and forever defend by these presents.
In witness whereof I have hereunto set my hand and seal,
this fifth day of January, one thousand eight hundred and
thirty-six.
Allen Araistrong..
Sealed and delivered in presence of
Another— w^ Bill of Sak of Goods.
Know all men by these presents. That I, Jacob Goodman,
of Heidelberg township, Berks county, state of Pennsylvania,
merchant, for and in consideration of the sum of five hundr^
dollars, to me in hand paid by Francis Polmi of the saine
CONVEYANCING. 239
\
place, at or before the sealing and delivery of these presents,
the receipt whereof I do hereby acknowledge, have granted,-
bargained and sold, and by these presents do grant, bargain
and sell unto the said Francis Polm, his executors, adminis-
trators and assigns, all the goods, household stuff, imple-
ments and furniture, and all other goods and chattels what-
soever mentioned and expressed in the schedule hereunto an-
nexed. [_0r thus, hereinafter particularly mentioned, that is
to say, one bureau, &c.] now remaining and being in the
house of Jacob Goodman : to have and to hold all and singu-
lar the said goods, household stuff* and furniture, and other
the premises above bargained and sold, or mentioned or in-
tended so to be, to the said Francis Polm, his executors, ad-
ministrators and assigns forever. And I, the said Jacob
Goodman, for myself, my heirs, executors and administrators,
all and singular the said goods, &c. unto tlie said Francis
Polm, his executors, administrators and assigns, against me
the said Jacob Goodman, my execlitors and administrators,
and against all and every other person and persons whomso-
ever shall and will warrant and forever defend by these
presents. Of all and singular of which said goods, &c. I the
said Jacob Goodman, have put the said Francis Polm in full
possession, by delivering to him the said Francis Polm one
silver spoon, at the sealing and delivery of these presents, in
the name of the whole premises hereby bargained and sold, or
mentioned or intended so to be, unto him the said Francis
Polm, as aforesaid.
In witness whereof I have hereunto set my hand and seal,
the first day of February, one thousand eight hundred and
thirty-six.
Jacob Goodman.
Sealed and delivered in presence of
Letter of Attorney.
Know all men by these presents, That I, Jesse Denny, of
Newlin township, Chester county, in the state of Pennsylva-
nia, merchant, have made, constituted and appointed, and by
these presents do make, constitute and appoint, and in my
place and stead put and depute my son Samuel Denny, of the
borough of Oxford, of the county and state aforesaid, painter,
8i9 OONVETANOIKG^
mj true and lawful attorney for me and in my name, and for
my use, to ask, demand, sue for, recover and receive all such
sum or sums of money, debts, goods, wares, dues, accounts
and other demands whatsoever, which are or may be due,
owing, payable and belonging to me, or detained from me, by
any manner of ways or means whatsoever, or in whose hands
soever the same may be found ; [and also to pay and discharge
all sums of money, due and owing by me, to any person
or persons whatsoever,] giving and granting unto my said
attorney, by these presents, my full and whole power,
strength and authority in and about the premises, to have, use
and take all lawful ways and means in my name, and for the
purposes aforesaid ; and upon the receipt of any such debts,
dues or sums of money, acquittances or other sufficient dis-
charges for me and in my name to make, seal and deliver :
and generally, all and every act or acts, thing or things, device
and devices in the law, whatsoever needful and necessary to
be done in and about the premises, for me and in my name to
do, execute and perform as fully, largely and amply to all in-
tents and purposes, as I myself might or could do if person-
ally present ; and attornies one or more under him, for the
purpose aforesaid, to make and constitute and again to revoke
at pleasure.— Hereby ratifying, allowing and holding for firm
and effectual, all and whatsoever my said attorney shall
lawfully do in and about the premises aforesaid by virtue
hereof.
In witness whereof I have hereunto set my hand and seal,
the first day of June, in the year of our Lord one thousand
eight hundered and thirty-six.
Sealed and delivered in presence of
Chester county, ss.
On the 14th day of June, in the year of our Lord one thou-
sand eight hundred and thirty-six, personally appeared before
me the subscriber, one of the justices of the peace in and for
said county, the above named Jesse Denny, and acknowledged
the foregoing letter of attorney to be his act and deed.
Witness my hand and seal on the day and year above
written.
JoKN Wa.&NER»
CONVETANOIirO. 241
Letter of Attorney — To receive Debts.
Know all men by these presents, That I, William Carey,
of the city of Lancaster, state of Pennsylvania, chairmaker,
(for divers good causes and considerations, me hereunto mov-
ing,) have made, ordained, authorised, constituted and ap-
pointed, and by these presents do make, ordain, authorise,
constitute and appoint Joseph Neeld of the same place, my
true and lawful attorney, (irrevocable) for me and in my
name and to my use, (or to the use of him the said Joseph
Neeld) to ask, demand, sue for, recover and receive of Sam-
uel Coale, of Middletown township, state aforesaid, all and
every sum and sums of money, debts and demands whatso*
ever, which now are due and owing unto me the said William
Carey, by and from the said Samuel Coale; and in default of
payment thereof, to have, use and take all lawful ways and
means, in my name or otherwise, for the recovery thereof, by
attachment, arrest, (distress) (re-entry) or otherwise, (and to
compound and agree for the same,) and on receipt thereof, to
make, seal and deliver acquittances or other sufficient dis-
charges for the same, for me and in my name ; and to do all
lawful acts and things whatsoever concerning the premises,
as fully in every respect as I myself might or could do if I
were personally present, and an attorney or attornies under
him for the purposes aforesaid, to make, and at his pleasure
io revoke ; hereby ratifying, allowing and confirming all and
whatsoever my said attorney shall in my name lawfully do or
cause to be done, in and about the premises, by virtue gf
these presents.
In witness v/hereof I have hereunto set my hand and seal,
the first day of January, one thousand eight hundr^ and
thirty-six.
William Caret.
Sealed and delivered in presence of
Conditions of Public Vendue.
The conditions of the present jmblic vendue, made and
held this twentieth day of April, A. D. one thousand eight
hundred and thirty-six, for the sale of a messuage and tract
of about sixty-five acres of Land, with the appurtenances,
situate in Tredyfifria township, Chester county, now in the
242 c}onV£tanC1n(».
tenure of Henry Greatrake, are as follow j The highest and
best bidder to be the buyer ; and if any dispute arise as to the
last and best bidder, the property shall be put up at a former
bidding. That the purchaser shall, within one hour after the
property is struck oiF to him, pay down the sum of two hun-
dred dollars, lawful money of Pennsylvania, or give his note
of hand, payable ten days after date ; and to pay the further
sum of two thousand dollars, like money aforesaid, on the
first day of April next, and give satisfactory security for the
payment of the residue, in two equal annual payments there-
after, with lawful interest from the said first day of April
next, payable annually. On the purchaser performing as
afforesaid, the subscriber hereby obligates and binds himself,
his heirs, executors, administrators or assigns, that he or
either of them shall and will, at the proper cost and charges
of such purchaser, his heirs or assigns, sign, seal and deliver,
' or cause so to be done, a good and sufficient deed, in fee sim-
ple, for conveying and assuring the said premises with the
appurtenances, unto the said purchaser, his heirs or assigns ;
and shall and will on the first day of April next, (the pur-
chaser having performed as aforesaid,) give a quiet and
Eeaceable possession of said premises to the purchaser, his
eirs or assigns. [Here make the necessary reserves, such
as grain in the gi'ound, &c.] And for the true performance
of all and singular the covenants aforesaid, I, Edmund Jones,
do for myself, my heirs, executors, administrators and assigns,
hereby obligate and bind myself to comply with the aforesaid
conditions. In witness whereof, I have hereunto set my
hand and seal, the day and year first above written.
Edmund Jones.
Signed and sealed in the presence of
Sale of Goods and Chattels.
The conditions of this present public vendue, held this
twentieth day of March, A. D. one thousand eight hundred
and thirty-six, for the sale of the £oods and chattels of the
subscriber are as follow : — The highest and best bidder to be
the buyer ; any person buying to the amount of four dollars,
and under, to pay cash, and for all sums exceeding, the pur-
chasers to have lour months' credit from this date, by giving
f
*
GONTEYAKCINO. 249
their notes of hand, [before the removal of the goods,] with
approved security, if required,
William Fleming*
Mortgage^
This indenture, made the first day of March, in the year
of our Lord one thousand eight hundred and thirty-six, be-
tween Eli Kling, of Richland township, Bucks county, and
state of Pennsylvania, of the one part, and John Downing, of
Tinicum township, county and state aforesaid, of the other
part, witnesseth. That whereas the said Eli Kling, in and by
a certain bond or obligation, duly executed, bearing even
date herewith, doth stand bound unto the said John Downing
in the penal sura of two thousand dollars, lawful money of th«
state of Pennsylvania, conditioned for the payment of one
thousand dollars, lawful money aforesaid, on the first day of
April next ensuing the date hereof, with lawful interest for
tlie same, as in and by the said recited obligation and condi-
tion thereof more fully appears. Now this indenture wit-
nesseth, that the said Eli Kling, as well for and in considera-
tion of the aforesaid debt or sum of one thousand dollars, and
for the better securing the payment thereof, with interest till
paid, unto the said John Downing, his executors, adminis-
trators and assigns, in discharge of the said recited obliga-
tion, as of the further sum of one dollar to hjm in hand paid
by the said John Downing, at the time of the execution here-
of, the receipt whereof is hereby acknowledged, hath granted,
bargained, sold, released and confirmed, and by these present*
doth grant, bargain, sell, release and confirm unto the said
John Downing, his executors, administrators and assigns, all
that, &c. yHere insert the premises^]
Together with all and singular the buildings, improvements,
ways, waters, water-courses, rights, liberties, privileges,
hereditaments and appurtenances whatsoever, unto the said
hereby granted premises belonging or in any wise appertain-
ing, and the reversions and remainders thereof; to nave and
to hold the said messuage, &c. hereditaments and premises
hereby granted or mentioned, or intended so to be, with the
appurtenances, unto the said John Downing, his heirs and
assigns, to the only proper use and behoof of the said John
Downing, his heirs and assigns, forever. Provided always.
4
344 eOMVETANCIKG.
nevertheless, that if iht saad Eli Kling, his heirs, executors,
administrators or assigns, shall and do well and truly pay or
cause to be paid, unto the said John Downing, his executors,
administrators, or assigns, the aforesaid debt or sum of one
thousand dollars, on the day and time hereinbefore mention-
ed and appointed, together with lawful interest for the same,
according to the condition of the said recited obligation, with- I
out fraud or further delay, and without deduction, defalca- •]
tion or abatement to be made for, or in respect of taxes, !
charges or assessments, whatsoever, then, as well this present
indenture and the estate hereby granted, as the said recited
obligation, shall become void and of no effect, any thing here-
in before contained to the contrary in any wise notwithstand-
ing. In witness whereof, the said parties have hereunto set
their hands and seals, the day and year above written.
Sealed and delivered in presence of
•Acknowledgment of u Mortgage.
The first day of March, A. D. one thousand eight hundred
and thirty-six, before me, the subscriber, one of the justices
of the peace in and for the county of Bucks, came the above
named Eli Kling, and acknowledged the above indenture to
be his act and deed, and desired the same might be recorded
Witness mj hand and seal,
ISAAO HiCKS, J. P.
DEED-'-^Common Form.
This Indenture, made the first day of March, in the year
of our Lord one thousand eight hundred and thirty-six, bj
and between William Mulberry, of the township of Sadsbury,
in the county of Chester, and state of Pennsylvania, farmer,
and Sarah his wife, of the one part, and Gerard G. Leopold,
of the borough of Harrisburg, in the county of Dauphin, and
state aforesaid, nursery-man, of the other part, witnesseth,
that he the said William Mulberry and Sarah his wife, for and
in consideration of the sum of four thousand dollars, to them,
in hand paid by the said Gerard G, Leopold, at and before the
sealing ^nd delivery hereofp the receipt and payment whereof
tiiey do hereby acknowledge, and thereof do forever acquit
aud discharge the said Gerard G. Leopold, his heirs, execu*
tors and administrators, by these presents, have granted,
bargained and sold, and by these presents do grant, bargain
and sell unto the said Gerard G. Leopold, and to his heirs
and assigns, a certain Tract of Land, situate in Sadsbury
township, and county of Chester aforesaid, boundednis follows,
viz: Beginning at an Italian mulberry tree, thence by land
of Jason M. Mahan, south five degrees west one hundred and
twenty-six perches, to a sugar maple tree; thence by land of
Job Pyle, north eighty-five degrees west, one hundred and
thirty -four perches, to an ailanthus tree; thence by land of
James Latta, north five degrees east one hundred and twenty-
six perches, to a linden tree; thence by land of John Yates,
south eighty-five degrees east one hundred and thirty-four
perches, to the place of beginning ; containing one hundred
and five acres and eighty-four perches, be the same more
or less ; it being the same premises which Job Pyle and Mary
his wife, by indenture bearing date the first day of May,
Anno Domini one thousand eight hundred and thirty -two, for
the consideration therein mentioned, did grant and confirm
unto the said William Mulberry, (party hereto,) and to hi»
heirs and assigns forever, as in and by the said in part recited
indenture, recorded in the ofiice for recording of deeds, at
Westchester, in and for the county of Chester, in Book D,'
vol, 9, page 213, relation being thereunto had more fully ap-
pears : together with all and singular the rights, privileges,
hereditaments and appurtenances thereunto belonging, and
the remainders, tents, issues and profits thereof; and also all
the estate, right, title, interest, property, claim and demand,
whatsoever, of them the said William Mulberry and Sarah
his wife, in law or equity or otherwise howsoever, of, in, to
or out of the same or any part thereof; to have and to hold
the said demised premises, hereby granted and sold, with the
appurtenances, unto the said Gerard G. Leopold and his
heirs and assigns forever. And the said William Mulberry
and Sarah his wife, for themselves, their heirs, executors and
administrators, *do hereby covenant, promise, grant and
agree, to and with the said Gerard G. Leopold, his heirs and
assigns, by these presents, that they the said William Mul-
berry and Sarah his wife, the above described premises here-
by granted and sold, with the appurtenances, unto the said
346 OONTEt\NOIKG.
Gerard G. Leopold, his heirs and assigns, against the said
William Mulberry and Sarah his wife, and their heirs, and
{gainst every other person and persons lawfully claiming or
to claim the same or any part thereof, shall and will warrant
and forever defend by these presents.
In testimony whereof the said William Mulberry and Sarah
his wife have hereunto set their hands and seals, the day and
year first above written.
William Mulberry, j l. s. >
Sarah Mulberry. ^ l.s. f
Sealed and delivered > ^ ^-^y^ ^
in the presence of i
William W. Eachus,
Philip Hathaway.
Receipt,
Received, on the day of the date of the above written inden-
ture, of and from the within named Gerard G. Leopold, Four
Thousand Dollars, being in full of the consideration therein
~ mentioned.
William Mulberry,
Witnesses present. Sarah Mulberry.
William W. Eachus,
Philip Hathaway.
Acknowledgment of a Deed.
Chester county, ss. •
The first day of March, in the year of our Lord one
thousand eight hundred and thirty-six, personally appeared
before me the subscriber, one of the justices of the peace in
and for the county aforesaid, the above named William Mul-
berry and Sarah his wife, and acknowledged the above writ-
ten indenture to be their, and each of their a^t and deed, and
desired the same as such mig:ht be recorded according to
law. She, the said Sarah, being of lawful age; separate and
apart from her said husband, by me examined, and the full
contents of the said indenture unto her made known.
Whereupon she did declare that she did voluntarily, and of
ker free will and accord, seal, and as her act and deed, de-
liver the same without anj concern or compulsion of her said
husband whatever. .^i^IHj
Witness my hand and seal,
George W. Parke, J. P. :
The form of a Will, with the devise of a Real Estate, Lease'
hold, ^'c.
The last Will and Testament of Caleb Taylor, of Tinicum
township, Bucks county. 1, Caleb Taylor, considering the
uncertainty of this mortal life, and being of sound mind and
memory, (blessed be Almighty God for the same,) do make
and publish this my last will and testament, in manner and
form following, (that is to say,) First, I give and bel[ueath
unto my beloved wife, Mary Taylor, the sum of two thousaijd
dollars. Item, I give and bequeath to my eldest son, Samuel
Taylor, the sum of nine hundred dollars: Item, I give and
• bequeath unto my two younger sons, John Taylor and Peter
Taylor, the sum of seven hundred dollars each. . Item, I give
and bequeath to my daughter-in-law, Mary Watson, single
woman, the sum of six hundred dollars, which said several
legacies, or sums of money, I will and order to be paid to the
said respective legatees, within one year after my decease.
I further give and devise to my said eldest son, Samuel Tay-
lor, his heirs and assigns, all that messuage or tenement,
situate, lying and being in Tinicum township, and county
aforesaid, together with all my other freehold estate whatso-
ever, to hold to him the said Samuel Taylor, his heirs and
assigns, for ever. And I hereby give and bequeath to my
said younger sons, John Taylor and Peter Taylor, all my
leasehold estate, of and in all those messuages, or tenements,
with the appurtenances, situate in Newtown township, coun-
ty aforesaid, equally to be divided between them. And
lastly, as to all the rest, residue and remainder of my per-
sonal estate, goods and chattels, of Nwhat kind and nature so-
ever, I give ajid bequeath the same to my said beloved wife,
Mary Taylor, whom I hereby appoint sole executrix of this
my last will and testament; hereby revoking all former wills
by me made. .In witness whereof, I have hereunto set my
hand and seal, the first day of January, in the year of our
Lord, one thousand eight hundred and thirty -six,
Caleb Taylor.
248 CONVEYANCING.
Signed, sealed, published and declared, by the above named
Caleb Taylor,* to be his last will and testament, in the
presence of us ; who, at his request and in his presence,
have subscribed our names as witnesses thereunto.
James Smith,
Thomas Williams,
. Henry Rieth.
* Caleb Taylor should say, in the presence of the witnesses
when he signs this—** I sign and publish this as my last will
and testament."
Common Bond of Arbitration.
Know all men by these presents, that I, Aaron Wiley, of
the township of Swatara, in the county of Dauphin, gentle-
man, am held and firmly bound to John Thomas, of the town-
ship and county aforesaid, yeoman, in the sum of five hun-
dred dollars, of good and lawful money of the United States,
to be paid to the said John Thomas, or to his certain attorney,
executors, administrators or assigns, for which payment to be
well and faithfully made, I bind myself, my heirs, executors
and administrators, firmly by these presents. Sealed with
my seal — dated the first day of August, in the year of our
Lord one thousand eight hundred and thirty- six.
The condition of this obligation is such, that if the above
bound en Aaron Wiley, his heirs, executors and administrators,
on his or their parts and behalfs, shall and do in all things
well and truly stand to, obey, abide by, perform, fulfil and
keep the award, order, arbitrement and final determination of
Job Ward, James Fox and David Rule, of the township and
county aforesaid, arbitrators, indifierently elected and named,
as well on the part and behalf of the above bounden Aaron
Wiley, as of the abov^ named John Thomas, to arbitrate,
.iward, order, judge and determine of and concerning all and
all manner of action and actions, cause and causes of action,
suits, bills, bonds, specialties, judgments, executions, ex-
tents, quarrels, controversies, trespasses, damages' and de-
mands whatsoever, at any time heretofore had, made, moved,
brought, commenced, sued, prosecuted, done, suffered, com-
mitted or depending by and between the said> parties, so as
the said award be made in writing, under the hands of the
said Job Ward, James Fox and David Rule, or any two of
.COVVETAKCINO. 249
them, and r&idj to be delivered to the said parties in differ-
ence, or sTtch of them as shall desire the same, on or before
the first day of June, one thousand eight hundred and thirty-
six, then this obligation to be void, or else to remain in full
force.
Award — By three Arbitrators,
To all to whom this present writing of award indented
shall come, we. Job Ward, James Fox and David Rule, send
greeting : Whereas, divers controversies and debates have
been and yet are depending between Aaron Wiley and John
Thomas, for the appeasing and determining whereof, the said
jparties have submitted themselves, and are become bound
each to the other by their several obligations, bearing date
the first day of April, one thousand eight hundred and thirty-
six, in the sum of five hundred dollars, witli conditions
theretader written for the performance of the award, arbitre-
ment, determination and judgment of us, the said Job Ward,
James Fox and David Rule, arbitrators indifferently elected
and chosen, as well on the part and behalf of the said Aaron
Wiley, as on the part and behalf of the said John Thomas, to
award, arbitrate, determine and judge of and concerning all
and all manner of actions, suits, judgments, executions, ac-
counts, quarrels, controversies, trespasse's, damages and de-
mands whatsoever had, made, moved, commenced or depend-
ing between the said Aaron Wiley and John Thomas, so as
the said award, determination and judgment of us, the said
Job Ward, James Fox and David Rule, of and concerning the
premises, be made and put in writing, under our hands and
flMals, on or before the first day of April, as by the said obli-
faitions and conditions thereof, doth more fully appear. Now
BOW ye, that we the said Job Ward, James Fox and David
Hule, arbitrators as aforesaid, taking upon us the charge and
burden of the said award and arbitrement, and having heard
and understood the sayings and allegations of both parties,
concerning the premises, and being minded to settle unity
and friendship between them, concerning the same, do there-
upon make and put in writing this our award, arbitration and
judgment between the said parties, for and concerning the
premises, in ttianner and form following, that is to say : ]nrst,
we do awards arlntrate. and 4eterxnine by these presents,
R
350 COKVETAKCIKO.
that the said Aaron Wiley, his heirs, executors or admini^
trators, do and shall pay or cause to be paid unto the said
John Thomas, the sum of three hundred and forty dollars
and fifty cents, and that upon payment thereof, each of them,
the said John Thomas and Aaron Wiley, shall seal and sub-
scribe, and as his several act and deed, deliver unto the
other of them a general release in writing, of all matters,
actions, suits, cause and causes of action, bonds, bills,
covenants, controversies and demands vrhatsoc^er, either of
them hath, may, might, or in any wise ought to have, against
the other of them, by reason of the matters aforesaid, or by
reason or means of any matter, cause or thing whatsoever,
from the beginning of the world unto the day of the date of
the said obligation: And for the better attestation and con-
firmation of this award, we the said arbitrators have hereunto
set our hands and seals, the first day of June, in the year of
our Lord one thousand eight hundred and thirty-six.
Job Ward,
James Fox,
David Rule.
Petition for laying ovi a Road,
To the honorable the judges of the Court of Common Pleas of
the county of Lancaster, now composing a Court of Quar-
ter Sessions of the Peace, in and for the said county.
The petition of divers inhabitants of the township of Leacock^
in the said county ^ humbly sheweth :
That your petitioners labor under great inconveniences for
want of a road or highway, to lead from — — to .
Your petitioners therefore humbly pray the court to appoint
proper persons to view and lay out the same according to law.
And they will pray, &c.
|C?* There must be no intermediate points made in the
road prayed for.
BETUBK
To the honorable the Judges unthin named.
We, the persons appointed by the within order of court, to
view and lay out the road therein mentioned, do report, thik
CONVfiTAKCINC% iSI
in pursuance of the said order^ we have viewed and laid out,
and do return for public for private] use, the following road,
to wit : Beginning, &c. [here describe the courses and dis-
tances in letters, not figures, with references to the improve-
ments through which it passes,] a plot or draft whereof is
hereunto annexed* Witness our hands the first day of July,
one thousand eight hundred and thirty-six.
|C7* At least five of the viewers must view the ground,
and any four of the actual viewers may lay out the road.
•Another.
We, tKe subscribers, do report, that in pursuance of the
within order of court, we have viewed the place where the
road within mentioned is requested, and are of opinion that
tiiere is no occasion to lay out the same. Witness our hands,
&c.
Petition /or review of a Hood*
To the honorable the judges of the Court of Common l^leafc
©f the county of Lancaster, now composing a Court of
Quarter Sessions of the Peace, in and for the said county.
7%6 petition of divers inhabitants of the township of CocaHco,
in the said county, humbly sheweth :
*
That a road hath been lately laid out, by order of the court,
from — , &c. which road, if confirmed by the court, will
be very injurious to your petitioners, and burthensome to the
inhabitants of the township through which the same runs.
Your petitioners therefore pray your honors to appoint proper
persons to review the said rqad and parts adjacent, and make
report to the court according to law. And they will ptay, &c.
REPORT.
To the honorable the Judges within named*
We, the persons appointed to review the road within men-
tioned, and parts adjacent, do report: That in pursuance of
the said order we did review the same, and have laid out for
public use, the following road, to wit: Be^nning, &c, [or,
after ' same,' say ' and in our opinion there is no occaaioo for
6iu^ftroad»'3 Witness our hasdi, &c«
25fl CONTSTAHOINO.
Petition for vacating a Road,
To the honorable, fyc. The petition of, Spc. Humbly sheweth r
That a road has been long since laid oiit from, &c.— — ^
which road, [or part of which road, beginning, &c.] jour pe-
titioners humbly conceive is now become useless, inconveni-
ent and burthensome to the inhabitants thereabouts. — Your
petitioners therefore humbly pray your honors, that the said
road may be vacated, agreeably to th€ act of general assem-
bly, in such case made and provided. And they win ever*
pray, &c.
REPORT.
To the honorable, fye*
We, the subscribers, appointed by the within order of
court, to view the road therein mentioned,^ do report. That
in pursuance of said order, we have viewed the said road^
and that the same is, in our opinion^ useless, inconvenient,,
and burthensome, [or, that, in our opinion, there is no cause
for vacating the same.] Witness our hands this first day of
June, one thousand eight hundred and thirty- six.
Petition for valuing Lands,
To tihe honorable, ^c. The petition of, fyc* Humbly sheweth :
That a public road or highway was lately laid out and
opened, by order of this court, from ; which road is
laid out and opened through the land of your petitioners.
Your petitioners, therefore, humbly pray your honors to ap-
point proper persons to view and adjudge the value of so much
of their lands, respectively, as is or may be taken up for the
use of the said road. And they will pray, &c.
REPORT.
To the honorable, ^c.
We, the subscribers, appointed by the within order of court,
to view and adjudge the value of so much of the lands of C. D.
as are taken up by me road therein mentioned, do report. That
in pursuance of the said order, we have viewed the lands
taken up by the road therein mentioned, and do valoo ftnd
|}ONTSTANCXXCU S5S
adjudge the loss thereby occasioned to the within named
C D. at the sum of dollars ; and the loss thereby
occasioned to E. F. at the sum of dollars, respectively.
Witness our hands the first day of Aprils one thousand eight
hundred and thirty-six.
Another,
We, the subscribers^ within appointed to view and assess
the damages sustained by the petitioner, C. D. by reason of
the premises in the within order mentioned, do report, that,
having been previously sworn and affirmed, according to law^
we did view the lot through which the within mentioned road
passes, and that upon due consideration, as well of the ad-
vantages as disadvantages arising to the petitioner, we are
of opinion, that he has received damage to the amount of —
dollars, and we do accordingly assess tiiie same. Witness
«ur hands, &c.
A general release from one to one^
Know all men by these presents, That I, Amos Vansant,
of Vincent township, Chester county, have remised, released
and forever discharged, and by these presents do, for me, my
heirs, executors and administrators, remise, release and for-*
«ver discharge Enos Philips, of Schuylkill township, county
Aforesaid, his heirs, execirtors and administrators, of and for
all, and all manner of actions, causes of action, suits, debts,
dues, sums of money, accounts, reckonings, bonds, bills,
specialties, covenants, contracts, controversies, agreements,
promises, variances, damages, Judgments, extents, executions,
claims and demands whatsoever, in law and equity, which
against the said Enos Philips, I ever had, now have, or which I,
my heirs, executors or administrators, hereafter can, shall, or
may have, for, upon, or by reason of any matter, cause or
thing whatsoever, from the beginning of the world to the day
of uie date of these presents. In witness whereof I have
hereunto set my hand and seal, the first day of July, one
tliousand eight hundred and thirty-six.
Amos Yansamt.
Sealed aodddivered in pvesenycd of
254 CONTEYAKCIKG.
Release of a Legacy^.
Know all men bj these presents, That whereas Hiram
Bojer, of Whitemarsh township, Montgomery county, by hi&
last will and testament in writing, bearing date the first day
of January, one thousand eight hundred and thirty-six, did,
among other legacies therein contained, give and bequeath
unto me, Willis Pirn, of thft town^ip of Upper Merion, and
county aforesaid, the sum or legacy of three thousand dollars,
and of his said will made and constituted Jesse Trewig sole
executor, as in and by the said will may appear. Now know
ye, that I, the said Willis Pim, do hereby confess and ac-
knowledge that I have had and received of and from the said
Jesse Trewig, the legacy or sum of three thousand dollars, so
as aforesaid given and bequeathed unto me, by the said Hi-
ram Boyer. And therefore I do by these presents acquit,
release and discharge the said Jesse Trewig, of and from all
legacies, dues, duties and demands, whatsoever, which 1, my
executors or administrators, may have, claim, challenge or
demand, of or against the said Jesse Trewig, his executors or
administrators, by virtue of the said last will and testament
of or out of the estate of the said Hiram Boyer, deceased, as
aforesaid.
In witness whereof I have hereunto set my hand and seal»
the first day of June, in the year of our Lord one thousand
«ght hundred and thirty-six*
Willis Pim*
Sealed and delivered in presence of
Release to a Gmtrdian,
Know all men by these presents, That John Marple, son
and heir of Lot Marple, deceased, hath remised, released and
forever quit -claimed, and by these presents doth remise, re-
lease, and forever quit claim, unto Thomas C. James, of
New Britain township, Bucks county, his guardian, all and
all manner of actions, suits, reckonings, accounts, debts*
dues and demands whatsoever, which he, the said John Mar-
ple, ever had, now hath, or which he, his executors or adtiiin^
istrators, at any time hereafter, can or may have, claim or
demand, against the said Thomas C. James, nis executors or
administrators, for touching or concerning the management
and disposition of any of the lands^ tenements or heredita^
OOKVEYANCING. 255
ments of the said John M^irple, situate in Dojlestown town-
«hip, and county aforesaid, or any part thereof, or for or by
reason of any money, rents or other profits by him received,
out of the same, or any payments made thereof, during the
minority of the said John Marple, or by reason of any matter,
cause or thing whatsoever, from the beginning of the world
to the day of the date hereof.
In witness whereof I have hereunto set my hand and seal,
Hiej first day of January, in the year of our Lord one thousand
eight hundred and thirty-six.
John Marple.
Sealed and delivered in presence of
Remarks. -^K release must be by an instrument sealed ; and
Ihe most beneficial release which a man can have, is one of all
tlemands.
Where a person has a cause of action against several,
either for a debt due, or a wrong done, and for which they are
jointly and separately liable, it seems tliat a release to -one is
a release to all.
'jPor Money recHved on a Purchase,
Know all men by these presents. That I, Philip Hathaway,
of Moyamensing township, Philadelphia county, do hereby
acknowledge myself, upon the day of the date hereof, to
have received of Jesse James, of the township and county
aforesaid, the sum of four hundred dollars, of lawful money
of the state of Pennsylvania, being the last payment, and in
full of fifteen hundred dollars, by him paid, as the considera-
tion of the purchase of a certain plantation and tract of land,
situate in Byberry township, and county aforesaid, by me,
the said Philip Hathaway, sold and conveyed to the said
Jesse James. And of the said whole sum of fifteen hundred
dollars, and of every part and parcel thereof, I, the said
Philip Hathaway, do by these presents, for me, my heirs,
executors and administrators, acquit and discharge the said
Jesse James, his heirs, executors and administrators, forever.
Witness my hand this first day of January, in the year of
our Lord one thousand eight hundred and thirty-six.
FntLIP HATftAWAYt
MESfSlTRATIOJr/
Mensuration is the art of measuring, and consists of thred
parts, viz. lineal measure, (or, as it is commonly called,
long or running measure,) superficial or square measure,
and cubic or solid measure ; for the denominations see pages
37, 39 and 46.
OF THE SQUARE.
A square is a plane superficies, having each of its opposite
sides parallel and equal ; and all its angles, are right angles.
A side given, to Jmd the areas or the area given, to find the
length of a side^
Rule.
1. Multiply a side by itself, and the product will be the
superficial content, or area.
2. Extract the square root of the area, and this root will be
the length of a side.
JExamples.
D C
1. What is the area of a square whose
side AB is 37 perches ?
37 X 37= 1369 perches = 8 A. 2 R. 9 P. Ans.
2. Required the side of a square field whose area » 10 A^
2 R. 1 P.
10 A. 2 R. 1 P.=1681 P, ; and ^"1681 =41 per. Ans.
3. How many square yards are in a floor 39 feet square?
Ans. 169.
4. A square plantation contains 255 acres 4 perches — ^I
wish to know the length of one of its sides. Ans. 202 P.
5. How many fields of 25 perches square may be made of
one of 100 perches square ? Ans. 16.
6. How many lots of 25 square perches may be made of a
field 100 perches square? Ans. 400.
7. Required the area of one mile square.
Ans, 640 acres, or 1 section
MXNaURATION* 3ST
S. How mmj sectkms of Iqid in a township fire miles
square? Ans. 25.
OF THE RECTANGULAR PARALLELOGRAM OR
OBLONG.
A rectangular parallelogram, or oblong, is a plane super^*
licies, having each of its opposite sides parallel, and all its
wangles are right angles.
The length nnd breadth given, to Jind the area ; or the area
iind one side given^ to Jind the length of the other aide.
Rule.
1. Multiply the length by the breadth, and the product
will be the area.
2- Divide the area by one of the sides, and the quotient will
be the adjacent side.
Examples*
1. What is the superficial content of an oblong piece of
ground, whose length AB is 60 perches, and breadth BC 40 ?
D IC
e0x40»2400per.=>15 Acres. Ans.
2. Purchased a field of an oblong form, 40 perches in
breadth, containing 25 acres^-^I wish to know 'the length.
25 acres»4000 perches ; and 4000-f-40:sl00. Ans«
8. What is the superficial content of an oblong, whose
length is 32 and breadth 30 perches ? Ans. 6 acres.
4. Required the breadth of a field whose length is 95
perches, and contains 19 acres. Ans. 32 perches^
5. What is the length of a board that contains 24 square
feet, and is li feet broad ? Ans. 16 feet.
6. A board contains 30 square feet, and is 1? feet broad ;
if 5 feet in length be sawn off at one end, what will be the
leiig;th of the remaining part ? Ans. 19 feet
7. Required the area of a field whose length is 35 perches^
and bteadth 20 perches. Ans. I A. 1 R. 20 P.
2SS HfiKSXTRATlOK.
OF TliE RIGHT ANGLED TRIANGLE,
A right angled triangle is a plane superficies, having one
right angle : the side opposite the rigtit angle is called the
hypothenuse, the side on which the triangle stands is called
the base, and the other side the perpendicular. The base
and perpendicular are sometimes called the legs.
The legs given, to find the area and hypothenuse ; or the area
and one leg given, to find the other leg and hypothenuse*
Rule.
1. Multiply the base and perpendicular together, and half
the product will be the area.
2. Divide the double area by the length of one leg, and the
quotient will be the length of the other leg.
The hypothenuse may be found by the note at page 187.
Examples.
1. The base AB of a right angled triangle is 60, and per-
pendicular BC 32 — Required the area, and hypothenuse AC*
C
60x32=1920;
and 1920-^2= 960= Area.
602 x322= 3600+1024=
4624.
and v/4624=68=hypoth-
enuse.
2. The area* of a triangular field is 600 perches, and the
base 50 — I wish to know the length of the perpendicular and
hypothenuse.
600x2=1200=double area,
and 1200-T-50=24«= perpendicular.
502 +242 ^2500+576=3076,
and v/3076=55.461 Answer.
B. What is the area and hypothenuse of a triangle whose
base is 64 and perpendicular 47 perches ?
Ans. Area, 9 A. 1 R. 24 P. Hypothenuse, 54.845«
4. Required the area and base of a triangle whose perpen*
dicular is 71 perches, and hypothenuse 2521 perches.
Ans. Area 559 A. 20 P. Base 2520 percheti4
MBvsuRATioir. il59
Note. — ^When the hypoihenuse and one leg are given, if
you multiply their sum by their difference, the product will
be the square of the other leg.
6. What is the base of a triangle whosi? hypothenuse is 45
and perpendicular 27 ?
45+27=72 sum
45—27=18 difference
1296 product ; and ^/1296 =- 36 Answer.
6. The hypothenuse of a triangle is 261, and the base 189;
required the perpendicular. Ans. 180.
Note. — When the area and hypothenuse are given, raise
the hypothenuse to the 4th power ; deduct 16 times the square
of the area from this power, and extract the square root of
the remainder, one half this root deducted from half the
square of the hypothenuse, will give the square of the shorter
leg, and if added thereto will give the square of the longer
leg.
7. The area of a triangle is 84, and the hypothenuse 25—
Required the other sides.
25* = 390625
84« Xl6 = 112896
277729, and ^/277729«=527, and 5274-2^202^
25^=625, and 625-^2-3124
312i— 263i= 49, and v'49= 7 shorter leg7 .
812i+263i=576, and x/576=24 longer leg 5 ^''^'
8. The area of a triangle is 5280, and the hypothenuse 146;
required the other sides. Ans. 110 and 96«
To find the area of any triangle, having the three sides
given.
Rule.
Add together the three sides and take half the sum, deduct
each of the several sides from that half sum, then multiply
that half sum and the three differences continually together,
imd extract the square root of the product, which will be the
area of the required triangle.
960 MENSURATIOV*
1. The sides of a triauigle are as follow, viz. AB 90, BC 80
and AC 70 — Required the area.
C
/
rso 1 30-)
-< 80 40 I differences.
170 I 50 J
2)240
120 half sum.
120 X 30 X 40 X 50=7200000
and v/7200000-= 268.328 Ans. a
2. The sides of a triangle are 189, 170. and 89— What is
tlie area ? ' Ans. 7560.
3. What is the area of a triangle whose sides are 48, 60
and 72 perches ? Ans. 8 A. 3 R. 28 P. +
4. The sides of a triangular garden are 8, 10 and 13
perches— Required the area. Ans. 39.68 perches +
OF THE TRAPEZIUM.
A trapezium is a plane superficies, bounded by four straight
lines, no two of them being parallel to each other. A line
connecting the opposite angles is called a diagonal.
The four sides and diagonal given, to find the area.
Rule.
Divide the trapezium into two triangles, by drawing a di-
agonal across it, then find the area of each triangle separately,
as before taught, and the sum of these will be the area of tha
trapezium.
Examples.
1. Required the area of a four sided field, whose south side
is 100 perches, east side 90 perches, north side 80 perches,
and west side 70 perches ; the diagonal from north-east to
south-west being 120 perches.
ItfiKSVlUTIOV.
^m
r 80 I 551 jjr
1 70 I 65 J ^'^^''-
J)
2)270
135 half sum.
135x55x15x65= o
7239375 ^
& ^7239375=2690.619]
area of ADC.
Sidesf^ I 65 j J;^^;-
ClOOJ55j^^^^-*
2)310
80
^/
100
155 half sura.
155x35x65x55= 19394375
and ^^19^94375=4403.904 area of ABC.
2690.619 area of ADC.
CO
4,0)709,4.523 area of ABCD.
4)177-14.523
44 A. 1 R. 14.523 P. Answer.
^ote. — Irregular figures are such as have more than four
sides, which, as well as their angles, are unequal. The su-
perficial content of all such figures may be found by dividing
them into trapeziums and triangles, by lines drawn from one
angle to another, calculating these separately, as before
taught, and adding all the areas together.
OF REGULAR POLYGONS.
A regular polygon is a plane figure, having all its side*
aad angles equal.
S62
MBMSURATION*
To find the superficial contents ^ having a aide and perpen^
dicutar let fall from the centre to the middle of one of it$
sides given.
Rule 1.
Multiply the sum of the sides by half the perpendicular;
or multiply the whole perpendicular by half the sum of the
sides, the product will be the area or superficial content.
Examples,
1. Required the area of an octagon, whose side is 4.9703,
and perpendicular 6.
4.9705x8=39.764, and 39.764-t-2= 19.882= half sum of
thfe sides.
19.882x6=119.292 Answer.
2. Required the superficial content of a hexagon, whose
side is 20 and perpendicular 17.320508. Ans. 103.92304a
A TABLE
For more readily finding the area and perpendicular of a
regular Polygon,
No. of
sides.
3
4
5
6
7
8
9
10
11
12
Names.
Trigon,
Tetragon,
Pentagon,
Hexagon,
Heptagon,
Octagon,
Nonagon,
Decagon,
Undecagon,
Duodecagon,
Areas.
The side 1.
.433013
1.000000
1.720477
2.598076
3.633912
4.828427
6.181824
7.694209
9.365640
11.196152
Perpendiculars.
The side 1.
.2886751
II III
.6881910
.8660254
1.0382617
1.2071068
1.3737387
1.5388418
1.7028437
1.8660254
Rule 2»
Multiply the tabular area by the square of the side, and
the product will be the area of the polygon ; or multiply the
tabular perpendicular by the side of the polygon, the product
trill be the perpendicular of the polygon : wn proceed bj
Rule h
MENSURATION. Sg3
Examples,
1. Required the area of a heptagon, whose side is 400.
400^ =160000, and 3.633912x160000=581425.92 Ans,
% Required the area of a pentagon whose side is 12.
•688191 X 12 = 8.258292 = perpendicular of the polygon*
12x5=60, and 60 -i-2 = half sum of the sides.
8.258292 X 30 = 247.74876 Answer.
3. What is the area of a hexagon whose side is 10 ?
Ans. 259.8076.
OF THE CIRCLE.
A circle i& a plane superficies, bounded by one line called
the circumference, which is every where equidistant from a
point within it, which is called the centre.
T'he circumference given, to find the diameter ; or the di-
ameter given, to find the circumference.
Rule.
1* As 7 is to the diameter, so is 22 to the circumference.
Or, As 113 is to the diameter, so is 355 to the circum-
ference.
Or, As 1 is to the diameter, so is 3.1416 to the circum-
ference.
2. As 22 is to the circumference, so is 7 to the diameter.
Or, As 355 is to the circumference, so is 113 to the di-
ameter.
Or, As 3.1416 is to the circumference, so is 1 to the di-
ameter.
Examples,
1. If the diameter of a circle be 31.8309,
what is the circumference ?
As 1 : 31.8309 :: 3.1416 : 100 Ans.
j 2. If the circumference of a circle be 29, what is the di-
, ameter ?
As 8.1416 : 39 :; 1 : 9.23 Answer.
364 M£NSURATIOir«
3. If the diameter of the earth be 7958 miles, (as it is very
nearly,) what is the circumference, supposing it to be exactly
round P Ans. 25000.8528 miles*
The diameter or circumference of a circle given, to find the
area ; or the area given, to find the diameter or circum-
ference.
Rule.
1. Multiply half the circumference by half the diameter*
and the product will be the area.
Or multiply the square of the diameter by .7854, and the
product will be the area.
Or multiply the square of the circumference by .07958> and
the product will be the area.
2. Divide the area by .7854, and the square root of tho
quotient will be the diameter.
Or, divide the area by .07958, and the square root of tKe
quotient will be the circumference.
JExampies,
1. If the diameter of a circle be 12, what is the area ?
12xl2===144, and 144 X. 7854= 113.0976 Answer.
2. If the circumference of a circle be 12, what is the area ?
12x12=144, and 144 X. 07958 =11. 45952 Answer.
3. If I drive a stake in my meadow, and fasten my horse
to it by a rope of such a length that he may graze exactly
half an acre, how long must the rope be P
Ans* 27.75 yards +
To find the area of an oval or ellipsis*
Rule.
Multiply the product of the two diameters by .7854, and
this last product will be the area.
Examples*
1. Required the area of an elliptical fish pond whose di-
ameters are 12 and 10.6 yards.
12X10.6=127.2, and 127.2 X.7854-> 100 sq. yds. Ana.
2. What is the area of an ellipsis whose diameters are IS
«nd9? Ana. 84.8232.
xsxsvRirFiov. its.
To find ih$ tide of a square piece cf tvatbetf thai nm/ he
sawn or hewn from a round piece.
Rule.
Extract the square root of half the square of the diameter.
Or, multiply the girth or circumference by 2, and divide
the product by 9, the quotient will be the side of the square,
near enough for common purposes.
Examples,
1. The girth of a tree is 5 ft. 7i in., required the side of a
i^quare post that may be hewn from it.
5ft7Hn.x2=llft. 3in.
and 11 ft. 3 in. -s- 9 =^ 1 ft. 3 in. Answer.
2. What must be the girth of a piece of round timber that
will hew 2 feet square ? Ans. 9 feet.
3. I wish to cut a tree that will hew 15 inches square—
What must be its circumference ? Ans. 5 ft. Ts in.
To measure the length of standing timber.
Provide a slight pole, about your height ; measure off on
your pole a length exactly equal to the height of your eye,
and at this place cut a notch. Fix your pole opposite that
*ide of the tree whicTi affords the best view of the summit of
its main stem, that is, up to that part which can be squared,
or made into merchantable timber. Proceed to such a dis-
tance from the tr^e as to you m^ay seem equal to its height;
set the pole in the ground perpendicularly, up to the notch,
and the station fixed upon must be level with the surface of
the ^ound at tl^^^ foot of the tree ; lie down on your back,
with»the soles of your feet against the pole and your head di-
rectly from the tree ; look over the top of the pole, and see
where the sight strikes the tree ; the pole may be removed
nearer to or fuither from the tree, until 4;he sight taken strikes
that part of the tree up to which you calculate timber.
Measure the distance from the tree to the foot of the pole,
that added to the height of the p<^e from the notch, is the
length of the timber. An allowance mujst, however, be made
for the stump.
Example*
1. The distance from the foot of the tree to the pole is '31
feet; the height of the pole or eye 5 feet 6 inches, and an al-
S
XXNSUlUlTIOjr.
Ipwance of 2 feet 6 inches is to be made for 1ke height of the
stump and waste- in cuttings— Required the length of mw:*
chantable timber.
C
\^
1
I
A D
ft. in.
31 = AD.
5 6 = DE = DB.
36 6 = AB = AC.
2 6 = stump and wastage.
34 = length of the timber.
% From the foot of a trea to the pole measures 47 fe^i
height of the pole 5 feet, allowance for stump 2 feet — ^Re
quired the length of the stick. Ans. 50 feet.
BOARD MEASURE.
Case I.
To find the superficial contents of boards.
Rule.
Multiply the length in feet by the 'width in inches, and
diride the product by 12, the quotient will be the superficial
content.
HSKSURATIOK* 36T
jffbte:^^lt frequently h^pens in measuring boards, that
they are found to be wider at one end than the other ; in
which case take the width in the middle, if it be a straight
edged board ; or which results the same thing, add the width
of the two ends together, and take half their sum for the mean
breadth; but if it be not a straight edged board, and wider in
some places than others, take the width in several places, and
divide their sum by the number of breadths for the mean
breadth ; then proceed as before.
Examples,
1. What number of feet is there in a board 17 feet long
and 11 inches broad ?
17x11=187, and 187-5-12=15 ft. 7 in. Answer.
2. Required the number of feet in a board 13 feet long, 16
inches wide at one end and 20 inches at the other.
16+20=36, and 36—2=18 mean breadth.
13x18=234, and 234—12=19 ft. 6 in. Ans.
3. An irregular board of 14 feet long measures at the ends
15 and 9 inches, the intermediate widths are 16, 13, 8, 6 and
10 inches — ^Required the number of feti in said board.
16+13+8+6+10+15+9=77,
and 77-5-7=11 mean breadth.
14x11=154, and 154-t- 12=12 ft. 10 in. Ans.
Case II.
To find the superficial contents of any square piece of timber,
Mcantling, plank, fyc. having the length, breadth and thick-
ness given*
Rule.
Multiply the length in feet by the breadth in inches, and
divide by 12 ; the quotient will be the content in feet, at one
inch thick, which multiply by the thickness in inches, the
product will be the whole content.
If the piece of scantling, plank, &c. be wider at one end
than the other, or be irregular, find the mean breadth as
taught in Case I. .
JExamples,
. 1. Required the number of feet in a piece of timber 20 feet
6 inches long, 7 inches wide, and 5 incnes thick.
20 ft. 6 in. x7= 143^, and 143^-5-12=11 ft. lU in.
Ilft.llix5=:59ft.9^in, Answer,
368 XBKSURATIOff*
% A piece of Bcaniling measni^s 19 feet 4 inches lo!^, 10
inches wide and 7 inches thick — How many feet does it con-
tain, board measure P Ans. 112 ft 4 in.
3. What is the content in board measure of 7 planks,
measuring each 21 ft. 9 in. long, 21 inches wide and 2i
inches thick P Ans. 666 ft 1^ in.
4. How many feet are there in a rafter, which measures Iff
feet long, 4s inches wide at one end, and 83 at the other, and
3 inches thick P Ans. 16 ft
5. Required the number of feet in 4 pieces of scantlings
one measuring 9 ft 5 in. long, and 7 inches by 5 ; another lO
feet 6 inches long, 6 by 4; a third 11 feet 2 inches long, 6i
by 5i, and a fourth 10 feet 3 inches long, 6 by 4.
Ans. 102 ft 2 in. 9J"
Case III.
To find the superficial contents of a round piece of timber,
when hewn or sawn square^
Rule.
Multiply half the square of the diameter in inches by the
length in feet : divide the product by 12, and the quotient
will be the superficial content.
Uxamples*
1. Required the superficial content of a round piece of
timber, whose length is 25 feet, and its mean diameter 20
inches.
20x20=400,
and 400-5-2= 200= half square of the diameter.
Then 200x25=5000, and 5000-^12= 416 ft 4in. Ana.
2. How many feet of square edged boards, one inch thick,
including the saw gap, can be made from a log 16 feet long
and 20 inches in diani^ter P ' Ans. 266 ft. 8 in.
SOLID BODIES.
Solid bodies are Such as consist of length, bread& and thick-
ness, as stone, timber, globes, &c.
iVb/e.— -In the common use of geometry, the term solid does
not only apply to absolute density* as is understood regarding
xxiraw&^TiOik
tlic timlier in a beim, but a chest or box, ihottgk emfty, li
tonsidcred a solid. If the object contains length, breadth aiid
ttickness, it is sufficient to constitute a solid.
OF A CUBE.
A cube is a square solid, comprehended under six geometri-
cal squares, bding in the form of a die.
To find the solidity.
Rule.
Multiply the side of the cube by itself, and that product
again by the side ; the last product will be the solidity.
Example*
1* A cellar is to be dug whose length, breadth and depth
are each 11 feet 6 inches — How many solid feet does it con-
^in, and what will it cost digging at 12 J cents per solid
jard ?
11 ft. 6 in. = 11.5 feet,
and 11.5x11.5x11.5 =1520.875 feet. Answer.
sq.yd. sq.ft. cts. S
As 1 : 1520.875 :: 12i : 7.041+ Ans,
OF A PABALLELOPIPEDON.
A parallelopipedon is a solid having six rectangular sides,
every opposite pair of which are equal and parallel.
To find the solidity*
Rule.
Multiply the length by the breadth^ and that product by
ihe depth*
JSxamples.
1. Required the nninber of cords in a pile of wood 100 ft*
long, 8 feet high, and 4 feet wide.
100x4x8 » 9200 solid feet,
liul SaoO-i-lSS «• as cords* Aaftw«r»
VtO MEXSVRATIOir.
2. I demand the number of cords in a pile' of wood GO feet
long, 6 feet high and 4 feet wide. Ans. 11 J cords.
3. In a stack' of bark measuring 24 feet 6^ inches long, 19
feet 6 inches wide, and 12 feet high, how many cords ?
Ans. 44 cords, 101 feet.
4. Required the solid content of a bale measuring 6 feet 6^
inches long, 5 feet 6 inches wide, and 4 feet deep.
6.5x5.5x4= 143 feet,
and 143-T-40 = 3 tons, 13 feet. Ans.
5. I demand the solid content of a load of bark measuring
18 feet 6 inches long, 3 feet 4 inches wide, and 2 feet lOj
inches deep. Ans. 1 cord, 1.475 feet.
OF A CYLINDER.
A cylinder is a round solid, having its base circular, equal
and parallel, in form of a roller used for rolling land.
To find the solidity.
Rule.
Multiply the area of the base by the length, and the pro-
duct is the solid content.
Bxamples,
1. If a piece of timber be 6 feet in circumference, and 25-
feet long, how many feet of timber are contained in it, sup-
posing it to be perfectly cylindrical ?
6x6x.07958 = 2.86488,
and 2.86488x25 = 71.622 feet. Answer.
2* I have a rolling stone, 14 inches in diameter, and 6 feet
long, required the solidity .^ Ans^ 6.4141 feet
t)F A CONE.
A cone is a solid, having a circular base, and growing
smaller and smaller, till it ends in a point, and may be
nearly represented by a sugar loaf.
To find the solidity.
Rule.
^ Multipljr the area of the base by a third part of the perpen-^-
diculap height, and the product will be the solid content*
ifole.—^To^nd the perpendictilar height, add the square of
the slant height to the square of half the diameter of the base,
the square root of this sum is the perpendicular heights
Examples,
1. What is the solidity of a cone, whose slant height is 10
feet, and diameter 16?
10x10 = 100 square of the slant height
8x 8 = 64 square of half the diameter.
36 square of the perpendicular height,
and \/36 = 6 perpendicular height.
18 Xl6 X .7854 = 201 .0624 area of the base,
2 = I the perpendicular height.
402.1248 An^Lwer.
!2. A heap of grain on a barn floor, (in a conical form,)
measures 10 feet in diameter, and the perpendicular height is
Z feet — I wish to know how many bushels it contains.
Ans. 63 bu. 3 qts.+
8. How many bushels of oats in a heap that measures 20
feet in diameter, and the perpendicular height 6 feet?
Ans. 504 bu. 3 pecks, 4 qts.+
OF A GLOBE OR SPHERE.
A globe or sphere is a round, solid body, having every part
t)f its surface equidistant from a certain point within it, call-
ed its centre.
To find the solidity »
Rule.
Multiply the cube of the diameter by -5236, and the pro-
"duct will be the solidity required.
Examples,
1. The diameter of the earth is about 7964 miles, required
its solidity in cubic miles. '
7964x7964x7964 = 505119057344
and 505119057344 X. 5236 =»264480S38425.3184 Ans.
«. The circumference af a globe is 31.416— What is the'
solidity? Ans. 523-6.
4^{p^$ tonnage % cmjpmitrs^ meoHsre.
Rule.
Multiply the length, breadth at the main beam, and depth
of the hold together, and divide the product bj 95, the quo-
tient will be the required tonnage for a single decked v«88el :
for double decked vessels, take half the breadth of the main
beam for the depth of the hold^ and work as for a single deck-
ed vessel.
Examples,
1. Required the tonnage of a single decked vessel, mea-
suring as follows, viz. length 72 feet, breadth 24 feet, and
depth of the hold 10 feet.
72x24x10= 17280.
and 17280-5-95=181.85 tons. Answer.
2' I demand the tonnage of a double decked vessel, whose
length is 100 feet and breadth 32 feet.
Ans. 539 tons^ nearly.
By government measure.
9utE.
Multiply the length, less three -fifths of the breadth, by the
breadth, and this product again by the depth of the hold ; di-
vide by 95, and the quotient will be the tonnage required.
If the vessel be double decked, take half the breadth for the
depth of the hold> and work as for a single decked vessel.
Examples.
1. Required the government tonnage of a single decked
vessel, whose length is 80 feet, breadth 25 feet, and depth lO
feet.
I of 25 feet » 1 5 feet, and 80—15 ^ 65 feet.
Then 65 x25 X 10 = 16250,
and 16250-^95 =^ 171 tons. Answer.
2. I demand the government tonnage of a double decked
Teasel, whose length is 90 feet, and breadth 30 feet.
Ans. 341 tons.
Note l.^*-For Aips of war, divide the continual product of
^ lengthy breadtli and depth in feet by 100» and the qaotitnt
will be the tonnage required*
JBxample*
Required fhe tonnage of a ship of war, length 100 feet,
breadth 32 feet, and depth 16 feet. Ans. 512 tons.
Note 2. — To find the length of the mast of a ship, add
ihe breadth of the beam to two-thirds the length of the keel,
and the sum will be the length of the main mast.
Example.
1. What is the length of the main mast for a ship of 105
feet keel, and the breadth of the beam 38 feet ? Ans. 108 ft.
STONE MEASURE.
Stone and stonework, or mason's work, is measured by the
standard* perch of 24.75 cubical or solid feet, which is 16i
feet long, li feet wide, and 1 foot high.
Rule.
1. Divide the continued product of the length, width and
height in feet by 24.75, and the quotient will be the number
of perches.
Or, divide the continued product of the length and height,
in feet, and width in inches, by 297, and the quotient will be
the number of perches required.
If the wall be no more than the standard thickness, multi-
ply only the length and height together, and divide the pro-
duct by 16.5.
2. Place the length and height of the wall in feet, and the
width in inches, for dividends, and the numbers 3, 9 and 11,
fqr divisors ; .divide each of the dividends by one of the di-
visors, and the continued product of the quotients will be
the number of perches required. It makes no difference in
the result which divisor and dividend be used together; the
work will, however, be abridged, by using such together as
will leave no remain,der, (if there be any such.)
Uxamples,
1. Required the number of perches in a pile of stone 27 ft.
long, 9 feet high, and 55 inches wide.
3
9
11
27 191
9 I 1 [-quotients.
55 I 5 J 9xlx5s=45 perches, Ans.
274
ItKNStiRXTtOir.
3
94.5
9
22
11
21
3
64
9
24
11
20
2. Required the number of perches in a wall 94.5 ft. long,
22 feet high and 21 inches wide.
10.5= 94.5- 9
2 =22 -r-11
7 =21 -7- 3
10.5x2x7=147 perches. Answer.
3. What quantity of stone is there in a wall 64 feet long,
34 feet high and 20 inches wide ?
7.11 =64-r- 9
8 =24-7- 8
1.818=20-7-11
7.11x8x1.818=103.4 perches. Answer.
. Note 1. — In mason's work, the dimensions of a building
are taken from corner to corner, that is, the girth of a building
is reckoned the length of the wall. The dimensions of chim*
nies are taken separately, the girth and half girth of which is
reckoned the length of the wall.
Note 2. — When the wall is less than li feet in width, no
deduction is to be made, but reckoned at the standard thick*
ness ; nor is any deduction to be made for doors, windows and
corners, except in reckoning the quantity of stone actually
made use of, when all doors, windows, &c. are deducted.
4. A certain building measures as follows, viz: side wall*
each 90 feet 6 inches, ends each 74 feet 3 inches ; thickness
of each 20 inches ; a partition wall 70 feet 11 inches, and I
foot thick, and all 18 ft. 9 in. high ; in the outside walls are
four doors, 7 ft. 3 in. by 3 ft. 3 in. each, and twelve windows
5 ft. 4 in. by 3 ft. each, and in the partition wall are 2 doors,
6 feet 6 in. by 3 feet 2 in. each — Required the number of
perches of mason's work, also the number of perches of
stone.
A«o..,« S Mason's work, 496.622 perches.
Answer. \ g^^^^^ ^^^^^ I' ^^^
To measure stone in a well.
Add the thickness of the wall to what it measures in the
clear ; then say, As 7 is to this sum, so is 22 to the circum-
ference or length of the wall.
■ 'ini "••
ji«Nti;RATioif. 275
Examples,
1. Required the number of perches of stone in a well
whose diameter in the clear is 3 feet 6 inches, thickness of
the wall 18 inches, and depth 44 feet 11 inches.
Ans. 42|^ perches-
2. A certain well measures 4 feet 9 inches in the clear, the
wall is 15 inches thick and 48 feet deep — Required the num-
ber of perches of stone. Ans. 45.7 perches +
3. Required the number of perches of stone in a well 30
feet deep, diameter in the clear 2 feet 4 inches, and thick-
'ness of the wall 1 foot 2 incjies. Ans. 15.555 perches +
PAVING AND PLASTERING.
Paving and plastering are measured by the square yard*
Rule.
Reduce the area of the pavement to square inches, and di-
vide this by the product of the length and breadth of the
brick or stone.
Or, divide by the length of the brick, and that quotient by
the breadth, for the number of bricks.
Or, multiply the length of the pavement by the breadth,
and divide by 9, for the area in square yards.
Examples.
1. A certain yard 161 feet square, is to be paved with
brick 9 inches long and Ah, broad ; required the number of
bricks, the number of square yards, and price of paving at 8
cents a square yard.
161 xl6j=272|, and 272|-^9=30| sq. yards,
30i square yards = 89204 square inches.
9x4s=40i square inches = area of a brick.
39204-r-40i=968=number of brick.
30i X. 08 =82.42 = price of paving.
2. What will the plastering of a room come to at 9 eents a
square yard, and measuring as follows, viz. two sides 13.25
feet by 8.75 feet each, and two ends 10.5 by ^75 feet each,
with a deduction for a door that is 6 feet long by 3.25 feet
wide, and 3 windows 3.25 by 4 feet each. Ans. £3.57^.
t27S llEKSURATIOX*
3. Suppose a certain payement contains 3240 stones, 10
inches long and 8 inches wide, I require the number of sqnart
yards. Ans. 200 sq. yards.
SHINGLE OR ROOF MEASURE.
Tb compute the number of shingles for a Roof
Rule.
1. Divide the breadth of the space to be roofed, in inches,
by the average width of the shingles, and the quotient will be
the number of shingles in a course.
2. Divide the length of the space to be roofed, in inches,
by the number of inches the shingles are to be laid to the
weather ; this quotient will be the number of courses-
3. Multiply the number of shingles in a course by the num-
ber of courses, and the product will be the number of shin-
gles required.
Examples,
1. How many shingles will be required for a roof 25 feet
square, the courses to be laid 7i inches to the weather, and
the shingles to average 6 inches in width ?
25 feet = 300 inches.
800 -r 6=50 = number of shingles in a course.
300 -7-73 =40 = nnmber of courses;
and 50x40=2000 Answer.
2. Required the number of shingles it will take to make a
roof 24 feet long and 20 feet broad, the shingles to be laid 8
inches to the weather, and to average 7$ inches in width.
Ans. 1152.
3. How many shingles will be required to roof a house 40
feet in length and 36 in breadth, the average width of the
shingles 4$ inches, and to be laid 10 inches to the weather ?
Ans. 4608.
To find the side of a square piece of timber^ that may be heton
or sawed from a roundpiece.
Rule,
Extract tiie square root of half the square of the diameter.
Or, multiply the girth by 9 and divide by 40, for the aide of
the square. Or, multiply the girth by 2 and divide by 9, the
quotient will^be the side of the square, near enough for conk'*
mon purposes.
MBCHANICS* S77
Examples.
1. The girth of a tree is 8 feet 9 inches— I wish to know
the side of a square piece of timber that may be hewn from it.
8 ft. 9 in. x9 =78 ft.. 9 in.
and 78 ft. 9 in. -f- 40= 1 ft. 11| in. Answer.
Or, 8 ft. 9 in.x2=17 ft. 6 in.
and 17 ft. 6 in. -7-9=1 ft. 11| in. Answer, nearly.
2. I wish to procure a piece of timbex' that w^ill square 20
inches — What girth will be required ?
20in.x9=180;
and 180 -r- 2=90 in. = 7 ft. 6 in. Answer, nearly.
3. The diameter of a tree is 30 inches — How much will it
square ?
30x30=900;
and 900 -T- 2= 450, ^/450='21.2 in. Answer.
MECHANICS.
OF THE LEVER.
There are three varieties of the lever, whereby the prop,
moving power or weight maybe applied differently to the in-
flexible bar or vectis, so as to effect mechanical operations in
a convenient manner.
Of the Lever of the first order*
A lever of the first order has the power applied at one end,
the weight to be raised at the other, and the prop or fulcrum
ftt some point between them^ as the common handspike or
steelyards ; therefore, the power applied at one end of this
order of levers will be reciprocally proportional to the dis-
tance of the fulcrum or prop from those ends : Or, as thQ
distance from the point oi suspension is from the weight.
Examples*
1. What weight will a person be able to raise who presses
with the force of 120 pounds on the end of an equipoised
handspike 12 feet long, which is to meet with a convenient
]Hrop, just 9 inches above the end of the handspike ?
898 MEOHANIOS.
12 feet = 144 inches, and 144—9=135.
in. in. lbs. lbs.
Then, As 9 : 135 : : 120 : 1800 Ans.
2. A gentleman, in giying directions for making a chaise,
the length of the shafts between the axle-tree and back -band
being settled at 8 feet, a dispute arose whereabout on the
shafts the centre of the bodj should be fixed. The chaise -
maker advised to place it 27 inches before the axle-tree ;
others supposing that 18 inches would be a sufficient incum-
brance for the horse. — Now suppose two passengers to weigh
820 pounds, and the body of the chaise 80 pounds more, what
will the beast in both these cases bear more than his harness ?
A .J 1125 lbs. at 27 inches.
' C 75 lbs. at 18 inches.
3. What weight can I raise by pressing with a frrce of 100
pounds on the end of a handspike, 24 feet long, which has a
prop exactly one foot above the end of the handspike ^
Ans. 2300 pounds.
Of the Lever of the second order.
A lever of the second order is where the prop is fixed at
one end, the power being applied to the other, and the weight
somewhere between them. The force of this order of levers
is in contra proportion to their length.
JSxamples,
1. A handspike 6 feet long being so placed that one end
rests on a pavement 9 inches from a weight of 700 pounds,
what weight applied to the other end will be sufficient to raise
this weight ?
6 ft.— 9 in. = 5 ft. 3 in.
Then, As 5 ft. 3 in. : 9 in. : : 700 lbs. : 100 lbs. Ads,
2. If a handspike 11 feet long, be so placed as to rest on a
prop at one end, the weight to be raised I65 inches from the.
prop, and moved with a force of 200 pounds, I demand the
weight it will raise. Ans. 1400 lbs.
Of the Lever of the third order.
A lever of the third order is where the prop is at one end,
Ae weight at the other, and the moving power or force some*
where between them.
XXOHANIOS. Sra
Example,
A certain water wheel turns a crank which works three
pump rods, fixed exactly 5 feet from the joint or pin bj
which their several levers, each 8 feet in length, are fastened
for the sake of the intended motion at one end, the suckers of
the pump being worked by the other, shews them to be leyers
of the third order. — Now I wish to know what the length of
the stroke of each of the barrels will be, admitting the crank
to play just 8 inches round the centre.
8 X2=16 diameter of the crank.
Then, As 5 ft. : 8 ft. : : 16 in. : 25.6 in. Ans.
OF THE WHEEL AND AXLE.
When the weight is to be raised by a rope, which coils about
the axle as the wheel turns around, and the poiyer applied to
the circumference of the wheel — say, As the diameter of the
axle, is to the diameter of the wheel, so is the power applied
to the wheel, to the weight to be raised.
Uxamples.
1. Suppose the axle of a windlass be 4s inches in diameter,
the diameter of the wheel 3 feet, and 2 pounds applied to the
wheel — I wish to know how many pounds may be raised.
As 4i in. : 8 ft. :: 2 lbs. : 16 lbs. Ans.
2. I wish to make a windlass, in such a manner that H
pounds applied to the wheel shall equal 16^ pounds suspend-
ed from the axle — ^Now supposing the diameter of the wheel
to be 2 ft. 9 in., required the diameter of the axle.
Ans. 3 inches.
3. The diameter of the axle is 7h inches, the weight appli-
ed 40 lbs. and the weight to be raised 320 lbs. — Required
the diameter of the wheel. Ans. 5 feet
4. The diameter of the axle is 5 inches, the diameter of the
wheel 5 feet, and the weight to be raised 240 lbs. — What
weight is sufficient ? Ans. 20 lbs.
OF THE SCREW.
The power of the screw is to the distance between the
threads, as the weight which is to be raised is to the circum-
ference of a circle applied at the end of the lever or hand-
spike, by which the screw is turned.
8PEOIFI0 ORATITT.
ExcanpltSm
1, What weight will a screw of a half inch thread raise,
the lever being 40 inches, and the pressing power or force t»
be 50 pounds ?
40 X 2=80 inches = diameter.
3.1416 X 80 =251.328= circumference.
As ^in. : 251.328 :: 50 lbs. : 25132.8 lbs. Ans,
2. There is a screw whose threads are one inch asunder ;
the lever or handspike by which it is turned is 25 inches
long, and the weight to be raised 2000 pounds — What power
or force must be applied to the end of the lever or hand-
spike, sufficient to turn the screw by which the weight is to
be raised?
25 >< 2 »= 50 = diameter.
and 50 >«i 3.1416 = 157.08 circumference.
in. in. lbs. lbs.
Then, As 157.08 : 1 :: 2000 : 12.732+ Ans.
OF THE SPECIFIC GRAVITIES OF BODIES. '
The specific gravities of bodies are as their weights or den-
sities, bulk for bulk ; tlius we say a body ha^ twice as much
matter when it contains twice as much matter in the same
space.
If a body be immersed in any fluid, it will sink if it be
heavier than its bulk of that fluid ; but if it be lighter it will
swim. Rain water is taken as the standard for immersing
bodies in, in order to determine their specific gravitji one
cubic or solid foot of which weighs about 62i pounds or lOOQ
ounces avoirdupois. Now, if any body heavier than water
be suspended therein, it will lose so much of what it weighed
in air, as the bulk of the water it displaces would weigli ; all
bodies, therefore, that will sink in water, if of equal bulks,
lose equal weights when suspended therein, and unequal
bodies lose in proportion to their bulks.
Specific gravities are found by hydrostatic scales, which
may be constructed in the form of a common balance, except
that a hook should be fixed at the bottom of each scale, from
which a body may be suspended, and immersed in the water,
without wetting ue scale.
VPEOIVIO GRATITY.
!»I
TABLE OF SPECIFIC GRAVITIES.
Ji cubic foot of
ounces.
Platina, rendered malle-
able and hammered, 20170
Gold, pure, 19637
old standard^ 22
carats fine, 18888
new do. 21|f » 1^739
Quicksilver, 13600
AUoj, such as used
with pure gold, 13306
Lead, 11325
Silver, pure 11087
standard 10535
Copper, 8843
Plate brass, 8000
Steel, 7852
Cast brass, 7850
Bar iron, 7645
Block tin, 7321
Cast iron, 7135
Load stone^ 5106
Slate, 3500
Diamond, 3400
Chrystal glass, 3150
White marble, 2707
Black do. 2704
Rock chrystal, 2656
Green glass, 2624
Clear do. 2600
Flint stone, 2582
Pavine do. 2570
Cornelian do. 2568
Common do. 2520
Free do. 2352
^ cubic foot of
Nitre,
lyory or horn,
Brimstone,
Alum,
Clay,
Brick,
Pitch,
Ebony,
Mahogany,
Human blood,
Sea water.
Cow's milk.
Box wood.
Rain water.
Bee's wax.
Red wine,
Linseed oil.
Dry oak.
ounces.
1900
1832
1800
1714
1712
1517
1150
1117
1063
1054
1030
1030
1030
1000
996
993
935
925
Proof spirits or brandy, 925
Olive oil, 913
Spirits of turpentine, 864
Beech wood, 854
Gun powder, 852
Alcohol or pure spirits, 850
Elm and ash, 800
Wheat, ^ 771
Rye and Indian com, 746
White pine, S^
Cedar, 513
Sassafras, 482
Cork, 242
Common air, H
Inflammable air,
The specific gravities of several solid and fluid bodies are
«hown in the preceding table, from whence the magnitude of
any given body may be found by its weighty or the weight
may be found by its magiutade.
T
289 SPECIFIC GRATITT.
RutE.
1. Divide the weight in ounces by the specific gravity, and
the quotient will be the magnitude in cubical feet.
2. Multiply the specific gravity by the magnitude in cubical
feet, and the product will be the weight in ounces.
Examples,
1. What is the weight of eight cubical feet of gunpowder ?
852x8=6816 ounces=426 pounds. Ans.
2. What is the weight of a brick 9 inches long, 4i broad,
and 2k thick? Ans. 5 pounds,
3. How many bushels of wheat in a granary containing 49
cubical feet, each bushel weighing 60 pounds ^
Ans. 39 bu. 1 peck, 3.3 qts.
4. Required the content of a load of white pine boards
whose weight is 3414 pounds.
Ans. 9^ cubical feet, =1152 ft. board measure.
To find the specific gravity of a body having its weight giveru
Rule.
If the body be heavier than water, weigh it both out of the
water and in the water, and the difference of these weight*
will be the weight lost in water : then say —
As the weight lost in water.
Is to the whole weight of the body.
So is the specific gravity of water, or 1000,
To the specific gravity of the body.
Examples.
1. A piece of plate brass weighs 8 pounds in air and 7
pounds in water — ^Required its specific gravity.
8 — ^7=1= weight lost in water.
Then, As 1 lb. : 8 lbs. : : 1000 oz. : 8000 oz. Answer.
2. A piece of diamond weighs 17 grains in air, and 12 in
water — What is its specific gi'avity ? Ans. 3400.
Note, — If the body be lighter than water, and will not
sink, affix a piece of another body, heavier than water, to it,
so that both may sink; then weigh the heavier and the com-
pound mass separately, both in the air and in the water, sub-
tract their weight in water from their weight in air, and again
take the difference of these remainders. Then say—
aPSOIFIO ORAYITT. 283
As this last remainder,
Is to the weight of the lighter body in air.
So is the specific gravity of water, or 1000,
To the specific gravity of the body.
Examples.
3. A piece of cork weighs two pounds in air, and a piece
of glass that weighs l3 pounds in air and 8 pounds in water,
is affixed to it, and the compound weighs If pounds in water:
I wish to know the specific gravity of the cork.
13^ loss
5
8i remainder.
As 8J : 2 :: 1000 : 240 Answer.
To find the quantity of two ingredients in a given compound.
Rule.
Find the difference of each pair of specific gravities, viz.
the specific gravity of the compound and each ingredient ;
multiply the difference of every two specific gravities by the
third : then say —
As the sum of the products.
Is to each of the other products respectively.
So is the weight of the compound,
To the two weights of the ingredients.
Examples,
1. The weight of the American Eagle, coined prior to July
31, 1834, is 270 grains, and its specific gravity 18888; it is
composed of pure gold and alloy — I wish to know what
weight of each metal it contains, the specific gravity of pure
gold being 19637, and that of the alloy 13306.
19637—18888= 749, and 749x13306 = 9966194
18888—13306=5582, and 5582x19637=109613734
119579928 '
As 119579928 : 9966194 :: 270 : 22J grains of alloy ^ >
119579928 : 109613734 :: 270 : 247i pure gold 5 S
384 sraonrio ouavitt.
2. The weight of the American Eagle, coined after July 31,
1834, is 258 grains, and its specific gravity 18739—1 wish to
know how much pure gold, also how much alloy it contains.
19637—18739= 898, and 898 X! 13306- 11948788
18739—13306=5433, and 543 >< 19637=106687821
118636609
As 118636609 : 11948788 :: 258 : 26 grains of alloys >-
118579928 : 106687821 :: 258:232 pure gold i S
To ascertain whether spirituous liquors be above or below
proof.
Rule-
An 1728 inches, or one cubic foot.
Is to 231, the cubic inches in a gallon,
So is the specific gravity of proof spirits,
To the weight of one gallon of proof spirits.
Note. — ^The better spirits are, the lighter they are ; and
the worse, the heavier.
Examples.
1. How much ought a gallon of proof spirits to weigh ?
As 1728 : 231 :: 925 oz. : 123.6545 oz. Ans.
2. I demand the weight of a gallon of alcohol or pure
spirits.
As 1728 : 231 :: 850 oz. : 113.6284 oz. Ans.
• To find the pressure of water against a sluice or bank.
Rule.
Multiply the depth of the centre of gravity (which is always
equal to half the depth of the water,) in feet, by the area of
the sluice under water: multiply that product again by 62i
pounds avoirdupois, for the pressure required.
Examples.
1. Required the pressure of water against a sluice or bulk
head, 40 feet long, depth of water 6 feet.
40x6=240, area of the side, and 3x240=^700 cubic ft.
Then, 720 X 62i «45000 pound*. Answer.
GUAGINO« 285
2. What is the pressure on the bottom of a vessel 3 feet
wide, 4 feet long and 5 feet deep ? Ans. 3750 pounds.
3. The pressure of atmospheric air on a cubic foot is found
to be 2125 pounds, I wish to know what height of water this
is equal to. v Ans. 34 feet.
4. I demand the pressure of atmospheric air on an ordinary
sized chaise body, whose surface is estimated at 14 square
ket Ans. 29750 pounds.
GUAGIJfG.
Gu AGING is the art of measuring and computing the capa-
city or content, in gallons or bushels, of any vessel, granary,
box, &c.
The dimensions are commonly taken in inches and tenths
of an inch, and the capacity or content computed in bushels
or gallons.
The standard bushel for the measurement of grain, &c.
contains 2150.42 cubic inches, and a gallon for the measure-
ment of liquids contains 231 cubic inches. [See section 2 of
the acts of Assembly, at page 33.] These are divisors for
square or oblong vessels.
Multipliers and divisors for circular vessels are thus found :
If the diameter of a circle be 1, the area is .7854 ; this being
divided by 2150.42, gives .000365, and divided by 231, gives
•0034 nearly ; these are therefore multipliers for circular ves-
sels, the former for bushels and the latter for gallons. Or, if
2150.42 be divided by .7854, the quotient will be 2738, and
231 divided by the same number, quotes 294.12 ; these quo-
tients are divisors for like vessels for bushels ^ind gallons.
Case L
To find the capacity of an oblong or square box, granary, or
cistern, having the length, width and depth given.
Rule.
Multiply the length, width and depth together, and divide
the product by the cubic inches in a bushel or gallon.
286 OUAGING.
Examples.
1. I demand the number of bushels a granary \vill hold 96
inches long, 60 inches wide, and 50 inches deep.
96x60x50=288000;
and 288000-r-2150.42 =133.927 bushels. Ans.
2. Required the number of gallons a cistern will hold, that
is 100 inches long, 75 wide, and 60 inches deep.
Ans. 1948+
S. Required the number of gallons in one cubical foot.
Ans. 7,48+
4. Required the quantity of wheat contained in a cubical
•foot. Ans. 3 pecks, 1.714 qts.
Note, — Heaped measure is about three-sixteenths more
than level measure, the bushel of which isr 2553.62 cubical
inches. [See page 41.]
5. How many bushels of charcoal will a box hold that is
150 inches long, 50 inches wide and 48 inches deep P
Ans. 141 bushels, nearly.
6. How many bushels of lime are contained in a wagon 110
inches long, 42 inches wide and 18 inches deep ?
Ans. 32s bushels +
Case II.
To find the tapftdty- of a cylindrical or circular vessel, having
the same diameter throughout.
RlTLE.
Multiply the square of the diameter by .000365 for bushels^
struck measure ; by .0003076 for heaped measure, and by
•0034 for gallons, which being multiplied by the length or
depth of the vessel, will give the capacity required*
Examples.
!• Required the capacity, in bushels, level measure, of a
vessel in form of a cylinder, the- length or depth 60 inches^
and diameter 67.5 inches.
67.5x67.5x.000365x60=99.781875,
or 100 bushels> nearly. Answer.
2. A ba£ of potatoes is 40 inches long and 20 inches in di-*
•meter— How many bushels does it contain P
Ans. 4«9316 bu<.
GUAGIK6. 287
3. Required the capacity in gallons of a circular cistern, 90
inches in diameter and 120 inches deep ?
Ans. 3304^ gallons.
4. I demand the capacity in gallons of a vessel in form of a
cylinder, diameter 10 inches, and the length or depth 20
inches. Ans. 6.8 gallons*
Case III.
To find the capacity of a circular vessel, wider at one end
than at the other.
Rule.
1. Add } of the square of the difference of the diameters
to the product of the diameters, this sum will be the square
of the mean diameter ; then proceed as in case 2, for the ca-
pacity required.
2. To the product of the diameters add the sum of their
squares ; multiply this sum by one -third the height, and that
{»rod^ct, multiplied by .0034, will give the capacity in gal-
ons, and by .000365, the capacity in bushels.
Examples.
1. Required the capacity in gallons of a vessel, the greater
diameter being 30 inches, that of the lesser 24 inches, and the
length 50 inches.
30x24 =720 >^„«
30— 24=6, and 6^-t-3 12$^'*^
Then, 732 X. 0034x50== 124.44 gallons. Answer.
2. What is the content in gallons of a tub, the diameters
being 45 and 36 inches, and depth 54 inches ; also how many
bushels will it hold ? a 5 302.3892 gallons.
Ans. ^ 32.46237 bushels.
3. What is the content in gallons of a tub whose diameters
are 22 and 18 inches, and depth 12 inches ? Ans. 16.3744.
iVb/e.— To Jind the capacity of a vessel whose bottom is
hollowing or uneven.
Rule.
Take the depth in several places; add the several depths
together^ and divide the sum by thid nukiiber of depths taken^
J
ff88 GUAOINO.
for a mean depth. The capacitj may theji be found either bj
Ca^e 2 or 3, as it is a straight or tapering vessel.
Examples.
1. The diameter of a kettle is 48 inches, the depth in the
middle 26 inches, at the edge 22, and half way between tiie
middle and edge 24 in. — How many gallons does it contain?
26+22+24=72, and 72-^-3=24 mean depth.
Then 48 x48 x .0034 x 24 =188.0064 gallons. Ans.
2. The diameter of a copper kettle is 40 inches, and the
several depths 12, 13, 15 and 16 inches — ^Required the con-
tent in gallons. Ans. 76.16 gallons.
CASE IV.
To find the content of a still or boiler »
Rule.
Add together the square of the greater end, the square of
the less, and four times the square of the section parallel to
and equidistant from the two ends ; this sum being multiplied
by one-sixth of the depth in inches, and again by the proper
multiplier, will give the capacity in gallons or bushels, as re-
quired.
Examples.
1. I wish to know the capacity in gallons of a spherical
boiler^ the diameter of the mouth (inside) being 90 inches, that
of the bottom 50 inches, that of the middle section (equi-dis-
tant from the mouth and bottom) 75 inches, and the depth 36
inches.
90x90= 8100")
50x50= 2500 > 36-5-6=6 one-sixth the depth.
75x75x 4=22500 J
33100 and 33100x6 X. 0034 =675.24 galh.
Answer.
2. The body of a still measures as follows, viz : the diam-
eter of the greatest section (inside) 40 inches, mouth 8 inched,
bottom 27 inchesi middle Beixtion between greatest section and
OUAGING, 289
mouth 3S inefaes, middle section between greatest and bottom
87 inches, depth from the mouth to the greatest section 12
inches, and from that to the bottom 28 inches — I wish to know
the capacity in gallons.
40x40=1600
8x 8= 64
33x33x 4=4356
6020X12-T-6=12040"
40x40=1600
27x27= 729
37x37x 4=5476
> 25130 sum.
7805x28-4-6=13090
and 25130 X. 0034= 85.442 gallons. Answer.
Note, — The content of a corn crib, cistern, &c. whose
sides or,bases are parallel, but unequal, may be found by the
following
Rule.
Find the area of each side or base separately ; add the square
root of the product of these areas to their sum ; multiply this
last sum by one third of the depth or height, and divide by the
number of cubical inches in a bushel or gallon, for the content
required.
Examples.
1. Required the number of bushels (heaped measure) in a
corn crib 20 feet in length at the bottom, and 4 feet wide, 24
feet at the top, and 4 ft. 6 in. wide, the height being 7 feet.
240x48=11520 > Sum, pounds.
288x54=155525 27072 and 11520x15552=179159040
v^l79159040= 13385
Last sum =40457x84^3=1132796
and 1132796-7-2553.62 = 443.6 bu. nearly. Answer.
2. I wish to know the capacity of a cistern of the follow-
ing dimensions, viz: the length of the greater side 80 inches,
and that of the less side 64 inches; the breadth at the top 56
n
290 6UAGIN6.
inches, and that at the bottom 45 inches, the height or depth
being 50 inches. Ans. 810.4 gallons.
CASK GUAGING.
In order to perform this part of guaging, the three following
dimensions of the cask must be accurately taken, viz. the
bung diameter, the head diameter, and the length of the cask,
all taken inside of the cask, or by proper allowance reduced
to inside measure.
Rule.
Multiply the difference between the bung and head diame-
ter, in inches, by .67, by .64 or by .6, according as the cask
is more or less arching ; add the head diameter to this pro-
duct, the sum will be the mean diameter, or that of a cylin-
der ; the continued product of this mean diameter, the length
of the cask in inches, and .0034, will give the capacity in
gallons.
Note. — The multiplier .67, is used for casks of the greatest
curvature, .64 for those of a moderate curvature, and .6
when of the least curvature, or when the staves are nearly
straight.
Examples,
1. I wish to know the capacity in gallons of a cask whose
bung diameter is 40 inches, head diameter 28 inches, and
length 36 inches.
40—28=12, and 12 X. 67=8.04
To which add 28.00 head diameter.
36.04 mean diameter.
36.04 >i 36.04 XZQ^ .0034=159 gallons, nearly. Ans.
2. Required the capacity in gallons of a cask whose bung
diameter is 32 inches, head diameter 25 inches, and length
41 inches, (second form.)
82— 25= 7, and 7 M. 64= 4.48
add 25 head diameter.
29.48 mean diameter.
S9.48 X 29.48 X41 ><l»0034=121 gall8.+ Ans.
OUAGIKO. 291
S. I demand the capacity in gallons of a cask whose bung
diameter is 22 inches, head diameter 18 inches, and the length
25 inches, (third form.)
22—18=4, and 4x.6= 2.4
add 18
20.4 mean diameter.
20.4 X 20.4 X 25 ><!.0034= 35.3736 gallons. Ans.
Note. — Some guage by what is called "Ivin's rule," viz:
take the diagonal of the cask, from the middle of the bung
hole to the end of the opposite stave ; cube the said diagonal,
and divide the cube by 370, the quotient will be the capacity
required. If the bung hole be not exactly in the middle of th&
cask, measure the diagonal each way, add the diagonals to-
gether, and take half their sum for a mean diagonal.
Examples,
1. Required the capacity in gallons of a cask whose diago-
nal is 24 inches.
24:X2iX 24= 13824, and 13824-r-370== 37.36 galls. Ans.
2. I demand the capacity in gallons of a cask whose diago-
nal is 33s inches.
38.5 X 33.5 X 33.5=37595.375,
and 37595.375-7-370=101.6 gallons. Answer.
3. I wish to know the capacity in gallons of a cask whose
diagonal is 36 inches.
S6X36X 36= 46656, and 46656-^370= 126 galls. + Ana.
4. Required the capacity of a cask whose diagonal is 29
inches.
20 X 29 X 29=24389, and 24389-7-370=65.9 galls. Ans.
292
GUAOINO*
A TABLE
Shewing the capacity of any cask whose du
computea to the nearest quart.
In.
gal. qt.
In.
gal. qt.
In.
gal. qt.
In.
gal.qt
12
4 3
181
16 2
24|
241
40
305
79
12*
5
m
17
41
31
80 2
12i
5 1
185
17 3
25
42 1
3U
82 2
12i
5 2
19
18 2
251
43 2
31J
84 2
13
6
I9i
19 1
251-
44 3
315
86 2
lai
6 1
19^
20
255
46 1
32
88 2
13.i
6 2
195
20 3
26
47 2
321
90 3
135
7
20
21 2
261
49
32i
92 3
14
7 2
20i
22 2
26i
50 1
325
95
14i
7 3
20i-
23 1
265
51 3
33
97
141
8 1
201
24 1
27
53 1
331
99 2
141
8 3
21
25
27i
54 3
331
101 2
15
9
214-
26
27}
56 1
335
103 3
loj
9 2
211-
26 3
275
57 3
34
106 1
15il
10
215
27 3
28
59 1
341
108 3
15J
10 5
22
28 3
281
61
341
111
16
11
22i
29 3
281-
62 2
345
113 2
161
11 2
221-
80 3
285
64 1
35
115 3
m
12
225
31 3
29
66
351
118 1
m
12 3
23
33
291
67 3
351
121
17
13 1
23i
34
29|
69 2
355
ISfJ 2
17i
13 3
33J
35
295
71 1
36
126
17i
14 2
235
36 1
30
72 3
361
128 3
17i
15
24
37 1
m
74 3
361
131 2 f
134 1
18
15 3
24J
38 2
30|
76 3
365
OF THE ULLAGE OF CASKS.
The ullage of a cask is what it wants of being full.
Rule.
Divide the dry inches of the bung diameter by the bung di-
ameter; then multiply the corresponding multiplier in the
following table, by the whole capacity, the product will be
the ullage ; deduct the ullage from the whole content, and
the remainder will be the quantity left in the cask.
6UAOIK6.
293
TABLE.
Quot.
Mult.
Quot.
.11
Mult.
.0598
Quot.
.21
Mult.
Quot.
.31
Mult.
.2640
Quot.
.41
Mult.
.01'
.0017
.1527
.3860
.02
.0048
.12
,0680
.22
.1631
.32
.2759
.42
.3986
j03
.0087
.13
.0767
.23
.1738
.33
.2878
.43
.4110
.04
.0134
.14
.0851
.24
.1845
.34
.2998
.44
.4238
.05
.0187
.15
.0941 .25
.1955
.35
.3119
.45
.4364
.06
.0245
.16
.1033 .26
.2066
.36 1.3241
.46
.4491
.07
.0308
.17
.1127
.27
.2178
.37
.3364
.47 .4618
.08
.0375
.18
.1224
.28
.2292
.38
.3487, .48
.4745
.09
.0446
.19
.1336
.29
.2407
.39
.3611
.49
.4873
.1
.05201 .2
.1454
.3
.2523
.4
.3735
.5
.5000
7> find the multiplier for any quotient from this table.
Rule.
Take the multiplier answering to the two first quotient
figures ; take also the difference between this multiplier and
the next greater, and multiply this difference by the given
number, exclusive of the first two figures, crop off at the
right hand of the product as many figures as you had figures
of the given number, to multiply by, then add the remaining
left hand figures of this product to th|^ multiplier taken from
the table*
Examples.
1. Required the multiplier answering to the quotient
.176455.
»1224 next greater multiplier.
.1127 given multiplier.
97 difference,
X.6452 given number^ exclusive of the first two figures.
625844 product.
and .1127+63 =.1190 multiplier. Answer.
Here 63 is added because 625844 is nearer 630000 than
020000.
2. Required the multiplier aaswering to the quotient
.8861. Ans. .3687.
294 GUAGINO.
3. Required the multiplier answering to the quotient
.4875. Ans. .4841.
4. Required the multiplier answering to the quotient
.2567. Ans. .2029.
5. Required the multiplier when the bung diameter is 30
inches, dry inches 10. Ans. .2918.
6. Suppose the bung diameter of a cask to be 31.4 inches,
of which 7.8 inches were dry, whole capacity 122.4 gallons;
required the ullage,^ and also the quantity of liquor in the
cask.
7.8-1-31.4= .2484 quot., and .1937= multiplier.
.2484 X 122.4=23.70888 ullage.
and 122.4—23.70838=98.63112 galls, of liquor. Ans.
7. The bung diameter of a cask is 32 inches, of which 12
inches are dry, whole capacity 100 gallons ; I wish to know
how many gallons are contained in the cask.
Ans. 65 galls. S qts.
8. The bung diameter of a cask is 21 inches, of which 7
inches are dry, whole capacity 32 gallons — I wish to know
the quantity of liquor in the cask. Ans. 22.6624 galls.
Note, — If more than one half of the bung diameter be dry,
use the wet inches the same as directed for the dry in the
rule, and the result will be the quantity of liquor in the cask.
9. Suppose the bur^ diameter of a cask be 28 inches, of
which 175 are dry, whole capacity 80 gallons — I wish to
know the quantity of liquor in the cask. Ans. 27.4 galls.
To ullage a standing Cask.
Rule.
Multiply the square of the distance of the liquor's surface
from the middle of the cask, by the difference between the
squares of the bung and head diameters, and divide the pro-
duct by the square of half the length of the cask ; subtract
one-thirdof the quotient from the square of the bung diame-
ter, and multiply the remainder by the distance of the liquor's
surface from the middle of the cask. The last product di-
vided by 294.12, will give the quantity above or under half
the content of the cask, according as the wet inches exceed
or fall short of half the length of the cask.
GUAOINO. 296
JSxaMples*
1. Suppose the length of a cask to be 40 inches, the bung
diameter 32 inches, the head diameter 24 inches, the wet
inches 26, and content 117 gallons ; how many gallons are in
tlie cask P
32x32=1024 square of the bung diameter.
24x24= 576 square of the head diameter.
448 difference of the squares of the diameters.
40-t-2=20, and 26 — ^20=6 distance of the liquor's surface
from the middle of the cask.
6x6=36, and 36x448=16128.
20x20=400, and 1 6128 -i-400= 40.32 quotient.
40.32-7-3=13.44=-} of the quotient.
1024—13.44=1010.56, and 1010.56x6=6063.36
6063.36-T-294.12=20.615 gallons above the half content.
117-^2=59.5, and 59.5+20.615=80.115 Answer.
2. The bung diameter of a standing cask is 35 inches, head
diameter 28.7, length 40, wet inches 10, content J 48.5 gal-
lons — required the content in the cask. Ans. 33.74 galls.
8. The length of a standing cask is 48 inches, the bung
diameter 36 inches, the head diameter 33 inches, whole ca-
pacity 195.376 gallons, and 40 wet inches — I wish to know
now many gallons are in the c^sk. Ans. 166.521 gallons.
TABLE
Showing the weight, contents in pure gold, old value, and
new value of the principal gold coins throughout the world, as
established by act of Congress of session 1833-'4.
Old standard, 22 carats — ^New standard, 21 carats 2^ grs.
by which the actual value of the Eagle coined prior to July
31st, 1834, is g 10.668 ; that coined since, SIO.
Note. — The tables at pages 54, 55 and 130 were prepared
previous to the passage of this act, and were inadvertently
put to press without the necessary alterations being made.
The pupil is requested to compute the gold coins according ||
this table. •
298
Ti,BLB OF GOLD COINS.
Names of Coins.
Weight.
Contents in
Old
N.W
pure gold.
value.
▼alae.
Austrian Dominions.
grains
grains.
g
%
Souverain,
86
78.6
3.176
3.S88
Double Ducat,
108
106.4
4.299
4.5R6
Hungarian do.
Bavaria.
531
53.3
2.154
2.297
* Carolin,
U9i
115
4.646
4.956
Max d'or or Maximillian,
100
77
3.111
3.818
Ducat,
531
52.8
2.133
2.278 ' 1
Berne.
Ducat — double in proportion,
47
45.9
1.854
1.977
Pistole,
117
105.5
4.262
4.546
Brazil.
Johannes — 5 in proportion.
432
16.
17.068
Dobraon, • %
822
759.
30,666
32.714
Moidore — i in proportion.
166
152.2
6.149
6.500
Crusado,
16i
14.8
.DSto
.637
Brunswick.
Pistole—- double in proportion.
1171
105.7
4.271
4.556
Ducat,
531
51.8
2.092
2.231
Cologne.
Ducat,
531
52.6
2.125
2.267
Colombia.
1
Doubloon,
4m
14.56
15.532
Denmark.
Ducat, current.
48
42.2
1.705
1.818
Ducat, specie.
53*
52.6
2.125
2.267
Christian d'or.
108
93.3
8.77
4.021
East Indies.
Rupee, Bombay, 1818,
179
164.7
6.654
7.096
Rupee of Madras, 1818,
180
165.
6.667
7.11
Pagoda, star,
521
41.8
1.689
1.801
England.
Guinea — i in proportion.
129i
118.7
4.796
5.116
Sovereisn, do
Seven shilling piece,
im
113.1
4.57
4.875
43
39.6
1.60
1.706
France.
.
Aottble Tioai9, coined before
^1786,
251
224.9
9J067
9.684
TAdtB OF 60IJI GOIK8.
39*
Names of Corns.
Louis, coined before 1786.
Doable Louis, coined since
1786,
Louis, do. do«
Double Napoleon, 40 francs
Napoleon, or 20 do.
Frankfort on the Maink.
Ducat,
Geneva.
Pistole, old.
Pistole, new,
Hamburg^
Ducat — double in proportion
Genoa^
Sequin,
Hanover.
George d'or,
Dacat,
Gold Florin--Kiouble in pro.
Holland.
Double Rjder,
Ryder,
Ducat,
Ten Guilder piece— S do* in
proportion,
Malta •
Double Louis,
Louis,
Demi Louis,
Mexioo.
DoublooAs — shftres. in prop.
Milam.
Sequin,
]}oppia, or pistole,
Fortjr Lire piece, 1808, .
NaplIss.
fiix Ducat piece, 1788,
Two do. or Sequin, 1762,
Tlireedo« or Oncetta, 1818,1
Weight.
grains.
125^
236
118
199
99i
531
103i
841
531
581
102J
531
50
309
153
104
256
128
64
4l6i
531
97i
200
186
44J
581
Contents in
pare &old.
grams.
112.4
212.6
106.3
179.
89.7
52.9
80.
52.9
53.4
92.m
53.3
39.
283.2
140.
52.8
98.2
215.8
108.
54.5
53.2
88.4
179.7
121.9
37.4
58.1
8.59
4.293
7.232
8.624
2.137
3.737
3.232
2.137
2.158
3.741
2.154
1.576
11.442
5.655
2.133
3.766
«:699
4.364
^202
14.56
2.15
8.572
7.261
4.925
1.511
2.849^
U
New
value.
4.844
9.163
4.581
7.713
3.866
2.279
4.086
3.448
2.279
2.302
3.939
2.297
1.687
12.206
6.048
2.276
4017
9.2f2B
4.655
2.349
15.532
2.298
3.801
7.746
5.254
1.611
S.S08
398
TABIE OF GOLD COfKS.
Names of Coins.
Netherlands.
Gold Lion, or 14 florin piece
Ten florin piece, 1820,
Parma.
Quadruple Pistole — double
in proportion,
Pistole of Doppia, 1787,
do. do. 1796,
Waria Theresa, 1818,
Piedmont.
PistoIe» coined since 1785 —
half in proportion.
Sequin — ^half in proportion,.
Carlinp, coined since 1785—
half in proportion.
Piece of 20 Francs, called
Marengo,
Poland.
Ducat,
Prussia.
Ducat, 1748,
do. 1787,
Frederick double, 1769,
do. do. 1§00,
do. do. 1778,
do. do. 1800,
Portugal^
Dobraon,
Dobra,
Johannes,
Moidore — ^lialf in proportioiii
Piece of 16 Pestoons, or
1600 Reas,
Old Crusado of 400 Reas,
New do. of 480 Reas,
Millrea, coined in 1755,
Rome.
Sequin, coined since 1760>
.Scudo of the republic^
Weight.
eontentt'in
pure gold.
Old
value.
' New
value.
grams.
grains.
1271
117.1
1031
93.2
441
386.
110
97.4
110
' 95.9
m
89.7
145
125.6
531
52.9
702
< 634.4
991
82.7
531
52.9
531
52.9
531
52.6
206
185.
206
184.5
103^
92.8
108
92.2
828
759.
438
401.5
432
166
152.2
54
49.3
15
13.6
16i
. 14.8
19i
18.1
v52i
25.2
4084
367.
s
4.731
3.7661
15.59616
3.935
3.875
3.624
5,075
2.1271
5iW
4.017
.638
4.198
4.138
3.87
5.414
2.J879
25.632^^.^49
3.341
2.137
2.137
2.125
7.475
7.454
3.749
3.725
3.565
2.279
2.279
2.367
7.974
7.952
3.999
3.973
^0.66632.714
16^17.305
1:7.063
6.56
16.
6.149
1.992 2.125
.549 .585
.598 .637
.732 .789
2.109 2.258
14.838X5.818
TABLE OF GOLD OOtMS.
!»9
Names of GoIds.
Weight.
Contents in
pure gold.
Old
value.
New
value.
Russia*
grains.
grains.
S
S
Ducat, 1796,
54
53.2
2.15
2.293
do. 1763,
535
52.6
2.125
2-267
Gold Ruble, 1756,
24i
22.5
.909
.969
do. 1799.
181
17.1
.691
.737
Gold Pollin, 1777,
8.2
.331
.353
Imperial, 1801,
195i
181.9
7.349
7.84
Half do. 1801,
92i
90.9
3.673
3.924
do- do. 1818,
99i
91.3
3.689
3.935
Sardinia.
Carlino — half in proportion,
2471
219.8
8.881
9.474
Saxony.
Ducat, 1784,
531
52.6^
2.125
2.^67
do, 1797,
53|
52.9
2.137
2,279
Augustus^ 1754,
102i
91.2
3.685
3.921
do. 1784,
102i
92.2
3.725
3.974
Sicily.
Ounce, 1751
68^
58.2
2.351
2.508
Double Ounce, 1758
137
117.
4.727
5.043
Spain.
Quadruple Pistole or Doub-
loon, 1772, double and sin-
.
gle, and shares in propor-
tion.
416^
3772
15.03
16.034
Doubloon, 1801,
417
360.5
14.56
15.532
Pistole, 1801,
104i
90.1
3.64
3.882
Coronilla gold dollar or vin-
teur, 1801,
27
22.8
.921
.982
Sweden.
Ducat,
53
51.9
2.097
2.237
Switzerland.
Pistole of Helvetic republic,
117i
105.9
4.279
4.504
Trever,
Ducat,
5^
52.6
2.125
2.267
Tuscany.
Zechino or Sequin,
5&i
53.6
2.166
2.31
Ruspone of the kingdom of
Etruria,
161J
161.
6.503
6.939
XiBLB OF OOIil> OOm.
value*
Names of Coins.
weight.
Turkey.
Sequin Fonducli of Constan-
tinople, 1773,
do. do. 1789,
Half Misseir, 1818,
Sequin Fonducli,
Termeebesklek,
United States of America
Eagle coined before July 81,
[1834,
do. coined since July 31,
1834, shares in proportion
Venice.
Sechino or Sequin — shares
in proportion,
WURTEMBURG,
Carolin,
Ducat,
Zurich.
Ducat, double and half in
proportion,
grains.
531
531
18i
53
73i
270
258
54
147i
53
531
contents in
Old
pure gold.
value.
grains.
S
43.3
1.749
42.9
1.733
12.6
.491
42.5
1.717
70.3
2.84
247.5
232.
53.6
113.7
51.9
52.6
10.
2.166
4.594
2.097
2.125
2
1.865
1.848
.521
1.831
3.029
10.668
10.
2.31
4.898
2.237
2.267
iVb/c,-^Four pennyweights of gold being divided into 24
equal parts, these parts are called carats ; but gold is often
mixed with some baser metal, which in the mixture is called
alloy ; and according to the proportion of pure gold which is
in every 4 pennyweights, so the mixture is said to be so manr
carats fine. Thus, if only 20 carats of pure gold and 4 of
alloy, it is 20 carats fine ; if 22 carats of pure gold and 2 of
alloy, 22 carats fine ; and if there be no alloy, it is 24 carat*
fine or pure gold. A carat is 4 grains.
To comjnjUe the Jineneaa of any gold coin from the foregoing
table.
Rule*
As the weight of the coin. Is to its contents in pure gold»
So is 24 carats. To the fineness required.
J
KI80ELLANE0U8 ^UEStTONt. 801
JExatnples,
1. The weight of the American Eagle, coined prior to
July 31st, 1834, was 270 grains, its contents in pure gold is
247.5 grains— I wish to know how many carats fine it is.
As 270 : 247.5 : : 24 : 22 carats fine. Answer.
2. Required the fineness of the American Eagle coined
after July 31st, 1834.
As 258 : 232 : : 24 : 21 carats 2^ grains. Ans,
3« I wish to know the fineness of the Turkish Sequin
Fonducli-
As 53 : 42.5 :: 24 : 191 nearly. Answer.
4. I demand the fineness of the sequin of Rome.
As 52.5 : 52.2 : : 24 : 23.86 carats fine. Ana.
5. Requir-ed the fineness of Rupee of M adnis.
As 180 : 165 :: 24 : 22 carats fine. Ans.
8. Required the fineness of the Spanish Doubloon.
As 417 : 360.5 :: 24 : 201 nearly. Answer.
7. I wish to know the fineness of Ruspone of the kingdom
of Etruria.
As 161.25 : 161 :: 24 : 23*96 carats fine, or nearly
pure gold. Answer.
MISCEl.IiANEOUS CIUESTIONS^
1. A hare starts 5 rods before a greyhound, and is not
perceived by him until she has been up 34 seconds ; she
scuds away at the rate of 12 miles an hour, and the grey-
hound on view makes after her at the rate of 20 miles an
hour — How long will the course hold, and what ground will
he run, beginning with the outsetting of the g;reyhound ?
Ans. 58^\ seconds : 1702$ feet run.
2. A. leaves New Italy at 4 o'clock in the morning for
Harrisburg, and goes at the rate of 6 miles an hour, without
intermission : B^ sets out of Harrisburg for New Italy at 5
o'clock the same morning, and tides at the rate of 5 miles an
hour constantly — the question is, whereabouts on the road
will they meet, and at what time ; the distance being 55
miles ? Ans. 32y^7 miles from Harrisburg, at 27^^ min.
past 9 in the morning.
i . '^^'^TT'^^f^mmm
' SOS IflSCBLLANEOUS qUESTIOKS.
3. There is an island which is 36 miles in circumference ;
now if at.the same time, and from the same place, two foot-
men, A and B, set forward to travel round about the sud
island, and follow one another in such a manner that A trav-
els every day 9 miles and B 7 miles — the question is to find
in what space of time they will meet again, and also how
many miles, and how many times round the island each foot-
man will then have travelled.
Ans. They will meet at the end of 18 days from their first
parting, and then A will have travelled 162 miles, (or 4h iimes
the circumference of the island) and B wi'll have travelled
126 miles, (or 3i times the circumference of the island.)
4. An Italian Mulberry orchard in New Italy measures as
follows, viz: south side 42.9 perches, west side 37.2
perches; north «ide 33.4 perches, east side 36.1 perches ; the
north-east and south-east corners are each a right angle — I
wish to know how much longer the diagonal from the north-
east to the south-west corner is than that from the nort\v-west
to the south-east corner. Ans. 6.89 perches.
5. During the memorable storm of sleet and snow on the
8th and 9th of January, 1836, a tree (near the coinpUer*3
door,) 80 feet in height, was broken in such a manner as to
touch the ground 60 feet from the foot of the tree — I wish to
know the length of the piece broken. Ans. 62^ feet.
JRule for such questions .
Add the square of the height of the tree to the square of
the distance from the foot of the tree to the top (after it fell):
divide the sym by twice the height of the tree, the quotient
will be the length of the broken piece.
6. Required the diameter of a circle that will compreheod
within its circumference the quantity of an acre of land.
Ans. 235 ft. 6 in.
7. A may pole 50 ft. 11 in. in length, at a certain \\our of
the day casts a shadow 98 ft. 6 in. long ; I would hereby find
the breadth of a river, that, running 20 feet 6 inches from the
foot of a steeple, 300 feet 8 inches high, the extremity of the
shadow of the steeple reaching 30 feet 9 inches beyond the
stream. Ans. 530 ft. 5 in. nearly.
8. If 6 men can perform a piece of work in 4^ days, how
many men will accomplish another four times as large in one
fourth the time ? * Ans. 96.
J
p
MISCBLLAKE0179 (JCaMttOVi* 808
9. A. set out from. Lancaster for Philadelphia, at the verj
»%me time' that B. set out from Philadelphia for Lancaster;
distant 62 miles : at 4 hours' end they met on the road, and
it then appeared that A. had ridden 1 mile an hour more
than B.— At what rate an hour did each of them travel ?
Ans. A 81 miles, B 7ir
10* A father and his son upon a time,
Were laden with some bottles of French winej
The son unto the father did complain.
That the weight of them his arms did sorely pain j
The father said, if one of yours I take.
My number double unto yours will make,
But if I Ont of mine to you do give.
As many as you have in all I still shall have-
How many bottles of this wine
Had each of them I pray define ?
AnS. father 7, and son 5.
^ote.'-^k. law was passed at the last session of the legisla*
ture of . Pennsylvania, regulating the standard weight of
grain. By weight is undoubtedly the most correct way to
arrive at the value of grain. The act of March 10th, 1835^
says: ** The several kinds of grain hereafter mentioned, which
are now usually bought and sold by measure, shall, from and
after the passage of this act, be regulated according to the fol-
lowing standard weight per bushel, to wit: the weight of each
bushel of barley, 47 pounds ; of each bushel of biickwheat,
48 pounds, and of each, bushel of oats, 32 pounds ; Provided,
that nothing in this act contained shall be constnied so as to
prevent any person or persons selling and buying the several
kinds of grain aforesaid by measure."
11. A farnier mixes barley, buckwheat and oats together,
80 as to have a mixture of 50 bushels that will weigh 42
pounds per bushel — I wish ia know tfie quantity of each kind
of grain.
Ans. 28 bu. of barley, 5 of buckwheat and 17 of oats.
Or, 12 of barley, 20 of buckwheat, and 18 of oats^
12. Required the superficies of & board whose mean
breadth is 15 inches, atid length 16 feet. Ans* 20 feet.
13. Required the quantity of bai'k in a caf 1 10 feet long, 8
feet 2.4 inches wide, and 4 feet deep. An0« 1 cord*
*
J
sol IIISOBtLANfiOUS qUSSTlONS^
iVo^c— 'The solid contents of similar figures are in propor-
tion to each other as the cubes of their similar sides or di^
ameters.
14. If a bullet 8 inches in diameter weighs 64 pounds, what
will a bullet of the same metal weigh whose diameter is 2
Inches? Ans. 1 pound.
15. If a man drink daily a dram which costs 61 cents, how
much will he expend in this manner in 40 years of 365| days
each? Ans. S913.12I.
16. If a parcel of cloth be sold for g678, and at 13 per
cent, gain, what was the prime cost ? Ans. 2600*
17. Two merchants trade together : A. put into stock SlSO,
and B. 8275, they gained gl70 — What is each person's
share? Ans. A. S60; B. gllO.
18. If tV of a ship be worth g6000, what is the worth of
the whole ? Ans. $82000*
19. A captain and 150 sailors took a prize worth £3000,
of which the captain had one-half for his share* and the test
was equally divided among the sailors— What was eacli
man's share ? Ans. I^e captain gl500; and each sailor 810.
20. An ancient lady being asked how old she was, to avoid
a direct answer, said, I have 12 children, and there are two
years between the birth of each of them ; the eldest was bom
when I was 20 years old, and the youngest is now 25 yea«
old— How old was the lady ? Ans. 67 years.
21- If a pound of ginger be sold for 6 cents, and therein
2 cents lost on it, what is the loss per cent. ? Ans. 25.
22. A perspn being asked the hour of the day, said, the
time past noon is equal to f of the time till midnight — ^What
Was the time ? Ans. 48 min. past 4.
23. If f of an ounce of silver cost ^ of a dollar, what will
i of a pound cost ? Ans. 812.M)
24. Twenty knights, 30 merchants, 24 lawyers, a.nd 24
citizens spent at a dinner 8192, which sum was divided
among them in such a manner that 4 knights paid as much as
5 merchants, 10 merchants as much as 16 lawyers, and 8
lawyers as much as 12 citizens. The question is, to know
the sum of money paid by all the knights, also by the mer-
chants, lawyers and citizens.
Ans. The. 20 knights paid 860; the 80 merchants, 873 1
tiie24 lawyers, 836$ and the 24 ei1iz«iis 824.
THE END.
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