Bryant and Stratton's commercial arithmetic Designed for the counting room, commercial and agricultural colleges, normal and high schools, academies, and universities

University of California • Berkeley

THE THEODORE P. HILL COLLECTION

of

EARLY AMERICAN MATHEMATICS BOOKS

.

'

BRYANT AND STEATTON'S

• COMMERCIAL ARITHMETIC.

IN TW OPART S.

DESIGNED

FOR THE COUNTING ROOM, COMMERCIAL AND AGRICULTURAL

COLLEGES, NORMAL AND HIGH SCHOOLS,

ACADEMIES, AND UNIVERSITIES.

BY

E. E. WHITE, A.M., J. B. MERIAM, A.M.,

SUIT. PUB. SCHOOLS, POBTSMOTJTU, OHIO. CASHIER CITY BANK, CLEVELAND, OHIO.

AND

H. B. BRYANT, \AND H. D. STRATTOX,

FOUNDERS AND PROPRIETORS OF THE "NATIONAL CHAIN OF MERCANTILE COLLEGES,"

LOCATED AT NEW YORK, PHILADELPHIA, ALBANY, BUFFALO, CLEVELAND,

DETROIT, CHICAGO, AND ST. LOUIS.

NEW YOEK:
OAKLEY AND MASON.

1866.

Entered, according to Act of Congress, in the year 1860, by

>T. Jb. BRYANT & H. D. STRATTON,
In the Clerk's Office of the District Court tor tne Southern District of New York.

ELECTBOTTPED BY

SMITH & McDOUGAL, J. M. JOHNSON,

82 & 84 Beekman St. printer and Binder,

BUFFALO, N. Y.

PREFACE.

EVERY book — and especially every text-book — should have
a twofold reason for its existence : first, a want which it is
desigi d to meet, and, secondly, an adaptedness to supply that
want. A work which meets these conditions needs no apology
for its appearance.

The preparation of the present treatise was undertaken at
the earnest solicitation of Messrs. BRYANT and STRATTON.
Their intimate acquaintance with the wants of business students,
resulting from an extensive experience in Commercial Instruc-
tion, revealed to them an urgent demand for such a work, and
suggested its general plan.

The Authors have also been engaged, many years, as teachers
of Arithmetic and Commercial Calculations in the first schools
and commercial colleges of the country, or in some of the most
practical departments of business. The result of this experience
is the conviction that a work presenting fully the applications of
arithmetic to actual business, and discussing thoroughly the gen-
eral principles of mercantile transactions, has long been a desid-
eratum. True, there are some excellent works on arithmetic,
in which considerable space is devoted to business forms and
transactions. In no one of these, however, with which we are
acquainted, are these subjects treated with sufficient fullness or
thoroughness for commercial students. By searching through
half a score of the best arithmetics now published, most of the
mformation designed may possibly be obtained. The present
treatise embodies this information in one volume, and presents,
in part, our idea of what is needed.

IV PREFACE.

PART FIRST is designed to afford a review of elementary
arithmetic. In its preparation it has been assumed that the
student possesses some knowledge of numbers. Fractions,
common and decimal, and Ratio and Proportion are treated
with considerable thoroughness on account of their great im-
portance.

PART SECOND is devoted mainly to Commercial Calcu-
lations. Aside from clear and exact definitions, concise rules,
and lucid explanations, we have endeavored to present a system
of general principles relating to the different subjects which
will enable the student more fully to understand the nature and
true theory of business transactions. To secure accuracy, por-
tions of the manuscript have been submitted to the supervision
of business men familiar with the subjects treated of.

As the value of such a work as this greatly depends upon the
character of its problems, we have aimed to present, as far as
possible, those occurring in actual business, without specially
preparing them for the place they occupy.

Experience and observation have taught us, in relation to
money, banks, interest, and exchange, that business students
need something more than rules, forms, and tables. They want
the theory too. The various and contradictory opinions upon
these subjects set forth by business men of even considerable
experience, prove a lack of knowledge of first principles which
should incite the student to a very thorough examination for
himself. Money has intrinsic properties, and is controlled by
natural laws, some of the most important of which we have
endeavored to present.

The nature of Interest, and the principles of Exchange and
Balance of Trade are also fully explained, and, if found correct,
will necessarily expose some radical but popular errors. The
problems submitted will be found to contain satisfactory facts
and statistics supporting our views.

PREFACE. V

The difference between simple, annual, and compound inter-
est, and the operation of the different rules for finding the
amount due on notes when "partial payments" have been
made, are illustrated by diagrams. The treatment of annual
interest is the joint work of the authors, and is believed to be
worthy of special attention.

In the Equation of Payments and the Equation of Accounts
we have aimed to make the student a rule to himself. The
rules and processes recommended are the results of a clear
analysis, leading the student with "open eyes" into the usual
perplexities of these subjects.

The first 116 pages of the work, also the articles on Equation
of Payments, Equation of Accounts, Cash Balance, Annuities,
Partnership, Alligation, Duodecimals, Involution and Evolution,
were prepared by Mr. E. E. WHITE ; the articles on Interest,
Partial Payments, Currency and Money, Banks and Banking,
Exchange, Prommissory Notes, Stocks and Bonds, Progression
and Mensuration, by Mr. J. B. MERIAM. Partnership Settle-
ments aod a portion of the Supplement were written by Messrs.
BRYANT and STRATTOX, to whom we also acknowledge our
indebtedness for valuable materials and suggestions.

The work has been extended beyond its first design, to adapt
it to advanced classes in our High Schools and Academies, and
is now believed to be sufficiently elementary and extensive for
that purpose.

E. E. WHITE.
J. B. MERIAM.

December, 1860.

IN committing this work to the hands of the gentlemen who
are known as its authors, we have been actuated by the sole
purpose of producing a book which should possess all the requi-
sites of a first-class business Arithmetic in a greater degree than
any previous work. We are aware that many books are already
extant which may well dispute the ground as elaborately scien-
tific essays upon the properties of numbers, but we are as fully
conscious that few, if any, can be found which will so completely
answer the demands of the student of Accounts or the practical
business man, as the present treatise.

The principal authors of this work are men of large expe-
rience and ripe judgment, both in the general acceptation and in
their respective departments of life. Mr. WHITE has been for
many years connected with public education in such capacities as
would essentially prepare him to appreciate the wants of the
learner, while his associate, Mr. MERIAM, has had equal advan-
tages in the more practical details of business, as well as ample
experience in teaching. We think it would be difficult, if not
impossible, to combine better qualifications for this particular
work.

To be brief, the book suits us ; and while we shall heartily
adopt it in our extensive chain of business schools, we shall
have no delicacy in pressing its , claims upon educators and
business men throughout the country, feeling, as we do, that in
promoting its general circulation, we are doing much for the
cause which is dearer to us than all others; that of PRACTICAL
EDUCATION.

H. B. BRYANT.
H. D. STRATTON.

TABLE OF CONTENTS.

PART FIRST.

PAGE

NUMERATION AND NOTATION, 13

ANALYSIS OF NUMBERS, 15

ADDITION, 17

LEDGER COLUMNS, 18

THE ADDING OP SEVERAL COLUMNS, 20

SURTRACTION, 21

MULTIPLICATION, 22

DIVISION, 23

CONTRACTIONS IN MULTIPLICATION AND DIVISION, 23

When the Multiplier is 14, 15, 16, etc., 24

When the Multiplier is 31, 41, 51, etc., 24

To Multiply by any two figures, 25

To Multiply by a convenient part of 10, 100, 1000, etc., 25

To Divide by a convenient part of 10, 100, 1000, etc., 26

FEDERAL MONEY, 27

BILLS, 28

GREATEST COMMON DIVISOR, 32

LEAST COMMON MULTIPLE, 34

COMMON FRACTIONS, 36

To Reduce a Fraction to its Lowest Terms, 37

To Reduce a Fraction to its Higher Terms, 38

To Reduca an Improper Fraction to a "Whole or Mixed Number, 39

To Reduce a Whole or Mixed Number to an Improper Fraction, 39

To Reduce Compound Fractions to Simple Ones, 40

CANCELLATION, 41

To Reduce Fractions to a Common Denomination, 42

ADDITION OF COMMON FRACTIONS, 43

SUBTRACTION OF COMMON FRACTIONS, 44

MULTIPLICATION OF COMMON FRACTIONS. 45

To Multiply a Fraction by a Whole Number, 45

To Multiply a Whole Number by a Fraction, 45

To Multiply one Fraction by another, 46

Viii CONTENTS.

PAtfB

DIVISION OF COMMON FRACTIONS, 47

To Divide a Fraction by a Whole Number, 47

To Divide a Whole Number by a Fraction, 47

To Divide one Fraction by another, 48

To Keduce a Complex Fraction to a Simple One, 49

MISCELLANEOUS PROBLEMS IN COMMON FRACTIONS, , 50

DECIMAL FRACTIONS, ; 52

NUMERATION OP DECIMALS, 54

NOTATION OF DECIMALS, 55

REDUCTION OF DECIMALS, 56

To Reduce a Decimal to a Common Fraction, 56

To Reduce a Common Fraction to a Decimal, 57

ADDITION OF DECIMALS, 58

SUBTRACTION OF DECIMALS, 59

MULTIPLICATION OF DECIMALS, 60

.DIVISION OF DECIMALS, 60

To Divide a Decimal by 10, 100, 1000, etc., 62

To Multiply a Decimal by 10, 100, 1000, .1, .01, .001, etc., 62

REDUCTION OF DENOMINATE NUMBERS, 63

To Reduce a Denominate Number of a Higher Denomination to a Lower, 63

To Reduce a Denominate Number of a Lower Denomination to a Higher, 65

To Find what part one Denominate Number is of another, 66

To Reduce a Fraction of a Higher Denomination to Integers of a Lower, 67

ADDITION OF DENOMINATE NUMBERS, 68

SUBTRACTION OF DENOMINATE NUMBERS, 69

MULTIPLICATION OF DENOMINATE NUMBERS, 70

DIVISION OF DENOMINATE NUMBERS, 70

MISCELLANEOUS PROBLEMS, 71

PRACTICE, 73

RATIOS, 77

SIMPLE PROPORTION, 78

COMPOUND PROPORTION, 81

PART SECOND.

PERCENTAGE, 84

To Express the Rate Per Cent. Decimally, 84

To Find a Given Per Cent of any Number, . . '. 85

To Find what Per Cent, one Number is of another, 87

To Find a Number when a certain Per Cent, is given, 88

A Number being given, a certain Per Cent, more or less than another, to

find the latter, 89

APPLICATION OF PERCENTAGE, 90

CONTENTS. IX

PAGB

PROFIT AND Loss 91

COMMISSION AND BROKERAGE 96

INSURANCE — Fire and Marine , 98

LIFE INSURANCE 102

TAXES 103

TAX TABLES 105

DUTIES OR CUSTOMS 106

Specific Duties 107

BANKRUPTCY 109

STORAGE 110

GENERAL AVERAGE. . . t 114

INTEREST 117

Simple Interest 119

Computation of Time in Interest 123

PRESENT WORTH AND DISCOUNT c 127

ANNUAL INTEREST 128

COMPOUND INTEREST 131

PARTIAL PAYMENTS — Three Rules 138

Vermont Rule 138

United States Rule 139

Mercantile Rule 142

Merits of the Three Rules 143

Diagram Illustrating Simple, Annual, and Compound Interest 145

Diagrams Illustrating Partial Payments , 149-151

METALLIC CURRENCY «... 152

PAPER CURRENCY 155

BANKS OF DEPOSIT 159

BANKS OF DISCOUNT 1G1

BANKS OF ISSUE 161

BANKS OF EXCHANGE 163

EXCHANGE 163

PAR OF EXCHANGE „...._ 165

RULE FOR COMPUTING STERLING EXCHANGE 166

NOMINAL EXCHANGE OR AGIO 167

COURSE OF EXCHANGE 169

BALANCE OF TRADE AND BALANCE OF PAYMENTS 170

STATISTICS 173

EXAMPLES IN EXCHANGE 175

BILLS OF EXCHANGE 180

PROMISSORY NOTES 181

NEGOTIABLE PAPER 182

^ Liability of Parties connected \vith Negotiable Paper 183

PRESENTMENT, PROTEST, AND NOTICE c . . 185

DAYS OF GRACE AND TIME OF MATURITY 186

DISCOUNTING NOTES 188

*

X CONTENTS.

PAGE

BANK DISCOUNT 190

BANKERS' ACCOUNT CURRENT 192

ROLES FOR DETECTING ERRORS IN TRIAL BALANCES. 194

STOCKS AND BONDS 197

Railroad Stocks 198

State Stocks 198

Government Stocks 198

Consuls 198

NEW RULE FOR FINDING THE VALUE OF A BOND 201

EQUATION OF PAYMENTS 204

To find the Equated Time for the Payment of several Sums of Money

with Different Terms of Credit 204

Method by Products 205

Method by Interest 205

Proof of Correctness of Mercantile Method 206

" Accurate Rule" not accurate „ , 207

To find Equated Time for Payment of several Sales made at Different

Dates and at Different Terms of Credit 211

To find what Extension should be given to the Balance of a Debt, Par-
tial Payments having been made before the Debt was Due 215

EQUATION OF ACCOUNTS 217

Two Methods 218

Another Method 221

CASH BALANCE „ 224

Account of Sales 227

ANNUITIES 230

Annuity Tables 231

To find the Final Value of an Annuity Certain 232

To find the Present Value of an Annuity Certain 232

To find the Present Value of a Perpetuity 233

To find the Present Value of an Annuity Certain in Reversion 233

To find the Annuity, the Present or Final Value, Time, and Rate being

given 234

Contingent Annuities, 235

To find the Present Value of a Lifo Annuity 236

ALLIGATION .' 237

Alligation Medial 237

Alligation Alternate „ 239

Method by Linking" 240

PARTNERSHIP 243

Capital Invested same Length of Time. 244

Capital Invested for Different Periods of Time. . . 246

DUODECIMALS -f» 249

Multiplication of Duodecimals W. » 249

INVOLUTION.. .., 251

CONTENTS. Xi

PAGE

EVOLUTION 253

SQUARE ROOT 254

The Eight-Angled Triangle 258

CUBE ROOT .* 260

ARITHMETICAL PROGRESSION 264

GEOMETRICAL PROGRESSION 267

MENSURATION 270

Triangles 272

To Find the Area of a Triangle 272

Quadilaterals, Pentagons, &c 273

To find the Area of any Quadrilateral having Two Sides Parallel.. . 273

To find the Area of a Regular Polygon 273

To find the Area of an Irregular Polygon of Two Sides or more 273

Circles 274

To find the Circumference of a Circle, the Diameter being known. . 275

To find the Diameter of a Circle, the Circumference being known. . 275

To find the Area of a Circle, the Diameter being known 275

To find the Area of a Circle, the Circumference being known 275

To find the Area of a Circle, the Circumference and Diameter both

being known 275

To find the Diameter or Circumference of a Circb, the Area being

known 275

To find the Side of the largest Square that can be inscribed in a

Circle 275

To find the side of the largest Equilateral Triangle that can be in-
scribed in a Circle 275

Ellipse 276

To find the Area of an Ellipse, the two Diameters being given 276

MENSURATION OP SOLIDS 276

Prisms and Cylinders 276

To find the entire Surface of a Right Prism or Right Cylinder 277

To find the Solidity of a Prism or Cylinder 277

Pyramids and Cones 277

To find the entire Surface of a Regular Pyramid, or of a Cone 278

To find the Solidity of any Pyramid or Cone 278

To find the entire Surface of a Frustrum of a Right Pyramid or of a

Cone 278

Spheres 278

To find the Surface of a Sphere 279

To find the Solidity of a Sphere 279

Gauging 279

PARTNERSHIP SETTLEMENTS 280

The Investment, the Resources, and Liabilities being given, to find the

nr "- Gam cr Loss. . . 281

Xll CONTENTS.

PAGE

The Investment, the Resources, and Liabilities at Closing, and the Pro-
portion in which the Partners share the Gains or Losses being given,
to find each Partner's Interest in the Concern at Closing 282

The Resources, the Liabilities (excefrt the Investment), and the net Gain

or Loss being given, to find the net Capital at commencing 285

("When the Firm commence Insolvent.) The Resources and Liabilities at
Closing, and the net Gain or Loss being given, to find the net In-
solvency at commencing 287

Miscellaneous Examples 290

SUPPLEMENT 299

Rates of Interest and Statute Limitations in the United States 299

Exchange Tables 300

Foreign Coins— Gold 304

« « —Silver 305

Tables of Weights and Measures. , 306

Practical Hints to Farmers 312

Table of Money, "Weight, and Measure of the Principal Commercial Coun-
tries in the "World 312

Miscellaneous Table of Foreign "Weights and Measures 322

Rates of Foreign Money or Currency, fixed by Law 323

A Table of Foreign Weights and Measures, reduced to the Standard of
the United States, and as received at the United States Custom

Houses • 324

Table giving th% Currency, Rate of Interest, Penalty for Usury, and Laws
in regard to the Collection of Debts, &c., in the several United
States.. 326

PART FIRST,

NUMERATION AND NOTATION,

ART. 1. Numbers are composed of orders, the value of
whose unit increases from right to left in a ten-fold ratio, that
is, ten units of any order make one unit of the order next
higher. The names of the first twelve orders are as follows :

indieds of liil

\
2

<D

a
•5

indivds of Mi

CO

g

i

1

indreds of Tli

ns of Thoimi

ousands.
ndrods.

-

I

-

—

i

p^

H

rfl »

H B

1 1

E

8

5

8

8

5

5

8

8 8

8 3

£

4: Ji

1

0

a

o

o

0

0

0

o o

0 0

000000000000
For convenience in reading or writing numbers, we divide
the orders into periods of three figures each. The three orders
which compose any period are called Units, Tens, Hundreds
of that period. The following table presents the names of the
periods and the manner of reading them :

£ 5 a H t§

£n;5 SH& ££3 «££ £££
333 333 333 333 333

Wi Period. Uh Period. 3d Period. Zd Period. 1st Period.

14 NUMERATION AND NOTATION.

The names of the periods above Trillions are Quadrillions,
Quintillions, Sextillions, Septillions, Octillions, Nonillions,
Decillions, etc.

ART. 2. To read a number composed of more than three
figures, we have the following

R- U JL, E) .

Begin at the right hand and divide the number into periods
of three figures each. Then, commencing at the left hand, read
the figures of each period as if it stood alone, adding the name
of the period.

Remark. — 1. The name of the first or unit period is gener-
ally omitted.

2. Beginners should first be taught to read and write num-
bers composed of not more than three figures. Perfect accu-
racy in this is very important.

Examples.

1. 203.

2. 230.

3. 40404.

4. 3060800.

5. 402300060.

6. 3700070707.

7. 30303030303.

8. 4000400040004.

9. 32400423000203.
10. 801001089006007.

Note. — In separating a number into periods, use a comma.
ART. 3. To write a number by figures, we have the follow-
ing

R.TJLE.

Beginning at the left hand, write the figures of each period
as if it were to stand alone, taking care to fill up the vacant
orders or periods with ciphers.

Note. — We may begin at the right hand instead of the
left. The latter is preferable, however.

NUMERATION AND NOTATION. 15

E x a, m pies.

1. Express in figures forty millions, four hundred and six
thousand, and five.

Explanation. — First write 40, and place after it a comma
to separate it from the next lower period, thus : 40, ; next
write 406 in thousand's period, and place a comma, thus :
40,406, ; then write 5 in unit's period, and fill up the two
vacant orders with ciphers, thus : 40,406,005.

2. Express in figures sixty-five billions, twenty thousand,
and eighty.

Explanation. — Write 65, and place after it a comma, thus :
65, ; then, as the next period (millions) is not given, fill it
with ciphers, and place after it a comma ; thus : 65,000, ;
then write 20, with a comma after it, in thousand's period, fill-
ing the vacant order with a cipher, thus : 65,000,020, ; lastly
write eighty in unit's period, filling the vacant order with a
cipher, thus : 65,000,020,080.

3. Express in figures thirty thousand and thirty.

4. Four hundred millions, five thousand and six'ty.

5. Forty billions, forty thousand and forty.

6. Ten trillions, two hundred millions, one hundred and
one.

7. Thirty-five millions and twenty-five thousand.

8. Two billions, three hundred and forty-five millions.

9. Nine trillions, ninety-nine millions, nine hundred and
ninety-nine.

10. Forty trillions and ten.

ANALYSIS OF NUMBEKS.

ART. 4. In addition and multiplication of numbers it is
necessary to reduce units of a lower order to units of a higher ;
in subtraction and division to reduce units of a higher order to
units of a lower. It is, also, often necessary to change the
form of a number, that is, take from it as many hundreds, or
tens, etc., as possible, and read the rest in units ; or to reduce a

16 NUMERATION AND NOTATION.

part of the units of a higher order to some lower, and express
the true value of the whole. A few examples will make these
changes plain to the pupil.

1. How many units in 4 tens ?

2. How many units in 4 hundreds ?

3. How many tens in 6 hundreds ?

4. How many tens in 6 thousands ?

5. How many hundreds in 3 millions ?

6. How many hundreds in 2 ten- thousands ?

7. How many tens in 25 thousands ? Ans. 2500.

8. How many tens in 40 units ?

9. How many tens in 400 units ? Ans. 40.

10. How many hundreds in 2000 units ?

11. How many hundreds in 200 tens ?

12. How many millions in 2400000 tens ? Ans. 24.

13. How many thousands in 400 tens ?

14. What is the greatest number of hundreds that can t)<?
taken from 34674 ? Ans. 346.

15. Divide 30460 into hundreds and units.

Ans. 304 hundreds and 60 units.

16. Divide 23046203 into ten-thousands and units.

Ans. 2304 ten-thousands and 6203 units.

17. Change the form of 23046.

Explanation. — By reducing the orders, a great number of
forms may be given to the number. The following are some
of the results : 1 ten-thousand, 130 hundreds, and 46 units ;
129 hundreds, 14 tens, and 6 units ; 22 thousands, 9 hundreds,
13 tens, and 16 units ; and 2 ten-thousands, 304 tens, and
6 units. By writing the changed form above the natural, we
may have :

1129146 2210316 11210316 20-29-13-16

23046; or 23046 ; or 23046 ; or 2 30 46.

Note. — The student should study the above changes closely.
See that they are clearly understood.

ADDITION. 17

ADDITION.

ART. 5. The two most important qualities of an accountant
are accuracy and rapidity. Every accountant must know that
his results possess absolute accuracy. In business, he is some-
times obliged to spend hours, and even days, in detecting an
error of a few cents in a trial balance sheet. Kapidity in the
performance of his work is of almost equal importance. The
most rapid computers are, generally, the most accurate.

It is not good policy to wait for the practice of actual
business to impart this skill. The persevering student can
easily acquire a high degree of proficiency, and thus bring to
his business one of the surest elements of success.

Addition is not only the basis of all numerical operations,
but is actually the most frequently used in all departments of
business. It is, also, in adding that the young accountant pos-
sesses the least skill and is most liable to make mistakes. For
these reasons, the student should regard no labor too great
which is necessary to master it. To aid him in acquiring
facility and certainty in adding columns of figures, the follow-
ing methods and suggestions are recommended.

Let it be required, for example, to add the following num-
bers :

637

584

796

839

376

458

749

276

968

Ans. 5683

Process. — Beginning at the bottom of the right hand
column, and naming only results, add thus : 14, 23, 31, 37, 46,
52, 56, 63 ; then adding the 6 tens to the second column, add
it in the same manner— 12, 19, 23, 28, 35, etc. The student
should never permit himself to spell his way up a column of

2

18 ADDITION.

figures in this manner, viz. : 8 and 6 are 14, 14 and 9 are 23,
23 and 8 are 31, 31 and 6 are 37, etc. It is just as easy to
name only the results, and much more rapid.

Proof. — To test the accuracy of the result, add the columns
downward.

Examples.

1. Add 57, 63, 246, 788, 565, 399, 464, and 555.

2. Add 36, 69, 304, 5698, 4536, 40864.

3. Add 28, 47, 55, 66, 77, 88, 99, and 23.

4. What is the sum of 309 + 384+679+436 + 358+804+
506 + 988+777?

5. What is the sum of 14+16 + 34+86+37+65+56+
78+35+49 + 12 + 15+8+9+76 ?

LEDG-ER COLUMNS.

*

ART. 6. In adding long columns of figures, as in a Ledger,
the following method is sometimes used :

Add the columns in order, and place the footings under
each other upon a separate piece of paper (testing the accuracy
of the same by proof) ; point off the right hand figure (except
in the last column) and add the left hand figure or figures to
the next column, thus :
' $57.45

28.75 Process.

36.87 4.7
4.56 4.7

98.88 6 1~~
6.25 29

49.38
9.63

$291.77

The figures, expressing the sum of the left hand column,
together with the figures cut off on the right, read upivards7
will be the sum total. The advantage of this method is two-
fold : 1. The partial results being preserved, it is easier to de-
tect errors. — Any column may be re-added without the trouble

ADDITION.

19

of adding the preceding. 2. The total sum when written is
correct, and the page is not defaced by erasures and corrections.

The student should write out long ledger columns on slips
of paper, and daily practice in adding them, being as careful
to obtain a correct result as he would be in actual business.

The following ledger columns are given merely as examples.
The student can easily increase the number of them to any
extent.

1.

3.25

8.37
2.50
12.35
9.00
.88
.93
4.65
5.48
10.12
1.20
9.15
7.75
18.64
9.15
13.48
4.96
8.30
4.55
3.08
1.13
2.63
7.87
4.33
0.00
.85
.90
5.00
8.00
12.00
15.00
6.50
5.80
7.26

2.

32.56
8.15
6.33
17.09
.90
.75
3.25
21.87
22.20
7.15
4.32
78.90
18.88
3.33
1.38
.63
.49
50.63
24.88
15.33
10.00
16.56
7.77
5.00
4.33
12.34
17.15
20.00
8.50
8.76
5.48
17.10
22.05
7.29
8.99

3.
75.50

284.38
3287.15

111.01
43.96

263.55
1900.09
1356.63

15.20
7.15

13.48
3456.38

348.54
2.75

52.30

900.90

4658.30

222.56

914.53

64.50

49.87

302.58

1256.29

10.10
100.98

78.60

44.50
253.63

77.88

1860.12

973.53

19.10

28.25

39.10
135.00

4.

19.50
23.86
12.45
14.52
25.48
42.54
8.60
9.37
8.80
.65
.73
.38
11.25
.86
2.95
5.92
9.52
.88
.99
6.01
7.83
1.50
2.00
3.85
5.38
1.53
12.60
19.30
22.33
10.19
9.81
8.76
12.57
18.19
7.63

20 ADDITION.

THE ADDING- OF SEVERAL COLUMNS.

ART. 7. Considerable practice will enable the accountant to
add two or more columns at one operation. There is often an
advantage in adding in this manner. Beyond two columns, or
at most three, the method may be more skillful than practical.
The following will illustrate the method of adding two columns :

86
75

68

34

__59

Ans. 322

Process.— 59 plus 30=89, plus 4=93, plus 60=153, plus

8=161, plus 70=231, plus 5=236, plus 80=316, plus 6=322.

It will be seen that the process consists simply in adding

the tens first and then the units. By naming only the results,

we have 89, 93 ; 153, 161 ; 231, 236 ; 316, 322.

The units may be added first and then the tens, thus : 63,
93 ; 101, 161 ; 166, 236 ; 242, 322.

Three or more columns may be added in a similar manner,

thus :

223
425
384
256

Ans. 1288

Operation.— 256+4=260, 260+80=340, 340+300=640,
640 + 5 = 645, 645+20 = 665, 665 + 400 = 1065, 1065 + 3=
1068, 1068+20=1088, 1088+200=1288.

By naming only results, we have : 260, 340, 640 ; 645, 665,
1065 ; 1068, 1088, 1288.

Examples.

1. Add 25, 68, 67, 83, 37, 46, 99, 87, and 34.

2. Add 38, 46, 92, 37, 83, 46, 52, 53, and 46.

3. Add 286, 356, 396, 423, 345, 660, and 780.

4. Add 384, 236, 112, 345, 784, 569, and 963.

SUBTRACTION. 21

SUBTRACTION.
AET. 8. Ex. 1. From 3084 take 2793.

2 9 IS 4 Minuend changed in form.

3084 Minuend.
2793 Subtrahend.
291 Kemainder.

Remarks. — 1. That the changed minuend above is equiva-
lent to the given minuend is evident from the fact that 30
hundreds + 8 tens=29 hundreds + 18 tens.

2. Upon the principle that the difference between two
numbers is the same as the difference between these numbers
equally increased, instead of changing the form of the minu-
end, we can add 10 to the minuend figure when it is less than
the lower subtrahend figure, and add 1 to the next higher order
of the subtrahend. It is plain that 1 added to a higher order
is the same as 10 added to the next lower. We do not borrow
this 10 however, nor do we pay any thing by adding the 1.
These terms ought not to be used.

Examples.

2. From 406309 take 347278.

3. From 100102 take 90903.

4. From 5000050 take 86432.

5. From one billion take one million and one.

6. From 32670804 take 3867498.

7. From 30006070 take 4906007.

8. From 40 hundreds take 25 tens. Ans. 3750.

9. From 205 tens take 264 units.

10. From 230 tens take 12 hundreds. Ans. 1100.

11. From 2 millions take 2 thousands.

12. From 16 tens take 75 units.

13. From 101 thousand take 56 hundreds.

14. From 1 ten take 8 units.

22 MULTIPLICATION.

MULTIPLICATION.

ART. 9. Ex. 1. Multiply 3464 by 306.

Multiplicand, 3464
Multiplier, 306

20784
10392

Product, 1059984

Proof ~by excess of 9's. — Add the figures of the multipli-
cand, casting out the 9's and setting the excess at the right.
Proceed in the same manner with the multiplier, setting the
excess under that of the multiplicand. Multiply these excesses
together and cast the 9's out of the result. Then cast out the
9's in the original product, and, if the work is correct, the last
two excesses will agree. Although this is not always an abso-
lute test of the correctness of a result, it is sufficiently so for
common purposes.

Ex. 2. Multiply 23045 by 70800.

Proof.
23045 5 Excess.

70800 _6 "

184360 30 ) 3 "

161315 (

Product, 1631586000 •} 3 "

Examples.

3. Multiply 405678 by 34006.

4. Multiply 38674506 by 30080.

5. Multiply 46923000 by 46702.

6. Multiply 83400607 by 33000.

7. Multiply 843464 by 30706.

8. Multiply 708000 by 4700.

9. How many feet would a horse travel in 109 days at the
rate of 35 miles per day ? (A mile contains 5280 feet.)

10. How much can 508 men earn in 65 days, if each man
receives 3 dollars per day ?

DIVISION. 23

DIVISION.

ART. 10. Ex. 1. Divide 2920464 by 60843.
60843)2920464(48 Quotient.
243372

486744
486744

Suggestion. — Make 6 your trial divisor and 29 your first
trial dividend. The second trial dividend is 48.
Ex. 2. Divide 2406874 by 30400.

304 00)24068 74(79 Quotient.
2128
2788
2736

5274 Remainder.

Examples.

3. Divide 304608 by 304.

4. Divide 6743207 by 6200.

5. Divide 340068 by 27.

6. Divide 84306200 by 308000.

7. Divide 8408 by 24.

8. Divide 345602 by 18. *

9. Divide 4060703 by 33.
10. Divide 412304 by 30300.

CONTRACTIONS IN MULTIPLICATION AND
DIVISION.

ART. 11. There are abbreviated methods of multiplying
and dividing numbers, which the expert accountant can often
use with great advantage. With a little practice a person
may readily multiply by two, three, or even more figures, at a
single operation. The process of division, may be abbreviated
in a similar though less practical manner. Many of these

24 DIVISION.

methods, together with their explanations, are too complex for
insertion here. The living teacher can best present such pro-
cesses. Unless the student is made familiar with them, they
are of no practical importance.

ART. 12. When the multiplier is 14, 15, 16, etc.
Ex. 1. Multiply 3425 by 15.
Operation.
3425 x 15
17125

51375 Product.

Remark. — It is not necessary to put down any part of the
operation. The result may be written at once by the following

RTJLE.

Multiply by the unit's figure, adding, after the unit's place,
the figures of the multiplicand.

Examples.

2. Multiply 34809 by 13.

3. Multiply 4876 by 18.

4. Multiply 369403 by 17.

5. Multiply 369403 by 13.

6. Multiply 369403 by 16.

7. Multiply 369403 by 15.

8. Multiply 369403 by 14. ,

ART. 13. When the multiplier is 31, 41, 51, etc.
Ex. 1. Multiply 3425 by 51.

Operation.
3425x41
13700

140425 Product.

RULE.

Multiply by the ten's figure and add the p* )duci to the
proper orders of the multiplicand.

Examples.

2. Multiply 3486 by 71.

3. Multiply 864 by 51.

DIVISION. 25

4. Multiply 86047 by 41.

5. Multiply 38967 by 91.

ART. 14. When the multiplier consists of two figures, the
product may be written at once.

Ex. 1. Multiply 675 by 56.

675x56=37800.

Explanation. — The process is based upon the fact that
units multiplied by units give units, tens by units tens, tens by
tens hundreds, hundreds by units hundreds, hundreds by tens
thousands, etc.

We first multiply 5 units by 6 units =30 units =3 tens and
0 units. Write 0 units. Multiply 7 tens by 6 units =42 tens,
and add 3 tens, (received from the units,) =45 tens, and to this
add 5 tens by 5 units =25 tens, which gives 70 tens =7 hun-
dreds and 0 tens. Write 0 tens.

Multiply 6 hundreds by 6 units =36 hundreds, and add the

7 hundred, received from the tens, which gives 43 hundreds.
Then multiply the 5 tens by 7 tens =35 hundreds, and add 43
hundreds =78 hundreds =7 thousands and 8 hundreds. Write

8 hundreds. Multiply 6 hundreds by 5 tens =30 thousands,
and add the 7 thousands received from hundreds =37 thou-
sands. Write 37 thousand. The product is 37800.

Examples.

2. Multiply 38765 by 34. By 45.

3. Multiply 68753 by 48. By 84.

4. Multiply 23086 by 96. By 69.

5. Multiply 6784 by 37. By 73.

6. Multiply 8745 by 43. By 34.

7. Multiply 6321 by 98. By 89.

ART. 15. When the multiplier is a convenient part of 10,
100, 1000, etc.

RULE.

Multiply ~by 10, 100, 1000, etc. (by annexing ciphers) of
which the multiplier is a party and take the same part of the
product.

26 DIVISION.

Ex. 1. Multiply 357 by 33}.
Operation.
3)35700

~TT900 Product.

Explanation.— Since 33 } is one third of 100, 33J times 357
must equal i of 100 times 357.

Note. — The following are some of the convenient parts
often occurring : of 10— 2}, 3J ; of 100— 12}, 16}, 25, 33}, 50 ;
of 1000—125, 166|, 250, 333}, 500, 666|.

Examples.

2. Multiply 528 by 3}. By 2}.

3. Multiply 124860 by 12}. By 16|.

4. Multiply 80648 by 25. By 33}.

5. Multiply 10368 by 125. By 166|.
.6. Multiply 62208 by 333}. By 666}.

ART. 16. To divide by a convenient part of 10, 100, 1000,
etc.

RTJJL.E.

Multiply by the quotient, found by dividing 10, 100, 1000,
etc., (as the case may be) by the given divisor, and divide the
result by 10, 100, 1000, etc.
Ex. 1. Divide 850 by 16|.

Operation.
850
_6

51.00 Ans. 51.

Explanation. — Since 100 is 6 times 16 f, 100 is contained
as many times in 6 times a given number as 16| is in the
number itself.

32 x a m. pies.

2. Divide 465 by 2}. By 3}.

3. Divide 54604 by 12}. By 16|.

4. Divide 8364 by 25. By 33}.

5. Divide 64575 by 125. By 500.

6. Divide 647500 by 166|. By 333}.

7. Divide 2564 by 6}. By 250.

i

FEDERAL MONEY. 27

FEDERAL MONEY.

ART. 17. TABLE.

10 mills (m) make 1 cent, marked ct.
10 cents " 1 dime, " d.

10 dimes " 1 dollar, « $

10 dollars " 1 Eagle, " E.

E. $ d. ct. m.
1=10=100=1000=10000

1= 10= 100= 1000

1= 10= 100

1= 10

Remark. — Dimes and eagles are not mentioned in ordinary
business transactions. In writing dollars and cents together,
a point, called the separatrix ( . ), is placed between the dollars
and cents ; and, since cents occupy two places, the first figure
at the right of cents is mills. It is not customary to separate
cents and mills.

Examples.

1. How many mills in 28 cents ? In 37} cents ?

2. How many cents in 15 dimes ? In 16} dimes ?

3. Keduce $12.50 to mills.

4. Change $90 to mills.

5. How many cents in 2 eagles, 5 dollars, and 8 dimes ?

6. Reduce 4360 cents to dollars.

7. Add the following: $9.60, $12.70, $45.37}, $.06, $1.50,
$4.98, $68.33, '$8.39, $60, and $.80.

8. Sold a carnage for $120.75, a horse for' $90.60, a har-
ness for $15.60, and a saddle for $13.12} ; what was the
amount received ? Ans. $240.075.

9. From $108 take 12} cents. Ans. $107.875.

10. Bought a barrel of flour for $6.37}, and sold it for
$5.87} ; what did I lose ? Ans. $.50.

11. Bought a house and lot for $1500. Paid $40 for a
front fence, $110.90 for painting house, $9.75 for fruit trees,

28 BILLS.

and $15 for other improvements. I then sold the property for
$1800. What did I gain ?

12. What will be the cost of 45 barrels of flour at $5.80
per barrel ?

13. What will 80 bushels of coal cost at 15 cents per bushel ?

14. What will be the cost of 60 bushels of wheat at $1.12i
per bushel ; 146 bushels of corn at 66 1 cents a bushel ; and 45
bushels of oats at 25 cents a bushel ?

15. How many bushels of coal at 12 £ cents a bushel can be
bought for $125 ?

Suggestion. — The dividend and divisor must be reduced to
the same denomination. Change both to mills. 125. 000 -r-
.125=1000. Ans. 1000 bushels.

16. How many pounds of butter at 16 cents per pound
must be given for 15 barrels of flour at $8 per barrel ?

17. How many barrels of flour at $5.62| per barrel can be
bought for $225 ? Ans. 40 barrels.

18. How many half-dimes would it take to pay for 16 cows
at $16.37i per head ?

19. A drover bought 105 head of cattle at $57 per head.
He paid for their pasturage one month $250, and then sold
them at $60 per head. What did he gain by the transaction ?

Ans. $65.

BILLS.

ART. 18. A Bill of Goods, or simply a Bill, is a written
statement of goods sold and their prices.

It contains the time and place of the transaction and the
names of the parties.

A bill is drawn against the purchaser, and in favor of the
merchant or seller.

A bill is receipted by writing the words Eeceived payment at
the bottom and affixing the seller's name. A bill may be receipted
by a cl rk, agent, or any authorized person, as in bills 2 and 3.

When sales are made at different times, the dates of the
several transactions may be written at the left.

BILLS. 29

A bill presenting a debit and credit account between the
parties and the balance due, may be written as in bill 7.

If the party against whom the bill is drawn is not able to
pay it when presented, he may acknowledge the same by giving
a due-bill. This will prevent all subsequent dispute as to the
correctness of the claim. A bill may be receipted by means of
a due-bill, as in bills 4 and 5.

1. CLEVELAND, July 1, 1859.

MB. JOHN COOK,

Bought of Samuel Bliss.

15 Ibs. Kio Coffee, . . . @ 16c. . $2.40

50 Ibs. W. I. Sugar, . . @ 8ic. . 4.25

36 Ibs. Pearl Starch, . . @ 12ic. . 4.50

8 gals. Molasses, . . . @ 40c. . 3.20

90 Ibs. Butter Crackers, . . @ 9c. . 8.10

45 Ibs. Picnic Crackers, . . @ lie. . 4.95

Keceived payment, SAML. BLISS.

BUFFALO, Jan. 1, 1860,

PETER HIND,

1859. Bought of James Fink & Co.

July 15. 9 yds. Silk, . @ $0.95 . '

" " 8 yds. Kibbon, . . . @ .45 .

" " 12 yds. Muslin, . . . @ .15 .
Sept. 9. 3 yds. Cassimere, . . @ 1.75 .

" " 2i yds. Broadcloth, . . © 4.50 .

" " 6 yds. Doeskin, . . . @ 1.12i .

" " 1 Cravat, . © 1.25 .

Oct. 15. 4 prs. Boots, . . . @ 5.20 .

" " 2 doz. Hose, . © 2.40 .

" " i doz. Sleeve Buttons, . @ .48 .

" " 3i yds. Linen, . . . © .60 .
Nov. 30. li doz. Collars, . . @ 2.25 .

" " 2 doz. Handkerchiefs, . © 1.40 .

" " 3 Vests, . . . . © 2.40 . __

1,797765

Received payment, JAMES FINK & Co.

per SMITH.

it it

1C it

30 BILLS.

3. NEW YORK, Jan. 1, 1859.

MB. JOHN SMITH,

To Hurd & Brothers, Dr.
1858.

Aug. 20. To 12 yds. Broadcloth, . @ $3.50 .

16 yds. Cassimere, . @ 1.12 .

17 yds. Drilling, . . @ .11 .
Sept. 25. " 12 doz. Spools On. Thread, © .60 .

" " " 7 yds. Gingham, . . © .25 .
" " " 34 yds. Fine Muslin, . © .18 .
" " " 5 yds. Eed Flannel, . © .62J .
"• " " 21 yds. Silk Velvet . © 400 .
Oct. 9. " 12 gross Shirt Buttons, © .75 .
15 doz. Wool Hose, . © 3.00 .
" 3 prs. Kid Gloves, . © 1.25 .
" " " 2 doz. Linen Napkins, . © 2.40 .
" " " 2 doz. Shirt Bosoms, . © 4.80 .
Nov. 1. " 11 yds. Drilling, . . © .10 .
;< 5 yds. Jean, . . . © .75 .
" 2 Silk Kdks., . . © 1.00 .
« 12i yds. Vel. Kibbon, . © .20 . _

$171.485
Eeceived payment,

JOHN STILL,
for HUBD & BROTHEBS.

4. CHICAGO, July 1, 1859.

JOSEPH CAMP,

To Geo. W. Colburn, Dr.
1859.

Apr. 3. To 3 doz. Scythes, . . © $9.00 .

" 8. " li doz. Hoes, . © 5.00 .

Mayl. a 6 doz. Kakes, . © 1.75 .

$45XX)

Keceived payment by due-bill,
July 15, 1859. GEO. W. COLBUBN.

(C (( a
tt

" "

BILLS. 31

5^ CINCINNATI, June 20, 1859.

AMOS KENT, ESQ.,

To W. B. Cook & Co., Dr.

To 1 doz. Webster's Unabridged Dictionary, @ $50.00
" 12 doz. Kobinson's Arithmetic, . . @ 9.00
" 5 doz. Sanders' Fifth Headers, . . @ 7.20
" 9 doz. Wells's Grammar, . @ 3.00

" 2^ doz. Small Testaments, . @ 1.20

$224
Julyl. Settled by due-biU,

W. B. COOK & Co.

6.
MR. J. H. POE,

1859.

May 3. 75 Ibs. Sugar,

" " 9 Ibs. Tea, .

" " 21 gals. Golden Syrup, .

June 1. 10 Ibs. Spice,

" 12 Ibs. Pepper, .

" 12 Ibs. Ginger, .

" 15 Ibs. Coffee,

10. 20 Ibs. Dried Apples, .

" 18 Ibs. Dried Peaches, .

" 2 bu. Onions,

15. 13 Ibs. Mackerel, .

18. 9 Ibs. Smoked Herrings,

20. 25 Ibs. Kice, .

" 12 Ibs. Dried Beef,

" 5 Sacks Table Salt,

" 5 bu. Corn Meal, .

27, 17 Ibs. Soda Crackers, .

Keceived payment,

PORTSMOUTH, July 1, 1859.

Bought of Wm. Miller.

. @ 6jc .

. @ 65c .

. @ 70c .

. @ 20c .

. @ 25c .

' . @ 18c .

@ lOc
@ 12|c
@ 80c
@8c
@ 20c
@ 5c
@ 12ic
@ 20c
@ 80c
@ 9c

$52.24
WM. MILLER.

32

GREATEST COMMON DIVISOR.

7.
KEED &

1859.
July 7.

SPRY,

ST. Louis, Jan. 1, 1859.

To Hall, Smith & Co., Dr.

1C CC

CC CC

" 20.

CC CC

CC CC

To 15 yds. Cambric, . @ 9c .

" 50 yds. Print, . . @ 12ic .

" 6 yds. Cassimere, . @ $1.60

" 33 yds. Sheeting, . @ lie .

" 6J yds. Broadcloth, . @ $4.37^ .

" 3 yd. Velvet, . . @ 3.00 .

Aug. 30. " 20 yds. French Print, @ 17c .

" " "15 yds. Lyonese, . @ 70c .

Or.

Sept. 1. By 40 bu. Coal, . . @ lie .

" 9. " 6 Cords of Wood, . @ $ 3.00 .

Oct. 20. " Cash, . @ 16.00 .

Nov 25. " 8 Days' Labor, . . @ 1.50 .

Balance due, .....
Keceived payment,

HALL, SMITH &
per HIBBS.

$50.40
$15.02

Co,

GREATEST COMMON DIVISOR.

ART. 19. Integers, or whole numbers, are divided into two
classes, prime and composite.

A prime number can be exactly divided only by itself and
unity ; as 2, 3, 5, 7, 11, etc,

A composite number can be exactly divided by other num-
bers besides itself and unity ; as 4, 9, 21, etc.

The factor of a number is one of two or more numbers
which multiplied together will produce the given number.
The factors of 12 are 2, 3, 4, 6, 1, and 12, since each of these
numbers multiplied by another will produce 12.

GREATEST COMMON DIVISOR. 33

The prime factors of a number are all the prime numbers
which multiplied together will produce the given number.
The prime factors of 12 are 1, 2, 2 and 3.

Two or more numbers are said to be prime tvith respect to
each other when they have no common factor ; as 8, 21, and 35.

The divisor of a number is any number that will exactly
divide it. Thus 4 is a divisor of 12, 16, and 24.

Note. — Every factor is a divisor and vice versa.

A common divisor of two or more numbers is any number
that will exactly divide each of them. Thus 4 is a common
divisor of 16, 32, and 64.

The greatest common divisor of two or more numbers is the
greatest number that will exactly divide each of them. Thus
16 is the greatest common divisor of 16, 32, and 64.

ART. 20. To find the greatest common divisor of two or
more numbers.

Ex. 1. What is the greatest common divisor of 63 and 105 ?

Explanation. — 3 and 7 are the only

ro J?SToMET7OD' factors common to 63 and 105, hence

Oo — O X o X /

105=3x5x7 ™iey are the only common divisors,

. 3x7=21. Ans. an(^ their product must be the great-

est common divisor.
Explanation. — That the last divisor is

SECOND METHOD. , . .

63)105(1 the greatest common divisor is evident from

63 the following analysis :

42)63(1 42=21x2; hence 21 will divide 42.

63=42 + 21 = 21 x 2 + 21x1 = 21x3 ;

hence 21 wm divde 63.

21 105 = 63+42 = 21x3+21x2 = 21x5;

hence will also divide 105.

IR-TILE.

Resolve the numbers into their prime factors. The pro-
duct of the factors common to all the numbers will be the great-
est common divisor. Or,

Divide the greater number ~by the less ; the less number by
the first remainder; the first remainder by the second remain-

3

34 LEAST COMMON MULTIPLE.

der; the second remainder by the third, and so on until noth-
ing remains. The last divisor will be the greatest common
divisor.

Note. — The greatest common divisor is chiefly used in re-
ducing fractions to their lowest terms. See Art. 24.

Find the greatest common divisor of the following num-
bers :

2. 56 and 98.

3. 69 and 161.

4. 168 and 392.

5. 85 and 136.

6. 126 and 294.

7. 148 and 296.

8. 16, 32, and 86.

Suggestion. — First find the greatest common divisor of two
of the numbers ; then use the greatest common divisor of these
two numbers as a new number, and find the greatest common
divisor of it and the third number.
9. 92, 138, and 161,

10. 2048 and 2560.

LEAST COMMON MULTIPLE.

ART. 21. A multiple of a number is any number it will
exactly divide ; thus 24 is a multiple of 6.

A common multiple of two or more numbers is any number
each of them will exactly divide. Thus 96 is a common mul-
tiple of 8, 12, 16, and 24.

The least common multiple of two or more numbers is the
least number each of them will exactly divide. Thus 48 is the
least common multiple of 8, 12, 16, and 24.

It is evident that the multiple of a number must contain
all its prime factors, otherwise it can not contain the number
itself. It follows from this, that a common multiple of two
or more numbers must contain all the prime factors of each

LEAST COMMON MULTIPLE. 35

of the numbers, and that the least common multiple of two
or more numbers must contain all the prime factors only
the greatest number of times they are found in any^ of the
numbers.

ART. 22. To find the least common multiple of two or
more numbers.

Ex. 1. What is the least common multiple of 21, 63, 108 ?

Explanation. — The mul-

FIEST METHOD. tiple of 108 must contain

nQ~o * o , v the factor 3 three times and

— XOX/ -i /» r» • i

10§ =3x3x3x2x2 *ne *actor 2 twice ; the mul-

3x3x3x4x 7=756 Ans. ^P^e °f ^3 must contain the

factor 3 at least twice and

7 once ; the multiple of 21 must contain the factor 3 at least
once and 7 once. It is evident that a number that contains
the factor 3 three times, the factor 7 once, and the factor 2
twice, is the least common multiple of 21, 63, and 108.

R UJL.E.

fiesolve each of the given numbers into its prime factors.
The product of the different factors, each factor being taken
the greatest number of times it occurs in any of the number sy
will be the least common multiple.

Note. — This method is not often used.

Explanation. — It is evident that

SECOND METHOD. by this method the same result is

obtained as by the former method,

viz : the greatest number of times

o)l— 3— 36 eacfa prime factor enters in any of

the numbers. 756 contains the

3x3x12x7=756 ^4rcs. f , Q ,, ,. 0, . , „

factor 3 three tunes, 2 twice, and 7

once (12=2x2x3).

E.TJLE.

Arrange the numbers on a horizontal line, divide by any
prime number that ivill exactly divide two or more of the num-
bers, and write the quotients and undivided numbers in a line

36 COMMON FRACTIONS.

beneath. Divide this line of numbers in the same manner as the
first , and so on until no prime number will exactly divide two
numbers. The product of all the divisors and undivided num-
bers will be the least common multiple required.

Find the least common multiple of the following num-
bers :

2. 8, 12, 16, 24, and 36.

3. 9, 15, 21, and 75.

4. 3, 8, 9, 15, and 32.

5. 17, 34, 68, and 5.

6. 8, 12, 16, 35, and 84.

7. 3, 4, 5, 6, 8, 10, and 12.

8. 5, 4, 6, 9, and 7.

9. 7, 8, 49, 98, and 168.

10. |, f, |, and f .

Suggestion. — Reduce fractions to a common denominator,
and then find the least common multiple of their numerators.

11. 2|, 5, 3 J, and 4j.

COMMON FRACTIONS.

ART. 23. If a unit or a body, as an apple, an orange, etc., be
divided into four equal parts, one of these parts is one-fourth of
the whole ; two, two-fourths ; three, three-fourths ; four, four-
fourths — which are respectively written 1, f , f , f . These ex-
pressions are called fractions ; the number above the line being
called the numerator, and the number below the line the de-
nominator. Hence, "a fraction is an expression for one or
more of the equal parts of a unit."

It is evident that the denominator shows into how many
equal parts the unit has been divided ; the numerator, how
many of these equal parts are taken. The numerator and de-
nominator are called terms of the fraction.

A fraction may also be regarded as an expressed division,
the numerator being the dividend and the denominator the

COMMON FRACTIONS. 37

divisor. 3-7-4 may also be written •£ ; the value of the frac-
tion being the quotient. 4 is contained in 3 three-fourths of a
time.

A common or vulgar fraction is one in which both terms
are written ; as £, -f , T\, etc.

Common fractions are divided into three classes, simple,
compound, and complex.

A simple or single fraction has but one numerator and one
denominator, each being a whole number ; as £ and J.

A compound fraction consists of two or more simple frac-
tions connected by the word of ; as | of £, and f of -f of 2|.

A complex fraction has a fraction for one or both of its

terms ; as I, 1, and 5.

3J 7> 3

4

Simple fractions are divided into proper and improper.

A proper fraction is one whose numerator is less than its
denominator ; as |, J, etc.

An improper fraction is one whose numerator is equal to
or greater than its denominator ; as £• and | .

A mixed number is composed of a whole number and a
fraction ; as 12 J, 16|, etc. The fraction is added to the whole
number, 12| being the same as 12 + |.

It is evident from the very nature of a fraction that both of
its terms may be multiplied or divided by the same number
without changing its value.

The value of a fraction may be increased, 1. By adding to
its numerator. 2. By multiplying its numerator. 3. By sub-
tracting from its denominator. 4. By dividing its denominator.

The value of a fraction may be decreased, 1. By adding to
its denominator. 2. By multiplying its denominator. 3. By
subtracting from its numerator. 4. By dividing its numerator.

ART. 24. To reduce a fraction to its lowest terms.

Ex. 1. Reduce f £ to its lowest terms.

4)tA=2)T6T-3? Ans. Or, 8)f*=^ Ans.

Explanation. — Since both terms of a fraction may be di-
vided by the same number without changing its value, divide
both numerator and denominator by 4. The result is /?.

38 COMMON FRACTIONS.

Again, divide both terms of this fraction by 2 ; the result is --J,
which can not be reduced lower, since no number greater than
1 will divide both of its terms. Or divide by 8, the greatest
number that will divide both terms of the fraction ; the result

i« 3

is T.

E.TJ3L.E.

Divide both terms of the fraction by any number that will
divide each of them without a remainder, and proceed until
they are prime to each other. Or,

Divide both terms of the fraction by their greatest common
divisor.

E x am. pies.

2. Reduce f f to its lowest terms.

3. Reduce TW to its lowest terms.

4. Reduce TVj to its lowest terms.

5. Reduce TW to its lowest terms.

6. Reduce Iff to its lowest terms.

7. Reduce T\64 to its lowest terms. Ans. f.

8. Reduce T3/^- to its lowest terms. Ans. }f-

9. Reduce f iff to its lowest terms. Ans. -f.
10. Reduce fWV to its lowest terms. Ans. T4T.
ART. 25. To reduce a fraction to higher terms.

Ex. 1. Reduce f to twelfths.

1= T\, |= ' x ,3,= _?_ AnSm Or, f x 3= T<V Ans.

Explanation. — Since 1 fourth equals 3 twelfths, 3 fourths
must equal 3 times 3 twelfths, which is 9 twelfths. Ans. T\.
Or, since both terms of a fraction may be multiplied by the
same number without changing its value, multiply both nu-
merator and denominator by 3.

es

33 x am p 1

2. Reduce f to sixty- thirds. Ans. f J.

3. Reduce T\ to sixtieths. Ans. f £.

4. Reduce T\ to fifty-sevenths.

5. Reduce ¥8T to eighty-fourths.

6. Reduce J to fifteenths.

COMMON FRACTIONS. 39

7. Reduce -V~ to twenty-sevenths.

8. Reduce £, f , and f to twenty-fourths.

Ans. |}, |i, and if.

9. Reduce 4, f , and T3T to seventieths.

10. Reduce ^ f , f , and T<V to forty-eighths.

ART. 26. To reduce an improper fraction to a whole or
mixed number.

Ex. 1. Reduce -M- to a mixed number.
49-^5=9f Ans.

Explanation. — Since 5 fifths make 1, there will be |s many
ones in 49 fifths as 5 is contained times in 49, which is 9}.

RULE.

Divide the numerator by the denominator.

Examples.

2. Reduce -1/- to a mixed number.

3. Reduce -\5- to a mixed number.

4. Reduce f J to a whole number.

5. Reduce -W- to a mixed number.

6. Reduce JTy- to a mixed number.

7. Reduce -V/- to a mixed number. -^ws. 3/g-.

8. Reduce -\5- to a whole number. Ans. 25.

9. Reduce -J-J- to a mixed number. -4ws. 5T2T.
10. Reduce ^-f ^ to a mixed number. Ans. 17|.
ART. 27. To reduce a whole or mixed number to an im-

proper fraction.

Ex. 1. Reduce 5f to an improper fraction.

_a_3

Explanation. — Since there are 4 fourths in 1, in 5 there
are 5 times 4 fourths =20 fourths, and 20 fourths + 3 fourths =
23 fourths. Ans. -V-

Multiply the whole number by the denominator of the frac-
tion, to the product add the numerator, and under the result
place the denominator.

?

40 COMMON FRACTIONS.

Examples.

2. Keduce 4A"S to an improper fraction.

3. Keduce SyVj to an improper fraction. Ans. f

4. Keduce 56 £ to an improper fraction.

5. Reduce 1236?97 to an improper fraction. Ans. --V/—-

6. Reduce 5Tf ¥ to an improper fraction.

7. Reduce 23r9¥ to an improper fraction. Ans. -3Ty.

8. Reduce 133Tf to an improper fraction.

9. Reduce 563f to an improper fraction. Ans. & -M-2-.
lO.^Reduce 8006 ff to an improper fraction.

Ans. laa-Mi.

11. Reduce 24 to fourths. Ans. Y-

12. Reduce 35 to twentieths. Ans. -yy1-

13. Reduce 312 to twelfths.

14. Reduce 19 to twenty-fifths.

15. Reduce 1008 to ninths.

ART. 28. To reduce compound fractions to simple ones.
Ex. 1. Reduce f of | to a simple fraction.

fnf 5 _ 4^5 - 20 A M n
oi g __---— 3 w j±ns.

Explanation. — 1 of J is J-0-, and 1 of | is 5 times ^\ or /0,
and if | of | is /0, f of | is 4 times /„? or 1^=1 Ans. This
is in effect multiplying the numerators together and also the
denominators.

Multiply the numerators together for the numerator of the
simple fraction, and the denominators together for its denom-
inator.

Note. — If there are whole or mixed numbers, first reduce
them to improper fractions.

Examples.

2. Reduce | of f of f to a simple fraction. Ans. -r\.

3. Reduce 3^ of 2| of T\ to a simple fraction. Ans. 2j.

4. Reduce 2£ of 1^ of f to a simple fraction.

5. Reduce f of J of 2i to a simple fraction.

6. Reduce f of 1| of -f of 2i to a simple fraction. Ans. }.

7. Reduce f of 6 to a simple fraction.

8. Reduce f of 2£ of 3 to a simple fraction.

COMMON FRACTIONS. 41

CANCELLATION.

ART. 29. The above operations may be abbreviated by in-
dicating the multiplications to be performed, and then cancel-
ling the factors common to both terms, as shown in the follow-
ing examples.

Ex. 1. Keduce £ of £ of 4 of 2i to a simple fraction.

2 2

$x$x0x# 4
4x0xtfx3=3 = 13 Ans'

3
2. Reduce f of £ of f of f of .; of l£ to a simple fraction.

3

. — 1 remains as a factor in the numerator.

3. Reduce \ of 4i of T9T of J- to a simple fraction.

4. Reduce f of 2ff of •£-* of f to a simple fraction.

Ans. T7T.

5. Reduce | of | of f of T\ of 12 f to a simple fraction.

Ans. 3f.

6. Reduce f of 3 £ of T6T of }i of r7j of 7f to a simple fraction.
Remark. — The principle of cancellation may often be used

with great advantage. Whenever, to obtain a certain result,
several multiplications and divisions are to be performed, indi-
cate the operations and cancel the factors common to the mul-
tipliers and divisors.

7. Divide the product of 24, 16|, 8, 33i by 12, 16|, and 66|.

t

8. Multiply 48, 32, 5280 and 27 together, and divide the
result by 16, 264, 54 and 6. Ans. 160.

9. How many cords of wood in a pile 144 feet long, 12 feet
high and 3 feet wide ?

109 3

x 3

= Ans'

42 COMMON FRACTIONS.

10. Multiply 9, 8, 18, 45, 36, 90, 81 together and divide
the result by 72, 180, 27, 24, 4 and 18. Ans. 25TV

ART. 30. To reduce fractions to a common denominator.

Ex. 1. Reduce f, f, f, f and T7^ to equivalent fractions
having a common denominator.

Solution. First Method. — It is evident upon a little in-
spection that each of the fractions can be changed to twenty-
fourths. According to Art. 24, J = i£, f = H> f = f£, ? = ££,
and T73 = £J. Hence f, f, £, f and T\ are respectively equal to
if? if? IT? if an<l if? fractions having a common denominator.

Second Method. — The least common multiple of 4, 8, 6, 3
and 12 (denominators) found by Art. 22, is 24, which, being
divided by 4, 8, 6, 3 and 12 respectively, give the multipliers
by which both terms of their respective fractions are to be
multiplied 3Xe — 11 i^ — n 5x4 — 20. 2j<_s_i6 and-^^_

4X6 247 8X3 24? 6X4 24? 3X8 24? 12X2

if.

KULE FOR SECOND METHOD. — Find the least common mul-
tiple of the denominators. Then divide the least common mul-
tiple by the denominator of each fraction and multiply both
of its terms by the quotient.

Note. — The first method is the one generally used. In ordi-
nary examples, the common denominator can be seen at a
glance.

t

E x a m. pies.

Reduce the following fractions to equivalent fractions hav-
ing a common denominator.

2. I, f, 1, TV, JV.

3. | and ,V
4- t, |, i, f.

5. |, I, I, i-

6. i of l,2i, |. Ans. f,-V-,f.

7. i off, f,2i.

Q i i i i i i
°* "3? 4? IT? F? ¥> !!?•

9. !, !, f, 1-

COMMON FRACTIONS. 43

ADDITION OF COMMON FRACTIONS.

ART. 31. Ex. 1. What is the sum of f , £ , £ and J ?

|+t+t+»=
H+H-Kfi+H==tt==3i

Ex. 2. Add | of |, f of -f and 2i

tof }=f, f of i=i52i

= W= 341

RULE.

Reduce the fractions to a common denominator; then add
their numerators, and under their sum place the common de-
nominator.

Notes. — 1. First reduce mixed numbers to improper frac-
tions, and compound fractions to simple ones.

2. The integers may be set aside and subsequently added
to the sum of the fractions.

1C x a m pies.

3. Add |, f, | and i. Ans. 2jf.

4. Add | of f and TV Ans. 1/T.

5. Add |, f and f Ans. !}££.

6. Add 5i, 3f, 5|. ^s. 14jf .

7. Add | of 2J and f of 2j. -4w«. 2.

8. Add 1026ii, 1875| and 5634 f. Ans. 8536ff f.
Suggestion. — First add the fractions.

9. Add 37i, 18f , 33i and 81J. Ans. 170|.

10. Add |, J»T of 4i, 563f, and | of 3f.

11. Add i, i, J, i and 1.

12. Add |, f, T\, andf ofl}.

13. Add i, i, i, i, and J.

14. Add | of f and 12i.

15. Add 105| and 98TV

44 COMMON FRACTIONS.

SUBTRACTION OF COMMON FRACTIONS.
ART. 32. Ex. 1. From % take f .

Ex. 2. From 2 J take } of 2.

2i=f, Jof f=f

RTJLE.

Reduce the fractions to a common denominator; then sub-
tract their numerators, and under the result place the common
denominator.

Note. — Mixed numbers may be subtracted without reducing
them to improper fractions.

3. Subtract f from f . Ans. TV

4. Subtract T2T from f .

5. From 1 of f take f of T2T. Ans. //„.

6. From f of f take 1.

7. From i of J take T\ of J. ^ws. } j.

8. From 820| subtract 56}.

820|, A

_

763}i Ans.
9. From 250} subtract 225f

10. From 993f take 546|. Ans. 446f

11. From J + J + 4- take f of f + T\ off. Ans. ||.

12. From | of 12 take f of 9.

13. From 1000 take 156|.

14. From 9 take 1 of }.

15. From 56A-f 89| take 5} + 81TV

16. From J'of 13 take | of 8.

17. From 3| of 5 take 2j of 7. ^ws. Ij.

18. From 4 of 42 take f of 48. Ans. 16f.

19. From f of 19J take | of 7f. ^iw. 9}f

20. From 8751 take 599f

COMMON FRACTIONS. 45

MULTIPLICATION OF COMMON FRACTIONS.

ART. 33. To multiply a fraction by a whole number.
Ex. 1. Multiply T\ by 4.

5 X4 - 20 - 5 - 1 2 Ama Or - _ - 5 - I2 /4'MC

T2- — T¥— 3- — -"-3- -AnS. Ur? — — _ 3 _ 1 j ^TiS.

Explanation. — 4 times T\ is ff=f, or 1|. It is evident
that the same result is obtained by dividing the denominator
by 4.

Multiply the numerator of the fraction by the whole num-
ber, or divide the denominator.

2. Multiply /T by 16. Ans. If.

3. Multiply if by 3. Ans. 2f .

4. Multiply ff by 9. Ans. 6|.

5. Multiply T|fF by 25.

ART. 34. To multiply a whole number by a fraction.
Ex. 1. Multiply 15 by |.
15xJ = -y.=lli Ans. Or, 15-^4=3£, 3fx3=llf ^W5.

Explanation. — Since | = i of 3, f times 15 is \ of 3 times
15, or 45, and | of 45=11^ Ans. Or, since 1 times 15 is
15, } times 15 is \ of 15— 3f, and | times 15 is 3 times
32=111 Ans.

Ex.2. Multiply 5280 by | .

8)5280 5280

660 _j?

_

5 Or, 8)26400

_
3300 Ans. 3300 Ans.

Multiply the ivhole number by the numerator of the frac-
tion and divide the product by the denominator. Or,

Divide the whole number by the denominator of the frac-
tion and multiply the quotient by the numerator.

3. Multiply 56 by f . Ans. 35.

46 COMMON FRACTIONS.

4. Multiply 5280 by &. Ans. 316f.

5. Multiply 329 by 5J. Ans. 1809^.
Suggestion. — Multiply by \, and then by 5, adding results.

6. Multiply 435 by 16|. Ans. 7250.
Note. — By changing the whole number to a fraction

(12 =-j-)} the above ten examples may be solved as in the
following article.

ART. 35. To multiply one fraction by another.

Ex. 1. Multiply f by }.

*X*=T^ = H Ans'

Explanation. — Since £ is \ of 3, f times f must equal J of
3 times J. 3 times f- is -y-, and 1 of y- is f |.
Ex. 2. Multiply f by f of }|.

2

$ 2 ~t£ 4 ,
-X.- of — =— Ans.
il $ lo 15

RTJIL, K.

Multiply the numerators together, and also the denomina-
tors. Or,

Indicate the multiplication to be performed, and cancel the
factors common to the numerators and denominators.

Note. — It is not necessary first to reduce compound frac-
tions to simple ones.

Examples.

2. Multiply | by |.

3. Multiply -f7¥ by 2T- 4-ns- I-

4. Multiply f by J.

5. Multiply 56 by J. Ans. 49.

6. Multiply T<V by 24. Ans. 13f

7. Multiply 81 by 7|. -4»w. 65|.

8. Multiply 111 by 9f.

9. Multiply | of |f by T8o of f f >4rcs. T«¥.

10. Multiply f of T\ by T9T— |.

11. Multiply | of 8 by 9 times f .

COMMON FRACTIONS. 47

12. Multiply 8^—61 by 9|-f|. Ans. 19f.

13. Multiply 256 by 12^. Ans. 3152.

14. Multiply 12i by 16|. Ans. 208.

DIVISION OF COMMON FRACTIONS

ART. 36. To divide a fraction by a whole number.
Ex. 1. Divide TV by 3.

fP=T3o A™. Or, Tf-3 = ^=T\ Ans.
Explanation. — To divide a number by 3 is to take | of it ;
i of fV=T3o, or i of T«v=^T=T3r.

Divide the numerator of the fraction by the whole number,
or multiply its denominator.

32 x a m. p 1 e s'.

2. Divide f } by 9.

3. Divide JJ by 7.

4. Divide 6J by 9. ^715. if.

5. Divide 6084f by 5.

5)6084|

1216, 4| unolivided
4f =-y-5-5=-i-f Hence 6084|s-5=:1216i| Ans.

6. Divide 308| by 12. Ans. 25}f

7. Divide 32006} by 9. Ans. 3556^-

8. Divide 1000fV by 5. Ans. 200 rV
ART. 37. To divide a who^e number by a fraction.

Ex. 1. Divide 12 by f .

12 Or, 3)12

A 4

3)48 _4

16 Ans. 16 ^W5.

Explanation. — Since 1 is contained in 12 twelve times, | is
contained in 12 four times 12 times, or 48 times, and £, one

48 COMMON FRACTIONS.

third of 48 times, or 16 times. Or, 3 is contained in 12 four
times, and f , or 1 of 3, four times 4 times, or 16 times.

RTJ3L.E.

Multiply the whole number by the denominator of the frac-
tion, and divide the product by the numerator. Or,

Divide the whole number by the numerator, and multiply
the result by the denominator.

Examples.

2. Divide 16 by f .

3. Divide 256 by if Ans. 336.

4. Divide 225 by 12J.

5. Divide 30864 by 1. By -}. Ans. to last, 46296.

6. Divide 50 by 6f By 3i.

7. Divide 284 by f of f . Ans. 1136.
Note. — By reducing the whole number to an improper

fraction the above 15 examples may be solved as in the follow-
ing article.

ART. 38. To divide one fraction by another.

Ex. 1. Divide & by f .

Explanation. — -Since £ is equal to \ of 3, the quotient of
sV, divided by 3, or /¥, will be four times too small, and
hence the quotient of ^\, divided by 1 of 3, or f , is equal to
4 times /„, or |f ==|. Observe that this is, in effect, the same
as multiplying the dividend by the divisor inverted.

Invert the divisor and proceed as in multiplication of
fractions.

Examples.

2. Divide f by \.

3. Divide f by f. Ans. If

4. Divide 7i by 8^.

5. Divide 4| by 6|. Ans. ||.

6. Divide 18| by 15}.

DIVISION OF COMMON FRACTIONS. 49

7. Divide f of J by J of 5f. Ana. T2T.

8. Divide J of 4j by 1 of 5£.

9. Divide J of 8 by f of 7. Ana.

10. Divide 12 J of J by 8J of J.

11. Divide A + 4} by 4}— 3}i.

12. Divide TV of 44 — 1 of T7T by 5\— 4}.

13. Divide 125f-62} by 37*.

14. Divide 4i + 6f by T5T.

15. Divide 9TV+4j x f by 6|. u4w*. Iff
ART. 39. To reduce a complex fraction to a simple one.

Ex. Keduce I to a simple fraction.

Explanation. — It is evident that a complex fraction is only
an indicated division of one fraction by another, in which the
numerator is the dividend, and the denominator the divisor.
In the example J is the dividend, and | the divisor. "We may
proceed as in division, or it is plain that the same result may
be obtained by multiplying the extremes, 4 and 9, for a nume-
rator, and the means, 5 and 8, for a denominator.

RTJ3L.E,

Divide the numerator of the complex fraction by the, de-
nominator as in division of fractions.

E x a m pies.

2. Eeduce - to a simple fraction.

T72

2_

3. Eeduce - to a simple fraction. Ans. |.

4. Keduce - — *— to a simple fraction.

33i

5. Keduce -^r~ to a simple fraction. Ans. |.

**»

50 MISCELLANEOUS PROBLEMS.

6. Keduce -| to a simple fraction.

4"

7. Keduce I to a simple fraction. Ans.

8. Keduce r~^~i to a simple fraction. Ans.

~ ~

MISCELLANEOUS PROBLEMS.

ART. 40, 1. What is the sum of f , £, f , and T72 ?

2. What is the difference between } and f ?

3. Multiply | by 3£.

4. Divide f by 3j.

5. What is the sum, difference, product, and quotient of
3J and 2i ?

6. What will be the cost of 15^ pounds of butter at 16|
cents a pound ? Ans. $2.58i.

7. At $4| per yard, how many yards may be bought for
$11$ ? .^s. 2f

8. At 28$ cents per bushel, how many bushels of oats may
be bought for 16 1 cents ? • Ans. ^ bushels.

9. How many pounds in four bags, the first containing
360} , the second 580}, the third 296|, and the fourth 375 T\ ?

Ans. 1614jf Ibs.

10. In 5 hogsheads of sugar containing, respectively, 945^
1054^, 963$, 901f f, and 899f , how many pounds ?

11. A man has 4 lots ; the first containing 320}| acres,
the second 225f , the third 160|, and the fourth 278f ; how
many acres in all ? Ans. 986 ^ A.

12. A man owes the following sums : to A $32.56}, to B
$44.95T\, to C $32.72}, to D $53.31 A, to E 192.05TV How
much does he owe in all ?

13. A farm is divided into 5 fields, containing, respectively,
as follows : 20|, 56T9T, 36f , 9|, and 102jf acres. How many
in all ? Ans. 226f f f A.

14. A man purchased } of a yard of velvet at the rate of
$3.62^ per yard ; what did it cost him ? Ans. $3.17T36 .

MISCELLANEOUS PROBLEMS. 51

15. A man owned f of a boat, and sold i of f of his share
for $2400. At that rate, what was the whole worth of it ?

Ans. $19200.

16. James has f of an orange. He gives Horace ^ of this
amount, and then divides the remainder equally between three
boys. What part does each of the three boys receive ?

Ans. }.

17. If f of a barrel of flour costs $5, how much will 2 bags
of flour cost, one containing | of a barrel, and the other f of a
barrel? Ans. $12.

18. Bought | of f of 5 j yards of broadcloth at the rate of
§3.50 per yard. Required the cost of it. Ans. $8.02-^.

19. What will be the cost of 7£ yards of muslin at 12i
cents per yard, and 12 1 yards of gingham at 18 f cents per
yard? , Ans. $3.28}.

20. I purchased 7 loads of coal, each containing 15 f bushels,
at 12^ cents per bushel. Required the cost. Ans. $13.78j.

21. A owns f of a vessel, and sells f of his share to B for
$45000. What part of the vessel has he left, and what is it
worth at that rate ? Ans. ^ left, worth $15,000.

22. A owns f .of a ship. He sells | of his share to B for a
certain sum, and | of what he then owns to C for $5,000.
What was the value of the whole ship at C-'s rate of purchase ?

Ans. $72000.

23. A owns T% of an acre of land, and B f of an acre.
How much does A own more than B ? How many times
more ? How much do they both own ?

Ans. to the last, |f.

24. I have $1000 and wish to lay out $346f of it in sugar
at 8^ cents per pound, and the remainder in coffee at 11 f cents
per pound. How many pounds of coffee do I buy ?

Ans. 5561-fVa Ibs.

25. A merchant directed his agent to lay out f of $2354 in
wheat at 87| cents^per bushel ; T30- of it in rye at 56 £ cents per
bushel ; and the remainder in oats at 31 £ cents per bushel
How many bushels of each did he purchase ?

Ans. to last, 564f f bus. of oats.

52 DECIMAL FRACTIONS.

26. What will 8.J- pounds of sugar cost at 18f cents per
pound ?

27. A has 6| acres in one lot and 7| in another ; B has 5f
times as much as A. How many has he ? Ans. 83f ]• A.

28. What will f of f yards of cloth cost at f of f dollars
per yard ?

29. A merchant owns f of a mercantile establishment worth
$64,000. He sells f of his share to B, and | the remainder to
C. How much does he receive from B and C respectively,
and what part has he remaining ? Ans. From B, $33600.

From C, $11200.
Has left, TV

30. A merchant has 33T7F yards of cloth, from which he
wishes to cut an equal number of coats, pants, and vests.
What number of each can he cut if they contain 3f , 2|, and
1 j yards respectively ? Ans. 4.

31. A merchant owns T97 of a stock of goods; -f of the whole
stock were destroyed by fire, and -^ of the remainder damaged
by water. "What part of the whole stock remained uninjured ?
How much did the merchant lose, provided the uninjured

are sold at cost for $5400, and the damaged at half cost?

An$. -£•$ uninjured.
Merchant Loses, 33,918.75.

DECIMAL FRACTIONS.

ART. 41, A decimal fraction is a fraction whose denomi-
nator is some power of ten, thus T5¥, Tf ¥? T/O are decimal frac-
tions.

In writing a decimal fraction the denominator is omitted,
the numerator being written in such a manner as to indicate
the denominator. This is done by continuing the decimal
scale used in writing whole numbers below or to the right of
the order of units.

The first order at the right of units is tenths, the second
hundredths, the third thousandths, etc.

DECIMAL FRACTIONS. 53

A point ( . ), called the decimal point or separatrix, is
placed between the order of units and the order of tenths. The
orders at the left of the decimal point express a whole number;
the orders at the right a decimal fraction, or simply a decimal.

The names of the orders at the right and left of the decimal
point, and the relation of decimals to whole numbers, are shown
in the following

TABLE.

3 j S §

3 C « 2 O

I J j 1 4 I I 4 j

4 7 £ I jl -3-7, c o "S 3

1 1 I I I ,1 I I I

i a J e « I & 3 s s ;g s « s

3333333 333333

WHOLE NUMBER. DECIMALS.

The orders at the right of the decimal point are called
decimal places. Thus in .0223 there are four decimal places.

The denominator of a decimal fraction is 1 with as many
ciphers annexed as there are decimal places in the numerator.
Thus the denominator of .00035 is 100000.

Since the value of decimal orders decreases in a tenfold ratio
from left to right, every cipher placed between decimal figures
and the decimal point, thus removing them one place to the
right, diminishes their value tenfold. Thus .025 is one-tenth
of .25.

Ciphers placed at the right of decimal figures do not change
their value. Thus .250=.25 and .8700=.87.

A whole number and a decimal written together constitute
a mixed number, or a mixed decimal, as 25.037.

Note. — When the denominator of a decimal fraction is
written, it is usually considered a common fraction ; the term
decimal being only applied when the denominator is under-
stood. The above definition of a decimal fraction is, however,
strictly correct.

54 NUMERATION OF DECIMALS.

NUMERATION OF DECIMALS.

ART. 42. In reading a decimal expressed in figures, two
things are necessary : 1st. To ascertain what the figures ex-
press as a whole number. 2d. To ascertain the order of the
right hand figure. In a whole number, the right hand figure
is always units. In a decimal, it is found by commencing at
the decimal point and naming each order toward the right.

Ex. 1. Express in words .002015607.

Explanation. — Commence at the right hand and separate
the figures into periods as in whole numbers, thus : 2.015.607.
Next commence at the decimal point and name the orders to
the last decimal figure, which is billionths. Then read the
decimal as a whole number, adding the name of the last deci-
mal figure, thus : two millions, fifteen thousand, six hundred
and seven billionths. Hence the following general

Read the figures as in whole numbers and add the name of
the last decimal order.

DE x a m pies.

Express in words the following decimals :

2. .01012305

3. .000027

4. .500006

5. 207.0084

Suggestion. — Read the whole number as units, and then
the decimal.

6. 7080.00607008

7. .002005505

8. .006

9. 600.06

10. 1000.001

11. 25000000.000250
-12. 206.000000206

NOTATION OF DECIMALS. 55

NOTATION OF DECIMALS.

ART. 43. Ex. 1. Express in figures ten thousand five hun-
dred and five milliontKs.

Explanation. — Write the numerator of the decimal as a
whole number, thus : 10505. Then place the decimal point so
that the right hand figure may be millionths, filling up the
vacant order with a cipher, thus : .010505.

Write the decimal as a whole number, and place the decimal
point so that the right hand figure shall be of the same name
as the decimal.

Examples.

Express in figures :

1. Twenty-five thousandths.

2. Twenty-five millionths.

3. Twenty-five hundredths.

4. Two hundred and five ten-thousandths.

5. Two hundred and five ten-millionths.

6. Twenty thousand and five millionths.

7. Two thousand and four ten-thousandths.

8. Six hundred and fifty units and thirty-seven thou-
sandths.

9. One unit and one millionth.

10. Five thousand units and five thousandths.

11. Two thousand five hundred and six hundredths..
Note. — The above is an improper decimal. • The point falls

between the figures, thus : 25.06.

12. Nine millions, fifteen thousand, and twenty-five mil-
liontlis.

13. Eight thousand and forty ten millionths.

14. One million and one millionths.

56 REDUCTION OF DECIMALS.

REDUCTION OF DECIMALS.

ART. 44. A whole number may be changed to a mixed
decimal, or a decimal to an equivalent decimal of a lower order
by annexing ciphers. Thus : .025= .025000, and 325. = 325.000.
This is, in effect, multiplying both terms of a fraction by the
same number.

A mixed decimal may be reduced to an improper decimal
fraction by removing the decimal point and writing the de-
nominator, thus : 205.025=a-f l-jrl^. The following examples

will make the student familiar with these changes :

1. Keduce .205 to millionths. Ans. .205000.

2. Eeduce .0225 to ten-millionths.

3. Eeduce .14 to hundred-thousandths.

4. Keduce .0205 to billionths.

5. Keduce .02301 to billionths.

6. Keduce .5 to millionths.

7. Keduce 25. to thousandths. Ans. 25.000.

8. Keduce 404. to hundredths.

9. Keduce 4. to millionths.

10. Keduce 40. to ten-thousandths.

11. Keduce 62.5 to thousandths. Ans. 62.500.

12. Keduce 6.02 to millionths.

13. Keduce 4.506 to billionths.

14. How many tenths in 40 units ? Ans. 400.

15. How many millionths in 5 thousandths ? Ans. 500.

16. How many thousandths in 62.304 ? Ans. 62304.

17. How many millionths in 36.0394 ? Ans. 36030400.

18. How many hundredths in 400 ? Ans. 40000.

19. How many tenths in 6 tens ?

20. How many millionths in one million ?

ART. 45. To reduce a decimal to an equivalent common
fraction.

Ex. Keduce .25 to an equivalent common fraction.

= T- Ans.

REDUCTION OF DECIMALS. 57

Supply the denominator, and reduce the fraction to its
lowest terms.

E x am pies.

Eeduce the following decimals to equivalent common frac-
tions :

1. .20506. 7. 62.25. Ans. 62J.

2. .250. Ans. J. 8. 6.225.

3. .75. 9. 80.025. Ans. 80¥V-

4. .125. Ans. 1. 10. 8.0375.

5. .0075. 11. 15.02. Ans. l^\.

6. .0125. Ans. TV 12. 120.0125.

ART. 46. To reduce common fractions to an equivalent
decimal.

Ex. Keduce £ to a decimal.

4)3.00

.75 Ans.

Explanation.— -}=J of 3 ; but 3=3.00, hence } =iof 3.00
=.75.

33, TILE.

Annex ciphers to the numerator and divide by the denomi-
nator. Point off as many decimal places as there are annexed
ciphers.

IE x a m. p 1 e s •

2. Keduce £ to a decimal.

3. Keduce Y7T to a decimal.

4. Keduce Tf T to a decimal. Ans. .024.

5. Keduce ¥~ to a decimal.

6. Keduce 2570- to a decimal.

7. Keduce 12 f to a mixed decimal. Ans. 12.75.

8. Keduce 25T3¥ to a mixed decimal.

9. Keduce 300T|¥ to a mixed decimal.

10. Keduce ^-f-8- to a mixed decimal.

11. Keduce 6.37£ to a mixed decimal. Ans. 6.3775.

12. Keduce .07| to a pure decimal. Ans. .07125.

58 ADDITION OF DECIMALS.

ADDITION OF DECIMALS

ART. 47. Ex. 1. Add 6.025, 65.37, 100.0035, and .875.

6.025
65.37 Explanation. — Since decimals are written

100.0035 upon the same scale as whole numbers, they

****** are added in the same manner.

172.2735 Ans.

Write the numbers so that the figures of the same order
shall stand in the same column.

Add as in whole numbers, and point off in the result as
many decimal places as are equal the greatest number found in
any of the numbers added.

Note. — The decimal points of the several decimals added
and of the answer stand in the same column.

rf Examples.

Ex. 2. Add .37J, .02561, .00015, .5J, .27i, and .026.
.37| = .3775
.02561= .02565
.00015= .00015
.5i = .533331
.271 = .273331
.026 = .026

1.23596| Ans.

3. What is the sum of 256 thousandths, 3005 millionths,
207 ten-thousandths, 45 hundred-thousandths, 7 hundredths,
and 20037 millionths ?

4. Add .00675, 4.5689, 3.00007, 2.05, 3.6800|, .9375, 8.75,
6.4375.

5. What is the sum of 307 millionths, 56 1 ten-thousandths,
68f hundredths, 5 hundred-thousandths, 256i tenths, 18f ten-
millionths, and 25 hundredths ? Ans. 26.568483875.

6. Add 375 ten-thousandths, 375 thousandths, 375 hun-
dredths, 375 tenths, and 375 units. Ans. 416.6625.

7. A man bought 4 barrels of molasses, each containing

SUBTRACTION OF DECIMALS. 59

respectively 30.37|, 31 J, 33.6756, and 28.6 1 gallons. How
many gallons in all ?

8. A man bought 5 lots, containing, respectively, 26.62^,
220.2007, 56.9£, 5.8T\, and 150.68J acres. How many acres
in all ? Ans. 460.31945.

9. Add 360.00025, 3.75, 567.893, 60,000.637, 200.050006,
.0003625, 20.05.

10. Find the sum of 2|, .625, 6TV, 3.6TJT, 26.3125, 5.6,

SUBTRACTION OF DECIMALS.

ART. 48. Ex. 1. From 60.025 take 3.0825.
60.0250

3.0825 Explanation. — Same as in addition.

56.9425 Ans.

RTJIL.E.

Write the numbers as in addition of decimals, subtract as
in wJiole numbers, and point off as in addition of decimals.

Examples.

2. From .37^ take .0187}.

.37i =.375000
.0187| =.018775

.356225 Ans.

3. From 4.05 take 2.00075.

4. From 8.1 take 5.37f .

5. From 362 ten-thousandths take 1056 millionths.

Ans. .035144

6. From 875 thousandths take 62 ten-millionths.

7. From 100.001 J take 93.00075. Ans. 7.00105.

8. A man bought 8.75 T3FV yards of linen at one time and
29.0056 at another. He afterwards sold 25 ff yards. How
many has he left ?

9. From 7 tenths take 7 ten-millionths.
10. From 10001 ten-thousandths take 10001 ten-millionths.

60 DIVISION OF DECIMALS.

MULTIPLICATION OF DECIMALS.

ART. 49. Ex. 1. Multiply 2.5 by .25.

2.5 Explanation. — 2.5== H, -25=TVo; an(i hence

2.5 x .25= if x TV*= rWir=.625.

.625

RULE.

Multiply as in whole numbers, and point off as many figures
in the product as there are decimal places in the multiplicand
and multiplier.

Note. — If there are not enough figures in the product, prefix
ciphers. Thus: 1.6 x. 016=.0256 ; .01 x. 003 =.00003.

IE x a m. pies.

2. Multiply 37.5 by 4.5.

3. Multiply $16.37^ by 3 hundredths.

4. What is 12 hundredths of $100.15 ?

5. What is 7 tenths of .201 thousandths ?

6. Multiply .0015 by .125.

DIVISION OF DECIMALS.

ART. 50. All the examples in Division of Decimals fall
under one of three cases, viz. :

1. When the decimal places in the dividend equal those of
the divisor.

2. When the decimal places of the dividend exceed those of
the divisor.

3. When the decimal places of the dividend are less than
those of the divisor.

These three cases are illustrated in the following examples :
Ex. 1. Divide 6.25 by .25.

2 Explanation. — Since the quotient arising

J* ' '_ - — . from dividing one number by another of the

same denomination is a whole number, 625
hundredths divided by 25 hundredths must give 25 units.

DIVISION OF DECIMALS. 61

Ex. 2. Divide .864 by 3.6.

Explanation. — 36 tenths (3.6) is con-

3.6).864.(.24 Ans. tained in 8 tenths (the same denomina-
-YTT tion) 0 times ; hence there are no units

144 in the quotient. 36 tenths is contained

in 86 hundredths 2 tenths of a time and
14 hundredths remaining. 36 tenths is contained in 144 thou-
sandths 4 hundredths of a time. Hence .864-^-3. 6 =.24.
Ex. 3. Divide 13.2 by .033.

Explanation.— 132 = 13.200 = 13200 thou-
.033)13.200 sandths, which divided by 33 thousandths must
400. give 400, a whole number.

33, TILE.

FIRST CASE. — Divide as in whole numbers ; the quotient
will be in units.

SECOND CASE. — Divide as in whole numbers, and point out
as many places in the quotient as the decimal places of the
dividend exceed those of the divisor.

THIRD CASE. — Make the decimal places of the dividend
equal to those of the divisor by annexing ciphers, and then pro-
ceed as in whole numbers. The quotient will be in units.

Note. — In either case, if there is a remainder, the division
may be continued by annexing ciphers ; but each cipher thus
annexed will give one decimal figure in the quotient.

Proof. — It is well for the student to test the correctness of
his answer by multiplying the divisor by the quotient. If the
quotient is correct, the product will be the dividend.

E x a TOO. pies.

4. Divide 6.25 by 2.5. Ans. 2.5.

5. Divide 6.25 by .025. Ans. 250.

6. Divide .625 by 25.

7. Divide 25.6 by .016.

8. Divide'256 by .16.

9. Divide .256 by 160. Ans. .0016.

10. Divide .001 by 100.

11. Divide .0025 by 50.

62 CONTRACTIONS.

12. Divide 4.2 by 31i.

13. Divide $16 by $0.25.

14. Divide 3 by 1.25. Ana. .024.
Note. — In this example, we annex two ciphers to make the

division possible ; this gives two decimal places in the dividend.
We add another cipher to obtain the quotient figure 4 ; thus
making in all three decimal places.

15. Divide 5 by 400.

16. Divide 9 by 1500.

17. Divide 6.4 by 80.

18. Divide .1 by .121. . Ans. .08.

19. Divide 6| by .08.

20. Divide 16| by .033i.

CONTRACTIONS.

ART. 51. To divide a decimal by 10, 100, 1000, etc., re-
move the decimal point as many places to the left as there are
ciphers in the divisor.

Note. — If there are not figures enough in the number, prefix
ciphers.

IE x am. pies.

1. Divide 6.25 by 100. Ans. .0625.

2. Divide .25 by 10.

3. Divide .45 by 1000.

4. Divide .01 by 100.

ART. 52. To multiply a decimal by 10, 100, 1000, etc., re-
move the decimal point as many places to the right as there
are ciphers in the multiplier. Thus : 62.5 x 100 = 6250 ;
4.3 x 10=43.

$43.50
150.
1.68

Multiply

456.30
1000.
38.
5.60

by 100.

REDUCTION OF DENOMINATE NUMBERS. 63

REDUCTION OP DENOMINATE
NUMBERS.

ART. 53. A denominate number is composed of concrete
units of different weights, measures, etc.

Denominate numbers are of two kinds, simple and com-
pound.

A simple denominate number is composed of units of a
single denomination, as 10 pounds ; 12 hours.

A compound denominate number, or simply a compound
number, is composed of units of several denominations of the
same weight, measure, etc., as 5 days 16 hours 20 minutes.

Reduction is the process of changing the form of a denom-
jnate number without altering its value.

Remark. — In treating of Denominate Numbers, we omit
both tables and rules. The student is supposed to be familiar
with the tables in common use.

ART. 54. To reduce a denominate number of a higher de-
nomination to a simple denominate number of a lower.

Examples.

1. Kecluce 5 Ib. 6 oz. 10 pwt. 18 gr. of silver to grains.

lb. oz. dwt. er.

5 6 10 18 Ans. 31938 gr.

12

66 oz.
20

1330 pwt.

24
31938 gr.

2. How many seconds in 10 hours ?

10 h. Ans. 36000 s.

60

600 m.
60

36000 s.

64 REDUCTION OF DENOMINATE NUMBERS. .

3. Keduce J Ib. of butter to drams. Ans. 199£ dr.

ix16=ii5.;xl6=:-L-V--=199i dr.

4. Keduce g-J¥ yd. to inches. Ans. f £ in.

aVo x 3 = sVo, x 12=f f. Ans. Or, JLy^jj = .3 in.

5. Keduce .48 yd. to nails. Ans. 7.68 na.

.48 yd.

L92 qr.

4
~7j68na.

6. Reduce 12i bu. to pints. Ans. 800 pt.

7. In f- of an acre how many perches ? Ans. 140 p.

8. Keduce 12 h. 20 m. to seconds. Ans. 44400 s^

9. Keduce £ hhd. of wine to pints. Ans. 378 pt.

10. Keduce .375 T. to pounds (Avoirdupois).

Ans. 750 Ib.

11. In .7 of a bushel how many pints ? Ans. 44.8 pt.
IS. In 8.75 yd. how many nails ? Ans. 140 na.

13. Keduce 2| days to minutes. Ans. 3840 m.

14. Keduce 5f cords to solid feet. Ans. 736 s. ft.

15. In .45 of a rod how many inches ? Ans. 89.1 in.

16. Keduce 12 cubic feet to cubic inches.

Ans. 20736 c. in.

17. Keduce 13.5 hhd. of beer to quarts. Ans. 2916 qt.

18. Keduce 5 Ib. 6 oz. 12 pwt. of gold to pwt.

Ans. 1332 pwt.

19. Reduce 5.24 Ib. of calomel to ounces. Ans. 83.84 oz.

20. Keduce 7 Ib. (Troy weight) to grains.

Ans. 40320 gr.

21. Reduce .65 of a yard to quarters. Ans. 2.6 qr.

22. In .24 of a ream of paper how many sheets ?

Ans. 115.2 sheets.

23. In f of a barrel of flour how many pounds ?

Ans. 78f Ib.

24. Reduce 7 Ib. 8| oz. of butter to drams.

Ans. 1930| dr

REDUCTION OF DENOMINATE NUMBERS. 65

25. In j %-$ Ib. of brass how many ounces ? Ans. TV2j oz.
ART. 55. To reduce a simple denominate number of a lower
denomination to a denominate number of a higher.

Examples.

1. Reduce 15969 gr. to pounds.

Ans. 2 Ib. 9 oz. 5 pwt. 9 gr.
24)15969 gr.
20)665 pwt. 9gr.
12)33_ oz. 5 pwt,
~2~" Ib. 9oz.

2. Reduce f of an inch to the fraction of a yard.

in. ft. yd.

¥xrV— rls"? Xj=sjjy. Ans. ^|¥ yd.

Explanation. — J of an inch is J of TV of a ft., which is
ft., and T£¥ of a foot is Tlj of 1 of a yard=¥JT yd.

3. Reduce .48 of a nail to the decimal of a yard.

4).48 n. Ans. .03yd.

4)12 qr.
.03 yd.

4. Reduce 25.6 dr. to the decimal of a pound.

16)25.6 dr. Ans. .1 Ib.

16)1.6 oz.
.lib.

5. Reduce 414 gal. wine to hhd. Ans. 6 hhd. 36 gal.

6. Reduce 2461 pwt. to pounds.

Ans. 10 Ib. 3 oz. 1 pwt.

7. Reduce 1357 pts. to bushels. Ans. 21 bu. 6 qts. 1 pt.

8. Reduce 98 furlongs to miles. Ans. 12 m. 2 fur.

9. Reduce 307200 perches to square miles. Ans. 3 sq. m.

10. Reduce 4032 gills to hhd. of wine. Ans. 2 hhd.

11. Reduce T3F gal. to the fraction of a hhd. Ans. -^^j.

12. Reduce T7T hours to the fraction of a day. Ans. ^f -5.

13. Reduce 6| pt. to the fraction of a bu. Ans. T\.

14. Reduce 645 in. to yd. Ans. 17 yds. 2 ft. 9 in.

15. Reduce 2176 en. ft, to cords. Ans. 17 cords.

16. Reduce 1152f qt. to hhd. Ans. 4 hhd. 36.2 qt.

17. Reduce 523 nails to yards. Ans. 38 yd. 3 qr. 3 na.

66 REDUCTION OF DENOMINATE NUMBERS.

18. Reduce 23.04 drams to Ibs. Ans. .09 Ib.

19. Reduce 184.8 hours to weeks. Ans. 1.1 weeks.

20. How many acres in a street 5 rods wide and 2i miles
long ? Ans. 25 acres.

ART. 56. To find what part one denominate number is of
another ?

Note. — The first ten examples contain abstract numbers, and
are designed to introduce denominate numbers.

3S x a m. pies.

1. 8 is what part of 12 ? Ans. 1.
Explanation. — 1 is ^ °f 12, and 8 is 8 times TV of 12,

which is T\ of 12= f of 12.

2. 9 is what decimal part of 15 ? Ans. .6.
Explanation. — 9 is T9j of 15, and T9? changed to a decimal

is .6.

3. | is what part of £ ? Ans. f .

|=f. Or,f=TVand}=T'T; TV=-TV=i Since TV is i of A,
T33 is 8 times 1 of T9¥=f of T\.

4. What part of GI is 2| ? ^4rcs. if.
23 i

_ !L __ 2_ _ 1 6 Or 92 - 8 _ 16 o-nrl £ 1 - 1 3 - 3 9 • 16- 39 - 1 6

j.— • J_3 — 3T- Jr? ^3-— 3—- 8~ an(1 b2— "2~— F- ? -8-~"^~— 38^'

5. 15 is what part of 12 ? Ans f .

6. 27 is what part of 48 ? ^4rcs. T\ .

7. What decimal part of 72 is 54 ? Ans. .75.

8. What decimal part of f is f ? ^4rcs. .8.

9. What decimal part of 10 is 4£ ? Ans. .45.

10. What part of .45 is .09 ? Ans. }.

11. 2 ft. 6 in. is what part of a yard ? ^4rcs. f .
2 ft. 6 in.=30 in., and 1 yd.=36 in. ; 30 in.-f-36 in.=f.
Suggestion. — Reduce denominate numbers to the same de-

nomination.

12. What part of a week is 5 d. 10 h. ? Ans. f f .

13. What part of 2 acres is 3 R. 25 p. ? Ans. f }.

14. What decimal part of 5 hours is 40 minutes ?

Ans. .13i.

DENOMINATE NUMBERS. 67

15. What decimal part of 5 gals, is 3 qts. 1 pt. ?

Ans. .175.

16. What part of $5 is 87 J cents ? Ans. T\.

17. What decimal part of a gallon is 3 pints ?

Ans. .375.

18. What part of .45 Ib. Troy is .45 oz. ? Ans. TV

19. £ oz. is what part of f Ib. Avoirdupois ? ^TIS. T|T.

20. 4 quires of paper is what decimal part of a ream ?

Ans. .2.

21. What part of a mile is 6 fur. 16 rds. ? Ans. f .

22. What decimal part of a pound is 10 oz. 4 pwts. ?

Ans. .85.

23. What decimal part of a bushel is 3 pks. 4 qts. ?

Ans. .875.

24 What part of a week is 3 d. 17 h. 36 m. ? Ans. T«T.
ART. 57. To reduce a fraction of a higher denomination to
integers of a lower.

Examples.

1. Reduce £ of a day to integers. Ans. 14 h. 24 m.

d. b. h. b. m.

3X24 72 "IAS 2X60 f)A

J ~~5~ -"-^S? 5 ^r*'

2. Reduce .85 of a day to integers. Ans. 20 h. 24 m.

.85 d.
24
20.40 h.

60
2~400m.

3. Reduce .375 hhd. to integers.

Ans. 23 gals. 2 qts. 1 pt.

4. Reduce .9 Ibs. Troy to integers. Ans. 10 oz. 16 pwts. .

5. Reduce £ rod to integers. Ans. 4 yds. 1 ft. 9 in.

6. Reduce .5625 cwt. to integers.

Ans. 2 qrs. 6 Ibs. 4 oz.

7. Reduce 30 T\ hhds. to integers.

Ans. 30 hhds. 27 gals. 2 qts. 2 gills.

8. Reduce f mile to integers.

Ans. 4 fur. 17 rds, 4 yds. 10 in.

68 DENOMINATE NUMBERS.

9. Eeduce 250.35 Ibs. Troy to integers.

Ans. 250 Ibs. 4 oz. 4 pwts.

10. Keduce .8 mile to integers. Ans. 6 fur. 16 rods.

11. Keduce £f to integers. Ans. 13s. 4d.

12. Keduce .45 peck to integers. Ans. 3 qts. 1.2 pts.

13. What is the value of f week ?

Ans. 2 d. 19 h. 12 m.

14. What is the value of .75 bu. ? Ans. 3 pecks.

15. What is the value of T\ day ? Ans. 13 h. 30 m.

ADDITION OF DENOMINATE NUMBERS.

ART. 58. Ex. 1. Add together 5 Ibs. 6 oz. 13 pwts. 22 grs. ;

12 Ibs. 9 oz. 18 pwts. ; 7 oz. 19 pwts. 21 grs. ; 24 Ibs. 11 oz.

18 grs.

ibs. oz. pwts. grs. Explanation.— Having written

5 6 13 22 numbers of the same denomination in

12 9 18 00 the same column, add, reducing as

7 19 21 •

far as possible the lower denomina-
^4 11 UU lo

^o — Ti — To — To~ A tions to a higher. In this example.

4o 11 1^ lo Ans. .

the sum of the grains is 61 grs.=

2 pwts. 13 grs. Write 13 grs., and add the 2, pwts. to the
column of pwts., and proceed as before.

2. A man purchased 4 loads of corn : the first contained
25 bu. 3 pks. 7 qts. 1 pt. ; the second, 30 bu. 2 qts. ; the third,
37 bu. 1 pk ; the fourth, 29 bu. 1 pk, 7 qts. 1 pt. How much
did he buy ? Ans. 122 bu. 3 pks. 1 qt.

3. Find the sum of 5 gals. 3 qts. 1 pt. ; 10 gals. 1 pt. 1
gill ; 25 gals. 1 pt. ; 19 gals. 1 qt. 1 gill ; and 30 gals. 1 pt. 3
gills. Ans. 90 gals. 2 qts. 1 pt. 1 gill.

4. A man has 4 farms. The first contains 110 A. 3 K. 25
P. ; the second, 95 A. 1 K. 20 P. ; the third, 205 A. 0 R.
15 P. ; and the fourth, 90 A. 3 K. 35 P. How many acres in
all ? Ans. 502 A. 1 K. 15 P.

DENOMINATE NUMBERS. 69

5. I purchase of a merchant 19 yds. 3 qrs. of cloth ; of a
second, 25 yds. 3 qrs. 2 na. ; of a third, 17 yds. 3 na. How
many yards did I buy ? Ans. 62 yds. 3 qrs. 1 na.

SUBTRACTION OF DENOMINATE NUMBERS.

ART. 59. Ex. 1. From 12 Ibs. 6 oz. take 7 Ibs. 9 oz. 13 pwts.
22 grs.

11 17 19 24 Minuend changed in form.

Ibs. oz. pwt. grs.

12 6 00 00 Minuend.

7 9 13 22 Subtrahend.
4862 Remainder.

Ex. 2. From 3 m. 7 fur, 30 rds. take 5 fur. 38 rds. 10 ft.
9 in.

36 69 15* 12 Minuend changed in form.

m. fur. rds. ft. in.

3 7 30 00 0

5 38 10 9

3 1 31 5i 3

3 1 31 59 Ans.

3. From 1 m. take 4 fur. 3 rds, 4 yds. 2 ft. 6 in.

4. From 2 T. 4 cwt. take 17 cwt. 2 qrs. 8 Ibs.

5. How long from June 12, 1855, to April 3, 1859 ?

mo. da.

1859 4 3
1855 6 12

3 9 21 Ans.

6. How long from the signing of the Declaration of Inde-
pendence, July 4, 1776, to the battle of New Orleans, January
8, 1815 ? Ans. 38 yrs. 6 mo. 4 da.

7. From the battle of Lexington, April 18, 1775, to the
battle of Montebello, May 5, 1859 ? Ans. 84 yrs. 17 da.

8. How long from the battle of Saratoga, Sept. 7, 1777, to
Perry's victory, Sept. 19, 1813 ? Ans. 36 yrs. 12 da.

70 DENOMINATE NUMBERS.

MULTIPLICATION OF DENOMINATE NUMBERS.
ART. 60. Ex. 1. Multiply 5 fur. 35 rds. 16 ft. 9 in. by 5.

m. fur. rds. ft. in.

5

35

16 9
5

3

5

20

* 9
1=6

3 5 20 13 Ans.

2. What is the distance round a square field, each side of
which is 35 rds. 5 yds. 2 ft. 9 in. in length ?

Ans. 3 fur. 24 rds. 1 yd. 2 ft.

3. What is the weight of 5 watch chains, each containing
1 oz. 7 pwts. 13 grs. of gold ? Ans. 6 oz. 17 pwts. 17 grs.

4. Bought 7 loads of corn, each containing 29 bu. 3 pks.
7 qts. 1 pt. ; how much corn did I buy ?

Ans. 209 bu. 3 pks. 4 qts. 1 pt.

5. Bought 11 pieces of broadcloth, each containing 34 yds.
1 qr. 3 na. ; how many yards did 1 buy ?

Ans. 378 yds. 3 qrs. 1 na.

6. How much wine in 7 casks, each containing 75 gals.
3 qts. 1 pt. ? Ans. 531 gals. 0 qts. 1 pt.

DIVISION OF DENOMINATE NUMBERS.

ART. 61. Ex. 1. Divide 1 m. 3 fur. 28 rds. 5 yds. 2 ft. 8 in.
by 5.

m. fur. rds. yds. ft. In.

5)1 3_28 5__2 8_

2 13 ~4~ 1 5J.

2. A man divided 1578 acres of land equally between 7
children ; what was the share of each ?

Ans. 225 A. 1 R. 28^ P,

DENOMINATE NUMBERS. 71

3. A piece of cloth containing 36 yds. 3 qrs. will make
5 suits of clothes ; how much cloth in each suit ?

Ans, 7 yds. 1 qr. If na.

4. Seven men purchased 8 cwt. 3 qrs. 20 Ibs. of sugar.
What was the share of each ? Ans. 1 cwt. 1 qr. 2 Ibs. 13-f oz.

5. Four men agreed to share equally 3 sacks of coffee, each
containing 2 cwt. 1 qr. 15 Ibs. What was the share of each ?

Ans. 1 cwt. 3 qrs. 5 Ibs.

MISCELLANEOUS PROBLEMS.

ART. 62. Ex. 1. What will .65 of a ream of paper cost at
20 cents a quire ? Ans. $2.60.

2. What will f of a ream of paper cost at £ of a cent per
sheet? Ans. $2.25.

3. What will f of a barrel of beef cost at 6^ cents a pound ?

Ans. $4.69.

4. What mustjbe the height of a wood-bed that is 12 feet
long and 3^ feet wide to hold just one cord ? Ans. 3^T ft.

5. What will it cost to excavate a cellar 18| feet long, 15|
feet wide, and 9 feet deep, at 20 cents per cubic yard ?

Ans. $19.12.

6. How many cords of wood in a pile 40 feet long, 7| feet
high, and 4 feet wide ? Ans. 9| cords.

7. What will .75 of a hhd. of wine cost at 75 cents a pint ?

Ans. $283.50.

8. Bought 12 barrels of flour at $6.50 per barrel, and sold
the same at retail at 4 cents a pound. How much did I gain ?

Ans. $16.08.

9. The cabin of the steamer Bostona is 165 feet long and
18 feet wide. What will it cost to carpet the same with
Brussels carpeting f of a yard wide at 80 cents a yard ?

Ans. $704.

10. At 25 cents a sq. yd., what will it cost to plaster the
ceiling of a room 18| feet long and 16 feet wide ?

Ans. $8.22.

72 DENOMINATE NUMBERS.

11. At 20 cents a sq. yd., what will it cost to plaster both
sides of a partition wall 52 feet long and 13 1 feet high, and an-
other wall 149 feet long and 11 feet high ? Ans. $52.02.

12. A gentleman's garden 200 feet long and 180 feet wide
is enclosed by a tight board fence 5£ feet high ? What will it
cost to paint the fence at 10 cts. per sq. yd. ? Ans. $46.44.

13. How many bricks, each being 8 in. long and 4 in. wide,
will it take to surround the above garden with a walk 6 feet
in width ? What will be the cost of the bricks at $4 per 1000 ?

Ans. 21168 bricks ; $84.67 cost.

14. A miller ground 5000 bushels of wheat, taking from
each bushel 4 quarts of wheat as toll. How many bushels of
wheat does he grind for his customers, and what does he re-
ceive for the work, wheat being worth 87^ cents a bushel ?

Ans. 4375 bushels, $546.87*.

15. What will be the cost of 25 boards, each being 15 ft.
long and 10 in. wide, at $30 per thousand ? Ans. $9.37^.

16. What cost 9 cwt. 1 qr. 18 Ibs. 12 oz. at $6.40 per cwt. ?

Ans. $60.40.

17. What will 10 Ibs. 8 oz. 8 pwts. of gold cost at $300 per
pound? Ans. $3210.

18. What will 3 f hhds. of molasses cost at 10 cents per
quart? Ans. $94.50.

19. What will be the cost of papering the walls of a room
40 feet long, 30 feet wide, and 9 feet high, at 30 cents a
bolt, each bolt being 9 yards long and 18 inches wide ?

Ans. $9.33i.

20. A farmer sold 30 bu. 2 pks. 1 qt. If pts. of clover seed
at $3.60 per bushel. How much did he receive ?

Ans. $191.10.

21. How many bushels of coal will a boat 100 feet long,
42 feet wide, and 4 feet deep contain, a bushel of coal being 1^
of a cubic foot ? Ans. 10800.

22. If there are 6 yds. 3 qrs. 2 na. in one suit of clothes,
how many yards will clothe an army of 128,000 men ?

Ans. 880,000.

PRACTICE.

73

PRACTICE.

ART. 63, Many of the examples met with in common
business, may be easily solved by exercising a little tact, espe-
cially where the prices used contain an aliquot part of a dollar,
or where the cost of compound quantities is required.

A few examples will illustrate this method.

The aliquot parts of a dollar in common use are shown in

the following

50 cts.= i of $1.00

TABLE

I

25 cts. =4 of 50 cts.
12i « = | of 25 "

6i " = 4. of 12i "
16| " =1 of 33i "

81 " =|of!6f "

16| "

61 "

= i of 50

25 " = i of $1.00
12 .V " = i of $1.00

6} " =TV of 81.00
33} " = i of $1.00
16| " = i of 81 00

8} " = TVof $1.00

Ex. 1. Required the cost of 24 yds. of muslin at 12i cts.
a yd.

Solution.— At $1.00 a yd. it is worth $24.00.

At 12.i cts. a yd. it is worth only i of $24.00, which is
$3.00. Ans.

Ex. 2. Find the cost of 56 yds. at 37 J cts. a yd.

Solution.— At $1.00 a yd. the cost=$56.00.

At 25 cts. a yd. the cost=i of $56.00= $14.00.

At 12i cts. a yd. the cost=i of $14.00=$7.00.

The sum of the last two results =$21.00. Ans.

Ex. 3. Required the cost of 56 bbls. of flour at $6.87^ a bbl.
50 cts.= i $56.00=the cost at $1.00 a bbl.

25 " =

$385.00 = " " " $6.87,
Note. — See table of aliquot parts.

1

Ii

a bbl.

a

$336.00

28.00
14.00
7.00

=the cost at $6.00

it tt it KC\

= " « « .25

74

PRACTICE.

Ex. 4. Kequired the cost of 75 gals, of wine at $<

50 cts.= i $75.00=the cost at $1.00 a gal.

3.93f

$225.00 =the cost at $3.00 a gal.
37.50 = " " " .50 "
18.75 = " " " .25 "

f a gal.

25 " =

=

9.375 =

4.6875=

.121
.06}

$3.93£

Ex.

$295.3125= <
5. Find the cost of 25 bu. at ^.o.^-

"1 ft 2 r»j-a
J.UTT OLo.

Ex.6.
25 cts.=

6i " =

Re
i

4

i

1

2

$25.00 =the cost at $1.00 a bu.
4.16|= u " " .16| "

a yard.

$29.166= " " " $1.16} "
quired the cost of 75 yds. at 43 £ cts.
$75.00 =the cost at $1.00 a yd.

18.75 = " " " .25 a yd.
9.375 = " " " .12i «
4.6874= " " " .06} "

Ex.

50 cts
61 "

$32.8125= < " " .43 J "
7. Kequired the cost of 45 bu. at 56} cts. a bu.
_$45.00_ =the cost at $1.00 a bu.
~22.50~ = " " " .50 "
2.8125= " " " .06} "
~

Ex.
25 cts.

Ex.

2qrs.=

8. Find the cost of 9762 bu. at 25 cts. a bu.
I i | $9762. =the cost at $1.00 a bu.

$2440.50= " "~~« 25 "~

9. Kequired the cost of 7 yds. 3 qrs. at 75 cts. a yd.
i

$0.75 =the
7

cost of 1 yd.

" " 7 yds.
" " 2 qrs.
" "' 1 qr.

$5.25 = "
.375 = "
.1875= "

Ex.
a bu.

cts,

$5.8125= ' i 7 yds. 3 qrs.

10. Kequired the cost of 256 bu. of corn at 18f cts.

$256.00=the cost at $1.00 a bu.

6}

32.00= "
16.00= "

$48.00="^

.06} "

PRAC TICE.

75

Ex. 11. Find the cost of 15 Ibs. 15 oz. of butter at 25 cts. a Ib.

8 oz.=

4 " =
2 " =
1 " =

Ex.

cts. a Ib
4 oz.=

2 " =
1 " =

Ex.:

at $9.50
2 qrs.=

1 "

5 lbs.=

5 " =

Ex. ]

68 f cts.
2 qts.=

1 "

Ipt. =

Ex. 1

61 cts.=

i

2

1
i
1

12.

1

4

I

1
I

L3.
a

i
j

i

5
1

0

4.

as

1

j

I

5.

T

$0.25 = the cost of lib.
15

3.75 = " " " 15 Ibs.
125 = " « " 8oz.
625 = " " " 4 "
3125 — u " " 2 "
15625= " " " 1 "

$3.984375= " " " 15 Ibs. 15 oz.
Required tne cost of 9 Ibs. 7 oz. of cheese at 12i

$0.125 =the cost of 1 Ib.
9

1.125 = " ' " "9 Ibs.
3125 = " " " 4oz.
15625 = " " " 2 "
78125= " " " 1 "

$1.1796875= " " " 9 Ibs. 7 oz.
Required the cost of 5 cwt. 3 qrs. 10 Ibs. of sugar
cwt.

$9.50 =the cost of 1 cwt.
5

$47.50 = " " " 5 cwt.
4.75 = " " " 2 qrs.
2.375= " " " 1 "
475= " " " 5 Ibs.
475= " " " 5 "

$55.575= " " " 5 cwt. 3 qrs. 10 Ibs.
Find the cost of 15 gals. 3 qts. 1 pt. of molasses at
al
$0.6875 =the cost of 1 gal.
15

1.03125 = " " " 15 gals.
34375 = " " " 2 qts.
171875 = " " " 1 "
859875= " " " Ipt.

$10.9141125
Required the cost of 875 bu. at $1.06j a bu.
V $875.00= the cost at $1.00 a bu.
54.69= " " " .06i "

$929.69=

$1.06i

76 PRACTICE.

Ex. 16. If a man walk 24 m. 7 fur. 25 rds. in one day ;
how far can he walk in 5 d. 11 h. 50 m. ?

Ans. 137 m. 0 fur. 23T5¥\ rds.

Remark. — This example may be solved in the same manner
as the preceding ; the only difference is, the multiplicand (24
m. 7 fur. 25 rds.) is a compound number.

Ex. 17. What will be the cost of 3 qrs. 2 na. at $4.50 a yd. ?

Ans. $3.94.

Ex. 18. Kequired the cost of 13 cwt. 3 qrs. 20 Ibs. of cheese
at $9.12i a cwt. Ans. $127.29.

Ex. 19. Find the cost of a ham, weighing 15 Ibs. 13 oz. at
13 cts. a Ib. Ans. $2.06.

Ex. 20. What will be the cost of 17 A. 1 K. 15 P. of land
at $25.25 per acre ? Ans. $437.93.

Ex. 21. Find the cost of 19 yds. at $4.37i a yd.

Ex. 22. What are 156 bu. 3 pks. 7 qts. 1 pt. of wheat worth
at 93J cts. a bu. ? Ans. $147.17.

Ex. 23. Find the cost of 87i yds. at 87i cts. a yd.

Ans. $76.56.

Ex. 24. If a man walk 27 m. 5 fur. 15 rds. in one day ;
how far can he walk in 15 d. 10 h. 45 m. ?

Ans. 439 m. 1 fur. 26 rds.

Ex. 25. If a man earn 6 Ib. 15 oz. 15 dr. of cheese in one
day ; how much can he earn in 7 d. 7 h. ?

Ans. 51 Ibs. 5 oz. 6{ dr.

Ex. 26. A man can plow 2 A. 1 B. 25 P. in a day ? how
much can he plow in 5£ days ? Ans. 12 A. 3 K. 13 £ P.

Ex. 27. Find the cost of 6 T. 5 cwt. 3 qrs. 20 Ibs. of hay at
$16.62^- a T. Ans. $104.57.

Ex. 28. Kequired the cost of 10 loads of coal, each contain-
ing 15^ bu. at 12i cts. a bu. Ans. $19.37i.

Ex. 29. What will be the cost of making 29 m. 7 fur. 35
rds. of road at $975.75 a mile ? Ans. $29257.25.

Ex. 30. Kequired the cost of 10 cords 75 ft. of wood at
$2.87 i- a cord. Ans. $30.43.

Ex. 31. Kequired the cost of 55 bbls. of flour at $6.68| a
bbl. Ans. $367.81i.

RATIO. 77

RATIO.

ART. 64. Ratio is the relation of one number to another of
the same kind, and is expressed by their quotient. Thus the
ratio of 8 to 12 is expressed by 12-^-8, or -1/- ; and the ratio of
5 to 3 by 3-^5, or |.

A ratio is commonly expressed by separating the two num-
bers by a colon. Thus the ratio of 8 to 12 is written 8 : 12 ;
the ratio of 5 to 3 is written 5 : 3.

The two numbers are called terms of the ratio — the first,
or divisor, being called the antecedent, and the second, or divi-
dend, the consequent.

When the antecedent is less than the consequent, the value
of the ratio is greater than 1, and the ratio is called increas-
ing ; when the antecedent is greater than the consequent, the
value of the ratio is less than 1, and the ratio is called de-
creasing.

Ratios are of three kinds ; simple, complex, and compound.

A simple ratio is the ratio of two whole numbers, as 5 : 6,
and 12 : 5.

A complex ratio is the ratio of two fractional numbers, as
I : |, 2i : 5i, and 2.5 : .5.

A compound ratio is the product of two or more simple
ratios, as (5 : 4) x (3 : 2) x (3 : 4).

Compound ratios may be written in the form of fractions,
as i x | x f . In stating problems, the ratios are written under

5

each other without the sign of multiplication, as 3

3

A compound ratio may be reduced to a simple one by mul-
tiplying all the antecedents together for a new antecedent and
all the consequents for a new consequent.

Note. — The numbers that form a ratio must be either both
abstract, or both concrete. When concrete, they must be of
the same denomination, or such as may be reduced to the same

78 RATIO.

denomination, otherwise a division is impossible. 5 men have
no ratio to 10 hogs, nor 3 pens to 6 hens.

What is the value of each of the following ratios :

1. 7 : 14. Ans. 2. 10. 1.5 : .45.

2. 6:3. Ans. }. 11. .25 : .6.

3. 15 : 45. 12. 2.5 : 10.

4. 3:9. 13. 10 : 2.5.

5. 6:2. 14. $5 : $15.

6. 45 : 15. 15. $0.75 : $3.

7. f : f. 16. 2 ft. 6 in. : 10 ft.

8. 2i : |. 17. 2 Ib. 8 oz. : 10 oz.

9. f : T\. 18. 10 oz. : 2 Ib. 8 oz.

Ans.

PROPORTION.

ART. 65. A Proportion is an equality of ratios.

Four numbers are in proportion when the ratio of the first
to the second equals the ratio of the third to the fourth ; thus
4, 6, 8 and 12 are in proportion.

The equality of two ratios may be expressed by the sign of
equality, thus 4 : 8=6 : 12 ; or by four dots, thus 4 : 8 : : 6 : 12.
The last mpthod is the more common, and is read 4 is to 8 as
6 is to 12.

The first ratio of a proportion is called the first couplet ;
the second, the second couplet.

The first and third terms of a proportion, being the antece-
dents of the two ratios, are called antecedents ; the second and
fourth, being consequents of the two ratios, are called conse-
quents.

The first and fourth terms of a proportion are called ex-
tremes ; the second and third terms, means.

RATIO. 79

Both ratios of a proportion must be of the same kind, that
is, both increasing , or both decreasing, otherwise they cannot
be equal. Hence, in every proportion, if the first term is less
than the second, the third term is less than the fourth, and if
the first term is greater than the second, the third term is
greater than the fourth.

As ratios may be expressed in the form of fractions (see
Art. 64), the proportion 4 : 8 : : 6 : 12 may be written £=-V2-.
By multiplying each of these equal fractions by 6 (the denom-
inator of the second), we have 1^=12, and by multiplying
each of these equal quantities by 4 (the denominator of the
first fraction), we have 8x6=12x4. But 8 and 6 are the
means of the above proportion, and 12 and 4 its extremes.
Hence,

In every proportion, the product of the means equals the
product of the extremes.

Therefore,

1. If the product of the two means of a proportion be
divided by either extreme, the quotient will be the other extreme,

2. If the product of the two extremes of a proportion be
divided by either mean, the quotient loill be the other mean.

It follows from the above, that if any three terms of a pro-
portion are given, the remaining term may be found. Find the
missing term in each of the following proportions :

1. 15 : 20 : : 90 : — .

2. — : 16 : : 90 : 20.

3. 45 : 90 : : — : 28.

4. 27 : — : : 108 : 12.

5. i : f : : | : — .
6.2i:-::|:4.

7. i ; 3 . . — . i^

8. 2.5 : 62.5 : : 15 : — .

9. 3.6 : 7.2 : : — : 9.4.

10. 2i : 7i : : i : — .

11. J: A :: — :}.

12. i :*::*:-,

80 RATIO.

SIMPLE PROPORTION.

ART. 66. A Simple Proportion is an equality of two
simple ratios.

The method of finding the fourth term of a simple proportion,
the other three being given, or of solving problems by means
of a simple proportion, is sometimes called the Rule of Three.

In stating a problem in simple proportion, the first and
second terms must be of the same denomination ; also the third
and the answer sought.

Ex. 1. If 5 men can do a piece of work in 18 days, how
many men can do it in 10 days ?

Explanation. — The

.
term) is to be in men,

10)90 therefore 5 men is the

~9 men, 4th term, or Ans. tnird term- If 5 men

can do a piece of work

in 18 days, it will require more men to do the same work in 10
days (less time). Hence the second ratio is increasing, and the
first must be increasing, or 18 days must be made the second
term. Hence, 10 days : 18 : : 5 men : Ans. or 9 men.

RTJLIE. ,

Place the number of the same denomination as the answer
sought for the third term. If the answer is to be GREATER than
the third term, place the greater of the other tioo numbers for
the second term, and the less for the first; if the answer is to
be less than the third term, place the LESS of the two numbers
for the second term, and the greater for the first.

Then divide the product of the second and third terms by
the first; the quotient will be the fourth term, or answer.

Examples.

2. If 5 peaches cost as much as 7 apples, how many apples
can you buy for 35 peaches ? Ans. 49 apples.

RATIO. 81

3. What will 450 feet of lumber cost at $17 per thousand ?

Ans. $7.65.

4. If 150 cows cost $1800, how many cows can be bought
for $132 ?.

5. If 5 men can mow 8 acres of grass in one day, how many-
men can mow 32 acres in the same time ? Ans. 20 men.

6. If a horse travels 15 miles in 1 h. 40 m., how far, at
this rate, can it travel in 12 hours ?

7. If a 5 cent loaf of bread weigh 4 ounces when flour is $4
per barrel, what should be the weight of a loaf when flour is
$7.50 per barrel ?

8. If 5 yards of cloth cost $17, how many yards can be
bought for $102 ? Ans. 30 yds.

9. A man received $45 for 30 days' work, how much should
he receive for 25 days' work ? Ans. $37.50.

10. If 12 oz. of pepper cost 20 cents, what will 7 Ibs. of
pepper cost ? Ans. $1.86|-.

11. A merchant failing can pay but 70 cents on each dollar
of his indebtedness. He owns A $1690, B $2000, and C
$1100 : what will each receive ? Ans. C $770.

12. A merchant failing owes A $900, B $1200, C $1400,
and D $1500. His property is valued at $2800 ; what will
each creditor receive ? Ans. D $840.

COMPOUND PROPORTION.

ART. 67. A Compound Proportion is an equality of two
compound ratios, or of a compound ratio and a simple one.

In solving problems in Compound Proportion, sometimes
called the Double Kule of Three, the second ratio is always
simple. The first ratio may be reduced to a simple ratio by
multiplying ther antecedents together for a new antecedent, and
the consequents together for a new consequent. Hence, every

compound proportion may be reduced to a simple one.

6

82 RATIO.

The third term of a compound proportion must be of the
same denomination as the answer sought, and each of the simple
ratios that compose the compound ratio must be of like de-
nominations.

Ex. 1. If 5 men can mow 20 acres of grass in 3 days by
working 8 hours each day, how many men will it take to mow
80 acres of grass in 4 days, working 6 hours each day ?

Ans. 20 men.

STATEMENT.

20A. 80A. ) 80*3x8*5

4 days 3 days V : : 5 men : Ans. Or, _ ^=20

6 hours 8 hours \ 20x4x6

Explanation. — The answer required being in men, place 5
men for the third term. If it take 5 men to mow 20 acres, it
will require more men to mow 80 acres in the same time ;
hence, 80 acres must be made the second term of the first
simple ratio of the compound ratio. If it take 5 men when
they work 3 days, it will require less men when they work 4
days ; hence, 3 days is the second term of the second simple
ratio. If it take 5 men when they work 8 hours per day, it
will require more men when they work but 6 hours per day ;
hence, 8 hours is the second term of the third simple ratio.
Reducing the compound ratio to a simple one, we havo
20 x 4 x 6 : 80 x 3 x 8 : : 5 : Ans.} from which we find the fourth
term to be 20.

By Cancellation. — Instead of stating a problem in com-
pound proportion in the above form, it is more convenient to
arrange the third and second terms in one column, the first
terms in another column, and cancel the factors common to the
two. The correctness of the process is evident from the fact,
that the product of the third and second terms constitutes a
dividend, and the product of the first terms a divisor. The
quotient is the fourth term.

5 44

, 5 x $0 x # x

'4
5 x 4 = 20 Ans.

RATIO, 83

RTJ3L.E.

Place the number of the same denomination as the answer
sought for the third term. Arrange the first and second terms
of each of the simple ratios of the compound ratio as in SIMPLE
PROPORTION.

Then, multiply the second and tnird terms together, and
divide their product by the product of the first terms. The
quotient will be the answer. Or,

Arrange, the third and second terms in one column, the first
terms in another at the left hand, and cancel all the factors
common to the two. Then, divide the product of all the un-
cancelled factors of the right hand column by the product of all
the uncancelled factors in the left hand column. The quotient
ic ill be the answer.

Note. — In determining which number of each ratio is to be
the second term, reason from the number in the condition.

Examples.

2. If $900 produce $50 in 9 months, what sum will pro-
duce §450 in 5 months ? Ans. $14580.

3. If it cost $25 to lay a sidewalk 10 feet wide and 90 feet
long, what will it cost to make a walk 6 feet wide and \ of a
mile long ?

4. If 16 men can excavate a cellar 90 feet long, 40 feet wide,
and 10 feet deep in 15 days of 8 hours each, in how many days
of 9 hours each can 3 men excavate a cellar 60 feet long, 36
feet wide, and 8 feet deep ? Ans. 34r2y days.

5. If 30 men, by working 8 hours a day, can in 9 days dig
a ditch 40 rods long, 12 feet wide, and 4 feet deep, how many
men, by working 12 hours a day for 12 days, can dig a ditch
300 rods long, 9 feet wide, and 6 feet deep ?

PART SECOND,

PERCENTAGE.

ART. 68. Per cent, is a contraction of the Latin phrase per
centum, which signifies by the hundred.

Percentage includes all those operations in which 100 is the
basis of computation.

The rate per cent, is the number of hundredths. Hence,
any per cent, of a number is so many hundredths of it. Thus,

5 per cent, of a number is 5 hundredths of it.

30 per cent, of a number is 30 hundredths of it.

3i per cent, of a number is 3^ hundredths of it.

\ per cent, of a number is \ hundredths of it.

125 per cent, of a number is 125 hundredths of it.

And so on.

Note. — Instead of the words " per cent./' it is now custom-
ary to use the character % : thus, 12 per cent, is written 12% ;
2J per cent., 2j%.

ART. 69- The rate per cent, may be expressed decimally by
writing it as so many hundredths. Thus,
1 per cent, is written .01
7 per cent, is written .07
5^ per cent, is written .05 J- ; or .055
15 per cent, is written .15
100 per cent, is written 1.00

i per cent, is written .00^ ; or .005
j per cent, is written .OOJ ; or .0025
2j per cent, is written .02^
¥V per cent, is written .OO^V ; °r .0005

PERCENTAGE. 85

Exercises.

1. Express decimally 10 per cent.

2. Express decimally 12| per cent.

3. Express decimally If per cent. Ans. .01 £.

4. Express decimally f per cent.

5. Express decimally T\ per cent. Ans. .001

6. Express decimally 2 per cent.

7. Express decimally 120 per cent.

8. Express decimally 250 per cent.

9. Express decimally 1| per cent.

10. Express decimally f of 3 per cent. Ans. .015.

11. Express decimally ^ per cent.

12. Express decimally 500 per cent. Ans. 5.00.

I.

ART. 70. To find a given per cent, of any number or
quantity.

Ex. 1. Sold a house and lot, which cost me $1450.75, at a
gain of 15%. What was the gain ?

Explanation. — Since 15% is .15, the gain was
$2T7 6l25 I** hundredths of $1450.75.

Some persons prefer, and it is sometimes more convenient,
to find the percentage as follows :

Explanation. — 1 per cent, of any number is
' -. - .01 of it (which is found by removing the decimal
point two places to the left), and 15 per cent, is 15
times as much as 1 per cent.

Multiply the given number by the rate per cent. EXPRESSED

DECIMALLY. Or,

Remove the decimal point TWO places to the left, and mul-
tiply by the rate per cent. AS A WHOLE NUMBER.

E x a m pies.

2. What is 8 per cent, of 500 miles ?

3. What is 6 per cent, of $72.37^ ? Ans. $43425.

86 PERCENTAGE.

4. Find 32 per cent, of 1200 men.

5. Find 25 per cent, of 12 hours 30 minutes.

Ans. 3 h. 7 m. 30 s,

6. What is 1000 per cent, of $1000 ? Ans. $10000.

7. What is | per cent, of $320 ?

Note. — The second rule is most convenient in solving such
examples as the above. Thus, f of $3.20=$1.20.

8. What is J per cent, of $15.80 ?

9. What is li per cent, of 1050 sheep ? Ans, 14 sheep.

10. Find 2-V per cent, of 134500 bushels. Ans. 67} bu.

11. 33} per cent of any number is what part of it ?

Ans. £.

12. What is 33i per cent, of 252 cattle ? Ans. 84 cattle.
Note. — When the rate per cent, is a convenient part of 100,

take the same part of the given number. Thus, 33^ per cent.
of 252 is i of 252 = 84.

13. What is 16| per cent, of 1200 hogs ? Ans. 200 hogs.

14. Find 66 J per cent, of 660 men. Ans. 440 men.

15. Find 75 per cent, (f) of 4852.. Ans. 3639.

16. Find 15 per cent, of 25 per cent, of $13.60.

Ans. $0.51.

17. Find 87^ per cent. (|) of 1632 feet, Ans. 1428 feet.

18. A merchant -failing was able to pay his creditors but 40
per cent. He owes A $3500, B $1200, C $1134, D $650.
What will each receive ?

Ans. A $1400, B $480, C $453.60, D $260.

19. A person at his death leaves an estate worth $1500 ;
12 per cent, of which he received from his wife ; 20 per cent,
from speculation ; 30 per cent, from rise of property ; 25 per
cent, from the estate of an uncle ; and the remainder from his
father. How much did he receive from each source ?

Ans. to last, $195.

20. A has an income of $1100 per year ; he pays 10 per
cent, of it for board ; \ per cent, for washing ; 2 per cent, for
incidentals ; 15 per cent, for clothing ; 9 per cent, for other
expenses. What does each item cost, and how much has .he
left ? Ans. He has left $698.50,

PERCENTAGE. 87

CASE II.

ART. 71. To find what per cent, one number is of another.

Ex. 1. 6 is what per cent, of 25 ?

/o, — -6^o — .24. Ans. 24 per cent,

Explanation. — 6 is •£$ of 25, which changed to a decimal
(Art. ) equals 24 hundredths ; or 24 per cent.

Ex. 2. 12 cents is what per cent, of $3 ?

5V2« = !-%[ £ £=.04. u4tts. 4 per cent.

Explanation. — Since only quantities of the same denomin-
ation can be compared, reduce $3 to cents, and proceed -as
above.

Reduce the numbers to the same denomination. Annex two
ciphers to the number which is to be the rate per cent., and
divide the result by the other number.

Examples.

3. What per cent, of $40 is $12 ? Ans. 30%.

4. What per cent, of 120 yards is 20 per cent, of 90 yards ?

5. 2^ dimes is what per cent, of $5 ? Ans. f// . •

6. 40 men is what per cent, of 150 men ?

7. 150 men is what per cent, of 40 men ?

8. The cent (new coinage) contains 22 parts copper and 3
parts nickle ; what per cent, of it is copper and what per cent,
nickle ? Ans. Copper 88'/0.

Nickle 121/,.
9. 15 per cent, is what per cent, of 60 per cent. ?

Ans. 25°/0.

10. A person whose annual income is $450 pays $125 for
board, $140 for clothing, $25 for books, and $30 for sundries ;
what percent, of his income is each item, and what per cent.
remains ? . • Ans. to last, 28}%.

11. A morchant failing owes $3500 ; his property is valued
at $'2100. What per cent, of his indebtedness can he pay ?

Ans. 60%.

88 PERCENTAGE.

S III.

ART. 72. To find a number when a certain per cent, of it
is given.

Ex. 1. A merchant sells 40 per cent, of his stock for $3500 ;
what is the value of his whole stock at this rate :

Explanation. — Since $3500 is

-- x 100=$S750. Ans. 40 per cent, of his stock, 1 per

cent, is TV of $3500, or $87.50,

and 100 per cent., or the whole stock, 100 times $87.50, or $8750.
Ex. 2. A person pays $13.50 a month for board, which is
30 per cent, of his salary, what is his salary ?

$13.50 $1350

-brk - x 100= -077- =$450. Ans.
ou ou

RTJ3L.E.

Divide the given number by the given rate per cent, and
multiply the quotient by 100. Or,

Annex two ciphers to the given number, and divide the
result by the rate per cent.

Note. — When the given number contains cents (see Ex. 2,
above), remove decimal point two places to the left, instead of
annexing two ciphers.

32 x a, m pies.

3. 45 is 10 per cent, of what number ?

4. $3.60 is 15 per cent, of what number ?

5. $5.62^ is 12^ per cent, of what number ? Ans. $45.

6. Sold cloth for $3.50 per yard, which was 70 per cent, of
its cost ; what was the cost of the cloth per yard ? Ans. $5.

7. A boy spent 60 per cent, of his money for toys, 'and 25
per cen't. for candies, and had 15 cents remaining ; how many
cents had he at first ? Ans. $1.00.

8. The assets of a merchant are $45000, which is 60 per
cent, of his indebtedness ; what is his indebtedness ?

Ans. $75000.

9. The deaths in a certain city, during the year, are 980,
wjiich is 3i per cent, of the population ; what is the number
of inhabitants ? Ans. ' 28000.

PEECENTAGE. 89

ART. 73. A number being given which is a given per cent.
more or less than another number, to find the required number.
Ex. 1. Sold broadcloth at $5 per yard and made 25 per
cent. ; what did the cloth cost per yard ?
JIQQ Explanation. — Since I gain 25 per

25 cent., I receive 125 cents for every 100

125)500 cents the cloth cost ; hence the cloth

4 cost as many tunes 100 cents as I re-

4 x 100=400 cents. ceive times 125 cents, which is 4, and
Ans. $4. 4 times 100 cents is $4.

Or thus : Qr thus :

Since I gain 25 per cent., the sum

-^— - received is 125 per cent, of the cost;

|j? ^ hence, $5 is f|f of the cost, which

is found by dividing by 1.25.

When the given per cent, is a convenient part of 100, it
maybe solved by using the common fraction; thus, T2-5-=i,
f + A = £ ; hence, $5 is f of the cost.

Ex. 2. A drover lost 12 per cent, of a flock of sheep by dis-
ease, and then had 2200 ; how many sheep in the flock at first ?

Explanation. — Since he lost 12
i c\c\
1~~ per cent, of his sheep, for every

"^^ sheep at first there remained
9, but 88 ; hence, the flock at first

95 x 100=2500 Ans contained as many times 100 sheep

Qr as there remained times 88, or 25

0900 x 100 times 100 sheep =2500 sheep.

-g-8 -- =2500 Ans. Or thus :

Since he lost 12 per cent, of his

flock, there remained 88 per cent. ; hence, 2200 sheep must
be T8/^ of his original flock, which is 2500 sheep.

Divide the given number by 100, inceased or diminished
by the rate per cent., and multiply the quotient by 100. Or,

Divide the given number by 1, increased or diminished by
the rate per cent, expressed decimally.

90 PERCENTAGE.

Examples.

3. 168 is 20 per cent, more than what number ? Ans. 140.

4. $63.75 is 15 per cent, less than what ? Ans. $75.

5. The population of a certain city is 25000, which is 25
per cent, more than it was in 1850 ; what was the population
in 1850 ? Ans. 20000.

6. A grocer sells flour as follows :

Extra Family, $5.50 per bbl.

Superfine, $4.75 " "

Fine, $4.25 " "

and makes a profit of 12^ per cent. ; what was the cost of each
brand ? Ans. to last, $3.77|.

7. A cargo of corn being injured, the owner was obliged to
sell the same for $28000, which was at a loss of 30 per cent. ;
what was the cost of the cargo ? Ans. $40000.

8. The sales of a dry goods firm amount to $90000 per
year ; f of the sales were made at a profit of 25 per cent. ; T\ at
a profit of 35 per cent. ; and the remainder at a profit of 20
per cent. ; what was the cost of goods ? Ans. $71300.

APPLICATIONS OF PERCENTAGE.

ART. 74. The four preceding cases underlie the whole sub-
feet of Percentage in all its numerous and important applica-
tions. The importance of fully understanding them can not
be urged too strongly upon one who wishes to become a
competent accountant. It is not enough to be able to solve
the examples in accordance with the directions of the rules.
Rule accountants are always liable to make serious errors. Do
I see- clearly why such a process gives the required result ?
To this question the student should be able to give an affirma-
tive answer. ,

There is such a thing as common sense, and the use of it in
solving practical business problems is a sine qua non. The
answer, of almost any question may be anticipated, at least
approximately, previous to its solution. The common-sense

PERCENTAGE. 91

student sees from the conditions of the question about what
answer he may expect. In solving a problem in discount, for
example, he knows whether the present worth will be nearest
§3, $30, or $3000. I have often known " rule students" to
hand in the most ridiculous answers to the simplest practical
problems.

PROFIT AND LOSS.

ART. 75. The price paid for an article, or the total expense
of producing it, is its cost ; the amount received for an article
by the vender is its setting price. It is evident, from this, that
the selling price of the vender, or salesman, may be the cost of
an article to the purchaser.

When an article is sold for more than its cost, there is a
profit, or gain ; when it is sold for less than its cost, there is a
loss. The actual gain or loss is the amount of this increase or
decrease.

Profit or loss is generally computed as a given amount upon
every hundred, or at a given rate per cent. The rate per cent,
is the number of hundredths of the cost gained or lost.

Profit and Loss, though usually, are not always limited
to transactions in money. When any quantity, whether it
is- money, or goods, or tune, or distance, or any thing else,
undergoes an increase or decrease, there is gain or loss, and it
may be computed at a rate per cent.

ART. 76. All the problems in Profit and Loss come under
one or more of the four following cases, which correspond to
the four cases of Percentage, already explained.

1. The cost and the per cent, of gain or loss being given, to
find the selling price.

KULE. — Multiply the cost by the rate per cent, of gain or
loss expressed decimally ; the product ivill be the gain or loss.
The cost increased by the gain or diminished by the loss ivill
be the selling price.

2. The cost and the selling price being given, to find the
per cent, of gain or loss.

92 PERCENTAGE.

EULE. — Divide the gain or loss ~by the COST, and express
the quotient decimally.

3. The actual gain or loss, and the per cent, of gain or loss
being given, to find the cost.

KULE. — Divide the gain or loss by the per cent, of gain or
loss, and multiply the quotient by 100.

4. The selling price and the per cent, of gain or loss being
given, to find the cost.

KULE. — Divide the selling price by $1 increased or dimin-
ished by the rate per cent, expressed decimally.

Note. — Keep in mind that gain or loss is computed upon
the COST.

E x a m. pies.

1. For how much per bbl. must I sell flour costing $4.50 per
bbl., to gain 16 f per cent. ?

Explanation. — It must be sold for the cost plus 16 f per
cent, of the cost (found according to Case I., Percentage) ; or,
since 16| per cent. = -J-, it must be sold for the cost plus -} of
the cost.

Remark. — When the given per cent, is a convenient part
of 100, it is best to use the common fraction, Instead of the
given per cent.

2. A man offers a farm, for which he gave $3450, for 20
per cent, less than its cost. What is his price ?

Explanation. — He offers it for the cost minus 20 per cent,
of the cost ; or, since 20 per cent. — }, he offers it'for the cost
minus } of the cost, or $2760.

3. How must I sell sugars that cost $7, $8.25, and jfclO.50
per cwt. to gain 12| per cent. ? Ans. to last, $11. ^lf.

4. Bought linen cloth for 45 cents, 50 cents, and 62^ cents
per yard ; for what per yard must I sell it (being damaged) to
lose 18 per cent. ? Ans. to last, 51 } cts.

5. A merchant is selling cloth that cost $3.75 per yard for
$5 ; twhat per cent, is his profit ? Ans. 33;,°fv

Explanation. — He gains $5.00 — $3.75 = $1.25 on each
yard, or on $3.75, which (Case II. Percentage) is 33 £ per cent. ;

PERCENTAGE. 93

or, since he gains §1.25 on $3.75, his gain is -J-f f or 1 of the
cost, or 33} per cent.

6. A grocer sells coffee that cost 15 cents per Ib. for 12 cents
per Ib. ; what is his loss per cent. ? Ans. 20 yc. .

Eemark. — The simple question in this problem is, what
per cent, of 15 is 3 ?

f 7. A grocer sells tea costing 62 1 cents per Ib. for 75 cents ;
sugar costing 9 cents for 12^ cents ; flour costing $5.20 for
$5.75. What does he gain per cent, on each article ?

Ans. to last, IQif0/;.

•» 8. Bought a horse for $130, paid for its keeping, two
months, $6, and then sold it for $124 ; what per cent, was my
loss? Ans. S]4%.

9. A merchant made a profit of $156 by selling a quantity
of silks at a gain of 12 per cent. What was the cost of the
silks, and for how much were they sold ? Ans. $1300 cost.

Explanation. — Since he gained 12 per cent., or TW of the
cost, $156 must be TVV of the cost, which (Case III. Percent-
age), is $1300 ; $1300 + $156=$1456, selling price.

10. A grocer bought a lot of apples, and sold them at 30
per cent, profit, by which he gained $36.60. How much did
they cost him, and for how much did he sell them ?

Ans. Cost $122 ; sold for $158.60.

11. Sold a cargo of wheat for $16000, at a profit of 25 per
cent. What was the cost of cargo ? Ans. $12800.

Explanation. — $16000 is 25 per cent, more than what
number ? (Case IV. Percentage). Or thus : Since I gained
25 per cent, or TYo = T, I must have sold it for f of the cost.

12. Gould & Brown sold a lot of goods for $16500, at a
profit of 33 i per cent. What did the goods cost them ?

Ans. $12375.

13. Sold tea at 90 cents per lb.? and gained 20 per cent.
What per cent, should I have gained had I sold it for $1.00
per Ib. ? Ans. 33i%.

Note. — This example involves Case IV. and Case II. of
Percentage. First find the cost and then the gain per cent, on
the cost by selling for $1.00 per Ib.

94 PERCENTAGE.

. 14. Sold a lot of books for $480, and lost 20 per cent. ; for
what should I have sold them to gain 20 per cent. ?

Ans. $720.

1/15. If tea, when sold at a loss of 25 per cent, brings $1.25
per lb., what would be the gain or loss per cent, if sold for
$1.60 per lb.? Ans. Loss '4$.

16. A merchant marked a piece of carpeting 25 per cent,
more than it cost him, but, anxious to effect a sale, and sup-
posing he should still gain 5 per cent., sold it at a discount of
20 per cent, from his marked price. Did he gain or lose ?

Ans. Neither.

Explanation. — Since the marked price was 125 per cent, of
the cost, 20 per cent, of the marked price must be 20 per cent,
of 125 per cent, of the cost, or 25 per cent, of the cost. 125
per cent.— 25 per cent. = 100 per cent., or cost

Or thus :

Since the marked price was \ (25 per cent.) more than the
cost, or f of the cost, 20 per cent., or £ of the marked price
must equal } of £ = £ of the cost.

17. My goods are marked to sell at retail at 40 per cent,
above cost. I furnish my wholesale customers at 12 per cent,
discount from the retail price. What per cent, profit do I
make on goods sold at wholesale ?

Illustration. — Suppose $1.00 to be the basis of computation.
We shall then have :

$1.00 cost. $1.40 retail price.

1.40 retail price. .16f amount to be deducted.

.16} 12 per cent, of 1.93] selling price,

retail price. ^.00 cost deducted.

.23 j profit.

18. My retail price for broadcloth is $4.75 per yard, by
which I make a profit of 33^ per cent. I sell a wholesale cus-
tomer 100 yards at a discount of 30 per cent, from the retail
price. What per cent, do I gain or lose, and what do I receive
per yard ? Ans. Lose 6:',;/.

$3.32i per yard.

19. A merchant asked for a quantity of dried fruit 22 per
cent, more than it cost him, but, being a little mouldy, he was

PERCENTAGE. 95

obliged to sell it for 10 per cent, less than his asking price. He
gained $98 by the transaction. How much did the fruit cost ?
For how much did he sell it ? What was his asking price ?

Ans. to last, $1220.

20. I bought a horse of Mr. A for 15 per cent, less than it
cost him, and sold it for 30 per cent, more than I paid for it. I
gained $15 in the transaction. How much did the horse cost
Mr. A ? How much did it cost me ? For what did I sell it ?

Ans. to last, $65.

21. By selling Java coffee at 18 cents per pound I make a
profit of 20 per cent., for how much must I sell it to make a
profit of 16f per cent. ? Ans. 17| cents.

22. The cost of purchasing and transporting a quantity of
goods from New York to Chicago is 9 per cent, of the first cost
of the goods. If a merchant in Chicago wishes to make a profit
of 25 per cent, on the full cost of the goods, what per cent, gain
on the first cost must he ask, for them ? What amount of
goods must he purchase in New York to realize a profit of
$3625 on the first cost ? W^hat would be the real profit on
full cost ? Ans. to the last, $2725.

23. What must be the asking price of cloth costing §3.29
per yard, that I may deduct 12£ per cent, from it, and still
gain 12^ per cent, on the cost ? Ans. §4.23.

24. I bought a lot of coffee at 12 cents per pound. Allow-
ing that the coffee will fall short 5 per cent, in weisrhino; it

O J- O O

out, and that 10 per cent, of the sales will be in bad debts, for
how much per pound must I sell it to make a clear gain of 14
per cent, on the cost ? Ans. 16 cents.

25. What must be the asking price of raisins costing §7.364
per box, that I may fall 10 per cent, of it and still gain 10 per
cent, on the cost, allowing 10 per cent, of sales to be in bad
debts? Ans. $10.

Note. — Other problems in Profit and Loss, involving In-
terest, etc., will be given in miscellaneous examples.

96 PERCENTAGE.

COMMISSION AND BROKERAGE.

ART. 77. Money received for buying and selling goods or
other property, collecting debts, or transacting other business
of like nature for another person or party, is called Commission.

Commission is usually estimated at a certain per cent, of
the amount of the purchase, sale, collection, or other business
transacted.

A person who buys and sells goods, or transacts other busi-
ness on commission, is called a Commission Merchant, Agent,
or factor.

When a person engaged in the Commission business lives
in a foreign country, or in a different part of the country, he is
called a Correspondent or Consignee ; goods shipped to such a
person to be sold are called a consignment, and the person who
sends the goods a Consignor.

The rate per cent, of commission, or the rate of commission
as it is called, varies with the amount and nature of the business.

Brokerage is money received for buying and selling stocks,
making exchanges of money, negotiating bills of credit, or
transacting other like business. Like Commission, it is com-
puted as a certain percentage of the amount of the money
involved in the transaction. Brokerage upon stocks is usually
computed upon their .par value.

ART. 78. The problems in Commission and Brokerage come
under one of the two following cases :

1. To find the commission or brokerage on any given sum
at a given rate per cent.

KULE. — Multiply the given sum by the given rate per cent,
expressed decimally.

2. When the given amount includes both the sum to be
invested and the commission or brokerage.

EULE. — Divide the given amount by $1, increased by the
rate per cent, of commission and brokerage, expressed deci-
mally; the quotient will be the sum to be invested.

PERCENTAGE. 97

The commission or brokerage may be found by subtracting
the investment from the given amount.

E x a m. pies.

1. A commission merchant in New Orleans purchased cotton
for a manufacturer in ^owell to the amount of $16576. What
is his commission at 2j per cent. ? Ans. $414.40.

2. Paid a broker 1 per cent, for exchanging $750 Ohio
money for Eastern funds. How much was the brokerage ?

Ans. $1.87^,

3. My agent charges me $25 for collecting $800. What is
his rate of commission ? Ans. 3 \%.

4. An architect charges f per cent, for plans and specifica-
tions, and li per cent, for superintending a building which cost
$32000. What is his fee ? Ans. $600.

5. I collected 65 per cent, of a note of $87.50, and charged
5 per cent, commission. What is my commission and the sum
paid over ? Ans. to last, $54.03.

6. My agent in Baltimore has purchased goods for me to
the amount of $1250, for which he charges a commission of If
per cent. What sum must I remit to pay for goods and com-
mission ? Ans. $1271.87|.

7. Sent to my agent in Cincinnati $765 to purchase a quan-
tity of bacon ; his commission is 2 per cent, on the purchase,
which he is to deduct from the money sent. What is his
commission, and what does he expend for bacon ? •

Ans. to last, $750.

Remark. — The $765 sent includes the sum to be invested
in bacon and the 2 per cent, commission on the money thus in-
vested. For every 102 cents sent, he will lay out 100 cents for
bacon; hence the $765 is }£?- of the amount invested. See
Case IV. Percentage.

8. I have received $11200 from my correspondent in Boston
with directions to purchase cotton, first deducting my commis-
sion, 2i per cent. What is my commission, and how much
must I expend for cotton ? Ans. to last, $10926.829.

9. My agent at Chicago writes that he has purchased for

98 PERCENTAGE.

me 4000 bushels of wheat at 80 cents a bushel, and wishes
me to send him a check on New York, which he can sell to a
broker for a premium of £ per cent. How large a check shall
I send him, his commission being 3 per cent. ?

Ans. $3271.464.

10. Field & Parsons sell for H. Johnson & Co. 3500 Ibs. of
butter at 20 cts. a lb., 2580 Ibs. of cheese at 9 cts. per Jb., at a
commission of 5 per cent. They invest the balance in dry
goods, after deducting their commission of 2^ per cent, for pur-
chasing. How many dollars worth of goods do Johnson & Co.
receive ? What is the entire commission of Field & Parsons ?

Ans. to last, $863.99.

11. I received of Brown & Lincoln $560 in uncurrent
money to purchase books. I pay a broker 3i per cent, for
current funds, and invest the balance, after deducting my com-
mission of 2 per cent. What do I pay for books, and what is
my commission ? Ans. to last, $10.596.

12. A broker bought 5 shares of K. K. stock at 35 per cent,
discount, what is the brokerage at 5 per cent., the par value of
each share being $100 ? Ans. $25.

INSURANCE.

ART. 79. Insurance is a contract by which one party en-
gages, for a stipulated sum, to insure another against a risk to
which he is exposed.

The party who takes the risk is called the Insurer or
Underwriter, and the party, protected by the insurance, the
Insured.

The sum paid for obtaining the insurance is called the
Premium, and the written contract is called the Policy.

Insurance is generally effected by a joint-stock company
or by individuals who unite to insure each other, called a
Mutual Insurance Company.

When the insurer agrees to pay the insured a certain sum
of money if he is sick, it is called Health Insurance.

PERCENTAGE. 99

When the insurer agrees to pay to the heirs of the insured,
or to some specified person, a certain sum in case of his death,
it is called Life Insurance.

Insurance on property is either fire or marine.

Fire Insurance is a guarantied indemnity against the loss
or damage of property by fire. It is generally effected for a
year or term of years.

Marine Insurance is a guarantied indemnity against the
loss or damage of property by the perils of transportation by
water. Insurance on the property carried is called Cargo In-
surance ; that on #10 vessel is called Hull Insurance.

In Mutual Insurance Companies, each person insured be-
comes a party to a certain extent in the losses of the con-
cern. The person insured pays a small cash premium at the
time the insurance is effected, and he also gives to the company
premium-note, upon which he is liable to be assessed to the

Amount of its face. After a sufficient sum has accumulated
from the premiums no further assessments are made on the
notes, and any surplus funds are distributed among the mem-
bers of the company.

ART. 80. Most of the problems in Insurance come under
one of two cases.

1. When the amount insured and the rate of insurance are
given to find the Premium.

KULE. — Multiply the amount insured by the rate of Insur-
ance expressed decimally.

2. To find for what sum a policy must be taken out, at a
given rate, to cover both property and premium.

RULE. — Divide the sum for which the property is to be in-
sured by $1, diminished by the rate of insurance expressed
decimally. (See Example 13.)

DElxa-inples.

1. What is the premiun for insuring goods valued at $4500
at 2i per cent. ? Ans. $112.50.

2. A hotel worth $15000 is insured for f of its value at f
per cent. The policy and survey cost $1.50 ; what will be the
premium ? Ans. $39.

100 PERCENTAGE.

3. An insurance company insured a block of buildings for
$350000 at | per cent., but thinking the risk too great, they
reinsured $150000 of it at £ per cent, in another company, and
$100000 of it at f per cent, in another. How much premium
did the company receive ? How much did it pay to both the
other companies ? How much did it clear ? What per cent,
of premium did it really receive on the part not reinsured ?

Ans. to last, -f^ per cent.

Note. — All property in one block, or in adjacent buildings,
having communications, or on one vessel, is considered as one
risk, and Insurance Companies seldom take more than $10000
in one risk. Some companies of very large capital take $20000,
but small companies do not take more than from $3000 to
$5000 in one risk.

4. A ship valued at $40000 is insured for £ of its value at
H per cent., and its cargo, valued at $36000, at f per cent.
What is the cost of insurance ? Ans. $738.

5. A merchant paid $1450 premium for the insurance of a
cargo of cotton, shipped from New Orleans to Boston, the rate
of insurance being 2| per cent. What was the value of the
cargo ? Ans. $58000.

6. Paid $7.20 for the insurance of a house at f per cent.
If the policy and survey cost $1.50, for how much was the
house insured ? Ans. $950.

7. I pay $50 for an insurance of goods valued at $32500,
and shipped from New York to St. Louis. What was the rate
of insurance? Ans. ^%.

8. A house valued at $1200 has been insured for f of its
value for 3 years at 1 per cent, per annum. Near the close of
the third year it is destroyed by fire. What is the actual loss
to the owner, no allowance being made for interest ?

Note. — The insurance company must pay him $800 ; but
of this sum he has paid to the company $24 premium ; hence
he actually receives but $800-24= $776.

9. My house was insured for $45000 for 5 years The first
year I paid $1.50 for policy and survey, and f per cent.
premium ; each succeeding year I paid | per cent, premium.

PERCENTAGE. 101

What was the total cost of insurance ? The house was burned
during the fifth year ; what was the actual loss of the com-
pany, no allowance being made for interest ?

Ans. to last, $43817.25.

10. A merchant ships $31360 worth of wheat from Chicago
to Buffalo. For what must he get it insured at 2 per cent, so
as to cover both the value of the wheat and the premium paid
for its insurance ? Ans. $32000.

Explanation. — Since the policy is to cover both the value
of the wheat and the premium, and, since the premium is 2
per cent., or T| „• of the amount covered by the policy, the value
of the wheat must be TW (or 98 per cent.) of the sum insured.
$31360 is TVo (98 per cent.) of what ? See Case III. Per-
centage.

11. For what must a cargo of R. R. iron worth $115200
be insured to cover both the value of the iron and premium,
the rate of insurance being 4 per cent. ? Ans. $120000.

12. A merchant shipped a cargo of flour worth $47880 from
Chicago to San Francisco via New York. To insure it from
Chicago to Buffalo he paid l£ per cent. ; from Buffalo to New
York j per cent. ; from New York to San Francisco 3£ per
cent. For what sum must it be insured to cover value of flour
and premium for the voyage ? Ans. $50400.

13. A policy covering property and premium is taken for
§12045. What is the value of the property insured, the rate
being f per cent. ? Ans. $12000.

Explanation. — Since the policy covers both property and
premium, $12045 is f per cent, more than the property. See
Case IV. Percentage.

14. A merchant insures a cargo of goods for $81800, cover-
ing both the value of the goods and the premium, What is
the value of the goods, the rate of insurance being 2{ per
cent. ? Ans. $80000.

15. The owners of the steamer Florence have, for the past
20 years, paid 5 per cent, per annum for her insurance. She
was sunk this morning. Have they gained or lost by having
the steamer insured ? Ans.

102 PERCENTAGE.

LIFE INSURANCE.

ART. 81. Life Insurance is a contract by which the insurer
agrees, for an annual premium, to pay to the heirs of him
whose life is insured, or some person specified, a certain sum
of money in case of his death during the time for which the
insurance of his life is effected.

When the contract extends only a given number of years,
it is called a temporary insurance.

The individual whose life is insured pays annually, during
life, a certain percentage of the sum for which his life is in-
sured. This sum is called an Annual Premium, and varies
with the age of him whose life is insured.

The basis of the percentage is the average number of per-
sons lives who have attained to the uge of the applicant. This
average extension of life, beyond a given age, is called Expec-
tation of Life. Tables showing the expectation of life for
every year of man's existence are deduced from life statistics,
or, as they are commonly called, Bills of Mortality.

The annual premium must be such a sum as will, when put
at interest, amount to the sum insured, at the close of the ex-
pectation of life. This sum is easily found upon the principle
of Life Annuities.

Life Insurance Companies have tables showing the premium
to be paid at any age to secure an annuity of $100, during the
remainder of life. As the computations of Life Insurance are
based upon these tables, it is unnecessary to add problems.

There are two tables showing the Expectation of Life.
One, called the Carlisle Table, based upon Bills of Mortality
prepared in England, is in general use in that country, and to a
limited extent in this. The other, called the Wigglesworth Table,
prepared by Dr. Wigglesworth, from data founded upon the
mortality of this country, is used to a considerable extent here.

The Expectation of Life, according to the two tables
named, is shown in the following

PERCENTAGE.

103

TABLE.

1

K\|K'ctntion by
C. Table.

\.\\ relation by
W.Tul.l...

§>

Kxpeotntion by
C. Tublo.

£.

c •-
.SS

¥.
1*

H

|

Exportation by
C. Tuble.

£

H

i*
i>

H

1

.fe-
ll

1

i

£

jl

2$

**

•s,

M

0

38.72 2S.15

ir

38.59

32.70

48

22.80

22.27

72

8.16 9.14

1

44.63

36.78

25

37.86

32.33

49

21.81

21.72

73

7.72

8.69

2

47.55

38.74

26

37.14

31.93

50

21.11

21.17

74

7.33

8.25

3

49.82

40.01

27

36.41

31.50

51

20.39

2061

75

7.01

7.83

4

50.76

40.73

28

35.69

31.08

52

19.68

20.05

76

6.69

7.40

5

51.25

40.88

29

35.00

30.66

53

18.97

19.49

77

6.40

6.99

6

51.17

40.69

30

34.34

30.25

54

18.28

18.92

78

6.12

6.59

7

50.80

40.47

31

33.68

29.83

55

17.58

18.35

79

5.80

6.21

8

50.24

40.14

32

33.03

29.43

56

16.89

17.78

80

5.51

5.85

9

49.57

39.72

33

32.36

20.02

57

16.21

17.20

81

5.21

5.50

10

48.82

39.23

34

31.68

28.62

58

15.55

16.63

82

4.93

5.16

11

48.04

33.64

35

31.00

28.22

59

14.92

16.04

4.G5 4.87

12

47.27

38.02

36

30.32

27.78

60

14.34

15.45

84

4.39

4.66

13

46.51

37.41

29.64

27.34

61

13.82

1486

85

4.12

4.57

14

45.75

36.79

38

28.96

26.91

62

13.31

14.26

86

3.90

4.21

13

45.00

36.17

39

28.28

26.47

63

12.81

13.66

87 3.71

3.90

16

44.27

35.76

40

27.61

26.04

64

12.30

13.05

88 3.59

3.67

17

4357

35.37

41

26.97

25.61

Co

11.79

12.43

89 3.47

3.56

18

42.87

34.93

42

26.34

25.19

66

11.27

11.96

90

3.28

3.73

19

42.17

34.59

43

25.71

24.77

07

10.75

11.48

91

3.26

3.32

20

34.22

44

25.09

24.35

OS

10.23

11.01

92 3.37

3.12

21

40.75 33.84

45

24.46

23.92

69

9.70

10.50

93

3.48

2.40

22

4!) 04 33.46

46

23.82

23.37

70

9.18

10.06

94

3.53

1.98

23

39.31

33.08

47

23.17

22.83

71

8.G5

9.60 95

3.53

1.62

TAXES.

ART. 82, A Tax is a sum of money assessed according
to law upon the person or property of a citizen,* for the use of
the nation, state, corporation, county or parish, society or
company.

Taxes upon property are direct or indirect, according to
the manner in which they are assessed.

A direct tax is assessed directly upon the taxable property
(determined by law) of citizens, and is generally collected an-
nually. Taxes are sometimes assessed at a certain per cent, of
the property taxed ; but more commonly as a given number of
mills on §1.

* The term citizen is used in its general sense.

104 PERCENTAGE.

Property, subject to taxation, is either real or personal.
Real Property or Real Estate consists of lands, mills, houses,
and other fixed property. All other property is called per-
sonal.

The value of taxable property is fixed either by the owner
under oath, as in case of personal property, or by an officer
chosen for the purpose, called an Assessor.

Indirect Taxes are assessed upon goods imported into the
country, and are collected at their port of entry. They are
called customs or duties.

Remark. — Duties are called indirect taxes, since, according
to the tenets of most political economists, the duty, imposed
upon imported goods and apparently paid by the importer,
enhances the price of these goods in market, and is thus in-
directly and really paid by the consumer. Other political
economists, called Protectionists, hold that, in most instances,
the protective duty really cheapens the price of goods. Such
duties can hardly be called taxes.

A tax assessed upon the person of citizens is called a poll
or capitation tax, since it is assessed at so much per head (poll
or caput), without reference to property.

Note. — In some states poll-taxes are only collected for
gtreet or road purposes.

Examples.

1. The taxable property of the city of Cleveland for 1857
was $21648938. The taxes were assessed as follows :

For State purposes, 3.1 mills on a dollar.

" County purposes, 2.5 "
" Corporation purposes, 8. "

What was the amount of tax assessed for each purpose ?
How much will be collected, allowing 8 per cent, to be uncol-
lectible ? Ans. to last, $270871.51.

2. The taxable property of the city of B. for 1857 was
$35500000 ; the assessment was 15 mills on a dollar. What
was the total tax of the city ? What tax was assessed upon
each of the following citizens ?

PERCENTAGE.

105

Mr. A who paid tax on $13560.

Mr. B
Mr. C
Mr. D
Mr. E
Mr. F

9850.59.
450.87.
60850.
119380.
1000000.

ART. 83. The labor of making out a tax list may be less-
ened by using tables.

The following table will be found very convenient for such
a purpose. One or two examples will illustrate the manner of
using it. The table is easily formed for any number of mills
on a dollar.

TABLE.
Kate of tax 15 mills on a dollar.

Prop.

Tax. Prop.

Tax.

Prop.

Tax.

Prop.

Tax.

Prop.

Tax.

$ 1

$.015

$21

$.315

$41

$.615

$61

$ .915

$ si

$1.215

2

.03

22

.33

42

.63

62

.93

82

1.23

3

.045

23

.345

43

.645

63

.945

83

1.245

4

.03

24

.36

44

.66

64

.96

84

1.26

5

.075

25

.375"

45

.675

65

.975

85

1.275

6

.09

26

.39

46

.69

66

.99

86

1.29

7

.105

27

.405

47

.705

67

1.005

87

1.305

8

.12

28

.42

48

.72

68

1.02

88

1.32

9

.135

29

.435

49

.735

69

1.035

89

1.335

10

.15

30

.45

50

.75

70

1.05

90

1.35

11

.165

31

.465

51

.765

71

1.065

91

1.365

12

.18

32

.48

52

.78.

72

1.08

92

1.38

13

.195

33

.495

53

.795

73

1.095

93

1.395

14

.21

34

.51

54

.81

74

1.11

94

1.41

15

.225

35

.525

55

.825

75

1.125

95

1.425

1G

.24

36

.54

56

.84

76

1.14

96

1.44

17

.255

37

.555

57

.855

77

1.155

97

1.455

18

.27

38

.57

58

.87

78

1.17

98

1.47

19

.285

39

.585

59

.885

79

1.185

99

1.485

20

.30

40

.60

60

.90

80

1.20

100

1.50

Explanation of Table. — Suppose, for example, we wish to
find the tax of Mr. A in the above example. $13560=$13000+
$500 + $60. The tax on $13000 is found from the tax of
$13 (.195) by removing the decimal point three places to the
right ($195.) ; the tax on $500 is found from the tax of $5
(.075) by removing the point two places to the right ($7.50) ;
the tax on $60 is found in the table ($.90). $195. + $7.50 +
$.90= $203.40 ; tax on $13560. B's tax in Ex. 2 is found

106 PERCENTAGE.

in the same manner. Thus : tax on $9=. 135, tax on $9000=
$135 ; tax on $8=. 12, tax on $800=$ 12 ; tax on $50=.75 ;
tax on 59 cents (found from tax of $59 by removing point two
places to the ^) = .Q885=.09 nearly.

$135.
12.75

J39

Tax on $9850.59 =$147.84

3. Find from the above table the tax assessed upon

E. Gr. who paid tax on $ 35867.50.
H. E. S. " " " " 115380.
A. K. " " " " 586789.99.
R. S. " " " " 480.48.

4. The cost of maintaining the Public Schools of the city
of B for 1858 is estimated at $56000. The taxable property
of the city is $22400000. How many mills tax on a dollar
must be assessed for school purposes ? Suppose the uncol-
lectible tax will equal 10 per cent, of the tax assessed ; how
many mills on a dollar must in this case be assessed ?

Ans. to last, 2J mills.

DUTIES OB CUSTOMS.

ART. 84. Duties or Customs are sums of money assessed
by government upon imported goods.*

Duties upon goods are collected at their port of entry, by
officers appointed by government and called custom-Jwuse
officers. At each port of entry for foreign goods is a custom-
house, where all custom business is done.

Duties are of two kinds, specific and ad-valorem.

Specific duties are assessed upon goods at a certain rate per
tun, hogshead, bale, gallon, etc., without reference to their
value.

Ad-valorem duties are a certain percentage of the cost of
goods as shown by the invoice.

* In some countries duties are also assessed upon exported goods.

PERCENTAGE. , 107

An Invoice or Manifest is a written account of the particu-
lars of goods shipped or sent to a purchaser, consignee, factor,
etc., with the actual cost or value of such goods made out in
the currency of the place or country from whence imported.

The invoice is exhibited at the custom-house by the master
of the vessel, or the owner or consignee.

When an invoice has not been received, the owner or con-
signee must testify to the fact under oath, and then the goods
are entered by appraisement.

When the currency of a country has a depreciated value
compared with that of the country into which they are im-
ported, a consular certificate showing the amount of deprecia-
tion is attached to the invoice.

ART. 85. In assessing specific duties, certain allowances
are made, called draft, tare, leakage, breakage, etc., before the
duties are estimated.

Draft is an allowance for waste. It must be deducted
before other allowances are made.

Tare or Tret is an allowance for weight of box, cask, etc.,
containing the goods. It is generally computed at a given rate
per box, cask, etc.

Leakage is an allowance for the waste of liquid.

Breakage is an allowance on liquors transported in bottles.

Gross Weight is the weight of goods before any allowances
are made.

Net or Neat Weight is the real weight of goods after the
allowances have been deducted.

Remark. — As specific duties in the United States were
abolished by the tariff-bill of 1846, the examples given below
will relate exclusively to ad-valorem duties. The rules
governing the entry of vessels and goods are deemed too
numerous and unimportant to merit more space.

Note. — In ad-valorem duties no allowances are made for
draft, tare, or breakage.

Examples.

1. A portion of the cargo of the ship Europa from Liver-
pool to New York was invoiced as follows :

108 PERCENTAGE.

650 yds. Broadcloth, cost 13s. sterling per yd.

1246 yds. Lace, " 2s.

1200 yds, Coach Lace, " lid. "

1950 yds. Ingrain Carpeting, " 3s. " "

2560 yds. Drugget, " 2s. 4d. " "

The duty on the broadcloth was 30 per cent. ; on lace 25 per
cent. ; coach lace 25 per cent. ; carpeting 30 per cent. ; drugget
30 per cent. What was the amount of duty in our currency,
allowing the pound sterling to be $4.84 ?

Ans. $1689.1358.

2. C. Hartwell & Co., of Baltimore, have imported from
Havana

100 hogsheads of Molasses, 63 gals, each, cost 25 cts. per gal.
50 hogsheads of Sugar; 500 Ibs. each, " 5 cts. per Ib.

150 boxes of Oranges, " $2.50 per box.

300 boxes of Cigars, " $8 per box.

160 boxes of Bananas, " $1.75 per box.

The leakage of molasses is 2 per cent. ; duty on same 30 per
cent. ; duty on sugar 30 per cent. ; on oranges 20 per cent. ;
on cigars 40 per cent. ; on bananas 20 per cent. What was
the duty on each article ? What was the amount of duties ?

Ans. $1900.05.

3. A wine merchant in New York imported from Havre

100 baskets Champagne, at $13 per basket.
80 casks Madeira, at $42 per cask.

56 casks Oporto, at $45 "

50 casks Sherry, at $25 "

If an allowance of 3 per cent, for leakage is made on the wine
in casks, what will be the amount of duty at 40 per cent. ?
For what must the wine be sold. .per basket or cask to make a
clear profit of 25 °/0 ? Ans. $3286.44 duty.

PERCENTAGE. 109

BANKRUPTCY.

ART. 86. Bankruptcy is a failure in business and an in-
ability to pay indebtedness.

A Bankrupt or insolvent is a person who fails in business
and has not means to pay all his debts.

An- Assignment is the transfer of the property of a bank-
rupt to certain persons called assignees, in whom it is vested
for the benefit of creditors.

It is the duty of assignees to convert the property into
money and divide the proceeds pro rata among the creditors,
after deducting expenses.

The entire property of an insolvent is called his assets ;
and the amount of his indebtedness his liabilities.

Ex. 1. A merchant failing in business owes A $950, B
$2500, C §1500, and D $3050. His assets are $6000, and the
expense of settling will be $800. What per cent, of his in-
debtedness can he pay ? What dividend will each creditor

receive ?

A's claim, $ 950 $ 950 x. 65=$ 617.50 A'sdiv.
B's " 2500 2500 x. 65= 1625.00 B's "
•C's " 1500 1500 x. 65= 975.00 C's "
D's '- 3050 3050x.65=_1982.50D's "
Liabilities, 88000 Proof, $520000

Assets, 6000

Expense of settling, 800
Net proceeds, $5200

5200.00-=-8000=.65, or 65 per cent.

Explanation. — Since his liabilities are $8000 and the net
proceeds of his assets $5200, he can pay $5200 on $8000, or
65 per cent, of his liabilities. Hence each creditor can receive
65 per cent, of his claim.

Note. — It is more common to ascertain how much can be
paid on a dollar. As 65 per cent, of $1 is 65 hundredths of it,
or 65 cents, the process is the same.

Divide the net proceeds of the assets by the amount of

110 PERCENTAGE.

liabilities, and the quotient will be the per cent, of the indebted-
ness (or the number of cents on a dollar) that can be paid.

To find each creditor's dividend, multiply his claim by the
per cent, thus found.

2. Best & Foster became embarrassed and failed in business.
Their indebtedness was $65000. The firm had cash and goods
convertible into cash, $12500 ; building and lot, $40000 ; bills
collectible, $2100. If the expense of settling is 5 per cent, of
the amount distributed to creditors, what per cent, of their
indebtedness can they pay ? What will C. Greene & Co. re-
ceive, whose claim is $25800 ? Ans. to first, 80 per cent.

Suggestion. — Divide assets by $1.05 ; the quotient will be
net proceeds.

3. C. Smith & Co. have become insolvent. They owe A
$3500, B $1500, C $1450, D $850, E $350, and F $450.
Their effects (assets) amount to $4981.50. The charges of the
assignees will be 2| per cent, of the amount distributed to
creditors. What per cent, of their indebtedness can they pay?
What will each creditor receive ? Ans. to first, 60%.

STORAGE.

ART. 87. Storage is the price charged for the safe keeping
of goods in a store or warehouse.

There is no uniform method of computing storage. The
Boards of Trade, or Chambers of Commerce of the different
cities, adopt such rules and rates for storage as they deem
equitable. The charges for storage are usually, however, a
certain rate per month for each box, bale, cask, etc.

When goods are withdrawn before the close of the month
no deduction is made, but storage is charged for the full month.
After the first month, for a part of a month less than one half,
no charge is made, but for a part greater than one half, charge
is made for a month. In some cities all fractional parts of a
month are considered full months.

If, however, goods are received and sold on account, as in
the commission business, or are received and delivered at the

PERCENTAGE. HI

pleasure of the consignor, an account is kept, showing the date
and number of casks, etc., received, and the date and number
sold or delivered. In computing the storage on such an account
it is customary to average the time, and charge a certain rate
per month of 30 days. If there is a fractional part of a barrel,
3tc., in the average, it is treated as in the case of parts of
months above.

Examples.

1. What will be the storage of 150 barrels of flour at 4
cents per barrel from May 20 to June 6.

150x.04=$6. Ans.

2. What will be the cost of storing salt at 2 cents per
barrel, received and delivered as follows : June 6, 1858, 120
bbls. : June 16, 140 bbls. ; June 26, 200 bbls. ; July 5^ 300
bbls ; July 16, 180 bbls. ; July 20, 160 bbls. AU delivered
Aug. 1.

Operation.

1858. bbl. d. prod.

June 6. Kec'd. 120x10= 1200
" 16. " 140

^60x10= 2600
" 26. " 200

~860X 9= 7740
July 5. " 300

1160x10=11600
" 15. " 18P

1340 x 5= 6700
" 20. " 160

1500x11=16500
Aug. 1. Deliv. 1500

30)46340
Bbls. chargeable for 1 month, 1544|

1545x.02=$30.90, storage.

Explanation. — The storage of 120 bbls. for 10 d. is the
same as the storage of 1200 barrels for 1 day ; the storage of
260 for 10 days, the same as the storage of 2600 bbls. for 1 day,
and so on. Hence the amount of storage is 1200+2600 + 7740+
11600+6700 + 16500 bbls.=46340 bbls. for 1 day=4635 (f
called 1 bbl.) bbls. for 1 month.

112

PERCENTAGE.

3. What will be the storage of flour at 5 cents per bbl. per
month, received and delivered as follows ?

Keceived July 1, 1858, 400 bbls. ; July 15, 350 bbls. ; July
26, 450 bbls. Delivered July 12, 200 bbls. ; July 20, 400
bbls. ; Aug. 1, 200 bbls. ; and Aug. 8, 400 bbls.

Operation.
1858.

July 1.
" 12.

" 15.
" 20.
" 26.
Aug. 1.
Aug. 8.

Kec'd.
Deliv.
Bal.
Kec'd.
Bal.
Deliv.

400 x
200

11= 4400
3= 600
5= 2750
6= 900
6= 3600
7= 2800

200 x
350

"550 x
400

Bal.
Kec'd.

150 x

450

Bal.
Deliv.

600 x
200

Bal.
Deliv.

400 x
400

30)1505.0
Bbls. chargeable 1 month, 502

502 x. 05= $25.10 Ans.

Explanation.— "From July 1 to July 12, 400 bbls. were
stored ; from July 12 to July 15, 200 bbls. ; from July 15 to
July 20, 550 bbls. ; from July 20 to July 26, 150 bbls. ; from
July 26 to Aug. 1, 600 bbls. ; from Aug 1 to Aug. 8, 400 bbls.

Commencing with the first date and ending with the last,
multiply the number of barrels, or other articles in store, from
each date to the one NEXT following it, ~by the number of days
between these dates. Divide the sum of the several products
by 30, and the quotient will be the number of articles stored for
one month, and this number multiplied by the rate of storage
for each article ivill give the amount of storage charged.

Remark. — The following form will give the student a very
good idea of an Account of Storage. The form can be filled
by the process used in solving Ex. 3.

4. Storage of goods on account of C. T. Wilder & Co.,

PERCENTAGE.

113

Chicago, 111., at 5 cents a bbl. per month, by Hubby & Hughes,
Cleveland, 0.

KECEIVED. DELIVERED.

1858.

Bbla.

Balance on hand.

Days.

Products.

1858.

Bbls.

Jan.

1 350

Jan.

20

700

tt

12 650

tt

31

200

Feb.

5 500

Feb.

24

800

«

10

•320

Mar.

20

350

tt

28

440

it

25

700

Mar.

15

850

Apr.

5

400

« J30

200

it

8

100

What is the storage on the above account, closed April 12,
1858, and how many barrels are on hand ?

ART. 88. Butchers and drovers sometimes hire their cattle
pastured or fed on account, entering and withdrawing them as
circumstances may require. The account is closed in the same
manner as an account of storage.

Account of pasturage of cattle at 60 cents a head per week
for Lewis & Vincent, Portsmouth, 0., by John Goodwin,
Wayne, tp.

KECEIVED. WITHDRAWN.

1858.

Head.

Balance on hand.

Days.

Products.

1858.

Head.

June

3

9

June

5

2

u

10

5

u

7

4

(C

18

15

it

12

5

July

1

20

it

15

3

tt

9

10

1C

21

10

(i

31

5

July

3

10

Aug.

3

12

tt

12

10

u

16

13

it

20

6

it

31

10

tt

28

2

Sept.

25

9

Aug.

7

5

a

30

3

n

13

15

Oct.

1

8

tt

20

9

Sept.

28

10

Oct.

4

5

tt

8

10

it

15

13

What is the average number of cattle pastured each week (7

days), and what is due John Goodwin ? Ans. to last, $159.

8

114 PERCENTAGE.

GENERAL AVERAGE.

ART. 89. When, for the safety of a ship in distress, any
destruction of property or expense is necessarily and voluntarily
incurred, either by cutting away the masts, throwing goods
overboard, or otherwise, all persons who have goods on board,
or property in the ship, bear their proportion of the loss.

The method of apportioning the loss among the several in-
terests, sacrificed or benefited by the sacrifice, is called General
Average, and the property thus sacrificed is called Jettison.

In ascertaining the amount of loss to be averaged, not only
the amount of goods thrown overboard is considered, but also
all damages to the ship, cost of repairs, and expense of deten-
tion for making repairs, including the wages of officers and
crew ; also the expense of entering a harbor to avoid peril, or
of setting afloat when stranded ; also towage in case of being
disabled, or salvage paid another vessel for affording relief, etc.

When the repairs made consist of new masts, rigging, etc.,
a deduction of | of their cost is usually made, since they are
considered better than the old.

In estimating the value of the three contributing interests —
vessel, freight, and cargo — it is customary to value the cargo
at the price it would have brought at its port of destination.
It is sometimes valued at its invoice price at the port of lading.

As the wages of seamen, pilotage, etc., are paid out of the
freight, a deduction is made from the gross freight for this
purpose. The amount to be deducted is not determined in a
uniform manner. According to some authorities, the gross
freight less 1 is the net freight, except in New York, where |
is deducted. The general practice, however, is to ascertain
what sum will actually be left to the vessel as net freight, after
paying seamen's wages, etc. Sometimes the vessel earns a net
freight of f the total amount, and sometimes the seamen's
wages, etc., absorb the whole of a very low freight. Each case
is estimated by its attendant circumstances.

PERCENTAGE. 115

The practical difficulty in General Average is to determine
whether the loss is. subject to a general average. In some cases
the loss is borne by only a part of the contributory interests.

When either a part or the whole of the ship or cargo or
both is insured, the insurers bear their proportion of the loss as
found by average. (See Ex. 1.) In some instances the adjust-
ment of the insurance becomes a very intricate problem.

Divide the total loss subject to average by the sum of the
values of the contributory interests, and multiply each interest
by the percentage thus found.

Note. — The jettison must be included in the contributory
interests, and bear its proportion of the loss.

IS x a m pies.

1. The ship Western World, in her passage from New-
York to Aspinwall was struck by a severe gale near the island
of Cuba. After throwing overboard cargo amounting to $4650,
she made the port of Havana. Here the cost of the necessary
repairs of the vessel was $1800, and the cost of detention in
port $450Voi The contribilcory interests were as follows : value
of ^ ship $35$)0; value of cargo $24000; net freight $4000.
Of the cargo, $8500 was shipped by Terry & Wheeler ; $7500
by Morse & Duty ; $5000 by T. C. Hood & Co. ; and $3000
by P. Kinney & Co. How ought the loss to be averaged ?

Operation.

Vessel, ..... $35000 Jettison, . . . $4650
Cargo, ..... 24000 Repairs, less 1, . 1200

Net freight, . . . 4000 Cost of detention, __450

Total contrib. interests, $63000 JTotal loss, . . $6300

6300.00-=-63000=.10 ; 3oss 10 Per cent-
$35000 x .10=|3500, loss borne by ship.
, 24000 x. 10= 2400, " " " cargo.
4000x10= 400, " " « freight.
8500 x. 10= 850, " « « Terry & Wheeler.
7500x10= 750, " « « Morse & Duty.
5000 x 10= 500, " " « T. C. Hood & Co.
3000x10=- 300, " « " P. Kinney & Co.

116 PERCENTAGE.

2. The steamship Asia sailed from Liverpool to Boston with
a cargo as follows : shipped by T. S. Foot & Co. $45500 ; by
C. S. Moore & Co. $10500 ; by T. Hope & Sons $7450 ; by C.
White & Co. $12550. During a storm the captain was obliged
to throw overboard cargo amounting to $8500, and the neces-
sary repairs of the ship cost $2700. In addition to repairs, the
charges for seamen's board, dockage, etc., were $500. How is
the loss to be shared, the value of the ship being $40000, and
the net freight $4000 ? Ans. Loss, %.

JKemarJc. — The following examples will give the student
some idea of Insurance as connected with General Average.

3. The schooner Michigan sailed from Chicago for Buffalo
with the following cargo : 25000 bushels of wheat owned by
Smith & Dewy ; 18500 bushels of corn owned by Fisk &
Hunter ; 850 barrels of flour owned by T. Ford & Co. The
schooner is insured in company A for $30000, which is f of its
value, at 3 per cent. ; the wheat in company B for $22500
(invoice price) at 2 per cent. ; the corn in company C for
$9250 (invoice price) at li per cent. ; and the flour in com-
pany D for $4250 (invoice price) at 2| per cent. The gross *
freight was $6000, and seamen's wages, etc., £ of the gross
freight. During a severe storm the flour was thrown overboard.
How is the loss to be borne ? How is the payment of the sum
for which the flour is insured to be adjusted ?

Explanation. — By general average we find that the average
loss is 5 per cent., and that the schooner must sustain $2250
of the loss ; the cargo $1800 ; and the freight $200. Insur-
ance Company A must pay 5 per cent, of $30000 =$1500 ;
company B 5 per cent, of $22500 =$1125 ; company C 5 per
cent, of $9250= $462.50 ; and company D 5 per cent, of
$4250= $212.50.

4. Suppose, in the above example, that when the schooner
reached her dock in Buffalo the flour could have been sold for
$6120 ; the wheat for $35780 ; the corn for $11100. How is
the insurance to be adjusted ?

INTEREST. 117

INTEREST.

ART. 90. Interest is the compensation allowed for the use
of money or capital.

It arises from voluntary loans, from certain investments
giving a periodical income, and from delay in payment of debts
already due.

The principal is the sum loaned, or the debt on which in-
terest is paid.

The amount is the principal and interest taken together.

The rate of interest is fixed by mutual agreement or by
law ; and is the ratio between the principal and interest for an
assumed length of time, expressed by percentage ; thus, " 6 per
cent, per annum," declares the interest for one year to be T£T
of the principal In expressing the rate per cent., one year is
generally assumed ; though in discounting " short paper/' a
month is frequently used ; as 1 per cent, per month.

Usury formerly was synonymous with interest, but now
signifies illegal interest. England having abolished all usury
laws, has no further use for that term. The practicability of
voluntary contracts in loaning money, restricted only as other
contracts are restricted, is gaining increased favor among intelli-
gent political economists, and not the least among money bor-
rowers. When the rate has not been previously agreed upon,
a legal rate is desirable, to avoid contention or oppression.
Government regulates all weights and measures, but not the
prices of the articles weighed and measured. So it regulates the
weight and fineness of coins, but it should not dictate the price
paid for the use of them. The injustice of restricting the rate
of interest may be seen by applying the principal to insurance
companies. If the premium for insurance be restricted to a low
rate, only the safest risks would be taken, those having greater
risks could not be accommodated. So in restricting the rate
of interest, only the rich and those who could offer the best

118 INTEREST.

securities would be able to borrow money. If the loan be made
at higher than the legal rate, the rate must be raised still higher
to cover the risk arising from illegality.

ART. 91. INTEREST may be simple, annual, or compound.

In simple interest the principal alone draws interest ; which
as it accrues remains unchanged until ultimate payment.

In annual interest the interest on the principal due at the
end of each successive year becomes a new principal to draw
simple interest until payment. When interest is made payable
semi-annually or quarterly, the interest, if not paid, is convert-
ible at those periods into the principal, as in annual interest.

In compound interest the entire amount due at regular in-
tervals of time, both of principal and interest, is converted into
one new principal. It is thus compounded annually, semi-
annually, or quarterly.

Note. — The difference between simple, annual, and com-
pound interest in their effect depends upon the time when in-
terest money, if not paid, begins to draw interest. In general a
debt should begin to draw interest as soon as it is due. The
time when a debt of interest becomes due is conventional. In
bank discounts it is payable in advance. In simple interest it
is not considered due until the ultimate payment of the prin-
cipal. In annual interest it is due after it has been accruing
for one year, except the interest on interest, which is not due
till ultimate payment. Compound interest supposes all in-
terest, whether upon principal or interest, to be due at the end
of equal successive intervals of time, generally of one year or
six months. When the interest is considered due the instant
it has accrued, and all interest is made to draw interest, it is
called instantaneous compound interest. The actual difference
between even instantaneous compound interest and simple in-
terest is not so great as at first might be supposed. For 6$
simple interest for one year will amount to more than 5f$ in-
stantaneous compound interest.

INTEREST. 119

SIMPLE INTEREST.

ART. 92, Inasmuch as the interest varies directly as the
principal, rate per cent., and time, these four terms bear such
a relation to each other, that any three of them being given
the fourth may be found. To find the interest is by far the
most common problem, and may be obtained by the following

GJ-E2STER-AL

I. Find the interest for one year by multiplying the prin-
cipal by as many hundredths as are expressed in the rate per
cent., then multiply by the number of years and fractional parts
of years expressed in the given time.

Note. — When the time is expressed in months and days, it
is usual for convenience to regard each month as TV, and each
day as ?J7 of the year. (See Art. 95).

Ex. What is the simple interest of $844.50 for 2 yrs. 3 mo.
6 da. at 1% ?

$844.50
_ .07

1 yr. = $59.1150

2 yrs.= $118.230
3mo.= i - 14.779
6d. =Fv _ .985

$133.99 Ans.

Remark. — The multiplication may be performed by aliquot
parts. The fractional parts of mills may be neglected when less
than a half — otherwise, they should be counted as one.

The following rules may be found convenient in practice,
and the pupil should become familiar with the principle of all,
to apply that one which will give the result with the least
work.

KULE II. — Set dozen the entire number of months in the
time as decimal hundredths, and one third of the number of
days as decimal thousandths; multiply half the principal by
this number. The result ivill be the interest at §f0 per annum.

120

INTEREST.

For 4 per cent, subtract £. For 7 per cent, add j.

tt ^1 a a u g a a ^

a K a a i a if) u a 2

j ¥. -LU , -3.

Or in general, for other rates than 6$, increase or diminish the
result obtained by the rule in the same ratio that the rate is
increased or diminished.

Taking the last example, we have by this rule the following
solution :

$422.25x0.272=$114.852=: the interest at 6$.
Adding 1, $133.99 = the interest at 1%.

RULE III. — Take one per cent, of the principal for the in-
terest for tivo months or sixty days ; then by aliquot parts find
the interest for the given time.

Note. — It will be observed that the interest for 6 days may
be found by removing the decimal point three places to the left.
For any multiple of 6 days the result may be obtained by a
simple multiplication.

This rule is convenient in cases of "short paper/' as in
bank discounts, which generally run 30, 60, or 90 days.

When not expressed, the rate is understood to be $% per
annum.

Ex. What is the interest of $420 for 30, 60, and 90 days,
respectively, days of grace included ?

60 d. \% = $4.20(1) Add (2) and (3) , =$2.31 =int. 33d.

30 d. take J = 2.10(2) " (l)and(3) = 4.41 =int. 63d.

3 d. take TV= .21 (3) " (1) (2) and (3)-= 6.51=int. 93d.

By this analysis most examples in banking may be wrought
mentally.

Examples.

ART. 93. To be wrought by each of the three rules given
above. Find the simple interest of

1. $120 for 1 yr. 2 mo. 12 d. at 6^ ? Ans. $8.64.

2. $340.50 for 2 yrs. 3 mo. 15 d. at % ? Ans. $70.23.

3. $1000.25 for 1 yr. 9 mo. 3 d. at 10$ ? Ans. $175.86.

4. $25 for 3 mo. 3 da. at 12$ ? Ans. $.78.
/ 5. $145.20 for 1 yr. 11 mo. 29 d. at 1% ? Ans. $20.30.

INTEREST. 121

•/ 6. $450 for 3 yrs. 2 mo. 21 d. at 8^ ? Ans. $116.10.
P 7. If a man borrows $10000 at 6$ interest, and loans it at
10$, what will be gain in 2 yrs. 3 d. ? -4/w. $803.33.

8. A merchant bought 400 yards of cloth at $4 per yard,
payable in 6 months, and immediately sold it at $4.10, giving
a credit of 3 months, at the expiration of which term he antici-
pated the payment of his own paper, getting a discount off of
10$ per annum. What did he gain by the transaction ?

9. A merchant bought 400 yards of cloth at $4 per yard,
payable in 3 months, and after holding it for 15 days sold it at
$4.25 per yard, receiving therefor a note payable in 4 months.
When the purchase money became due, he had this note dis-
counted at the bank to meet k. What did he gain by the
transaction ?

10. Taking the conditions of the last example, what would
he have gained if he had borrowed at 6% interest, until the
maturity of the note he had received, sufficient to pay for the
cloth, and why should there be any difference in the results ?

11. If I invest $1000 in wool, pay 5% for freight, and sell
at 15$ advance on cost price, giving 4 months credit, get this
paper discounted at the bank at 6% interest, and repeat the
operation every 15 days, investing all the proceeds each time,
what shall I gain in 2 months ?

12. If a man borrows $1000 at 10$ interest, and with it
buys a note for $1100, maturing in 5 mo., but which not being
paid when due runs 1 yr. 6 mo. beyond maturity, drawing 6$
interest, will he gain or lose, and how much ?

Ans. He gains $7.33.

13. Jan. 1st. a man borrowed $10000 at 6$ interest.
Fifteen days after he lent $4500 for 8 mo. 15 d., without grace,
at 10$. Feb. 1st, with the balance he purchased a note for
$5650, due July 4, which not being paid at maturity was
extended until the loan of $4500 became due, at the rate of
8$ interest. Both notes having been then promptly paid, he
immediately purchased a 7$ State Bond of $10000, which,
with its semi-annual interest, would mature Jan. 1st following,
for which he paid 1$ premium upon its par value, at the same

122 INTEREST.

time loaning the balance at the rate of 1 \% per month. What
was his profit for the year ? Ans. $249.49.

ART. 94. To find the interest for days, counting 365 days
for a year, the only strictly accurate

Reduce the whole, time to days, by which multiply the year's
interest, and divide by 365. Or,

fieduce the actual number of days to months of 30 days
each, then find the interest by Kule II, subtracting from the
result thus obtained TV part °f itself.

Examples.

1. Find the simple interest of $1000 from April 1 to Dec. 1.
Solution.— -244 x $60~365=Ans. $40.11.

2. Find the simple interest of $125 from April 1 to Dec. 7.
Solution.— -246 days = 8 mo. 6 d. Then $125 x .041 =

$5.125, and $5.125— ^r= $5.055, the interest required.

By the first rule we have the following equation : 246 x
$7.50-^365= $5.055.

3. Find the interest of $1250 for 360 days at 6% pel
annum of 365 days.

Solution.— T£T of $1250=$75. Then $75- 3 f T (or T\) of
$75 := $73.97.

4. Find the interest of $1250 for 365 days at $% per
annum of 360 days.

Solution.—^ of $1250=$75. Then $75-f ^f ¥ (or TV) of
$75=$76.04.

5. What would be the diiference between the accrued in-
terest for 90 days on $1000000 of 6% State Bonds, computed
first in Ohio, counting 360 days for a year, then in New York,
counting 365 days for a year ? Ans. $205.48.

Note. — In New York the interest for years and months is
computed in the usual way without reducing to days, but for
the odd days the interest is computed by the above rule.

6. A note for $1000 runs from Jan. 1, 1856, to Jan. 25,
1858, with interest at 6$. What amount is due according to

INTEREST. 123

the above rule ? What amount is due computed as it would
be in New York ? What amount is due computed as it would
be in Ohio ?

COMPUTATION OF TIME IN INTEREST.

ART. 95. While most of the States have enacted rigid laws
against taking usurious interest, they have left the mode of
computing legal interest very indeterminate. Nearly all the
rules in common use in this country are inaccurate and illegal,
and have only been sustained by ^decisions based upon custom ;
but custom varies, and the legal decisions have not been uni-
form.

The difficulties attending this question, which has occasioned
so much litigation and jeopardized so much capital, can be
briefly stated.

The fundamental principle upon which lawful simple in-
terest is computed is that the rate should be exactly propor-
tionate to the term for which interest is paid. The time
usually assumed for fixing the rate is one year, e. g., 6 per
cent, per annum ; that is, when the time is one year, the in-
terest should be T£7 of the principal ; and when the time
varies from one year, the proportion of interest should vary in
exactly the same ratio. If, then, we assume that the year
consists of 365 days (as that is regarded in law a civil year),
it must be . admissible, in computing the interest on a note
running from Jan. 1, 1856, to Jan. 1, 1857, to add one day's
interest to the interest for one year ; for in the case proposed,
February of a leap year intervening, the time was 366 days in-
stead of 365, the legal civil year.

One year being the standard of reference in expressing the
rate, all time in computing interest must be expressed in years
or aliquot parts of the year. But the year has no exact natural
or artificial subdivisions except the day, and the day is an ali-
quot part only as we assume the year to consist of a definite
number of days. The number 360 being a multiple of more

124 INTEREST.

whole numbers than 365, for convenience in reckoning it would
have been better to assume 360 days for the nominal year in
fixing the rate, rather than 365. The time in expressing the
rate is arbitrary, and as neither 360, 365, nor 366 is the exact
number of days in all years, either civil or astronomical, would
not the increased facility in computation, and the perfect ac-
curacy in the result, warrant the change ?

The division of the year into twelfths, called months, is
purely imaginary ; for no month, either lunar or calendar, was
ever known which occupied just one- twelfth of a year. Mani-
festly, if we assume a year of 365 days as the standard for refer-
ence in expressing the rate, we never can introduce the denom-
inations of months in any form whatsoever without inaccuracy,
unless we involve in the calculation fractional parts of days,
which would be as absurd as it would be difficult.

If, however, we assume a year of 360 days, we may have
assumed months of 30 days. Then 6 per cent, per annum of 360
days would be 1 per cent, for 60 days, and all time being reduced
to days or months of 30 clays each, or years of 360 days each, the
computation would be simple, rapid, and perfectly accurate. As
it is, the law having accurately determined when a paper matures,
however the time may be expressed in the paper, the only accurate
rule for computing interest is to ascertain the actual number
of days, and make each day's interest ^ ^ of the annual interest.
Some banks are restricted by their charters in their discounts
to " 6$ per annum," but are allowed to compute by Hewlett's
Tables. But Hewlett's rule " To find bank interest/' makes
all time reducible to days, and the interest for each ¥|¥ of the
year's interest, so that when the time in the note to be dis-
counted reads " two months," the interest for T\ of the year
should never be taken except when February 29th of a leap
year is included in the term, for in that case only will the
" two months" contain just 60 days and no more. In all other
cases, the interest should be 59, 61, or 62-360ths of the year's
interest, according to the actual number of days contained in
the time of the note. In Massachusetts and some other States
interest computed on the supposition that 360 days make the

INTEREST. 125

year is regarded valid. But in New York each day's interest
must be only ^ of the year's interest.

ART. 96. KULES FOR COMPUTING THE DIFFERENCE OF
TIME BETWEEN DATES — Besides counting the exact number
of days as referred to above, two rules are in common use.

RULE I. — By compound subtraction, reckoning 30 days for
a month.

RULE II. — By finding the number of entire calendar months
from the first date, and counting the actual number of days
left.

Note. — By " calendar month" is meant the time from any
day of one month to the corresponding day of the next month.
If the days of the first month is a higher number than the
greatest number of days in the last month, the calendar month
ends with the last day. Thus from Oct. 31 to Nov. 30 is a
calendar month.

From Aug. 20, 1854, to March 10, 1857, would be,
according to the 1st Rule, 2 yrs. 6 mo. 20 d. ;
" " 2d Rule, 2 yrs. 6 mo. 18 d.

From Aug. 31, 1854, to March 10, 1857, would be,
according to the 1st Rule, 2 yrs. 6 mo. 9 d.
•< " 2d Rule, 2 yrs. 6 mo. 10 d.

It will be observed that in these particular examples, though
the actual difference of time in the two cases is 11 days, the
result by the second rule shows only 8 days. A discrepancy of
2 days may also arise in the use of the first rule, for by it the
time from Feb. 28, 1857, to March 2, 1857, would be 4 days,
while the actual time is only 2 days. The first rule also shows
no difference of time between March 31 and April 1. Each rule
will give a result sometimes too large and sometimes too small.

The examples in this work, except those in Bank Discount,
and those otherwise restricted, may be wrought by the second
rule.

ART. 97. PROBLEMS IN WHICH THE INTEREST is KNOWN. —
Of the four quantities, the principal, time, rate per cent., and
interest, to find either one of the first three, the remaining
three being given, we have the following

126 INTEREST.

G- E ]ST E R A IL, R-TILE.

Find the interest by the given conditions, assuming one
dollar for the principal, one per cent, for the rate, or one year
for the time, in place of the unknown quantity, as the case may
be, by which divide the given interest, and multiply the assumed
amount by the quotient.

Unity is assumed for convenience only in multiplication.

Note. — When the amount is given instead of the interest,
to find the latter subtract the principal from the amount.

E x am. pies.

1. What is the rate of interest if I receive $20.96 for the
use of $126.75 for 2 yrs. 24 d. ?

Solution. — At \% I would have received $2.62, and since
the given interest is eight times this, the rate should be eight
times \%.

2. What sum invested at 10$ per annum will secure an
income of $1000 semi-annually ?

Solution. — One dollar thus invested would yield an income
of 5 cents semi-annually, and since $1000 is 20,000 times 5
cents, the sum loaned should be 20,000 times one dollar.

3. In what time will $512.60 amount to $538.31 at 1%
per annum ?

Solution. — The interest of $512.60 in one year would amount
to $35.88, and since the given interest is only $25.71, the re-
quired time would be ff:fj of 1 year, which by reduction will
be found to be 8 mo. 18 d.

Fractional days in the result may of course be neglected.

ART. 98. The same result may be obtained by making the
statement in the form of a proportion, though it is better to
work by analysis.

The above examples would be thus stated :

As $2.62 int. at \% is to $20.96 given int., so is \% the
supposed rate to 8% the required rate.

Or, $2.62 : $20.96 : : \% : 8$.

2. $0.05 : $1000 : : $1 : $20,000.

3. $35.88 : $25.71 : : 1 yr. : 8 mo. 18 d.

INTEREST. 127

4. In what time will any sum double itself by simple in-
terest at 5 per cent. ?

Solution. — The required interest must be 100$ of the prin-
cipal, and as there is a gain of only 5$ in one year, it will take
as many years as 5 is contained times in 100.

Note. — To treble itself, the required interest must be 200$
of the principal.

PRESENT -WORTH.

ART. 99. Simple interest varies directly as the principal,
time, and rate per cent. Either two of 'the latter terms re-
maining the same, interest varies as the other. The principal
being given or fixed, the amount, consisting of the sum of
principal and interest, or of a constant and variable quantity,
can not vary as the time and rate per cent. But if the time
and rate per cent, are constant quantities, the interest varies as
the principal, and the amount being in this case the sum of
two equally varying quantities, varies also as the principal.
From this we see the truth of the following

PROPOSITION. — For the same time and rate per cent., whether
the interest be -simple or compound, the amount due varies as
the principal.

The Present Worth of any debt is the sum or principal
which at the current rate of interest will amount to that debt
when it becomes due.

For example, $100 at 10$ will amount in one year to
§110. The Present Worth then of $110 due one year hence is
$100.

The amount, rate, and time being given, to find the prin-
cipal or Present Worth, we have the following

RTJLE.

Assuming any principal, determine the amount for the
given rate and time, by which divide the given amount, and
multiply the assumed principal by the quotient.

128 INTEREST.

Note. — To render the multiplication easy, assume $1 or
$100.

Remark. — The difference between the Present Worth and
the Amount of the debt is called the Discount ; and is really
the interest on the Present Worth. For Bank Discount, see
Art.

Examples.

1. What is the present worth and discount of a debt of
$1000 due in 1 yr. 6 mo., the current rate of interest being 6
per cent. ? Ans. Pres. Worth, $917.431 ; Dis., $82.569.

2. What sum must I put at interest at 10 per cent, to
liquidate a debt of $3000 due 3 years hence ?

3. A man can sell his farm for $5000 cash, or for $6000
payable in 2 years ; if he accept the last offer, and receive in-
stead its present worth at 8% interest, how much better would
it be than the first offer ? If he accept the first offer, and loan
the $5000 at 8% interest, how much less would he receive at
the end of the 2 years than if he accept the last ? What is
the present worth of that difference ?

ANNUAL INTEREST.

ART. 100. If a note reads " with interest payable an-
nually," or " with annual interest/' the interest may be col-
lected at the close of each year ; but, if not paid, the interest
due draws only simple interest to the time of maturity, or until
paid.

It is a principle in law, that money due or on interest al-
ways draws simple interest, unless a condition to the contrary
is expressly stated. The condition, "with interest payable
annually, applies to. the interest which accrues on the princi-
pal or face of the note, and not to the interest on the annual
interest.

INTEREST. 129

If, when the annual interest is not paid at the close of each
year, separate notes for the same, drawing simple interest,
should be given, the sum of the amounts due on the several
notes, including the original, would be the same as the amount
due on the one note with annual interest unpaid till the time
of maturity or settlement.

Ex. 1.

$500. CLEVELAND, May 10, 1850.

For value received. I promise to pay John Smith, or bearer,
five hundred dollars, four years from date, with interest at 10
per cent., payable annually.

JAMES HOLT.

Nothing being 'paid till time of maturity, what will be the
amount then due ?

Operation.

Principal, $500

Interest on the principal 1 vr. =$50

4yrs. = 8200

Simple interest on $50 for 3 yrs.=$15
" " 2yrs.= 10

" " JL yr. = _5

6yrs.= ' 30

Total amount due at maturity, . . $730

Explanation. — At the close of the 1st year, $50 annual in-
terest was due, but, being unpaid, draws simple interest to the
time of maturity, or 3 years ; at the close of the 2d year, $50
annual interest was again due, which, being unpaid, draws
simple interest 2 years ; at the close of the 3d year, $50 annual
interest is again due, and draws simple interest 1 year ; at the
close of the 4th year, or time of maturity, §50 is again due,
but, being paid, has no interest. Hence, the total interest due
consists : 1. Of the annual interest (§50) multiplied by 4, the
number of years to maturity. 2. Of the simple interest of the
annual interest (§50) for 3 years, for 2 years, for 1 year, or for
3^2 + 1 years— 6 years.

Note. — It will be noticed that the amount due consists cf
three parts : 1. Principal. 2. Total annual interest. 3. Simple
interest on annual interest.

130 INTEREST.

Ex. 2.

$1000. BUFFALO, Jan. 1, 1853.

For value received, I promise to pay Thos. Hunt, or order,
May 7, 1858, one thousand dollars, with annual interest at G
per cent. G-EO. SWIFT.

Nothing heing paid on the above note till time of maturity,
what will be the amount then due ?

Operation.
Principal, . . ...... $1000

Interest on the prin. 1 yr., or annual interest, — $60
" " * 5 yrs. 4 mo. 6 da., the entire

time of the note computed as in simple int.— 321
Simple interest on $60 for 4 yrs. 4 mo.- 6 d.

(( a 3 a 4 u 6 "

K a 2 a 4 u 6 u

ic a 1 " 4 " 6 "

cc tc 4 " 6 "

Total amount due at maturity, . . . $1363.30
Note. — In this case, the amount due consists of three parts
as in Ex. 1. The term " total annual interest" as used above,
though nothing more than the simple interest on the principal,
signifies that debt of interest which if not paid draws interest.
As all interest is due at settlement, that which has accrued at
the time of settlement, though for less than a year, as in the
last example, may still be classed with " annual interest/'

Find the simple interest on the principal for the entire time,
which will be the TOTAL annual interest.

Then find the SIMPLE interest on the annual interest for one
year, for a time equal to the SUM of the periods of time the
several annual interests draw interest.

The sum" of the principal, total annual interest, and simple-
inter est thus found, will be the amount due at maturity. Or,

On the annual interest due each year, compute SIMPLE IN-
TEREST till maturity, and to the sum of their several amounts
add the principal.

When the interest is payable semi-annually or quarterly,

INTEREST. 131

each semi-annual or quarterly interest draws simple interest
till paid.

IE x a, m. pies.

3. A note for $1200 is given' to run 3 yrs. 3 mo. 12 d. with
interest at 6 per cent., payable annually. Nothing being paid
till maturity, what is then due ? Ans. $1453.03.

4. Bought a city lot for $900, to be paid in 4 equal annual
payments with annual interest. Nothing being paid, what is
due 5 years from the date of the article or lease ? What, 4
yrs. 7. mo. 9 d. ? What, 10 years, interest payable semi-
annually ? Ans. to the last, $1593.90.

5.

§2000. CLEVELAND, March 15, 1853.

On the first day of January 1858, for value received, I
promise to pay John F. Whitelaw, or order, two thousand
dollars with annual ^interest. CHARLES L. CAMP.

WThat was due at maturity, no interest having been paid ?
What was due, supposing the annual interest to have been
paid promptly ?

COMPOUND INTEREST.

ART. 101. In Compound Interest, as before stated, the
entire amount due at regular intervals of time, whether prin-
cipal or interest, is converted into one new principal. It may be
thus compounded annually, semi-annually, or quarterly.

For illustration, consider $1 to draw interest at 6% and
compounded annuallv.

$1.

1st year's interest, .... .06 •

Amount due forming a new principal, 1.06

2d year's interest, . .0636

Amount due forming a new principal, 1.1236

3d year's interest, 067416

Amount due forming a new principal, 1.191016

4th year's interest, _.07146096

Amount due in four years, . . $1^26247696

132

INTEREST.

Amount of $1 at Compound Interest in any number of years.

Yrs.

2 per cent.

2^ per cent.

8 per cent.

oi per cent.

4 per cent.

4£ per cent

1
2
3
4
5

1.0200 0000
1.0404 OoiiO
1.0612 0300
1.0824 3216
1.1040 8080

1.0250 0000
1.0506 2500
1.0763 9062
1.1038 1289
1.1314 0821

1.0300 0000
1.0609 0000
1.0927 2700
1.1255 0881
1.1592 7407

l.t.350 0000
1.0712 2500
1.1087 1787
1.1475 2300
1.1876 8631

1.0400 0000
1.0816 0000
1.1248 6400
1.1698 5856
1.2166 5290

1.0450 0000
1.0920 2500 !
1.1411 6612 1
1.1925 I860
1.2461 8194

6

7
8
9
10

1.1261 6242
1.1436 8567
1 1716 5938
1.1950 9257
1.2189 9442

1.1596 9342
1.1886 8575
1.2184 0290
1.2488 6297
1.2800 8454

1.1940 5230

1.2298 7387
1.2607 7008
1.3047 7318
1.3439 1638

1.2292 5533
1.2722 7926
1.3168 0904
1.3628 9735
1.4105 9376

1.2653 1902
1.3159 3173
1.8685 6905
1.4288 11 SI

1.4802 4423

1.3022 6012

1.3ft. 8 6183
1.4221 0061
1.4860 9514
1.5529 0942

11
12
13
14
15

1.2433. 7431
1.26S2 4179
1.2938 0663
1.3194 7876
1.3458 6834

1.3120 8666
1.8443 8SS2
1.3785 1104
1.4129 7382
1.4482 9317

1.3842 3387
1.4257 6039
1.4685 3371
1.5125 8972
1.5579 6742

1.4599 6972
1.5110 6866
1.5689 5606
1.6186 9452
1.6753 4883

1.5394 5406
1.6010 3222
1.6650 7351
1.7316 7645
1.8009 4351

1.6228 5305
1.6958 8143
1.7721 9610
1.8519 4492
1.9352 8-44

16
17
IS
19

20

1.8727 8570
1.4002 4142
1.42.32 40 J5
1.4563 1117
1.4859 4740

1 4845 0562
1.5.' 10 1826
1.5596 5872
1.5986 5019
1.6386 1644

1.6047 0644
1.6528 4763
1.7 24 3306
1.75-35 0605
1.8061 1123

1.7339 8601
1.7946 7555
1.8574 8920
1.9225 0132
1.9897 8386

1.8729 8125
1.9479 0050
2.0253 1652
2.10G8 4918
2.1911 2314

2.0223 7015
2.1188 7681

2.2084 7s77
2.3u78 6031
2.4117 14U2

21

22
23
24
25

1.5156 6634
1.5459 7967
1.5768 9926
1.6 )84 8725
1.6406 0599

1.6795 8185
1.7215 7140
1.7646 1068
1.80S7 2595
1.8539 4410

1.8602 9457
1.9161 0341
1.9735 8651
2.0327 9411
2.0937 7793

2.0594 8147
2.1315 1158
22061 1448
2.2333 2349
2.3G32 4498

2.27S7 6S07
2.3699 1^,79
2.4647 155 1
2.5683 0417
2.6658 8633

2.5202 4116
2.6336 52 il
2.7521 6635
2.&760 1383
3.01,54 8446

26

27
28
29
30

1.6734 1811
1.7068 8648
1.7410 2421
1.7753 4169
1.8113 6158

1.9002 9270
1.9478 0002
1.9964 9502
2.0464 0739
2.0975 6753

2.1565 9127

2.2212 89', 1
2 2379 2768
2 3565 6551
2.4272 6247

2.4459 5356
2.5315 6711
2.6201 7196
2.7118 7798
2.8067 9370

2.7724 6979

2.8333 6358
2.9937 0332
3 1186 5145
3.2433 9751

3.1406 7901
3.2320 0956
3.4296 9999
3.5340 3649
3.7453 1813

31
•32
33
84
35

1.8475 8882
1.8345 4059
1.9222 8140
1 9606 7603
1.9998 8955

2.1500 0677
2.2037 5694
2.2583 5086
2.3153 2213
2.3732 0519

2.5000 8035
2.5750 8276
2.6523 3524
2,7319 0530
2.8138 6245

2.9050 3148
8.0067 0759
3.1119 4235
3.2208 6033
3.3335 9045

8.3731 3341
8.5080 5875
3.6483 8110
3.7943 1634
3.9460 8899

8.9138 5745
4.0899 8104
4.2740 3018
4.4663 6154
4.6673 4781

36
37
33
39
40

2.0393 8734
2.0306 8509
2.1222 9379
2.1G47 4477
2.2080 3966

2.4325 3532
2.4933 4370
2.5556 8242
2.6195 7448
2.6850 6384

2,8932 7833
2.9*52 2668
3.0747 8348
3.1670 2693
3.2620 8779

3.4502 6611
3.5710 2543
3.6960 1132
3.3253 7171
3.9592 5972

4.1039 3255

4.2630 8986
4.4388 1345
4.6163 6599
4.8010 2063

4.8773 7846
5.G9G8 6049
5.8/62 1921
5 5658 9908
5.8163 6454

41
42
43
44
45

2.2522 0046
2 2972 4447
2.3431 8936
2.890i > 5314
2.4378 5421

2.7521 9043
2.821)9 9520
2.S915 2008
2.9638 0803
3.0379 0328

3.3598 0-93
34606 9>S9
3 5645 1 )77
3.6714 5227
8.7&15 95s4

4.0978 8381
4.2412 5799
4.3897 0202
4.5433 4160
4.7023 5855

4.9930 C145
5.1927 8391
5.4004 9527
5.6165 1503
5.8411 7568

6.0781 0094
6.3516 1543
6.6374 SS18
6.93(11 2-_>!m
7.2482 4843

46
47

49
50

'2.4366 112!)
2.5363 4351
2.5s7i) 703!)
2 'I'!--; 117!)
2.6915 8803

3.1133 5086
8.1916 9713
3.2714 8956
8.3532 7630
3.4371 0872

3.8950 4372
4.0118 9503
4.1322 5183
4.25IV2 ]!>U
4..-3S30 0602

4.8669 4110

5o:;72 8404
5.2135 8S98
5.3960 <;!.v,»
5.5849 2636

6.0743 2271

6.3178 1562
«.57«'5 2824
6.8333 4937
7.1066

7.5744 1961
7.9152 G849
8.2714 f.557
f.<54«(5 7107
9.0326 3627

51

2.7454 1!»7''

-V;2°>0 •% U

4..MT4 '_'-;•-">

; 99!10

7 ."/)"'.) r>i!G3

9.IS91 049)

53
54
55

: 8475

2<n:!t um

2.9717 3067

:', 7 1 >> !>iiK>
3.7939 2«91
, 7808

-! 7!) 4 1247
4. 9341 2435
:>.oxU 4359

(1 '921 0824
640SS 3202
6.6331 4114

7.9910 :.22i;
s.;i!:;s 1 |:i;,
8.6463 6G92

10 3o77 8858
10.7715 8(577
11.2563 OS17

INTEREST.

133

Amount of §1 at Compound Int€rest in any number of years.

r»

1
2
3
4

5

5 per cent.

6 per cent

7 per cent.

8 per cent

9 per cent 10 per cent

l.tlSftO 000
1.1 '.'
1.153
1.2;:
1.27

1.0600 000
1 1-236 000
1.1910 160
1.2624 770
1.....352 256

1.0700 000
1 1449 000
l.-.'^oO 430
1.3107 960
1.4025 517

1.0800 000
1.1664 000
12597 120
1.3604 890
1.4693 231

1.0900 OCO

i.:>-i (MM)

1.2950 290
1.4115 816
1.5i>86 240

1.1 COO 000
1 2100 COO
1.3310 000
1.4641 000
1.01(5 100

6

T
8
9
10

1.3400 95<i

1.4071 o-4
1.4774 S:,4
1.5- :
L628S 946

1.4185 191
1.5036 8(i3

1.593- 4-1
- 4 790
1.790S 477

1.5007 304
1.6057 815
1.71S1 862
1.-3S4 592
1.9671 514

1.5863 743
L7133 243
1.5509 3(12
1.9990 046
2.1589 250

1.6771 001
1.8280 S91
1.9925 626
2.1718 983
2.3673 637

1.7715 610
1.94S7 171
2.1485 888
2.8579 477
2.5937 425

11
12
13
14
15

1.7103 394
1.7953 5t>3
• •» 491
1.9799 316
1 -J 232

1.8P-
•2.0121 965
2.1329 2S3
0 040
2.35

2.1043 520
2.2521 916
2.4<>93 450
2.5785 342
2.7590 315

23316 390
2.51S1 7ol
2.7196 237
2.9371 936
3.1721 691

2.5804 264

-6 64S
3.o»'.: -
3.3417 270
aC424 S25

2 8c31 167
3.1: -
8.4522 712
3.71-74 9S3

4.177.

16
17

13
19
20

B8 746

2.2920 1S3
24066 192
2.5269 502
2.6532 977

2.54C3 517
2.6927 7-2-
2.S543 392
156 905
3.2071 S55

2.9521 633
3 1533 152
3.3799 323
3.6165 275
3.8696845

3.4259 426
3.7000 181
3.9960 195
43157 01 1
46609 571

3.9703 059

43270 834
4.7171 204
5.1416 613

5.6044 1 3

45949 730

5J/44 7d3
5.5599 173
6. 1 1.'9 S90
6.7275 000

21

24
25

£B 626

2.92 -
3.0715 233
3.2250 999
3.3S63 54

3.3995 636
3.6035 374
7 497
4.0459 346
4.2&1

4.1405 624
4.4304 017
4.7405 299
5.0723 670
5.4274 326

5.0333 837
5.43G5 4i 4
5.S714 637
6.3411 -<7
6.34S4 752

6.1'-

6.6566 -".4
7.2^7
7.9110 852
8.6230 807

7.401-2 499
8.1402 749
8 (24
9.5497 3-7
10.8347 059

26
2T
28
29
M

3.5556 727
3.7334 563
3.9201 291
4.1161. 356
4.3219 424

4.5493 830

-_.
5.1116 867
5.41S3 S79
5.7434 912

5.8073 529
6.21:

6.G4S3 384
7.1142 571
7.6122 550

7.3963 532
7.9SSO 610
7! 064
9.3172 749
10.0626 5C9

9.3991 579

10.24:
11.1671 :-05
12.1721 821
13.2670 7;5

11.9181 765
13.1099 942
14.42(9 936
15.-f3o 930
17.4494 023

31
89

33

34
35

4.53^ 395
4.7649 415
5.0031 385

5.2.-: ->
5.5160 154

6.r.881 006
6.454

•1-405 899
72510 25=3
7.6360 8C8

8.1451 129
8.7.:..
9.3253 398
rSl 135
10.6765 815

10.8676 694
11. 7370 S30
12.6760 4!»0
18.6901 336
14.7853 443

144617 695

15.703:; i-3
l7.1S-_"' -'-4
IS 72S4 109
20.4139 679

19.1943 425
21.1137 768
:i 544
25.5476 C99
2J-.1024 S69

36

87
33
39
40

5.7913 161
6.0- ; ;
6.8354 773
6.70 ' '

7.031*.

S.I 472 520
10 S71
9.1542 524
9.70-
10.2857 179

11 4239 422
12.2236 1-1

13."7'.'2 714

13.9:> g

14.9744 573

15.9681 718
17.2-156 256
IS 6252 7:0
20.1152 !•"
21.7245 215

22.2: 1

26.4::,-
2e.S159 817
31.4<;94 200

30.9126 805
S4.U
43 434
4114-.1 77-
45.'25t2 656

41
42
43
44
45

7.391.
7.761:
8.1496 669
8.5571 5'3
8.9850 078

10.9023 610
11.557
122.-i.i4 546
12.9S54 -10
13.7t>4a 11.. s

1C,. ir2-26 699
17.1442 563
is 34 13 543
19.62>4 596
21.0024 513

23 4624 832
25.3394 £19
27.8660

29.5559 717
31.9204 494

34.2362 679
37.317
40.67
448»
48.3272 601

49.7851 811
86 9t.2
60.24

C6.2640 761
72.8904 637

46

47

49

50

9.4342 582
9.9 >59 711
1 ..4012 697
1 ».9-213 831
11.4673 993

14.5904 -75
15.4659 1> 7
16.3933 717
17.3775 H40
18.4201 543

•22 -1726 234
•J4."4.-7 i7-i
•2:. 72-9 065
.' 800
29.4570 251

S44740 853
20 122

4- i-.'li 5 7S1
4-U.74 I9i»
46.9016 1-5

52.6767 419

57.417
6_'5--
Cs-2179 OS3
74.3575 2'1

80.1795 ?21
88.1974 853
'.•- 0172*888
'106.7189 572
117.3908 529

51
53
53
54
55

1-2.0407 693
12.6423 083
13-2749 4b7
13.93-6 961
146356 809

19.52.V
20.69-N
21.9386 985
23.2550 204
246503 216

81.5190 163
58 450
M 224
-1 509
41.3150 015

50.6537 415
54.T06I

5 -241
63.8091 260
68.9133 561

SI .0496 9<-f>

96.2951 -449
1 1"4.961 7 079
114.4(82 616

129.1299 382
142.042!

156. '2-1 72 252
' ' '.' 477
1S9.I.591 425

134 INTEREST.

If compounded semi-annually, we should have the follow-
ing result :

$1.

Interest 1st six months, • . . . .03

L03

Interest 2d six months, . . . .0309

1,0609
Interest 3d six months, . . . .031827

1.092727

Interest 4th six months, . . . .03278181

Amount in two years, . . . $1.12550881
We have seen heretofore that simple interest varies directly
in the same ratio as the principal, time, and rate per cent.
Compound interest likewise varies as the principal, but when
the time or rate per cent, is increased, compound interest in-
creases in a still greater ratio, e. g.
Doubling the principal doubles the compound interest.
Doubling the time more than doubles the compound interest.
Doubling the rate more than doubles the compound interest,
as may be seen from the following figures :
When the interest of $100 is .... $5.
The interest of $200 would be ... $10.

The compound interest of $100 for 2 years at 6% is $12.36
« " " " " " 4 years at 6% is $26.2477

" " " " " 2 years at 5% is $10.25

1 « " " " " " 2 years at 10/0 is $21.

From the fact that compound interest (and therefore the
compound amount) varies as the principal, the time and rate
remaining the same, having ascertained the interest or amount
for any one principal, the interest for any other may be found
by a simple proportion. Tables have therefore been prepared
giving the interest or amount of $1 for different intervals of
time and at different rates per cent. The interest or amount
for any given principal may then be found by simply multiply-
ing the sum found in the table by the given principal. If the
intervals are less than one year, as when the interest is to be
compounded semi-annually or quarterly, tables computed with
yearly intervals may still be used by reducing the rate per cent.

INTEREST. 135

proportionably, and taking in the table the proper number of
intervals.

For the time used in expressing any rate of interest is en-
tirely arbitrary, and having . fixed the ratio between the prin-
cipal and interest at each compounding, the result depends
upon the number of times the operation be repeated. Thus,
if the interest be compounded a given number of times by add-
ing to each respective amount 4$ of itself, it matters not
whether it be considered 4$ per annum or 4^ per minute, the
result would be the same. If the interest is to be compounded
quarterly, when the rate is said to be 8^ per annum, 2^
should be used at each compounding, though it would amount
to more than 8$ compounded annually.

Examples.

1. What is the compound interest and amount of $1000
for 5 yrs. at Q% per annum, payable annually ?

" Ans. $338.22 and $1338.22.

2. What is the compound amount of $2200 for 3 yrs. 2 mo.
12 d. at 6/p per annum, payable annually ?

Ans. $2651.67.

Note. — After having computed the compound amount for
the number of entire intervals at the end of which the interest
is payable or to be computed, compute the simple interest on
that amount for any remaining time before the settlement.

3. What is the compound interest of $1400 for 10 yrs. 8
mo. at 8/£ per annum, payable quarterly.

Solution.— $2.29724447 x 1400 = $3216.1423 = the comp.
amount for 10 yrs. 6 mo., and $3216.1423 x l.Oli— $1400=
the comp. interest for 10 yrs. 8 mo. =$1859.024.

4. If the population of a city containing 10,000 inhabitants
should increase 10^ annually, what would it amount to in 10
years? Ans. 25,937.

5. If a farmer beginning with one bushel of wheat should
sow his entire crop each successive year, and the increase each
year should be 1900^, what would he have at the end of 5
years? Ans. 3,200,000 bushels.

136 INTEREST.

6. If a banker's rate in loaning money is 12$ per annum,
and lie reloans all his capital every two months, what must
have been the rate at simple interest to realize the same amount
at the end of one year ? Ans. 12^$ nearly.

What, at the end of two years ? Ans. 13T4¥$ nearly.

What, at the end of eight years ? Ans. 19T3¥/^ nearly.

What, at the end of fifteen years ? Ans. 33$ nearly.

What, at the end of twenty-five years ? Ans. 74$ nearly.

ART. 102. In compound interest, as in simple interest, the
four quantities, viz., principal, time, rate per cent., and interest
or amount, bear such a relation to each other as that when
any three of them are given, the fourth may be found. Hence
four cases arise.

i.

The principal, time, and rate being given, to find the com-
pound interest and amount.

This case has already been presented, but the rule may be
expressed in a more concise form.

KULE. — Find from the table the amount of $l/or the given
number of entire intervals, or times of compounding, at the
proper rate for each interval, and multiply it by the given
principal. Taking this product for a new principal, find the
amount at simple interest for any fractional interval, if any,
remaining before settlement. This will be the compound
amount, and the compound interest may be found by subtract-
ing from it the given principal.

II .

The compound interest or amount, the time and rate being
given, to find the principal.

RULE. — Assume $1 for the principal / compute for the
given time and rate its compound interest or compound amount,
by which divide the given compound interest or compound
amount, observing always to divide interest by interest and
amount by amount. See Art. 97.

For illustration of Present Worth see Art. 99.

INTEREST. 137

E x a rn. pies.

1. What sum, in 17 yrs., at 6^, payable annually at com-
pound interest, will amount to §1009.79 ? Ans. $375.

2. What sum, in 14 yrs., at 8,V', payable semi-annually at
compound interest, will amount to §10,795.34 ? Ans. §3COO.

3. What principal will yield §3251.50 compound interest
in 6 yrs. 2 mo. at 7$, payable semi-annually ? Ans. §6150.

4. How much must a father, at the birth of his son, set
apart for his benefit, so that with the interest at 7%, com-
pounded semi-annually, it may amount to §10,000, when his
son shall become 21 years of age ? Ans. §2357 79>.

5. What sum at 10/t, payable quarterly, will produce
§7197.22, compound interest, in 3 yrs. 6 mo. 9 d. ?

Ans. §17,280.

6. What is the present worth of §50,000, due 50 yrs. hence,
at 9 per cent., payable annually ? Ans. §672.43.

How much greater would be the present worth at simple
interest ?

CA.SE III.

The principal, time, and interest or amount being given,
to find the rate. See Case IV.

C.A.SE I^T.

The principal, rate, and interest or amount being given, to
find the time.

For the last two cases we have the following general
KULE. — Divide the given amount by the principal ; the
quotient will be the compound amount of §1 at the given rate
for the required time or for the given time at the required rate.
By reference to the table, the rate heading the column in which
this quotient is found opposite the given time or number of in-
tervals, ivill be the required rate; and the number in the left
hand column opposite the quotient under the given rate will be
the required time or number of intervals.

E x a m. pies.

1. At what rate will §7200 yield §12,665.02, compound in-
terest in 15 yrs. ? Ans. 7 per cent.

138 INTEREST.

2. At what rates will any sum of money double itself by
compound interest in 8, 10, 15 yrs. payable semi-annually ?

Ans. 4i$, 3$, 2i$, respectively.

3. In what time will $5428 amount to $27157.31 at 5$,
payable annually ? Ans. 33 yrs.

4. In what time will any sum of money triple itself by
compound interest at 4$, 7$, 8$, 10$, payable quarterly ?

7 yrs., 4 yrs., 3^ yrs., 3 yrs. nearly.

PARTIAL PAYMENTS.

ART. 103. When partial payments are made on mercantile
accounts which are past due, and on notes running only for a
year or less, it is customary to use the

RTJLE3.

Compute the interest on the whole debt or obligation from
the time it began to draw interest, and on each payment from
the time it was made until the time of settlement, and deduct
the amount of all the payments, including interest, from the
amount of the debt and interest.

Note. — When a partial payment is made on a note or obli-
gation before it is due, no part is applied to the discharge of
the interest, but the whole is used to reduce the principal in
accordance with the above rule.

$800. CLEVELAND, Nov. 18, 1856.

Ninety days after date, I promise to pay to the order of
William Penn six hundred dollars, with interest, value re-
ceived. WALTER JOHNSON.

Indorsements.— Nov. 30, $100 ; Dec. 10, $250 ; Dec. 20,
$100 ; Jan. 2, $80.

What was due at maturity ?

$600, with interest for 93 days, amounts to $G09.30

$100, " " « 81 " " " $101.35
$250, " « " 71 " " " 25296
$100, " " " 61 " " « 101.02
$80, " " " 48 " " " 80.64
Sum of payments, with their interest, $535.97

Amount due at maturity, Feb. 19, 1857, "$73^33

INTEREST. 139

The same result can be obtained more easily by the use of

the following

IRTJ JL.E.

Multiply the amount due at first, and the balance of the
principal due after deducting each payment, by the number of
days that elapse between the several payments, add all the pro-
ducts, and divide the sum by 6000. The quotient will be the
interest at 6 per cent.

Taking the same example as above.

§600 multiplied by 12= ...... 7200

§500 " 10= ..... . 5000

§250 " " 10= ...... 2500

§150 " " 13= ...... 1950

§70 " " 48= ...... J3360

Sum = ...... 20010

Which, divided by 6000, gives for the interest due . §3.33
This added to the balance of principal, gives . . §73.33

When the principal does not draw interest, the last rule
can not be used without some modification.

When the time of the note or obligation is more than one
year, the following rule has been adopted by the courts of
most of the States, and by the Supreme Court of the United
States, and may therefore bo called the

STATES

ART. 104. Apply the payment in the first place to the dis-
charge of the interest then due ; if the payment exceeds the in-
terest, the surplus goes toward discharging the principal, and
the subsequent interest is to be computed on the balance of
principal remaining due.

If the payment be less than the interest, the surplus of in-
terest must not be taken to augment the principal ; but interest
continues on the former principal until the period when the
payments taken together equal or exceed the interest due, and
then the surplus is to be applied toivard discharging the princi-
pal, and interest is to be computed on the balance as aforesaid.

This rule requires that the payment should in all cases be
applied to the discharge of the interest first, then the principal.

140

INTEREST.

Ex. 1. For value received, I promise to pay to the order of
C. D. Stratton $16*50 on demand, with interest at 7$.

J. 0. SNYDER.

CLEVELAND, 0., May 20, 1856.

Indorsements.— Sept. 1, 1856, $25 ; -Oct. 14, 1856, $150;
Mar. 20, 1857, $45 ; July 5, 1857, $300.

What was the amount clue Nov. 11, 1857 ?
Solution. — Interest on $1650 from May 20,
1856, to Sept. 1, 1856, 3 mo. 12 d., at 7% per

annum, . $32.725

The payment, $25, being less than the interest then
due, neglecting the former work, find the interest
on $1650 from May 20, 1856, to Oct. 14, 1856,
4 mo. 24 d.

46.20
1650.

Amount due, Oct. 14, 1856, ....
Sum of the two payments, $25 and $150, to be

deducted,

Balance due after the second payment,

Interest on $1521.20 from Oct. 14, 1856, to March

20, 1857 ($46.14), being more than the payment

made, find the interest on $1521.20 from Oct.

14, 1856, to July 5, 1857, 8 mo. 21 d.

Sum of the payments, $45 and

Balance due July 5, 1857,

Interest on $1253.401 from July 5, 1857, to Nov.

11, 1857, 4 mo. 6d.,

Balance due on settlement, Nov. 11, 1857, .

1696.20

175.
1521.20

J77.201
15987401

345.^
1253:401

30.708

. $1284.109

Note. — Frequently an estimate of the interest may be made
mentally with sufficient accuracy to decide whether it be not
more than the payment, whereby some labor may be saved.
2. A note of $1200 is dated June 10, 1854, on which,
Aug. 16, 1855, there was paid, . $100

Dec. 28, 1855, « « « . . 200

June 2, 1856, " " " . 25

Dec. 29, 1856, " " " . 25

June 1, 1857, " " " . 25

Oct. 28, 1857, " " " . 500

INTEREST. 141

What is the amount due Dec. 10, 1857, the interest being
6 ? Ans. §551.347.

3. BUFFALO, X. Y., April 10, 1852.

One year after date, I promise to pay to the order of James
Johnson one thousand dollars, with interest, value received.

THEODORE LELAND.

Note. — The legal rate of interest in New York is 7$.
On the note were the following indorsements :
Nov. 10, 1853, rec'd $ 80.50 Jan. 10, 1855, rec'd §450.80
5, 1854, " 100. Oct. 1, 1857, " 500.

remained due Jan. 1, 1858 ? Ans. §170.146.

CHICAGO, July 15, 1854.

>T\vo years from date, for value received, I promise to pay
the order of Peter Finney, six hundred and fifty dollars,
with interest at 10/£, payable annually. SILAS WARREX.

\Mr. Warren paid on the above note, Sept. 15, 1856, §105 ;
ay 9, 1857, §250. What amount was due Sept. 24, 1858 ?

Note. — In cases like the last, the payments should be ap-
plied first to the discharge of the interest on the annual interest,
then the annual interest, and finally the principal. The in-
terest on the principal, which has not yet become annual in-
terest, not being due, should not be cancelled by payments
except it be at the final settlement of the note.

Solution.

First annual interest, $65.

Interest on same from July 15, 1855, to Sept. 15, 1856, . 7.5SJ

Second annual interest, C5.

Interest on same from July 15, 1856, to Sept. 15, 1856, . 1.0S3

$138.66~6

First payment 105.

Interest on $33.666 from Sept. 15, 1856, to May 9, 1857, .
Original principal, ........

685.854
Second payment, 250.

Xo\v principal, '. $135.854

Interest on $650 from July 15, 1856, to May 9, 1857,

not due at time of payment, • $53.083

Interest on $435.854 from May 9, to July 15, . 7.990

Third annual interest,,

Interest on same from July 15, 1857, to Sept. 24, 1858,

Fourth annual interest,

Interest on same from July 15. 1858, to Sept. 24, 1858,

Fifth annual interest, due at settlement,

Amount due Sept. 24, 1858,

ra|'
in

142 INTEREST.

ART. 105. Another rule for applying partial payments is
in use among many business men, and has received the sanction
of several legal decisions. This rule, because it is used by
merchants, has been styled

THE MEPtC^LlNrTIIjirj RTJT^n.

Compute the interest on the principal or original debt for
one year, and add it to the principal. Find the interest also
on the payments made during the year, if any, from the time
they were made to the.- end of Ike year. Deduct the sum
payments and interest from the amount of principal ami
terest for a new principal. Do the same for each succeeding
year till the final settlement.

Note. — It will be observed that this is applying the
mont Rule to eaph separate year, beginning with the date
the note, and making yearly rests. Sometimes these rests, or
times of making a new principal in mercantile accounts, a
made to come at the end of each civil ^s-r, sometimes once i
six months, depending upon the custom of merchants in balanc-
ing their accounts. Bankers for the same*reason have been
allowed to make quarterly rests, carrying forward a new prin-
cipal every quarter, at the time of "balancing the ledger.

Ex. A note of $2000 is dated Feb. 1, 1850, on which were
the following

Indorsements. — March 1, 1850, $200 ; July 1, 1850, $300 •
Oct. 1, 1850, $500 ; July 1, 1851, $100 ; Oct. 1, 1852," $200 ;
Jan. 1, 1853, $600.

What was due July 1, 1853, the interest being 6;^ ?
$2000 will amount, Feb. 1, 1851, to ... $2120
200 " " " to . $211

300 " "• to . 310.50

500 " " " " to . 510

Sum of payments and interest, .... 1031.50

New principal, ....... 1088.50

$1088.50 will amount, Feb. 1, 1852, to . . 1153.81

100 " " " " to . . . 103.50

New principal, ....... 1050.31

[Carried over.]

INTEREST. 143

[Brought over.]

$1050.31 will amount, Feb. 1, 1853, to . . 1113.33

200 " " " " to . $204

600. " " " " to . 603 . 807

New principal, 306.33

$306.33 will amount, July 1, 1853, to ... 313.99
ART. 106. MERITS OF THE BULKS FOR PARTIAL PAY-
MENTS.— The method of computing interest when partial pay-
ti&ents have been made is a subject that has given rise to much
^itigation. In many States the only law relating to it consists
•bf decisions in particular cas.es, wliigk, from the peculiar cir-
jcunwtances, do not always clearly indicate a principle that may
* beiipplied justly to other cases. The aim in legislative enact-
ts appears to have been twofold, to avoid usury and the
ing of compound interest. Now all interest is in effect
compounded when it is paid, since it allows the lender to loan
again and draw interest on interest, while, if not paid, the debtor
the use of the interest money without paying interest. No
court ever objected to a man's paying interest as often as he
cho'se, and the statutes generally allow a collection of legal in-
terest as often as WJIB 'agreed upon by the parties in the original
coniract. They alsc*'allow$; collection of simple interest upon
any interest money a^t^it becomes due, if not paid. They
also allow compounding »t the legal rate as often as the debtor
chooses, provided tha.t thev-bld obligation be cancelled and a
new one given. Compound interest then is not of itself illegal.,
it is only certain forms of it.

The difficulty attending partial payments is in deciding
whether jfchey shall be applied to the debt of interest or princi-
pal. If applied to the debt of principal, there is only simple
interest ; if applied to the debt of interest, the practical effect
is that of compound interest.

The Vermont Rule is the only one involving no compound
interest. The objection to that rule, when the time is more
than one year, may be seen in the fact that the payments may
be no greater than the interest due at the time of the payment,
and still if the payments are sufficiently frequent, and the note
run sufficiently long, the entire debt of principal and interest

144 INTEREST.

may be discharged, and the holder of the note become indebted
to the debtor. (See Ex. 1, page 143.) Both the Mercantile and
the United States Rules involve compound interest, the former
compounding it once a year, the latter as often as a payment is
made which equals or exceeds the interest then due. When the
"payments occur at intervals of just one year, commencing with
the date of the note, bo th rules give the same result. When they
occur oftener than once a year, the Mercantile Rule is the
favorable to the debtor ; when more than a year intervenes, :
United States Rule is tjpie more favorable. The Vermont R
is usually more favorable than either, for by that there
no compound interest, and all the payments draw interest.
By the use of the United States Rule an inducement is offtred
to defer payment as long as possible, and the longer paying
be deferred, the greater the inducement to continue it. Strict
justice to all parties, in all cases, would be to have the interest
on the whole debt, whether of principal or interest, compoum
instantaneously. This method, though desirable, can not

•< O

present be made practicable. See Note, page 118,

Examples.

1. A holds an obligation against B for $1000, wnich
run 25 years at Q% interest. At the expiration of each year a
payment of $60 was made. What is the amount due, as com-
puted by each of the rules given above ?

By the United States Rule, B owes A $1000.
By the Mercantile Rule, B owes A $1000.
By the Vermont Rule, A owes B $80.

2. A note of $10000 runs 4 years at 8$ interest, on which
were made quarterly payments of $500. What was the amount
due at the time of settlement ?

By the Vermont Rule, $4000.

By the Mercantile Rule, $4322.30.

By the United States Rule, $4408.21.
Note. — It will be observed that generally the result obtained
by the Mercantile Rule will be intermediate between those ob-
tained by the other two.

INTEREST.

145

DIAGRAM

ILLUSTRATING

SIMPLE, ANNUAL,

AND

COMPOUND INTEREST.

10

146 INTEREST.

SIMPLE INTEREST.

ART. 107. The relation between the principal, time, rate per
cent., and interest, is exhibited to the eye in the diagram on the
opposite page. Let the single line A (which for convenience is
separated from the diagram, but which should be considered
as extending horizontally to the left from B, C, D, etc., re-
spectively,) represent the principal ; the perpendicular line BG
represent time with its divisions into years, at the points C, D,
E, and F; and the horizontal lines CH, DI, EK, FL, and GM
the accrued simple interest at the expiration of each successive
year. As no ratio can be expressed between time and money,
area can represent nothing in the diagram. As rate per cent.
is nothing but the ratio between the principal and interest, it
can only be represented by the degree of divergence of the
lines BC and BH, by which the lines CH, DI, EK, and FL
shall bear a proper relation to the line A. If the rate be 10$
per annum, the line CHrnust be TW or TV of the line A, DI r\,
EK T\, and so on. The line BM represents nothing but a limit
to the lines representing interest for any time on the line BG.

A + CH, A+DI, A+EK, etc., represent the amount due
each successive year at simple interest.

ART. 108. ANNUAL INTEREST.

Simple and annual interest are the same for the first year.
At this time in " annual interest," the accrued simple interest
on the principal forms a new principal to draw simple interest
till maturity. The same is true at the end of each following
year. This increase of interest will be represented by the lines
/i, JT3, LG, and Mi 0. The rate being 10^, Ii must be TV of
CH its principal; JK"3 = Tair of CH+T\ of NI=T^ of CH ;
£« = •& of CH+fv NI+j\ of OK=T°v of CH; and M, 0 =
TV of CH + T\ of NI+ A of OK+ TV of PL = [£ of CH= CH.
It will be observed that the line B\ 0 is not a straight line, but
composed of straight lines, the degree of divergence from the
line BG being increased at the end of each year ; also that the
numbers i, 3, c? i », etc., are the sums of the several series i ;

INTEREST. 147

x

i + 2 ; i + a + 3 ; 1 + 2 + 3 + 4, etc. ; and also that they express
the number of years that the simple yearly interest of the prin^
cipal must draw interest to equal the interest on all the several
amounts of annual interest. The line ab, though limited by
the straight line 6, i o, is still a correct representation of the
interest due at the end of 4| years with annual interest.

ART. 109. COMPOUND INTEREST.

Annual and compound interest are the same for two years.
Then the interest which has accrued on the first annual interest
becomes a part of the principal. In like manner all the interest
at the end of each year becomes a part of the principal for the
next year. The line ,, c, d, 2, limits the horizontal lines re-
presenting compound interest after the first two years. It
should be separated from the line Si 0 at the point 3, a distance
equal to TV of /,. At the point 6, a distance equal to 3c+ TV
of Kc. At the point i „, equal to 6d+TV of Ld.

Or, comparing simple interest with compound, the line B2
must begin to diverge from the line BM at the point H, and
be separated from BM at the point 7, a distance equal to TV
of CN. At the point K, equal to the I, + TV of D i . At the
point Lj equal to Kc-}- rV of EC. At the point M, equal to

"PARTIAL PAYMENTS" ILLUSTRATED.

ART. 110. The Diagrams on the following pages illustrate
the difference in the principle of the three foregoing rules for
" Partial Payments."

The problem used in each diagram is the following :

A note for $1000 runs 4 years with interest at 6$.
In 1 yr. frpm date a payment of ... $50 is made.
In lj yrs. from date a payment of . . . 250 "
In 2 yrs. from date a payment of . . . 224 "
In 2 yrs. 8 mo. from date a payment of . . 20 "
In 2 yrs. 10 mo. from date a payment of. . 110 "

What was due at maturity ?

148 INTEREST.

In the illustration, time is measured horizontally by the
distance between the perpendicular lines.

The horizontal base line in each figure separates principal
from interest, the perpendicular lines above representing the
former, and those below the latter. The perpendicular lines
above are limited by a horizontal line which is more or less re-
moved from the base line, as the payments are applied to in-
crease or decrease the principal. The perpendicular lines below,
representing interest, are limited by a line always diverging
from the base line, the degree of divergence depending upon
the rate per cent, and the size of the principal. When the
entire interest is cancelled by any payment, the diverging line
starts anew from the horizontal base line. The perpendicular
distance between these two limiting lines at any time repre-
sents the amount of principal and interest due at that time.

INTEREST.

149

$346.

$476.

10

b o

^ S r^ ^

•3l.^§

S950.

Principal. $10 00.

O -^ *'~~5 r5^ S^

l|?l,i:

§ I.I.S

s ^

150

i

INTEREST

$ 489.19.

$589.70.

Jo

ICO

0 0

fi t§ i

W rd

r^ -4— > cQ

5 - g

<j O -1-3

rj-j M QJ

•§ ^ s

5 G S

P^ R g

pi o" o

•^ £ ^

^ 3

fH +- o

o ^

EH ~
P ^

.-

^ o

5 3 §
Pn QQ "

§F

$1000

05

CO

a

"S

Principal. $ 1000.

^j ^p

£ g

<^ fc

o .a

bD

w

P 111

w *•! * ,

pq* ^ 'g o

• r-H O "^^

O o ^

«L§ ®

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^s J a

0>

rg

go ^ o o
O CM CM rH
CM CM rH

i «

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J- r-c

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INTEREST

151

S,

CO

tntfli

CO

M

05 ! I G*|<M

10

ko

30

00

CO

C5
O

r^»

$58910.

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152 CURRENCY AND MONEY.

to compounding so much of the interest then due. Had the
payments been more frequent, the amount due at maturity, by
the United States Rule, would have been larger, as compared
with the other rules, than in the present instance.

It is recommended to the pupil to study these diagrams tiD
he becomes perfectly familiar with the reason why different
rules give different results, and also to work other examples,
drafting diagrams to correspond. With the use of proper
mathematical instruments, tolerably accurate results may be
obtained by drafting alone. Especially should the pupil notice
that rate per cent, is the ratio between the principal and in-
terest, and is represented in the diagram by the degree of
divergence of the interest line from the horizontal base line.
In the same diagram the less the principal, the less the diver-
gence.

CURBElNrCY AND MONEY.

METALLIC 'CURRENCY.

ART. 111. BARTER is simply exchanging one or more com-
modities for others, as giving one bushel of wheat for two
bushels of corn.

MONEY is an instrument to facilitate exchanges, and, strictly
speaking, should possess an intrinsic value equivalent to that
for which it is exchanged.

Various articles have at different times and by different
nations been used for this purpose, as shells, leather, corn,
cattle, etc., but the precious metals, gold and silver, have been
found to be most serviceable for the following reasons :

1st. They possess great value in small bulk.

2d. Their value remains quite uniform, changing only by
slow degrees.

3d. They can be used or hoarded without much wear or
decay.

CURRENCY AND MONEY. 153

4th. The pieces can be united or subdivided without loss
of value.

5th. They are homogeneous in their structure, and easily
identified.

Gold and silver, by being used as money, become the stand-
ard of reference for expressing the value of other commodities.
The price of a commodity is usually its value expressed in the
denominations of money.

When prices or obligations in debit and credit and barter
are thus expressed, and business transacted without the inter-
vention of money, we have what is called the " money of ac-
count." The denominations in the " money of account" may
be even different from the denominations of the money in cir-
culation, and if the denominations of both be the same, the
values represented by them may be different. Still further,
there may be a " money of account" where there is no money
in actual use, in which case (as to a certain extent in all cases)
prices are only expressions showing the relative value of com-
modities, and, like the terms used in the measure of arcs and
angles, are indefinite until referred to other commodities, or to
the same commodity of different amount. Gold and silver
have an intrinsic value, depending upon their cost of produc-
tion and uses. They derive a value from their capacity to
facilitate exchanges, just as horses, mules, and railroads derive
their value from facilitating transportation. Government can
no more create a value to gold and silver than to sugar. It
does, however, increase their value by coining them into pieces
convenient for use, and declaring them legal tender in payment
of debt. Coinage being only a certificate of value already ex-
isting in the metal, it is not necessarily the work of govern-
ment, neither is legal tender a necessary element of even a
metallic currency, as is seen in the coinage of copper and nickle.
Coining gold and silver enhances their value in the same way
that manufacturing steel enhances the value of the iron used,
or as the brand of an official inspector renders certain articles
of merchandise more salable. Making gold and silver coins
legal tender increases their value because it increases their

154 CURRENCY AND MONEY.

demand. For when other articles of value can not be used
in liquidating indebtedness, these will always answer the
purpose.

Money, by being legal tender, becomes naturally a standard
of value for other property. But money itself is not an invari-
able measure of value, for the reason that its value, like that
of other kinds of property, is affected by cost of production,
supply, demand, etc. The debasement of coins by government
is not here taken into the account. If gold alone were used as
money and legal tender, its gradual change of value would be
perceptible only as it caused an increase or decrease of prices.
A diminution in value of gold would raise prices, and vice
versa. But frequently gold and silver both are legal tender, as
it was in the United States until A.D. 1853. In making both
legal tender, it is necessary for government to establish their
relative value. If the legal relative value be the actual com-
mercial relative value, then both will circulate equally well,
except so far as convenience may dictate. But as both are
constantly changing in their commercial value, while the legal
relative value remains the same, the metal that has the greatest
commercial value will be used to make foreign purchases, while
the cheaper metal will remain at home. It is a general prin-
ciple in currency, that if several different articles be allowed to
circulate as money, the cheaper will displace the dearer. If a
thousand silver dollars will pay a larger debt in a foreign coun-
try than a hundred gold eagles, then silver will be shipped in
payment.

By making silver legal tender for small sums only, its legal
relative value, or mint valuation, may be considerably higher
than its commercial or marketable value, and still the currency
will not be burdened by its abundance, and gold will be re-
tained for the reason that it will be demanded for the payment
of those debts that are above the silver limit. Whenever both
are legal tender for any amount, there must be frequent neces-
sity for government to change the legal or nominal value. In
A.D. 1853, silver coins in the United States were made " legal
tmderfor all sums not exceeding Jive dollars" and its nominal

CURRENCY AND MONEY. 155

value was made so great that it is not probable there will be
need of another change for very many years, if ever. The same
is true in England.

PAPER CURRENCY.

ART. 112. Bank notes, certificates of deposit, checks, bills
of exchange, etc., are in business used as money, but are not
money. They are representatives of money when an equiva-
lent amount of gold and silver is lying idle, and the paper takes
its place in the circulation. Otherwise, they are representa-
tives of indebtedness merely, and the man who receives them in
payment of any debt has only given up one claim for another
which may perhaps be more available. Bank notes, actually
representing gold or silver in store, may be used with profit,
for the reason that the coin lying in the vault is saved from
wear, and the inconvenience and risk attending the transfer of
large sums are to a great extent avoided. This is the case with
the certificates of deposit that are used by the associated banks
in New York in settling their balances at the " clearing house/7
It has been strongly advocated by some that a " gold-note
currency" on such a basis might with many advantages be
issued from the Sub-Treasury of the United States. Bullion
banks might also be formed that would furnish the same kind
of currency.

When gold or silver is received, it is an ultimate payment,
for they are supposed to contain intrinsically an equivalent
value. The policy of a paper currency, beyond an actual specie
basis, is a question upon which intelligent political economists
disagree. The use of certificates of deposit, checks, bills of
exchange, etc., greatly facilitates the transaction of business
and reduces the amount of metallic currency needed. To make
them serviceable and reliable, however, they should not be
issued as a basis of credit, or for procuring loans, but should
arise from legitimate business transactions in which the drawee

156 CURRENCY AND MONEY.

has previously become actually indebted for the amount of the
bill.

Examples relating to Coins and. M!oney of.A_cco\int.

1. If a pound of sugar be worth a half a peck of wheat,
what would be the price in wheat of 50 Ibs. of sugar ?

Ans. 6 1 bushels.

2. If a pound of sugar be worth 8 pounds of wheat or 10
yards of tape, how much tape can be bought for a pint of
wheat, a bushel of wheat weighing 60 Ibs. ? Ans. !£{• yds.

3. If an ounce of silver be worth 6400 ounces of iron, how
many tons of iron can be bought with 3£ pounds of silver ?

, Ans. 8 1 tons.

4. If the value of a bushel of wheat be represented by 1.
what would be the value of 5 bush. 1 pk. 3 qts. ?

Ans. 5H-

5. Before the federal currency was established by Congress
in 1786, and indeed for some time after, the denominations in
the money of account in the United States colonies were
pounds, shillings, and pence, as in England, while most of the
coin in circulation consisted of Spanish silver dollars, their
halves, quarters, and sixteenths. Owing to 'the scarcity of
metallic currency, and the fact that the relative value of the
money of account, compared with the silver dollar, had not been
generally determined or agreed upon, remarkable fluctuations
in the money of account arose, varying in different States, so
that when it became necessary to fix their relative values, it
was found that in the New England States £1 or 20 shillings
=3^ Spanish dollars, while in New York and Ohio £lr=:only
2^ Spanish dollars. How much below the New England
standard was the money of account in Ohio ? Ans. 25$.

6. Assuming the pound sterling of Old England to have
been equal at that time to 4f Spanish dollars, as is stated by
some, how much below that standard had the New England
money of account depreciated ? Ans. 25$.

7. Assuming the Spanish dollar to equal a ollar in federal
currency, how much less in cents would an article cost in New

CURRENCY AND MONEY. 157

York whose price was 7 shillings., than in New England where
the price was 6s. 6d. ? Ans. 20 f cts.

8. Paper currency frequently occasions great fluctuations in
the money of account. Continental money, when first issued,
was very nearly par with silver. In 1778 its depreciation was
as 6 to 1, in 1780 as 30 to 1, in 1781 as 1000 to 1. The money
of account would, however, soon cease to follow such extreme
fluctuations, but would adopt some other standard. Assuming
the paper currency of Chicago to have depreciated the money
of account 2% below that of New York city, how much more in
New York funds would an article be worth in New York than in
Chicago, the price in each place being $1000 ? Ans. §19.608.

9. In 1837 the fineness of the silver dollar United States
coin was changed from f llvl to TO-O-? but its weight, which was
416 grains, was so changed that the amount of pure silver in
the coin remained the same as before. What was the weight
after the change ? Ans. 412^ grs.

10. In 1853 the weight of the silver half-dollar was changed
from 20fi{ grains to 192 grains, the fineness remaining the
same, viz., /„. What is the value in new silver coin of the
dollar coined before 1853 ? Ans. 107f J cts.

11. From 1792 to 1834 the United States eagle weighed
270 grs., and was }| fine. Its weight was then reduced to
258 grs., its fineness remaining the same. In 1837 the fineness
was reduced to T\, the weight remaining the same, since which
there has been no change. What is the present value of an
eagle coined previous to 1834 ? Ans. $10.65 f^f.

12. Augustus Humbert, United States Assayer in Califor-
nia, under a legal provision of 1850, has issued fifty dollar
pieces of gold, purporting on their face to be 887 thousandths
fine and weighing 1310 grains each. Assuming them to be of
full fineness and weight, what is their value in United States
gold coinage ? Ans. $50.05JH-

In the above examples no account is made of the alloy.

13. If I take 20 Ibs. of bullion of standard fineness to the
mint to be coined, and pay a seigniorage of \%, what amount
of money, in gold coin, should I receive ? Ans. $4442.79.

] 58 CURRENCY AND MONEY.

14. In A.D. 671 a pound sterling was equivalent to a
pound Troy of silver. In the 14th century the same amount
of silver was coined into £1 5s., and a pound of gold into £15.
After successive debasements for the profit of kings, a pound
of silver now makes £3 11s. 2d., and a pound of gold makes
£50 9s. 5d. The average price of wheat in the 14th century
was £1 for what now averages £2i. Prices of other staple
commodities and wages have undergone a similar change. The
conclusion is apparent, that though governments may depre-
ciate the money of account, they can not force the sale of com-
mon merchandise at much less than its value. Though they
may change the conditions of legal tender, so that 6 shillings
worth of silver will pay a pound of debt, new contracts will
recognize the change, and ultimately not be affected by it.
Queen Elizabeth, using a pound of silver for coining £3 5s. for
England, put no more than that into £8 for Ireland. What
ought to have been the price of flour in Ireland for what in
England cost £1 ? Ans. £2 9T33 shillings.

15. James the Second manufactured four pennyworth of
silver into £10, with which he paid off his soldiers. What per
cent, of their just dues did they receive ? Ans. | per cent.

16. Suppose an estate to have been left, centuries ago, for
the support of the dean of a cathedral and four choristers, the
income then being £300 per year, out of which he was to pay
each chorister £30. If the debasement of current coin has
raised rents 250/£, and the increased supply of the precious
metals raised it 150/£ more, how do the relative salaries of the
dean and choristers compare with what they were evidently
designed to be by the testator ?

Ans. The dean should receive 6 times what a chorister re-
ceives, but actually receives 46 times as much.

BANKS AND BANKING. 159

BANKS AND BANKING-.

ART. 113. BANKS are of four kinds. Banks of Deposit,
Banks of Discount, Banks of Issue, and Banks of Exchange.
The first two and the last may be established by individuals or
associations, the other only by special authority from the State.

BANKS OF DEPOSIT.

ART. 114, BANKS OF DEPOSIT are for the safe keeping of
money.

A special deposit is made when the identical money is to
be returned to the depositor, the bank being responsible only
for the safe keeping ; the loss, for instance, attending the failure
of the banks whose notes are deposited being sustained by the
depositor. In other cases, the Lank or banker becomes in-
debted to the depositor, the banker being allowed to use the
money as he pleases, but obligating himself to pay the depositor
the whole or any part of the amount due him whenever it is
demanded, if demanded during business hours. The improba-
bility that all the depositors of a bank will call for the entire
balance of their account at the same time, renders it safe for
the banker to use a portion of the funds thus entrusted to him,
in loaning to those who need the money but for a short time,
and may therefore be relied upon for prompt payment. The
interest money thus received is the banker's compensation for
keeping the accounts of his depositors. Sometimes interest is
paid by the banker for the deposit, but, as a general rule, that
this interest may be refunded, there is a strong temptation to
loan too large an amount " on call," or to seek largely paying
investments, with doubtful securities, which is against the in-
terest of both banker and depositor.

When the depositor usually has a large balance with his
banker, there is an implied obligation with the banker to give

160 BANKS AND BANKING.

such a customer or dealer the preference in " bank accommo-
dation/' if he offer's equally good security.

The advantages to a business man in keeping a bank ac-
count are the following :

1st. If he has an honest prudent banker, his surplus funds
are ordinarily safer than if kept by himself.

2d. The settlement of bills with checks drawn upon bankers
is not only more convenient, but there is less liability of error,
and if errors do occur, the vouchers, which should always be
preserved, will aid in detecting them.

3d. He will lose less from counterfeit, broken, and uncur-
rent money, and will be relieved from frequent charges of pay-
ing out the same by throwing the responsibility upon his
banker.

4th. By depositing his Bills Receivable and Drafts, he
avoids much trouble and risk attending their collection. If by
mistake, oversight, or neglect, drawers and endorsers are re-
leased from liability, tho banker, by assuming the collection,
becomes responsible for the consequences.

5th. It aids him in establishing his own credit, and learning
the credit and responsibility of others with whom he wishes to
do business.

The Bank of Hamburg is exclusively a bank of deposit, the
silver in the vault always being equal to the amount of the
deposits. This may be withdrawn at pleasure by the deposit-
ors, but the business is mostly done by checks, which have the
effect merely of transferring the credits from one account to
another. The expenses of the bank are met by a small per-
centage charged the depositors on the amount of business done.
The currency of Hamburg being almost exclusively silver, ex-
changes are greatly facilitated through the means of this insti-
tution.

BANKS AND BANKING. 161

BANKS OF DISCOUNT.

ART. 115. Banks of Discount are closely connected with
Banks of 'Deposit , and, indeed, they generally exist together in
the same institution. Their ohject is the loaning of money, the
discount being the interest taken in advance. The capital may
1) .-long to one individual, or to a company forming a copartner-
ship, or to a corporation organized by authority of the State.
The securities usually taken are endorsed names, stocks, bonds,
and business paper. The primary object of banks of discount be-
ing to grant temporary loans, where the business requires at some
seasons more capital than can be profitably employed through
the year, and to aid in preserving an equilibrium in such regu-
lar business as may be disturbed by irregularity of receipts and
disbursements, it is unwise to depend upon such institutions
for any portion of the permanent capital needed in business.
Continued loans and renewals from a bank of deposit are very
unreliable. For when the bank calls for payment to supply
the withdrawal of deposits it will generally be found to be just
the hardest time to pay.

BANKS OF ISSUE.

ART. 116. Banks of Issue are those institutions that, by
authority of the general government, put in circulation, to be
used as money, their own notes, payable on demand in gold or
silver coin. When payable at some future specified time, they
are called post notes. Were banks of issue to retain in their
vaults sufficient gold or silver to redeem all their circulating
notes at once, there would be no profit to them from the circu-
lation except so far as the notes should be lost or destroyed,
and never presented for redemption, which has been found to
amount, extraordinary losses excepted, to about one tenth of
one per cent, per annum. If, on the other hand, they were
loaned as money, and no actual capital kept idle to redeem

them, the banker would receive the same revenue, until their

11

162 BANKS AND BANKING.

redemption, as lie would from an equivalent amount of capital
furnished him in gold and silver. In short, his credit would at
all times afford him as much working capital as his notes in
circulation amount to.

The value of bank notes as currency depends upon the ease
and certainty with which they may be converted into gold or
silver coin. Hence the importance of rigid restrictions being
imposed by government to insure a prompt and certain re-
demption. Without these the field is open to frauds, limited
only by the intelligence and forbearance of the community.

The paper currency of our country is furnished by twenty-
seven different States, each under somewhat different laws and
regulations. In general, they can be classified under three dif- '
ferent systems, a specie basis, a safety fund, and the "free
banking" principle.

The specie basis requires a part, or all its capital, to be paid
in coin, limits the amount of circulation in proportion to its
capital paid in, and makes the assets of the bank, with per-
haps the individual liability of the stockholders, furnish the
means to redeem the circulating notes.

The "safety fund" system requires each of several banks to
deposit, with a State officer or Board of Control, a certain per-
centage of its capital or circulation, which shall be safely in-
vested as a " bank fund" to redeem the notes of any insolvent
bank that may have contributed its due proportion for this
purpose.

In "free banking" the circulating notes are secured by State
stocks, to at least an equivalent amount at their marketable
value. The stocks are deposited with an officer of State, for
which he issues registered blank notes. These, when signed,
are used as money by the banker, while he receives at the same
time, the interest on the stocks deposited. If the bank fails
to redeem, the stocks are sold, and the proceeds applied to the
redemption.

E X C H A N G<E . 163

BANKS OF EXCHANGE.

ART. 117. Nearly all banks are Banks of Exchange, their
legitimate business being the buying and selling of drafts, by
which remittances and settlements of debt at distant places
are made without the transmission of money. The operation
of this department of banking will be more full explained un-
der the subject of " EXCHANGE." Those bankers who deal
exclusively in buying and selling gold, silver, and bank-notes,
are called " brokers" or " money brokers."

EXCHANG-E.

ART. 118. When a purchase is made a satisfactory equiva-
lent is rendered by the purchaser in various ways. It may be
by labor or services, or he may give other commodities in ex-
change, which last transaction is called barter. He may give
gold and silver, which are also commodities of an equivalent
value, but called money, because they are serviceable mainly
in making other purchases, thereby facilitating several trans-
actions in barter. Frequently, however, no equivalent is ren-
dered ; but an obligation merely on the part of the purchaser
for a fixed amount is recognized by both purchaser and seller.
This constitutes debt on the part of the purchaser, and credit
on the part of the seller, and is expressed in the denominations
of the " money of account." If now the debtor gives a writ-
ten obligation to pay, in the form of a due bill or promissory
note, this evidence of credit with the holder may he transferred
as other property, and another become the creditor. In book-
keepifig, the account with the seller is closed, and " Bills Pay-
able" receives the credit. Instead of giving his own promissory
note, he may use those which he himself has received in the
same way ; as for example, bank notes which were issued ex-
pressly for this kind of circulation. When bank-notes, or
certificates of deposit, are held as evidence of debt against a
bank, the debt is collected by the return of these to the bank

164 EXCHANGE.

If it be an account current, and kept by a pass-book, it is sub-
ject to drafts or checks.

The facility with which business is transacted by means of
drafts or other paper substitutes, for money, has given to the
term Exchange a technical use, and now signifies the method
of making payments at distant places ~by the use of Drafts or
Bills of 'Exchange , without the transmission of money. The
business is usually transacted through bankers, who buy the
credits payable in distant places, and sell to those having pay-
ments to make in those places.

To illustrate, suppose the pork dealers of Cincinnati to send
their pork to New York for sale, and receive therefor gold,
which is returned to them by express. Suppose also the dry-
goods' merchants of New York to send their goods to Cin-
cinnati for sale, and receive therefor gold, which is returned to
them by express. If the pork purchasers in New York had
paid the dry-goods' merchants there, and the dry-goods' pur-
chasers in Cincinnati had paid the pork dealers there, the whole
business might have been closed without the risk and expense
of transmitting gold either way. This would be done by the
pork sellers drawing drafts or orders on the pork buyers, in
favor of the dry-goods' buyers, who, having paid for these drafts,
would forward them to the dry-goods' sellers in payment of
their purchase. These drafts being presented to the pork buy-
ers would be cashed, and thereby the debts arising in both
cities liquidated without the transmission of any money. In
making this system general, to include all kinds of trade in
many different places, it would frequently be very difficult
for those having bills of exchange to sell to find buyers, and
vice versa. An exchange broker, or bank of exchange, will
obviate this difficulty. They bring the buyers and tscllers
together, by buying bills with their own capital, and sending
them forward for credit, then selling their own drafts drawn
against this credit, in amounts to suit purchasers. If between
any two places the amount of bills bought equal those sold,
then no gold need be transmitted, and the difference between
the buying and selling rate would be the commission charged

PAR OF EXCHANGE. 1C.1)

by the broker for his services, use of his capital, and risk in
buying such drafts as would not be honored.

PAH OF EXCHANGE.

ART. 119. To understand the quotations of premium or
discount in exchange, it is necessary to consider the currencies
of the different places. Supposing gold, as a metal, to be so
distributed as to have in all places a uniform intrinsic value,
and gold coin to be the only currency, the true par of ex-
change between two countries is the exact equivalent of gold in
the standard coin of one country compared icith the gold in
the coin of the other. If, however, gold is the standard of cur-
rency in one country, and silver in the other, the relative in-
trinsic values must be compared. This need be computed only
when the coins and money of account in the two countries are
different. Comparing the sovereign of England with the half
eagle of America, for instance, we find the sovereign to weigh
123.3 grains, but only 916^ thousandths of it pure gold. The
half eagle weighs 129 grains and 900 thousandths pure gold.
If we reduce the fineness of the sovereign to that of the half
eagle, without changing its value, it must weigh 125 rWV
grains. In this estimate the alloy is reckoned of no value.
To ascertain the true equivalent we have this simple propor-
tion, 129 grains : 125.583 grains : : §5 : §4.SG7j.

As the weight and fineness of the sovereigns coined previously
to the present reign were somewhat less than the value, as de-
rived above, the average value, as fixed by our mint, is $4.84
A new Victoria sovereign, however, is worth §4.86 f. A pound
sterling (£) is a denomination in the money of account only ;
the sovereign is a coin of an equivalent value. It follows from
the above that exchange on London is par when a bill for
£100 can be bought for §486.75 in American gold.

The common quotations are based upon a purely nominal
value of the pound sterling, viz. : $4.44£, for that is not now
its value in any other sense.

166 STERLING EXCHANGE.

True value of the pound sterling, . . . $4.8675
Nominal " " ... 4.4444 +

Difference=9i^ (nearly) of the nominal par, . .4230
When the quotations are 109^, sterling exchange is really
at par ; when 110/£, it is at a premium ; when 109^, it is at a
discount. Quotations are generally made on sterling bills
drawn at 60 days' sight. As the cost of transmitting gold, in-
cluding insurance, is about equal to the interest on the bill for
60 days, the time for the passage of both being the same, re-
mittances often are made in these time drafts, for which the
same is paid as for sovereigns of equivalent amount.

RULE FOB COMPUTING- STERLING-
EXCHANGE.

ART. 120. To $40 add the premium on $40, at the quoted
rate. By this sum multiply the amount of sterling exchange
expressed in pounds, and divide the product by 9. The quo-
tient will be the value in dollars.

E x a m. pie.

What will a bill for £224 5s. 6d. cost in New York when
sterling exchange is par, quoted at 109^ or §\% premium ?

£224 5s. 6d. 40

43.8 9i#= 3.80

~179T~ 43.80

672
896

10.95
1.095

9)9823.245
$1091.47 Aw.

By comparing French coin with that of the United States,
we find 20 francs Louis Napoleon equal to $3.84, or one dollar
in gold equal to 5 francs and 21 centimes nearly, or 5r\V
francs. The quotations of Paris exchange are usually made
in this way, without involving percentage. If a bill of ex-

NOMINAL ^EXCHANGE. 167

change for more than 521 francs can be bought for $100, Paris
exchange is at a discount ; if less, it is at a premium, and the
quotations express the. number of francs that can be thus
bought.

The sum mentioned in a bill of exchange on a foreign
country is usually expressed in the denominations of the money
of account in the place where it is made payable. Computa-
tions in foreign exchange therefore require the use of tables of
foreign money, including the comparative values of the coins
or currencies in those countries.

NOMINAL EXCHANGE.

ART. 121. In the United States, though the money of ac-
count be nominally the same, yet owing to the character of
the paper money in circulation, the currencies,. and hence the
moneys of account of different states and cities, are essentially
different. The relative value of paper money, as stated here-
tofore, depends upon the risk and cost of converting it into
coin.

If, for example, in Buffalo, it costs \% to convert the usual
paper currency into coin, the true, par of exchange between
that city and New York (where coin only, or its equivalent, is
current) would be expressed by the nominal rate of \% pre-
mium, in favor of New York. For the same reason the cur-
rency of Chicago being redeemable in coin at still greater cost,
exchange on New York may actually be at par when the nomi-
nal rate is 2^ premium. This 2^ no more expresses the actual
premium than does the 9^ the actual premium of exchange
on London. It is really the premium of New York currency
over Chicago currency. The true value of the denominations
in our money of account is represented by coin only, being
established by the law regulating legal tender. Practically,
however, by the use of a depreciated local currency, the money
of account for that place is equally depreciated. Thus, goods
bought in New York for §100, when sold in Chicago for $100

168 NOMINAL EXCHANGE.

are sold for less than their cost, counting transportation and
insurance nothing. Prices, however, will tend to appreciate
as tha value of the currency depreciates, so that the apparent
loss by an unfavorable nominal exchange is, in general, compen-
sated by increased prices. Inasmuch as increasing the supply
of even a metallic currency depreciates its relative value, the
nominal exchange between two places, using the same kind of
currency, with the same mint standard, will be in favor of the
place having the smallest amount of currency in proportion to
its business wants, and therefore having the least depreciation.
The nominal exchange is then measured by the excess of the
market price of bullion above the mint price, and is, so far,
unfavorable. A depreciation of metallic currency which affects
the nominal exchange may also be occasioned by abrasion or
wear of circulation, or by making only one of two metals legal
tender where the other is in general circulation. It will be
observed that, although this " exchange," which is merely nom-
inal, almost universally enters into the quotations of exchange
between different countries, it belongs rather to the exchange
of currencies in the same country, and expresses the difference
between the current and the standard moneys of that place.

Agio, meaning " difference/' is the proper term to express
this nominal exchange when considered alone. In the United
States the expense of sending coin to and from New York, by
the modern express companies, being so trifling, the premium
on New York exchange must always bo very nearly the same
as on coin. The fluctuations in the nominal rate of exchange,
or agio, where a depreciated paper currency is used, will be
much greater than if the currency were coin or its equivalent,
for the reason that the depreciation will be more variable.
Sometimes the scarcity of such currency, compared with busi-
ness wants, raises its current value temporarily to nearly par
with coin. Just so far the nominal exchange disappears. In
Bank notes that can be converted into coin at less expense
than the usual local currency are, for that place, at a pre-
mium. Those costing more are at a discount, and are called
uncurrent. Indeed, these notes, when removed from their

COURSE OF EXCHANGE. 169

native habitation, resemble bills of exchange on the places
where they are redeemed, and are bought and sold at nearly

the same rates as exchange.

COURSE OF EXCHANGE.

ART. 122. Having ascertained the par of exchange we have
a basis for computation. The nominal exchange modifies that
computation, by showing the relative value of the metallic
currency affected by scarcity and abundance or abrasion, and
also the depreciation arising from the use of a paper currency
not equivalent to coin, though bearing the same denomination
in the money of account.

The course of exchange relates to the relative supply and
demand for bills, or the relative amount of indebtedness be-
tween different countries or cities. If the debts and credits
between two countries are equal, the real exchange is at par,
if unequal it will fluctuate with the inequality. If New York
owes London more than London owes New York, bills on Lon-
don will bo at a premium. The range of this course of ex-
change will be limited by the expense of transmitting coin or
bullion, and the premium, cannot for a long time exceed that
expense. The current, or computed rate of exchange, includes
both the real and nominal exchange, taking the true par for a
basis. "Within the United States it is reckoned by percentage.
Between the United States and England it is reckoned also by
percentage, but the true par is at a premium above an assumed
fictitious par. So that an advance in quotation from 109 to
110 is not really 1$, that is, one on a hundred, but less, it
being only 1 on 109^.

With other countries the current exchange is generally ex-
pressed by equivalents, thus $1=5 francs 15 centimes, 1 marc
banco =35^ cts. If the depreciation of Chicago currency be
V/c, and the real exchange on New York \% premium, the
current rate will be the sum of the nominal and real, viz. :

170 BALANCE OF TRADE.

\\% premium. If? however, the real exchange be \% in favor
of Chicago, the current rate will be equal to the difference, or
\% premium.

The equilibrium in the course of exchange is only to a small
extent restored by the shipment of coin or bullion, for the rea-
son that almost always other articles of merchandise can be
shipped with more profit, gold and silver bearing a nearly uni-
form value among all civilized nations. When, however, new
productive mines are opened and worked, the metals depreciate
in value in the mining country, in which case they become
profitable articles of export to non-producing countries, until
the depreciation becomes general. The unequal depreciation
occasions a variation in the nominal exchange before the coin
or bullion is shipped. The transfer of the metal would affect
the real exchange, because it either pays or creates a debt.

"BALANCE OF TBADE."

ART. 123. If a country, in her trade with other nations,
buys more than she sells, so as to incur a debt, the payments
of which, in bullion Or coin, would reduce the amount of
metallic currency below her proper proportion, as compared
with the supply in other nations, she is said to " over- trade,"
and the " balance of trade" is against her. If the reverse be
true, the balance of trade is in her favor. Some restrict the
term " balance of trade" to the exchange of commodities other
than gold or silver. But why should not gold be considered a
staple article of export from California and Australia, as iron
is from Sweden or lumber from Maine ? It is not proposed
here to discuss this subject in its bearing upon the prosperity
of a country, but merely to offer a few suggestions to Iho
student, in its relation to the subject of exchange. It is raihei
the balance of payments between separate countries, and the
mode of estimating the amount, the direction, and means of
liquidating it, that ho should consider here. 1st. Although

BALANCE OF TRADE. 171

the direct commerce between two separate nations may be very
unequal, yet the total amount of importations to any country
are for the most part paid for by its exportations, through the
agency of bills of exchange, drawn against the latter, and
transmitted to other countries in payment of the former.
Sometimes it is effected by a succession of bills drawn by
bankers through intermediate points, or a more circuitous
route, which gives rise to Circular Exchange and an Arbitra-
tion of Exchange. For example, a merchant in New York
may remit to Hamburg by buying first a bill on Paris, and
then by his agent another on London, and there a bill on Ham-
burg. Kemittances to remote points are more frequently made
by bankers' bills drawn on some commercial center, where
other bankers are accustomed to keep an account, so that they
may be easily negotiated, making the place thereby a kind of
clearing-house. Thus, London has been styled " the clearing-
house of the world." Nearly all our foreign trade is settled
through England and France. In like manner, remittances
between inland towns in the United States are made in drafts
on New York. The course of exchange between London and
New York does not arise alone from the commerce between
the two cities, but from all that commerce that is settled for
through those places. Thus, if we pay for our importations
of tea with bills on London, our balance of payments with
London is affected the same as if the tea came directly from
London.

2d. So far as the commerce of any country is carried on by
its own capital and labor, a large share of the excess of imports
over the exports arises from the profit of the trade, which does
not increase the balance of payments. If, for example, an
American vessel leaves New York for Liverpool, with a cargo
of wheat, valued at §10,000, which is sold there for §12;000,
and that amount invested in manufactured goods, and taken
to China and sold for §15,000, and that amount, with §5,000
cash invested in tea, which is brought home to New York, it
is evident that, from that transaction, the importations exceed
the exportations $10,000, one half of which represents the

172 BALANCE OF TRADE.

gross profit for the round trip, not including the enhanced value
of the tea by being transported from China to New York.

3d. So far as foreign vessels, sustained by foreign capital
and labor, transport our exports and imports, the difference
between the two, as valued at our own ports, will show the
balance of payments.

4th. Goods lost at sea have been entered at the Custom
House whence they cleared as exports. But if the loss is sus-
tained by the exporting country, they pay for nothing abroad,
and foreign exchange is affected no more than if destroyed
before shipment. If the loss be sustained by the country
whither they were bound, exchange is affected the same as if
they had reached their destination.

5th. When capitalists emigrate from one country to another,
so far as they carry their capital, either in coin or goods, with
them, the real exchange is not materially affected ; but if they
remove their capital through the agency of certificates of de-
posit, letters of credit, or their own bills of exchange, it becomes
a debt of one country to the other, which, in the end, is gener-
ally paid in merchandise rather then money. This fact often
affects sensibly the course of exchange between the east and
west of the United States.

6th. The negotiation of bonds, stocks, and other loans in
a foreign country creates a debt against that country, which,
though nominally for money, is generally paid in merchandise.
After this debt is paid, though the bonds are truly the evi-
dence of debt against the country that issued them, yet, with
the exception of the payment of the interest, the balance of
payments and course of exchange are not affected ti]l the ma-
turity of the bonds.

7th. An excess of imports over exports, as shown by the
Custom House returns, by no means prove that a country is
in debt. Indeed, it is clear from what has been stated, that
with every nation engaged in the carrying trade the imports
will generally exceed the exports, and, so far as the latter pay
for the former, the greater the excess the more profitable the
commerce.

STATISTICS. 173

The fluctuations in the rate of exchange depend upon a
variety of conditions, a few only of which have here been
noticed. They cannot, to any great extent, be controlled by
an arbitrary decree of bankers or merchants. Excepting when
disturbed by a panic, or an unusual distrust in the credit of
those who draw or accept bills of exchange, which gives it a
fictitious value, the current rate represents the actual resultant
of all the movements in trade and currency, whether traceable
or not, and is, therefore, if properly analyzed, a better test of
the condition of accounts between different countries and cities
than any estimate that can be made, independent of it, based
upon exports and imports and other Custom House data.

To understand the current rate, however, requires, as stated
before, a thorough knowledge both of the par of exchange and
the nominal rate, for frequently the fluctuations in the cur-
rent rate are wholly due to the fluctuations in the nominal
rate, which latter depends entirely upon the relative condition
of the currency.

STATISTICS.

ART. 124. To exhibit the truth of the foregoing principles,
a few statistics have been compiled from reliable authorities.

Total imports to the United States, includ-
ing bullion and specie, from 1790 to
1857, inclusive, .... $7,658,722,496

Total exports for the same time, . . 6,860,004,549
Excess of imports for 68 yrs. ending 1857, "798/717,947
7 " 36,363,971

30 " 1850, 250,438,055

31 " 1820, 511,915,921
The valuation of imports, as obtained from Custom House

returns, owing to the ad valorem system of tariff, is, below
their cost, generally estimated to average even 10^. It will be
observed that allowing an undervalution of \% will increase
the excess of imports about

174

STATISTICS.

Excess of imports of bullion and specie for

30 years ending .1850, before the supply of

gold from California, . . . * . $69.995.789

Excess of exports of bullion and specie for 7

years ending 1857, . . . . . 269.797.1G8

From 1790 to 1820 the imports, including bullion and
specie, exceeded the exports each year except in 1811 and 1813.
From 1821 to 1857 the imports exceeded the exports each year
except in 1821-5-7, 1830, 1840-2-3-4-7, 1851-5-6-7.

Total amount of public and corporation debt held
in foreign countries against the United States
in the form of bonds, stocks, &c., is. generally

estimated at,

$300,000,000

On which there is probably paid an annual divi-
dend of about, 20,000,000

The average current rate of exchange on England at New
York, for No. I bankers' bills, as quoted on the first of each
month was, for —

1822 . .

12 1831

8f

1840 . .

8

1849 .. 9

1823 . .

7^

1832

9

1841 . .

?*

1850 .. 9

1824 ..

9~

1833

8

1842 . .

7?

1851 .. 10

1825 ..

81

1834

.. 31

1843 . .

<i

1852 .. 10

1826 . .

10

1835

Of

1844 . .

9

1853 . . 9

1827 . .

103

1836

8

1845 . .

91

1854 . . 9

1828 ..

101

1837

.. 13*

1846 . .

8J

1855 . . 9

1829 . .

9

1838

* * 4

1847 ..

h?
4

1856 .. 9

1830 . .

n

1839

.. 91

1848 . .

9j

1857 (to Sept.) 9

Average for the 9 years ending 1830,
" 10 " 1840,

" 10 " 1850,

" 7 " 1857,

It will be perceived that the average rate of sterling ex-
change at New York, for the twenty years ending 1850, was
\% below par, or \% in favor of New York ; while, for the
seven years following, it was above par, or in favor of England.

Of the $300,000,000 of gold deposited at the Mint and
branches, and Assay Office at New York, for the six years ending
1855, about 94^ per cent, was produced by California.

In San Francisco sight exchange on New York averages

EXAMPLES IN EXCHANGE. 175

about 3^ premium, the currencies of both places having a
metallic basis.

If we put 900 new sovereigns and 900 new shillings into
average ordinary circulation, in 12 months time the former
will be worth about 899 and the latter about 894.

In London, previous to the re-coinage in 1774, exchange
was uniformly about 2$ in favor of Paris, owing to the fact
that the old coinage, by wear, had sunk below its standard
weight about 2$, while the coinage of France was not thus de-
graded. As soon as the new coinage took the place of the old,
exchange became par. Before the re-coinage, in the reign of
William III, owing to the wear and clipping of the silver
coins, the nominal exchange between England and Holland
was 25/b against England, while at the same time the real ex-
change was in her favor, as was shown upon the issue of the
new coins.

EXAMPLES RELATING TO EXCHANGE.

ART. 125. 1. What is the cost of a draft on New York
for $1250, the rate of exchange being \\% premium ?

Ans. $1268.75.

2. What must be the face of a draft to cost $1000, at f
per cent, premium ? Ans. $993.79.

Remark. — For a strictly accurate solution assume, say $1,
for the face, and find its cost, then by it divide the given cost.
Custom, however, allows, for small sums, the percentage to be
computed on the cost instead of the face. By that rule the
answer to the last question would be $993.75. The ap-
proximation may be brought nearer by adding the premium
on the premium, which, in this case, is \% of $6.25= §0.04
nearly.

3. What would be the proceeds of $4000 invested in ex-
change on New Orleans, at a premium of \% ?

\% of $4000=^20, and \% of $20= $0.10.
$4000- $20 + $0.10= $3980. 10, Ans.

176 EXAMPLES IN EXCHANGE.

If the rate had been \% discount we should havo had
$4000 + $20 + $0.10= $4020~. 10.

4. What must be paid in New York for a draft on London
for £1374 5s. 9d., at 10% premium ? Ans. $6718.74.

5. What amount of sterling exchange can be bought for
$3122.25 the premium being 9f^ ? Ans. £640 Is. lUd

Find by the rule the cost of £1, by which divide the given
cost.

6. What will a draft on Paris for 12144.5 frcs. cost if
$1=5.35 frcs. ? Ans. $2270.

7. What will be the cost, at Milwaukie, of a bill on Lon-
don for £1500, the quotation at New York being 110, the agio
of Milwaukie current funds being 2% discount compared with
those of New York, and the real exchange, or course of ex-
change, being \% in favor of New York ? Ans. $7498.33.

8. New York quotations of Paris exchange being 5.18 frcs.,
and the agio of Cincinnati current funds being 1% discount
compared with United States coin, what will a bill of 1000
frcs. cost at Cincinnati, if the purchaser buys coin and sends
by express, at a charge of $1.50 per thousand dollars, and
buys the exchange in New York through a broker whose
charges are \% for commission ? Ans. $195.75.

9. The money of account in Hamburg is of two kinds, each
reckoned in marcs or marks, viz : marks banco and marks
current. The former is the account kept at the bank where
specie or bullion is deposited, and is generally the standard of
reference in quotations of exchange. The latter is current in
business, and is much depreciated, the agio of the two accounts
being subject to slight variations. The par of exchange be-
tween Hamburg and London is 1 mark banco=ls. 5{d. As-
suming £l=:$4.S6f , what is the par of exchange between Ham-
burg and New York ? Ans. 1 mark banco=35i cts. nearly.

10. Assuming the quotations of 109^ on London and 35 J
on Hamburg to represent the par of exchange, as they do very
nearly, how much per cent, higher is Hamburg exchange
sterling exchange, when the quotations are 110 and 36.

Ans. .9518$.

EXAMPLES IN EXCHANGE. 177

11. Assuming the mark current at Is. 2d. sterling, what is
the agio between the two moneys of account at Hamburg ?

Ans. The mark banco would be 25/^ premium.
It usually varies from 20 to 26^ premium.

12. What would be the cost, at Chicago, of a bill on Ham-
burg for 10,000 marks banco, the banker in Chicago drawing
direct, at New York quotations (37 cts. per mark), adding the
current rate of exchange on New York (\\% premium), and
\% commission ? Ans. $3792.50.

13. If the agio between New England paper currency and
coin be \%, and between Illinois currency and coin 2$, what
would it be if both circulated in equal proportions ?

Ans. \{%.

14. If the currency in circulation in Cincinnati have an
agio of \% compared with United States coin, what would be
the ultimate effect of making Illinois currency " bankable" if
its agio is 2$.

Ans. It would drive from circulation every thing but Illi-
nois currency or its equivalent, and depreciate the money of
account \\%.

15. A banker in New York sends 1000 eagles to London,
at a cost for freight and insurance of |^, which is paid in New
York, and receives credit at the rate of £3 16s. 2d. per oz.,
and 3/o per annum interest on the account. At the same time
he sells a 60 days' sight bill drawn against the proceeds of the
coin and the accrued interest, at the rate of 110^. Suppose
the bill to be accepted on the day of the credit, and payable
without grace, what profit does the banker receive in the trans-
action. Ans. $28.20.

16. At one time the laws of Spain rigidly restrained the ex-
portation of the precious metals from that country, still they
were secretly exported at a risk of about 2$. What, then,
was the nominal exchange between that and other countries
having a free-trade in bullion, arising from the depreciation
occasioned by relative excess ? Ans. About 2$ against Spain.

17. If from the large increase of California gold, or exces-
sive paper issues in the United States, the nominal exchange

178 EXAMPLES IN EXCHANGE.

between England and the United States should be 2$ in favor
of England, what should be the quotations of sterling ex-
change, other things being equal, to represent the balance of
payments in equilibrium ? Ans. \\\\%.

18. If the nominal exchange, at London, on Hamburg, be
16 \% discount, what would a London merchant make for his
net profit, the cost of transportion, insurance, &c., being 5^ on
the purchase price, and payable at London, if he sells in Ham-
burg for £12,000 what cost in London £10,000 ?

Ans. He would lose £500.

19. If the currencies of England and the United States
were in due proportion in amount compared with business
wants, what would be the effect upon the " movement" of
the precious metal between the two countries, if the United
States should add to its currency a large issue of paper money
or gold coinage, thereby raising prices and depreciating the
relative value of money ?

20. Why is any country better able to sustain an increase
of importations compared with the exportations, when it arises
from an excess of specie currency, than when it arises from an
excess of paper currency ?

Ans. Because nothing but metal will pay the balance, and
in the one case we can afford to part with it, while in the other
we cannot.

21. Suppose the circulating medium in San Francisco to be
depreciated below the currency of New York Y/o in consequence
of imperfect coinage, and the expense of transportation, includ-
ing risk, be \% more, and the broker's commission in New
York be \%, what does an exchange broker or gold exporter
in San Francisco make, if he sells sight drafts on New York
for 3% premium, and to make his exchange he is obliged to
ship gold ? Ans. \l%.

22. If a wheat merchant in Toledo buys wheat at $1.00
per bushel, and sends it to Buffalo for sale at $1.02^ per
bushel, the cost for transportation, insurance, and commission
being ~\.\%, what per cent, profit does he make, if, in view of the
difference in value, or agio, of the currencies of the two places,

EXAMPLES IN EXCHANGE. 179

he is able to negotiate at \% premium the drafts drawn against
the proceeds of the sale ? Ans. 1^.

Remark. — In the last example the rates were made to cor-
respond with those of the 21st, to show more clearly to the
pupil that in general the same laws govern the movement cf
gold in large quantities as regulate the movements of wheat.

23. During the year ending June 30, 1857, our exports, in-
cluding specie, to England, exceeded our imports from England
§54,216,623 ; but in our trade with Cuba, Brazil, China,
and France, our imports exceeded our exports, as follows :
Cuba, §30,319,658 ; Brazil, $15,915,526 ; China, $3,961,802 ;
France, $9,553,840. During the same time our total excess
of exports of specie was $56,675.123, of which $46,821,211
went to England, and we will suppose, for this example and
the one following, that the balance of excess went, in equal
amounts, to the other four countries. Why did the specie go
to England, when we were not in debt to her, and how was
our debt to the other countries probably settled ?

24. First, Suppose the last example to represent our entire
foreign commerce and trade for that year, after a full settle-
ment, and to include nothing else, and our due proportion of
specie for currency to have been preserved by supply from
California, and the Custom House value to be the exact ex-
changeable values of both importations and exportations, what
was the balance of net profit as shown by the excess of im-
ports ? Ans. $5,534,203.

Second, What per cent, would that profit be on the entire
exports to those countries which, for that year, specie included,
were about $240 millions ? Ans. About 2 j£.

Third, If the exports, as entered at the Custom House,
not including specie, were $170,000,000, and the imports, as
received, were entered $231,000,000, what was the balance of
payments in specie, if the exports, being carried by American
vessels, brought in the foreign market 10^ advance on their
Custom House valuation, and the imports were entered 5% be-
low their cost ? Ans. $56,157,895.
Actual balance of payments, $56,675,123.

180 BILLS OF EXCHANGE.

Fourth, If our due proportion of currency required no in-
crease of specie for the year 1857, and California, with other
American mines, furnished for the market §49,000,000, how
was our balance of trade for that year ?

Ans. $7,675,123, against us.

Fifth, Suppose we had redeemed, during that year, of our
foreign indebtedness in stocks and bonds, §10,000,000, what
would then have been our balance of trade ?

Ans. §2,324,877 in our favor.

BILLS OF EXCHANGE.

ART. 126. A bill of exchange is an order or draft, made
by one person upon a second, to pay a certain sum of money
to a third, or to his order, or to the bearer. For example :

CLEVELAND, 0., Nov. 6, 1858.

Sixty days after date, pay to the order of J. F. Whitelaw
one thousand dollars, and place to the account of

To Messrs. SMITH & BROWN, ALBERT CLARK.

New York.

The person making the order is called the drawer ; the
person to whom the order is addressed is called the drawee ;
and the one to whom the amount is payable is called the payee.
If the drawee accepts, by writing his name across the face of
the bill, under the word " accepted," he then becomes an
acceptor, and the instrument is then called an acceptance. Jf
the payee writes his name upon the back of the instrument,
he becomes an indorser. The person to whom it is afterward
transferred by indorsement is called an indorsee.

Foreign bills are' those which are drawn in one country but
are payable in another.

Domestic or inland bills are those that are payable in the
country where they are drawn.

The United States being separate sovereignties, are foreign
to each other, and bills drawn in one payable in another, like

PROMISSORY NOTES. 181

the example given above, are foreign bills, though apparently
inland.

Time bills are those requiring payment at a certain speci-
fied time after sight or after date. All others are payable on
demand. When time bills are drawn "acceptance waived,"
they may be held till maturity before being presented to the
drawee ; otherwise, they should be presented immediately for
acceptance.

PROMISSORY NOTES..

ART. 127. A promissory note is a written agreement by
one party to pay to another a specified sum at a specified time.
The one making the agreement or signing the note is called the
maker. The person to whom the amount is payable is called
the payee, and the owner of the note is called the holder. A
principal is one directly responsible for the payment of a bill
or note a£ maturity.

For different forms of notes, see examples under the sub-
ject of Interest.

Adjoint and several note is one signed by two or more dis-
tinct parties, in which case each one becomes liable as maker
or principal, the same as if no others signed with him. Some
of the features of a valid promissory note are the following :

A full consideration is implied from the nature of the in-
strument, but a want of consideration would be a valid defense
on the part of the maker as against the payee, but not as
against any other holder, into whose possession it may have
come without a knowledge of such want of consideration, in
which case he would be called an innocent holder.

It may be written with ink or pencil, or it may all be
printed except the signature, which must always be in the
hand-writing of the maker or his authorized agent. It should
be an unqualified promise to pay in money, definite in amount,
and independent of all contingencies. The amount should be
expressed in the body of the note, in words, and 'should be re-
lied on for accuracy rather than figures in the margin.

182 NEGOTIABLE PAPER.

If the time is not definitely stated, it is payable on demand.
If the place of payment is not specified it is payable at the
place of business or residence of the maker.

In the settlement of bills of exchange and promissory notes,
so far as their terms are subject to general law, as fixing the
rate of legal interest and day of maturity for example, the law
of the State where they are made payable should govern. If
a note is not paid at maturity, it continues to draw the same
interest as before, if it does not exceed the legalized rate ; but
if no rate be mentioned, it draws simple interest at the legal
rate till paid.

NEGOTIABLE PAPER.

ART. 128. Bank notes, checks, certificates of deposit, bills
of exchange, and promissory notes, when properly drawn, are
negotiable, except when made payable by the terms of the
contract, to one person only. If the amount is payable to
"bearer," or is subject to the "order" of the payee, they are
negotiable. But if neither the word " bearer" nor " order" ap-
pears in the instrument, but simply the name of the payee, it
is not negotiable, and the payee cannot give full title to a third
party ; for the account, as between the maker and payee, would
still be subject to a garnishee process from other creditors of
the payee.

In the negotiation of paper the transfer may be made by
delivery or ~by indorsement. If payable to " bearer," or to the
payee " or bearer," as are bank notes and most checks, the
transfer is by delivery. If payable " to the order of" the
payee, or to the payee " or order," the transfer is by indorse-
ment.

If the payee simply writes his name across the back of the
paper it is an indorsement in blank, and is afterward negoti-
able by delivery. But if above this indorsement it be made
payable to the order of another person, called an indorsee, it is
an indorsement in full, and is then negotiable only by the in-

NEGOTIABLE PAPER. 183

dorsement of the indorsee. By repeating this kind of indorse-
ment there may be several indorsees. When the indorsement
is in blank, any legal holder is allowed to write that above it,
which will make it an indorsement in full. A qualified in-
dorsement is one that affects the liability of the indorser, but
not the negotiability of the paper, as when made "without re-
course."

LIABILITY OF PARTIES CONNECTED
WITH NEGOTIABLE PAPER.

ART. 129, Bank notes designed to circulate as money,
checks, and other paper negotiable by delivery, may be legally
retained by an innocent holder, who receives them in good faith
for a valuable consideration, though the party from whom they
were received obtained them fraudulently.

Bank notes are a good tender if not objected to at the time
of payment, unless it should appear afterward that they were,
at the time of payment, worthless, or of less value than repre-
sented, as when counterfeit, altered, spurious, broken, or un-
current. Any unreasonable delay to return them, after the
discovery is made, whereby the payer loses the opportunity
or means of indemnity, would throw the loss upon the payee
or holder, on account of the neglect.

If a person receives a check on a bank, it is his duty to
present it for payment at the bank during the same or the
next day at the furthest; otherwise he holds it at his own risk,
tha loss being his if the bank fails meantime, provided that the
funds were there to meet the check before the failure. If he
lives at a distance from the bank he must send it for collection
by mail, or otherwise, during the same or next day. If the
check passes through the hands of several persons, each one is
allowed one day, and his liability, so far as above described,
ceases with the succeeding day. Bank drafts, or " bankers'
exchange," from their service in making remittances to distant
points, may be used to fulfill that mission, but should not be

184 NEGOTIABLE PAPER.

allowed to lie still or circulate as money beyond the reasonable
expectation of the drawer.

When the holder of a check gets it certified as good by a
bank on which it is drawn, the drawer is released though the
bank fail to pay.

As between the maker and payee of a note the maker is
allowed any defense that would be allowed in any other debt
between the two. But as between the maker and indorsee, or
other holder, no defense can be set up, except it be shown that
the holder had knowledge, at the time of the note's coming into
his possession, of a just ground of defense between the maker
and payee. If, however, the note came into the possession of
the holder, after it became due, the claim of the holder would
be subject to all the equities in favor of the maker that existed
at maturity, or that had arisen after maturity.

On a promissory note the maker is principal, and is directly
responsible to any bona fide holder. The indorsers are re-
sponsible in the order of their indorsements, that is, each one
to all those who follow, on condition of their being duly noti-
fied of non-payment, as explained hereafter. The liability of
those who indorse as guarantors is not so easily discharged
by a failure to give prompt notice of non-payment.

A bill of exchange involves no direct liability until pre-
sented for acceptance. If acceptance be refused by the drawee,
the drawer immediately becomes principal, and is bound to re-
deem the draft from the holder without delay, though it be a
time draft, and the time not yet expired. If the bill be ac-
cepted, the acceptor becomes principal, the same as the maker
of a promissory note, in which case the drawer sustains practi-
cally the position of first indorser, in case of non-payment on
the part of the acceptor. The liability of indorsers on bills is
the same as of those on promissory notes. That liability, how-
ever, may be avoided in both cases by their writing over their
indorsements " without recourse," or other words of equivalent
signification, except so far as to wan-ant that the bill or note
is genuine, that is, not forged or fictitious, a liability which
attaches not only to all indorsers, but to all who negotiate

PROTEST. 185

the paper by delivery, as owners, or even as agents, unless thac
agency, with the name of the principal, be distinctly stated at
the time of the transfer.

Indorsers are also released from liability, if they are not
duly notified of non-acceptance or non-payment, the paper
having been duly presented.

If a man lends his name and credit by making a note or ac-
cepting a bill of exchange for the accommodation of another
party, it is called an accommodation paper. He thereby be-
comes liable to any bona fide holder, to the same extent as if
he had received a full consideration, except to the person for
whose accommodation the credit was given. But for his in-
demnity for payment he has a valid claim on the party ac-
commodated.

PRESENTMENT, PROTEST, AND NOTICE.

ART. 130. The limits of this work will not allow the de-
tail of all the particulars necessary to be observed by the holder
of a bill or note, in making a proper demand for payment, and,
in case of non-payment, in properly notifying the indorsers, so
that they may not be released from liability. The importance
of the subject demands the careful study of those who deal in
negotiable paper, or who undertake the collection of it for
others. Business men, unless thoroughly posted, had better
intrust their collections with some responsible banker. A few
brief rules only will be given.

There should be no unnecessary delay in presenting for
payment any paper payable on presentation, and for accept-
ance all time drafts (unless drawn "acceptance waived"),
especially if the time of maturity is to be determined by the
time of sight or presentment.

When the time is definitely fixed by the date of the in-
strument or of the acceptance, it must be presented for pay-
ment on the exact day of maturity, as regulated by the law of

186 DAYS OF GRACE.

the State where it is made payable. A protest on any other
day would be of no avail.

The paper itself must be presented by the holder personally
to the acceptor Xor maker, or their authorized agent, at the
place where it is made payable, during reasonable business
hours. If no such person or agent is found with funds to meet
it, the paper may be treated as dishonored. In case of non-
acceptance or non-payment the paper should be protested, and
the drawer and indorsers notified.

" A protest is a solemn declaration on behalf of the holder,
drawn up by an official person, against any loss to be sustained
by the non-acceptance or non-payment of a bill." This pro-
test should be made by a notary public, who should also per-
sonally make due presentment or demand, and should on the
same day, or, at furthest, the next day, send written notices
of protest to the parties to be notified. If the residence of all
the indorsers be not known, and all the notices be sent under
one cover to the last indorser, he is allowed only one day to
forward the notices to antecedent indorsers. So also for each
of the others. Sundays and legally recognized holidays are
excepted. Notices to parties residing in the same town must
be delivered in person or by a messenger. Notices to all others
must be sent by mail. If an indorser writes over his name
" waiving demand and notice/' a protest is not necessary to
retain his liability.

DAYS OF GRACE AND TIME OF MATURITY.

ART. 131. It may be observed here that each of the United
States makes its own laws in regard to negotiable paper, and
probably the laws of no two States agree in all respects. The
laws of that State are applied in which the paper is made
payable, though it be drawn in another. For a valuable
comperid upon this whole subject the student is referred to a
" Manual for Notaries Public," published by J. Smith Homans,
New York.

DAYS OF GRACE. 187

As a general law in the United States the day of maturity
for all negotiable time-paper does not come till three days
after the expiration of the time mentioned in the instrument,
except when the time is limited by the expression " without
grace/' These days are called days of grace, but they give
the maker no special advantage, for interest is allowed on those
days the same as others, and no presentment need be made till
the last day of grace.

If the last day of grace falls on Sunday, or any legally re-
cognized holiday, the paper is payable on the preceding day.

Bills drawn at sight are sometimes allowed grace and some-
times not. The statutes of different States, so far as they
exist, do not agree, and in the absence of special statutes the
custom is not uniform. In New York, commercial bills, drawn
at sight, are payable loitliout grace, and all paper in which
either the maker, drawer, or drawee is a bank or banker, is
also payable without grace.

If the time be expressed in months, calendar months are
always to be understood. For example, three months from
January 31, without grace, would be April 30 ; including
grace, May 3.

If the time be expressed in days, the time of maturity may
be found by taking the remaining number of days in the month
of the date, and as many days of the following months sepa-
rately as will equal the given number of days plus three. The
number of days in the last month will be the date of the month
on which the paper matures.

For example, a note dated August 20, 1858, payable ninety
days from date, would mature November 21, 1858.

Solution.— 1 1 + 30 + 31 + 21 = 93.

Or, to the day of the date add the time of the note plus
three, from which subtract consecutively the number of days
of each following month, beginning with the month of the
date, until the remainder be smaller than the number of days
in the next month. The remainder will be the date of ma-
turity.

Solution.— 20 + 93=113, and 113-31-30-31=21.

188 DISCOUNTING NOTES.

Or, if the time be 30, 60, or 90 days, call each 30 days a
calendar month, and correct by subtracting 1 for each month
passed over containing 31 days, and adding 1 or 2, according
as it is a leap year or not, if the last day of February be in-
cluded.

Ttyus, 90 days from January 10, 1856, would be, counting
three calendar months, April 13, including grace.

Now, from 13 subtract 1 for January and 1 for March, and
add 1 for February, and we have April 12, for the result. The
last rule is convenient for bank paper, which usually runs 30,
60, or 90 days.

It is evident from the above rules that the day of the date
should be excluded from the calculation.

The following fact may be worth remembering by those
who get " accommodations" at bank.

A paper having 60 days to run PROOF.

will mature on the same day of 33 '== 7 x 5 — 2

the Aveek as that on which it was 63 = 7 x 9

made. Having 30 days to run, it = 7 )

will mature 2 days earlier in the week, and having 90 days
to run will mature 2 days later in the week.

DISCOUNTING NOTES.

ART. 132. In negotiating promissory notes and time-bills
of exchange their estimated value depends upon three con-
siderations, viz.

1st. The responsibility and promptness of the maker.

2d. The relative value of the currency, used in the pur-
chase, compared with that of the payment of the obligation at
maturity.

3d. The market rate of interest.

The range of the first consideration is from A No. 1 to
worthless.

The range of the second, in the United States, is generally
within 2$.

DISCOUNTING NOTES. 189

The range of the third may be said to be between 3 and
20^ per annum.

In view of the first, a man may make a bad bargain in
buying a note having sixty days to run, if he pay for it but 10
cents on a dollar. The United States may perhaps borrow
money at 4$ per annum, when individual States would have
to pay 5 or 6$, and railroad companies 10 or 15/c. A cor-
responding difference is found in promissory notes made by in-
dividuals and business firms.

The purchase of a draft on New York, payable in coin,
with Illinois paper currency, which is convertible into coin at
a cost, say, of 1^, will illustrate the force of the second con-
sideration.

In regard to the third, the market, or ruling rate of interest,
depends mainly upon the rate of profit with which capital can
otherwise be employed. New countries, rapidly developing,
furnish profitable investments, and therefore sustain a high
rate of interest. Sudden expansions and contractions of cur-
rency temporarily affect the rate, causing it to fall with the
expansion and rise with the contraction, but a continued in-
crease in the supply of money stimulates prices, awakens
enterprise, and increases the profits in business and specula-
tion, thereby raising the rate of interest proportionably.

The rate of interest does not express the value of money,
but only the value of the use of it for a limited time, or rather,
it expfesses the value of the use of the capital or credit mea-
sured by money. Money, from its nature, is always cheap
when prices are dear, and vice versa ; for as money measures
the value of other commodities, so the comparative price of
the standard articles of commerce meacures the relative value
of money. Generally, when money is cheap, interest is high.
For many years money has been cheaper in the United States
than in England, but during the whole time the rate of in-
terest has ruled higher. Ifi the early history of California
money was exceedingly cheap, but the rate of interest remark-
ably high. The current rate of interest is also made higher
from the effect of unwise usury laws, and laws under which

190 BANK DISCOUNT.

the collection of valid claims can bo enforced only after a pro-
tracted, uncertain, and expensive prosecution.

There are many other causes that occasion remarkable
fluctuations in the market rate of interest, as war, commercial
revulsions, &c. Unlimited confidence in business encourages
a high rate of interest, while excessive caution and distrust
cause it to decline.

As a general rule, the market rate of interest, like the price
of exchange, is not subject to arbitrary control, but is the re-
sultant of sundry contributing causes ; and whatever legisla-
tion is necessary should be expended on the cause rather than
on the effect.

BANK DISCOUNT.

AKT. 133. The banks of the United States are usually re-
stricted by charter in their rates of discount, but being allowed,
in the interior, to deal in time-drafts or bills on New York,
payable in coin, and being allowed frequently to pay out paper
currency of less value than coin in purchasing such drafts,
they are enabled by this and other means to realize more than
the nominal, legally restricted rate of interest. It is not pro-
posed in this work to discuss the policy of bank charters with
special privileges and special restrictions, nor any other ques-
tion of policy, but merely to furnish to the student and in-
experienced business man the fundamental principles upon
which money and negotiable paper do rest and should rest.

It may, however, be taken for granted, that although
banks, railroad companies, &c., may have been established for
" the accommodation of the people/' yet so long as they are
controlled by human nature, and the profits go into the pockets
of individuals, corporations no more than individuals can be
expected to furnish "accommodations" without their being
paid for. As a general rule, a business man may expect ac-
commodations from a bank only so far as he makes it for the
interest of the bank to grant them.

BANK DISCOUNT. 191

The interest which is charged on notes discounted at a
bank is generally paid in advance, and is computed upon the
amount due on the note at maturity. The difference between
the interest and face of the note is the proceeds, which is re-
ceived by the customer.

Thus the proceeds of a note for $2000, having 63 days to
run, including grace, would be, at 6^ interest, $2000— §21 =
$1979.

If "business paper," drawing interest, is discounted, the
amount due at maturity, including interest, is taken as the face
of the note upon which the bank discount is computed. It
will be observed that bank discount exceeds the "tru-e dis-
count," as heretofore explained ; for while the latter is the
interest on the present worth or principal, the former is the
interest on the amount of principal and interest, and the ex-
cess is equal to the interest on the true discount for the given
time. The ratio of this excess will also increase as the time is
lengthened, -so that, other considerations remaining the same,
the longer the time the more profit to the bank. If the note
run 16 1 years, the bank discount, at 6$, would absorb the
whole note, and the proceeds would be nothing. Frequent re-
newals, so far as the matter of interest is concerned, are un-
favorable to the bank. The reason for the custom among
banks of discounting only " short paper," as it is called, is two-
fold.

First, A large portion of the capital invested in discounts
is based upon deposits, which are subject to " call," and their
own "circulation," which must be redeemed on presentation.
In case of unusual demands for redemption, or withdrawal of
deposits, the early maturity of Bills Discounted is their main
reliance.

Secondly, The risk arising from the varying circumstances
of the makers and indorsers is lessened by shortening the time.

If, however, bills of exchange are discounted, payable in a
better currency than that used in the discount, or for which a
charge is made for collection, the shorter the time the greater
the pecuniary profit.

192 BANKERS' ACCOUNT CURRENT.

In considering the percentage of profit in " bank discount"
with frequent renewals, there is a partial offset in favor of the
banker by his being able to compound the interest at each re-
newal. But this advantage is very small if we consider its
effect for one year only (See Note, page 118), at which time sim-
ple interest, if paid, may also be compounded by re-loaning.

Comparing simple interest with " bank discount/' includ-
ing the advantage from compounding the interest, we obtain
the following result :

Bank discount at 6^ on paper,

Renewed once in 12 mos., is equivalent to 6.383^ simple interest.
" 6 " " 6.281^ "

" " 4 " " 6.248# "

" " 3 " " 6.232^ "

ic ie 2 " " 6.216$ "

" " 1 " " 6.200^

" every instant " 6.182^ "

From the above we see that the excess of bank discount
over true discount, as affecting the rate of interest received,
when the time is less than a year, can be but trifling, being for
§fo always less than

BANKERS' ACCOUNT CURRENT.

ART. 134. -Bankers frequently receive and pay interest on
the account current with their correspondents and depositors,
paying interest on the deposits and receiving interest on the
over-drafts. A settlement occurs once in 3, 6, or 12 months,
as custom or special agreement may dictate, at which time the
balance of interest is entered to the debit or credit of the ac-
count as the case may be, after which it draws interest the
same as other items in the account. The principle involved in
this kind of interest account forms the basis of the "MERCAN-
TILE RULE" in Partial Payments, as given in this work.

The process of computing the interest on such accounts is
made easy by the use of the following

RULE. — Divide the sum of all the daily balances by 6 and

BANKERS' ACCOUNT CURRENT.

193

the quotient, after pointing three places for decimals, will be
the interest required.

fiemark. — It is evident that each daily balance draws in-
terest one day. The interest, then, of the sum of daily balances
for one day is all that is required.

Note 1st. — If the daily balance remains the same for several
days, instead of setting down the amount as many times as
there are days, use the product of the balance into the num-
ber of days.

Note 2d. — If the balances are sometimes debit and some-
times credit, take the difference between their sums before
dividing.

Note 3d. — The above rule gives the interest at 6$. To
find the interest at 4.% divide by 9 instead of 6. For 3^, divide
by 12. In general, the divisor for any rate may be found by
dividing 36 by the rate. Or, having found the interest at 6$,
the interest for any other rate may be found by aliquot parts.

Note 4th. — If a different rate of interest is to be charged
on the over-drafts or debit entries, the footings of the daily
balances should be divided by their appropriate divisors before
subtraction.

The following abbreviated form will serve to illustrate the
foregoing rule :

Account Current

Daily Balances.

Total Daily Balances.

1859

Dr.

Cr.

Dr.

Cr.

Dr.

Cr.

July 1

$500

500

500

2

$200

100

400

400

3

75

325x17

— —

5525

20

500

825 x 10

—

8250

30

1000

175

x 5

=875

Aug. 4

375

200x10

2000

14

125

250

325x30

9750

Sept. 13

125

450 x 10

— •

4500

23

1000

1450 x 8

=

11600

Int. 4.63

42525

Bal.

1454.63

875

2854.63

2854.63

9)

41.650

Oct. 1

By Bal.

$1454.63

Int. at 4%

$4.63

13

194 TRIAL BALANCES.

RULES FOB DETECTING- ERRORS IN
TRIAL BALANCES

ART. 135. The first rule of the book-keeper should be to
make no error, but as all are fallible a few suggestions may
not come amiss.

1st. If the error is found to be in one figure only it is
probably an error, of footing or copying.

2d. If it involves several figures it may have arisen from the
omission of an entire entry or the entering of the same twice.

3d. If it be divisible by 2, without a remainder, it may
have arisen by posting an item to the wrong side of the account,
in which case the item would be half of the apparent error.

4th. If the error be divisible by 9, without a remainder, it
may have arisen from transposition, three cases of which may
be easily detected by rules founded on the peculiar property
of the number 9. They are —

First. When two figures are made to exchange places with
each other, the orders in notation remaining the same : e. g.}
372 made to read 327, or 732, or 273.

Second. When two or more figures are made to change their
places in notation, their arrangement in respect to each other
remaining the same : e. g.} $4275 made to read $42750, or
$42.75, or $427.50.

Third. When two significant figures are made to change
position both with respect to themselves and also the orders
of notation : e. g., $14 made to read $0.41.

To detect the first and second cases of transposition divide
the amount of the error in the trial balance successively by
9, 99, 999, 9999, dc., so far as possible without a remainder,
rejecting all ciphers at the right of the last significant figure in
the error.

The quotients that contain but one digit figure will express
the difference between the two digit figures transposed, which
will be adjacent to each other if the divisor contained but one
9, separated by one other figure' if it contained two 9s, by two
other figures if it contained three 9s, and so on.

TRIAL BALANCES.

195

Those quotients, which contain two or more figures will
express the number itself, which is transposed in notation
simply, the arrangement of the significant figures remaining
the same. In either case the order of the last significant
figure in the error will be the lowest order of the figures trans-
posed. The orders of the other figures can be easily determined
by referring to the error and applying the principles of no-
tation.

To detect the third case, divide the error in the balance by
as many 9s as is possible so as to give only a single figure in
the quotient, and then the remainder in the same way, reject-
ing all ciphers at the right of the last significant figure in both
dividends, after which there should be no remainder.

The first quotient will be the figurS filling both the highest
and lowest order in the transposition ; the second quotient
will be the other figure.

Note. — If the error of the trial-balance be not divisible by
9 it cannot be the result of transposition alone. But when-
ever the error becomes so reduced as to be divisible by 9 with-
out a remainder, a transposition being then possible, the above
tests should be given.

To illustrate the application of the foregoing rules, four
examples are given below, each one representing a balance-
sheet taken from the ledger, but erroneous, from the fact that
the footings of the Dr. and Cr. columns do not agree.

Dr.

Or.

Dr.

Cr.

Dr.

Cr.

Dr.

Cr.

25

34

184

74

100

22

184

22

100

981

24.50

10.25

320.60

36.40

23.50

185

87.50

73

30

200.75

400.90 20 |

126

71

300

90

20.40

80

10

31.20

81.44

137.80

18.40

92

120

110

10.44

10

326

323

7

93.50

100

50

495

800

3.51

6.44

94

12

90.60! 33

450

200

74.25

100

81.50

310

75 25

100.16

120.50

353

40

144

86.24

201.75

40

30

200.10

25

10

63

122.22

8.25

30

20.10

10

350

290

922.40 11.84

75

333.92

8

49.50

24

35.99

1,842.801,905.80

855.25

929.50

1,945.20

1,499.70

1,570.70

1.221.2.J

63 ,

74.25'

445.50

349.47

196 , TRIAL BALANCES.

The "errors" G3, 7425, 4455, and 34947 being each divisi-
ble by 9, transposition is possible. Taking the first example,
we have 63-^-9=7. As this is the only division we can per-
form, we conclude the transposition can occur only in those
amounts where the digit figures expressing the units and tens
of dollars differ by 7. In the Dr. column there are three num-
bers answering these conditions, and in the Cr. column two,
viz. : $18.40, $7, $81.50, $981 and $92. The transposition
could not have occurred in the third number for the footing is
already too small. If, then, either of the other numbers had
been transposed from $81.40, $70, $918, and $29 respectively,
the error is accounted for, a question easily settled by reference
to the ledger. In the second example, we have 7425-^9=825
and 7425-^99—75. The quotients containing two or more
figures in the transposition must be in notation simply. By
reference to the Dr. and Cr. columns it will be observed that
these quotients occur four times in the former and once in the
latter, viz. : $0.75, 201.75, $8.25, $75, and $200.75. The
transposition could not have occurred in the second number
without displacing other significant figures, nor in the fourth,
because the Dr. footing is already too small, nor in the fifth,
because the Cr. footing is already too large. The only two
numbers to be compared, therefore, are the first and third,
which, perhaps, should have been $75 or $82.50, either of
which would account for the error.

In the third example we have 4455 -r- 9 =495, 4455-r99
=45. Here the transposition must be in notation simply,
and may be found in one of two places only, viz. : $495 and
$450.'

In the fourth example we have 34947-^9=3883, 34947-f-
99=353, 34947^9999=3, with a remainder 495, which -^99
=5. We omit the division by 999, because the remainder is
not divisible by 99 without a remainder. For the same rea-
son we omitted it in the third example. In this case there
could be no transposition in the notation of 3883, because the
number does not occur. There may have been a transposition
of $353 from $3.53, or the figure 3 and 5 may somewhere have

STOCKS AND BONDS. 197

been made to change places with respect to themselves and
notation also ; as, when $0.53 had been made to read $350.

Remark. — In the use of these rules in practice, not only
the balances of the ledger accounts as they appear on the
balance sheet should be examined, but also all the separate
postings, as a transposition there will equally affect the final
balance.

STOCKS AND BONDS.

ART. 136. Capital is a term applied to the property in-
vested, by an individual or company, in trade, manufactures,
railroads, banking, &c. The capital of an incorporated com-
pany is generally called its capital* stock, and is divided into
equal parts of convenient size called shares : the* persons own-
ing one or more of these shares being called stockholders.

The management of such companies is generally vested in
officers and directors, who are elected by the stockholders, each
stockholder being entitled to as many votes as the number of
shares he holds.

It not unfrequently happens that the capital stock con-
siderably exceeds the actual capital paid in, which occurs when
it is made payable in installments, and is called in only as the
wants of the company demand. The profits which are distri-
buted among the stockholders are called dividends, and when
"declared" are a certain per cent, of the par value of the
shares.

Certificates of stock are issued by the company, signed by
the proper officers, indicating the size and number of shares
each stockholder is entitled to. These are transferable, and
may be bought and sold like any other property.

When their marketable value equals their nominal value
they are said to be at par. When they sell for more than
their nominal value or face they are above par, or at a pre-
mium ; when for less, they are beloio par, or at a discount.

198 STOCKS AND BONDS.

Quotations of their marketable value are generally made by a
percentage of their par value.

When States, cities, railroad companies, and other corpora-
tions borrow large amounts of money, instead of giving com-
mon promissory notes, they issue bonds, in denominations of
convenient size, payable at a specified time, with interest usu-
ally payable semi-annually.

When issued by governments these bonds are frequently
called government stocks or State stocks, but the terms should
be carefully distinguished from the capital stock of business
corporations.

To these bonds are attached what are called coupons*, each
of which is a due bill for the interest on the bond to which it
is attached, representing the amount of the periodical dividend
or interest, and the time of payment, which coupons are sever-
ally cut off and presented for payment as they become due.

These bonds and coupons are signed by the proper officers,
and, like certificates of capital stock, are negotiable by delivery,
being made payable " to bearer." The loan is made by the
sale of the bonds, with coupons attached, but they are rarely
negotiated at par. 'Their value depends upon the degree of
certainty of their being paid at maturity, and the market rate
of interest compared with the rate drawn by the bond.

Treasury notes are also issued by the United States govern-
ment for the purpose of effecting temporary loans, which more
nearly resemble bank notes, and are made payable with inte-
rest, but without coupoi

Consols is a term abbreviated from the expression "con-
solidated annuities," the British government having at various
times borrowed money at different rates of interest, and pay-
able at different times, consolidated the stock or bonds thus
issued, by issuing new stock drawing interest at three per cent,
per annum, payable semi-annually, and redeemable only at the
option of the government, becoming practically perpetual an-
nuities. With the proceeds of this the old stock was redeemed.
The quotations of these three per cent, perpetual annuities or

* Coupon, pronounced koo-pong'.

STOCKS AND BONDS. 199

consols, indicate pretty accurately the state of the money
market, as they form a staple credit and become a standard
for reference.

Examples.

ART. 137. 1. A person buys 25 shares, par value $100
each, in the Illinois Central Kailroad, at a discount of 12$ per
cent. To what did they amount ?

2. What will be the cost of $15,000 of Ohio State Bonds,
at a discount of 2^$ ?

3. Bought 40 shares ($100 each) of New York and Erie
Eailroad stock, at a discount of 3$, and sold the same at a
discount of 37^$. How much did I lose in the transaction ?

4. If the New York Central Railroad Company declares an
annual dividend of 14$, what will a stockholder receive who
owns 240 shares ($100 each) ?

5. How many shares of canal stock, of $100 each, at 14$
discount, can be bought for $1020 ? How much would be
gained by selling them at 33 \% discount ?

6. If the capital stock of a bank be $500,000, what amount
is necessary to declare a dividend of 5|$ ?

7. A person owns 20 shares ($100 each) of bank stock,
and receives a dividend of $150 ; what was the rate of divi-
dend ?

8. A certain stockholder draws $270 when a dividend of
9$ is declared ; what is the amount of his stock ?

9. Bought stock at 4 per cent, discount, and sold the same
at 5$ premium, and gained $450. How many shares of $100
each were transferred ?

10. A broker paid $9748.50 for bank stock, at a discount
of 3$. How many shares of $50 each did he purchase ?

11. Which is the better investment, railroad stock paying
a semi-annual dividend of 4$, bought at a discount of 25$, or
money loaned at 10$ interest, payable annually ?

Ans. Railroad stock by f$, besides the use, each year, of
one semi-annual dividend for six months.

12. Bought bank stock, paying 12$ dividend, at a discount
of 20$. What per cent, interest did the investment pay ?

200 STOCKS AND BONDS.

13. When the annual dividend of railroad stock is 15$,
and the interest of money is 10$, at what premium ought the
railroad stock to sell ? Ans. 50%.

14. At what per cent, discount must I buy bank stock,
paying 6$, that the investment may pay 9$. Ans. 33^$.

15. If the C. & E. KR. Co. declare a dividend of 15$ per
annum, what is the value of its stock, money being worth 8$ ?

16. The free banking law of New York requires that the
stocks deposited with the superintendent, as security for bank-
note circulation, shall be made equal to stock producing an
interest of 6$ per annum. What amount of circulating notes
could a bank receive on a five per cent, stock ?

Ans. 83 \% of the par value of the stock.
What on a 7$ stock ? Ans. 116|$.

17. In January, 1848, the total amount of British consols
was £378,019,855. What was the amount of interest paid on
them semi-annually ? Ans. £5,670,297f£.

18. The debt of Great Britain and Ireland, in round num-
bers, is £780,000,000, and the annual revenue £56,000,000.
Supposing the annual interest to average 3|$, what per cent,
of the revenue is needed to pay the interest on the debt ?

19. In July, 1859, forty-five New York Fire Insurance
Companies (out of fifty), on a capital of $8,712,000, divided
among the stockholders, as a semi-annual dividend, $679,950.
Compared with railroad stock paying 5$ semi-annually, which
would yield the greater income, railroad stock bought at 65$
or insurance stock at par ?

20. A man subscribed $20,000 stock in a mining company,
the capital stock of which is $500,000, but only 20$ paid in. A
cash dividend of 2$ on the par value is declared and a dividend
of 10$ to be credited to the stockholders as an installment on
their unpaid stock. What is the amount of cash he receives,
and what is the balance due on his subscription ?

21. I buy 100 shares of $100 each in a railroad company,
the capital stock being $3,000,000. The first year they de-
clare a cash dividend of 10$. The second year they increase
their stock by declaring a stock dividend of 10$. The third

STOCKS AND BONDS. 201

year they divide among their stocknclclers the same amount as
in the first year. What would be the per cent, of the last
dividend ? Ans. 9T\ per cent.

How much more would they need to declare a dividend
of 10$, the same as in the first year ? Ans. $30,000.

22. If the paid up stock in a railroad company be worth
100$, and a stock dividend of 10$ be made to the stockholders,
what would be the value of the stock after the dividend ?

Ans. 90} -J- per cent.

23. If the net earnings of a bank with $200,000 capital
be sufficient to pay an annual dividend of 10$, and reserve
$4000 as a surplus to provide for future losses, and it pay
6$ on its net earnings to the State in lieu of taxes, what
would be the rate of taxation on its capital ?

Ans. TW per cent.

NEW RULE FOB FINDING- THE VALUE
OF A BOND.

ART. 138. Most of the problems respecting stocks and
bonds, and brokerage in money and exchange, can be solved
by the application of the ordinary principles of percentage;
without special rules. One problem, however, not unfre-
quently arises, more complicated, to the solution of which the
attention of the student is now directed.

To find the present value of a bond having several years to run,
with interest payable semi-annually, in order to realize from
the dividends and final payment an equivalent to a given rate
per cent, per annum on the investment, use the following

RULE. — 1st. Taking a single dividend or semi-annual in-
terest on the bond for a principal, compute the simple interest
on it at the proposed rate, for one-fourth as many years as
would be the product of the number of semi-annual dividends
into the number less one. To this interest add the sum of the
several amounts of semi-annual interest, and the face of the
bondj setting this sum down for a DIVIDEND.

202 STOCKS AND BONDS.

2d. Suppose another bond, differing from the given bond
only in its rate of interest being the same as the proposed rate
for investment. Proceed with this as with the other, and use
jthe result for a DIVISOR.

The quotient, after division, wiU express, decimally, the
rate per cent, of the par value equal to the present value.

Ex. 1. What should I pay for a bond for $1000 due in 10
years, with interest at 6%, payable semi-annually, in order to
make it a 10$ investment ?

, Solution.

Interest on $25 at 10$. for AJIJIJL years, . . $237.50
Total amount of semi-annual dividends =$25 x 20= 500

Face of the bond, _1000_

Dividend, 1737.50

Interest on $50 at 10$ for AJ» ju. years, . . " 475

Total amount of semi-annual dividends =$50 x 20= 1000

Face of the bond, 1000

Divisor, ~2475~

$1737.50^$2475=.70202.

$1000x.70202=$702.02, the present value of the bond.

KEMABK. — A strictly accurate solution of the above pro-
blem requires the aid of logarithms, and the operation is tedi-
ous. The above rule is simple and brief, and gives a result
sufficiently approximate for all practical purposes. The ques-
tion involves compound interest, the interest on the investment
being supposed to be compounded annually, while the interest
on the dividends is compounded at the proposed rate at the
end of each year. Though annual interest gives a result some-
what less than compound interest, yet if two problems be
wrought, first by annual interest and then by compound, the
ratio between the results by the first operation will not differ
essentially from the ratio by the second. This principle forms
the basis of the rule given above. The work of computing the
"annual interest," or rather semi-annual interest, is much
shortened by incorporating in the rule an expression for the
sum of the arithmetical series of years, during which a single
dividend would draw interest. The approximation to strict

STOCK.S AND BONDS. 203

accuracy is furthermore increased by treating the supposed
bond or investment the same as the one given, so far as that
its interest should be payable semi-annual ly instead of annu-
ally, as proposed in the conditions of the problem.

The answer given to the above example in PRICE'S STOCK
TABLES, computed by logarithms, is 70^ instead of 70^, as
given by the above* rule.

If the rate per cent, to be realized be the same as the rate
of interest on the bond, the present value, by the above rule,
would be the par value. By Price's Stock Tables it would be
at a premium ; if 7/c, and running 50 years, the premium would

be 1TVV Per cen*-

Ex. 2. Mosney being worth 10$ per annum, what is the
present value of a 7$ bond, interest payable semi-annually,
running 20 years ? Ans. 76 TW per cent.

By Price's Stock Tables. " 75TVo "

Note. — As the ratio only is sought, any convenient amount
may be assumed for the face of the bond.

Ex. 3. In 1813 the United States government borrowed
§16,000,000, selling their bonds to run 12 years, at 6$ in-
terest, payable semi-annually, at 12$ discount. At what dis-
count should the purchasers have taken them, to realize on
their investment an average annual interest of 8$ ?

Ans. 14ryo-<V$.

KEMARK. — It is manifest that, if a corporation sells in New
York its bonds, drawing 7$ interest, for less than-par value, it is
borrowing money at a higher rate of interest than the legal rate,
and the contract under the general law of that State, regu-
lating interest, becomes tainted with usury. But for the ac-
commodation of corporations, and the security of capitalists in-
vesting in such bonds, it was enacted by the Legislature of
New York, in 1850, that " no corporation shall hereafter in-
terpose the defense of usury in any action/' With this restric-
tion upon them, corporations can negotiate their bonds more
readily and at better rates than without such restriction. A
large class of individual borrowers desire a similar legal prohi-
bition for a like accommodation.

204 EQUATION OF PAYMENTS.

EQUATION OF PAYMENTS.

ART. 139. Equation of payments is the process of finding
the mean or average time for the payment of several sums of
money due at different dates. The mean or average time
sought is called the equated time.

The common methods of finding the equated time are based
upon the principle that money kept after it is due is counter-
balanced by an equal sum of money paid the same length of
time before it is due.

This principle obviously depends upon another which may
be expressed as follows : The payment of $100 down, and
$100 in two years without interest is equivalent to the pay-
ment of $212 in two years, without interest, the rate of in-
terest being 6 per cent. ; or to express the same abstractly, the
use of any sum of money is worth its interest for the time it is
used.

ART. 140. To find the equated: time for the payment of
several sums of morily with different terms of credit.

Ex. 1. A owes B $1200, of which $300 is due in 4 months,
$400 in 6 months and $500 in 12 months. What is the
equated time for the payment of the whole sum ?

FIRST METHOD.

300 x 4—1200 Explanation. — Suppose the sums

400 x 6—2400 to be paid respectively, 4 months,

500x12=6000 6 months, and 12 months before

1200 ~ ]9600 due. The amount to be paid will be

8 mos. Ans. $300 — its discount for 4 months ;

$400 — its discount for 6 ^months ;

and $500— its discount for 12 months. The interest or dis-
count of $300 for 4 months equals the discount of $1 for 1200
months ; the discount of $400 for 6 months equals the dis-

EQUATION OF PAYMENTS. 205

count of $1 for 2400 months ; the discount of $500 for 12
months equals the discount of $1 for 6000 months ; or, the
discount on the whole sum equals the discount of $1 for 1200
+2400 + 6000—9600 months. Now, the discount of $1 for
9600 months equals the discount of $1200 for on*e-twelve hun-
dredths of 9600 months =8 months, the equated time.

RULE. — Multiply each payment or debt ~by its time of credit,
and divide the sum of the PRODUCTS by the sum of the PAYMENTS.

Note. — 1. By the term discount, as used above, is meant
mercantile discount or simple interest.

2. If we suppose all the sums to be paid in 12 months, the
time upon which the last debt becomes due, the amount to be
paid will be $300+ its interest for 8 months, $400+ its interest
for 6 months, and $500, or $1200 + the interest of $1 for 4800
months. It is plain the debts will be cancelled by paying
$1200 four months before the last debt is due ; or, which is
the same thing, eight months after the first debt is due.

For convenience we have commenced at first date and dis-
counted.

SECOND METHOD.

Discount on $300 for 4 months, at 6$=$ 6.00

400 for 6 " " = 12.00

500 for 12 " " = 30.00

Discount on $1200 =$48.00

$12= Discount of $1200 for 2 months

6= " 1200 for 1 "

48-^6=8. Ans. 8 months.

Explanation. — The interest of $1200, or the sum of the
payments, being $6 a month, A is entitled to the use of $1200
as many months as $6 is contained times in $48=8. Hence,
8 months is the equated time.

RULE. — Find the interest of each payment, or debt, for its
term of credit, and divide the amount of interest thus found by
the interest of the sum of payments for one month or one day.

Note. — As the result will be the same for any rate of inte-
rest, take that rate which is most convenient.

206 EQUATION OF PAYMENTS.

ART. 141. That the equated time obtained by both of the
above methods is correct, will appear from the following proofs :

First Proof.— By paying the $1200 at the close of 8
months A gains the use of $300 for 4 months=$6 interest,
and $400 for 2 months=$4 interest, and loses the use of $500
for 4 months=$10 interest. Hence, A gains $6 + $4=$10
interest, and loses $10 interest. On the other hand B loses $6
+ 4= $10 interest, and gains $10 interest.

Second Proof. — If neither payment should be made till the
last debt is due A would then owe B $300 + its interest for 8
months=$300+$12=$312; $400+its interest for 6 months
=$400 +$12 =$412; and $500 without interest: that is,
A would owe B in 12 months $312 + $412 + $500= $1224.
Now, the present worth of $1224, four months before it is due,
is $1200. Hence, A's paying B $1200 at the close of eight
months is the same as his paying him $1224 in 12 months, or
$300 in 4 months, $400 in 6 months, and $500 in 12 months.

Third Proof. — If A should pay each debt when it is due,
and B lend the money received to C, at the time A's last
payment is due C would owe B $24 interest. If A should
pay the sum of the debts, or $1200, at the equated time (8
months), and B lend as before, he would also receive from G
$24 interest. Hence, the amount of interest is the same in
either case, and 8 months is an equitable time for the payment
of the debts.

The correctness of the above methods is called in question
by a number of good authors. I can account for this only
by the well known fact that a specious error, well authenti-
cated and often repeated, sometimes passes current among
good scholars, without being submitted to the rigid test of ex-
amination. The following is the common method of demon-
strating the incorrectness of the above methods of finding the
equated time :

" If I owe a man $200, $100 of which is now due, and the
other hundred in two years, the equated time is not one year.
For in deferring the payment of the first $100' one year I oughjb
to pay the amount of $100 for the time, which is $106 ; but

EQUATION OF PAYMENTS. 207

for the $100 which I pay one year before it is due, I ought
to pay the present worth of $100, which is §94.35f|; and $106
+ §94. 35f£= $200.33 f£ ; whereas by the mercantile method I
only pay $200."

This argument is fallacious. For if I ought to pay the
present worth ($94.33 1£) of the $100, I pay one year before
it is due, I ought not to pay the amount ($106) of the $100 I
pay one year after it is due. The $6 interest in this amount
is not due until the close of the two years. I ought to pay
$100+ the present worth of $6 due in one year, which is
$5.66/3 ; and $100 + $5.66/3 + $94.33fi= $200.

The mistake is in considering the sums of money payable
at different times as separate from each other ; whereas, by
the very nature of the problem of finding a common time of
payment, they must be regarded as parts of the same contract.
Suppose, for example, I buy a horse, and agree to pay $100 in
one hour, and $100 in two years, without interest. Failing to
pay the $100 due in one hour until the close of one year, which
I then pay luithout interest, how much must I pay at the close
of the second year? Evidently $106 (if the legal rate is 6),
since I paid at the close of one year only the principal ($100),
leaving the interest ($6) unpaid, which cannot draw interest.
Now, in finding the equated time for the payment of several
debts due at different dates, the question is to find a time for
the payment of the several principals loithout interest. Instead
of paying the amount of $100 in the problem proposed, the
principal alone is paid.

The following is given by these authors as the " only accu-
rate rule :"

. Find the present worth of each of the given amounts
due; then find in what time the sum of these present ivorths
iv iU amount to the sum of all the payments."

The inaccuracy of this " accurate rule," tested by the logic
of its authors, will appear from the following :

The equated time for the payment of $200, $100 of which
is now due, and the other $100 due in two years, as found by
this rule, is 11.32075 months. Now, the amount of $100 for

208 EQUATION OF PAYMENTS.

11.32075 months, at 6 percent., is $105.660387; the present
worth of the other $100, due in 12.67925 months, is $94.03832,
and $105.660387+ 94.03832 =$199.698707, whereas it ought
be $200.

It is also evident that the equated time, as found by this
" accurate" rule, will not be the same for all rates of interest.
At 50 per cent, the equated time of the above example is 8
months, and the error, by the above test, $8.33^ ; at 100 per
cent, it is 6 months, with an error of $10.

This supposed accurate rule is based upon the principle
that the amount to be paid on a debt due at a future date,
without interest, at any time previous to this date, is the pres-
ent worth of the debt at any prior date, plus the interest of the
present worth up to date of payment. The incorrectness of
this principle is easily shown. Suppose I owe a man $100,
due in two years, without interest ; how much ought I to pay
in one year ?

The present worth of $100, due in two years (at 6 per
cent:), is $89.2857, and the interest on this sum for one year
is $5.3571 ; hence the sum to be paid is $89.2857 + $5.3571 =
$94.6428. The true amount to be paid, however, is the pres-
ent worth of $100, due in one y^ar, which is $94.339.

In finding the equated time for the payment of a bill of
goods or of an account current, the exact number of days be-
tween the different dates is used. The pupil may commence
with the first dates or with the last. In commencing with
the first dates, each item, except the first, is subject to dis-
count; if the last date is taken, each item, except the last,
draws interest. ^

Ex. 2. A merchant sold goods to one of his customers, at
different dates, as by the statement annexed. What is the
average time for the payment of the same ?

June 16, 1858, a bill amounting to $500, no credit.

" 30, " " " 220 "

July 30, " " " 300 "

Aug. 15, " " " 250 "

Sept. 1, " « " 112 «

Oct. 1, " « " 100 «

EQUATION OF PAYMENTS. 209

OPERATION BY FIRST METHOD.

days. days,

June 16, 1858, §500 x 00=

" 30, '" 220 x 14= 3080
July 30, " 300 x 44=13200
Aug. 15, " 250 x 60=15000
Sept. 1, " 112 x 77= 8624
Oct. 1, " 100x107=10700 ^

1482 50604_34 days.

4446J
6144
5928

Counting forward 34 days from June 16, the date of the
first bill, we have July 20, the equated time for the payment
of the above bills.

Note. — A little reflection will make it evident that the
above example is similar to one requiring the equated time for
the payment of §500 cash ; §220 due in 14 days ; $300 due
in 44 days ; §250 due in 60 days ; §112 due in 77 days ; and
§100 due in 107 days. The average date of purchase of several
bills is found in the same manner.

OPERATION BY SECOND METHOD.

days. dis.

June 16, 1853, §500 for 00=

" 30, " ' 220 " 14= J .51*
July 30, " 300 " 44= 2.20
Aug. 15, " 250 " 60= 2.50
Sept. 1, " 112 " 77= 1.44
Oct. 1, " 100 " 107= 1.78
§1482~ ~§8^3

§14.82 dis. for 60 days.
.247 " 1 day.
.247) 8.430 (34 Ana. 34 days.

__
L020

.988
32

Counting forward 34 days from June 16, we have July 2C,
the equated time.

210 EQUATION OF PAYMENTS.

Note — As the result will be the same for any rate of inte-
rest (discount), it is generally most convenient to compute the
interest at 6 per cent. When the time is in days, as in the
second example, the interest is readily found by removing the
point, or separatrix, two places to the left, and taking such
aliquot parts of the result as the given days are of 60 days.

Suppose, for example, we wish to find the interest of
§230.60 for 39 days. Since 39=30+6 + 3, the interest for 39
days will be the sum of |, TV and ^ °f the interest for 60 days.
Thus : Interest for 60 days =$2.306

" " 30 " (i) = 1.153
" " 6 " (TV)= .231
" 3 " (¥v)= jJ15
" 39 " =$1.50"

Note. — 2. If the equated time contains a fraction greater
than i add 1 to the number of days ; if less than J disregard it

Examples.

3. I owe $450, due in 6 months ; $300, due in 8 months ;
$125 due in 10 months ; and $100, due in 12 months. What
is the equated time for payment ? Ans. 7f f months.

4. Bought a farm for $3500 ; | of it is to be paid down, \
of it in 8 months, -} in 12 months, and the remainder in 15
months, without interest. What is the equated time for the
payment of the whole ? Ans. 5£ months.

5. A merchant owes a bank $1500, of which $300 is due
in 30 days, $250 in 45 days, $350 in 60 days, $450 in 80 days,
and $150 in 90 days. What is the equated time for the pay-
ment of the whole ?, Ans. 61 days.

6. Bought of Ivison & Phinney the following bills of goods :

June 3, 1858, a bill amounting to $300
July 1, " " " 220

" 20, " " " 400

Aug. 15, " " " 330

Sept. 13, " 240

What is the average date of purchase ? Ans. July 22.

7. A merchant has charged on his ledger $120, due May
15, 1858 ; $90, due July 3, 1858 ; $75, due Aug. 30, 1858 ;

), due Sept. 10, 1858 ; $160, due Oct. 18, 1858 ; $150, due

EQUATION OF PAYMENTS. 211

Dec. 20, 1858. What is the equated time for the payment of
these accounts ? ^ns. Sept. 10.

ART. 142. To find the equated time for the payment of
several sales, made at different dates, and for different terms
of credit.

Ex. 1. James Russell bought of Fink, Hall & Co., several
bills of goods, as below stated :

April 3, 1858, a bill of $220, on 3 months' credit.
May 1, " " 125, on 5 "

" 15, " " 200, on 6

June 24, " " 140, on 8 " "

July 1, " " 190, on 9 " "

What is the equated time of payment ?

Operation.

days. days.

Due, July 3, 1858, $220 x 00=
" Oct. 1, " 125 x 90= 11250
" Nov. 15, " 200x135=27000
" Feb. 24,1859, 140x236= 33040
" April 1, " 190x272= 51680

875 ) 122970(141 nearly.

875
3547
3500

470

The equated time for the payment of th*e above bills is
141 days from July 3, which is Nov. 21.

METHOD BY DISCOUNT.

dis.

Due, July 3, 1858, $220 for 00=
" Oct. 1, " '• 125 for 90=$ 1.88
" Nov. 15, " 200 for 135= 4.50
" Feb. 24, 1859, 140 for 236= 5.51
" April 1, " ' 190 for 272= 8.61

$875" .1458 )§20.5000(141 days.

8.75 1458

G'o)-1458 5920

5832

880

141 days from July 3, is Nov. 21, the equated time as above.

Explanation.— The bill of $220 falls due 3 months from
April 3, which is July 3 ; the bill of $125 falls due 5 months

212 EQUATION OF PAYMENTS.

from May 1, which is Oct. 1, and so on : the time of maturity
of each bill being found by adding its term of credit to its date
of purchase. The average time of maturity is the equated
time for the payment of the bills.

KULE. — First find the MATURITY of each bill (or the time
when it falls due) and then proceed as in the previous case.
The equated time is found by counting fonoard from the date
of the first amount falling due.

Notes. — 1. The bill having the earliest date does not always
fall due first. It sonietimes happens that the term of credit
of the first bill is longer than that of the succeeding bills. It
is most convenient to arrange the statement of maturity so
that the bill maturing first shall stand first.

2. The equated time for the payment of several bills may
be found by commencing at the last date and finding how long
each bill draws interest. Thus, the last example may be
equated as follows :

' days. days.

Due, April 1, 1859, §190 x 00=
" Feb. 24, " 140 x 36= 5040
" Nov. 15, 1858, 200x137=27400
" Oct. 1, " ' 125x182= 22750
" July 2, " 220x273= 60060

875~ )115250(132 nearly.
875_
2775
2625

1500

The equated time is 132 days previous to April 1, 1859,
which is Nov. 20, 1858. The difference of one day between
the results of the two methods is due to the fractional parts
of days being omitted.

Examples.

2. T. W. Cook & Co. sold to Murray & Co. several bills
of goods, as shown in the statement annexed. What is the
average time of maturity ?

April 15, 1857, a bill amounting to $450, on 5 months' credit.
June 16, " ' " 560, on 2

July 31, " " " 180, on 6

Sept. 19, « " " 760, on 5

u u

a a

« u

Ans. Nov. 19.

EQUATION OF PAYMENTS. 213

3. Bought goods of Smith '& Moore, at sundry times, and
on different terms of credit, as follows ?

Dec. 18, 1857, a bill of $375.50, on 6 months' credit.
Jan. 10, 1858, " 290.60, on 6 "
March 13, " " 800.00, on 8 "

April 30, « " 650.80, on 7 "

June 15, " 460.25, on 4 "

What is the equated time for the payment of the whole ?

Ans. Oct. 8, 1858.

4. 0. Blake & Co. sold goods to J. B. Foster, at sundry
times, and on different terms of credit, as follows :

Sept. 30, 1858, a bill of $ 80.75, on 4 months' credit.
Nov. 3, " " 150.00, on 5 " "

Jan. 1, 1859, " 30.80, on 6 " "

March 10, " " 40.50, on 5 " "

April 25, " 60.30, on 4 "

How much will balance the account June 2, 1859 ?

Ans. $364.04.

Note. — The equated time for the payment of the above ac-
count is May 5, 1859 ; hence the several bills above are equiva-
lent to a bill of $362.35 due May 5. It is evident that the
$362.35 should draw interest from May 5 to June 2, the time
of settlement. When it is required to know the amount due
at any date previous to the equated time, the present worth*
of the sum of the several bills must be found.

5. A merchant sold to one of his customers several bills of
goods, as follows :

May 9, 1857, a bill of $340 on 4 months' credit.
June 6, " " 400 on 3 "

July 8, " " 345 on 5 " "

Aug. 30, " " 130 on 5 " "

Sept. 30, 240 on 6 " "

How much money will balance the account Jan 1, 1858 ?

Ans. $1466.40.

6. J. D. Stuart bought of Geo. A. Davis & Co. several
bills of goods, as follows :

* The mercantile method of finding the present worth in such cases is to de-
duct interest for the time.

214 EQUATION OF PAYMENTS.

March 3, 1850, a bill of $250, on 3 months' credit.

April 15, " ' " 180, on 4 "

June 20, " " 325, on 3 "

Aug. 10, " " 80, on 3 "

Sept. 1, " 100, on 4 "

What is the equated time of payment, and how much money
would balance the account July 1, 1850 ?

Ans. Aug. 30 ; $925.65.

7. Purchased goods of a merchant at sundry times and on
different terms of credit, as follows :

Nov. 9, 1857, a bill of $ 20.00 on 5 months' credit.
" 30, " " 50.60 on 3 "

Dec. 31, " " 90.00 on 4 " "

Feb. 1, 1858, " 120.00 on 3 "

What is the average date of purchase, and what the average
time of maturity ? Ans. to first Jan. 4, 1858.

8. A merchant sold goods to one of his customers, as stated
below :

April 6, 1857, a bill of $450, on 4 months' credit.

May 12, " " 600

June 20, "" " 750

Aug. 1, " " 300

When must a note for the whole be made payable ?

Note. — When the sales have the same term of credit, as in
the above example, it is most convenient to find first the aver-
age date of purchase. The equated time of payment is then
readily found by adding the common term of credit to this
average date of purchase. The average date of purchase in the
above example is 54 days from April 6, which is May 30 ; the
equated time of payment is 4 months from May 30, which is
Sept. 30.

The days of grace generally allowed may be added to the
equated time.

9. Sold John Smith, on a credit of 90 days, the following

bills of goods :

Jan. 10, 1858, a bill of $20.

April, 12, " " 45.

May 27, « " 60.

June 30, « " 75.

What is the equated time of payment ? Ans. July 13, 1858.

«

tt a

a a

EQUATION OF PAYMENTS. 215

10. Purchased goods of Stratton & Co, at different dates,
and on a credit of 6 months, as below stated :

Oct. 12, 1858, a bill of $460 on 6 months' credit.

" 30, " • " 95 " "

Dec. 1, " " 180 " "

" 25, " " 390 " "

Jan. 20, " " 410 " "

How much money will balance the account July 1, 1858 ?

Ans. $1542.907.

ART. 143. To find what extension should be granted to
the balance of a debt, partial payments having been made be-
fore the debt was due.

Ex. A owed B §1200, due in 6 months, but to accomodate
him paid $400 in 2 months. When ought the balance to be
paid ? Ans. in 8 months.

Explanation. — Since A paid B $400 four months before it
was due, B, at the close of the 6 months, owed A the interest
of $1 for 400x4 months^ 1600 months. To balance this in-
terest due A, he can keep the $800 unpaid ¥£ 0- of 1600 months
=2 months after the debt is due.

Ex. 2. Singer & Morton sold Wm. Williams, June 10,
1858, goods to the amount of §1300, on 6 months credit.
Aug. 20, Mr. Williams paid $200 ; Sept. 18, $250 ; Oct. 30,
$350. When, in equity, ought the balance to be paid ?

Operation.

days.

200 x 112 = 22400

250 x 83 = 20750

350 x 41 = 14350

$800" "~_57500

57500^-500=115

The balance ought to be paid 115 days from Dec. 10, 1858,
which is April 4, 1859.

KULE. — Multiply each payment by the time it was paid
before due, and divide the sum of the products by the balance
unpaid.

3. A sold B, July 1, 1858, goods to the amount of $1500,
on a credit of 90 days. Aug. 5, B paid $400 ; Sept. 3, $600;
Sept. 15, $300. When ought B to pay the balance.

Ans. April 26, 1859.

216 EQUATION OF PAYMENTS.

4. A merchant sells a customer to the amount of $600,

1 of which is to be paid in 3 months, | in 4 months, and the
balance in 7 months. The customer pays 1 down. How long
may he keep, in equity, the remainder ? Ans. 7f months.

5. A owes B $600, payable in 6 months. At the close of
3 months he wishes to make a payment so as to extend the
time of the balance to one year. How great a payment must
B make ? Ans. $400.

Explanation. — B wishes to pay such a sum of money three
months before it is due, as will extend another sum 6 months
after it is due. It is evident the sum paid must be twice as
great as the sum extended. Divide $600 into two parts, which
shall be to each other as 2 to 1.

6. A owes B $1000, payable in 6 months. At the close of

2 months A pays B $1200, and B gives A his note for the
balance. When ought the note to be dated ?

Ans. 24 months back.

Explanation. — Since B paid A $1200 four months before
the $1000 was due, A, at the close of the 6 months, owed B
the interest of $1200 for 4 months, or $1 for 4800 months.
It is evident that a note for the balance, $1200— $1000= $200,
must be dated ^7 of 4800 months, or 24 months previous to
the time the $1000 was due.

7. July 10, 1858, A paid B $600 ; Sept. 12, 1858, B paid
A $800. When ought A to pay the balance ?

Explanation. — Sept. 12, B owed A $600+ its interest for
64 days. He paid A $600 + $200. Hence, A is entitled to
the use of the balance ($200) until its interest equals the in-
terest of $600 for 64 days, or 192 days. 192 days from Sept.
12, 1858, is March 23, 1859.

8. July 10, 1858, A paid B $800 ; Sept. 12, 1858, B paid
A $600. What should be the date of a note for the bal-
ance ?

Explanation. — Sept. 12, B owed A $800 + its interest for
64 days. He paid A but $600. Hence, he owes A the bal-

EQUATION OF ACCOUNTS.

217

ance (§200) and the interest of §800 for 64 days, or the inte-
rest of $200 for 256 days. A note for the balance must there-
fore be dated 256 days previous to Sept. 12, 1858, which is
Dec. 30, 1857.

Jlemark. — The above eight examples, if well understood,
will aid the student in equating accounts which contain both
debits and credits..

EQUATION OF ACCOUNTS.

ART. 144. Equation of accounts (also called "Averaging
of Accounts/' and " Compound Equation of Payments") is
the process of finding the equated time for the payment of the
balance of an account that contains both debits and credits.

Since the debit and credit sides of an account are respect-
ively equivalent to the sum of their several items, due at the
equated time (See Note, page 213), the first step in equating
accounts is to find the time when each side of the account be-
comes due.

This may be found by equating each side of the account,

without any reference to the other, commencing either at the
first or the last date of each, or by using the first or last date
of the account as a common starting-point for both sides.

The solution of the following example will sufficiently illus-
trate these two methods of equating the debit and credit sides
of an account.

Note. — In the following solution we have commenced at
the first date and discounted :

Ex. 1.
Dr. Fisk, Hull & Co. in account with Jas. Russell. Or.

1838.

\ Time of credit.

1858.

April 3

ToMdse.

$220 3 mo.

July 1 By Cash.

$200

May 1

«

12.3 5 "

Oct. 3 "

150

" 15

a

200 6 "

Dec. 20 "

300

June 24

a

140 8 "

i

July 1

tt

190 9 "

i

218

EQUATION OF AC. COUNTS.

FIRST

Debits.

Due,
July 3,1853, $220 X 00 =

oct i « 125 x 90=11250
NOV. 15, » 200x135=27000

Feb 84 1859 140 X 236 = 33040

April i, •« 190x272=51680

$875

METHOD.

Credits.

Due.
July 1, 1858, $200 X 00=

oct. 3, « 150 x 94=14100
Dec. 20, » 300x172=51600

$650

) 65700

101 ds.

Credits are due 101 days from
July 1, which is Oct. 10.

) 122970
141 ds.

Debits are due 141 days
from July 3, which is Nov. 21.

The above account thus equated will stand as follows :
Dr. Cr.

Due, Nov. 21, 1858, $875. I Due, Oct. 10, 1858, $650.

Or tlius :

Debits.

Due,
July 3, 1858, $220 X 2= 440

oct. i, « 125 x 92=11500
NOV. 15, .« 200x137=27400

Feb. 24, 1859, 140 X 238 = 33320

April i, « 190x274=52060

$875 .

Credits.

Due,
July 1, 1853, $200 X 00=

oct. 3, •« 150 x 94=14100
Dec. 20, •• 300x172=51600
$650

)124720
T43 ds.

) 65700
101 ds.
Credits due 101 days from

July 1, which is Oct. 10.

Debits due 143 days from
July 1, which is Nov. 21.

The account thus equated stands as before :

Dr. Cr.

Due, Nov. 21, $875. | Due, Oct. 10, $1650.

Note. — In the above operation, we start from the earliest
date upon which any item of either side of the account be-
comes due.

The next step is to find when the balance of the account,
as thus equated, becomes due.

Debits, .... $875 650

Credits, ... 650 42

Balance, . . . $225

Difference in time 42 days. _

225)27300

121 days.

1300

EQUATION OF ACCOUNTS. 219

Or thus, by Discount :
$6.50 $4.55--.0375 (dis. of $225

3~25 Dis. for 30 days. for 1 day) =121 days.

1.30_ ^ 12 "

$455T3is. for 42 days.

Balance is due, 121 days from Nov. 21, 1858, which is
March 22, 1859.

Explanation. — Assume the account settled Nov. 21, the
latest date. The credit side of the account has heen due from
Oct. 10 to Nov. 12, or 42 days. Nov. 21, the credit side is
equal to $650, and the interest of the same 42 days. That tjie
debit side of the account may be increased by an equal amount
of interest, it is evident that the balance of the account must
remain unpaid 121 days, or the 121 days must be counted for-
ward from Nov. 21.

Or thus :

The above account may be stated as follows : Oct. 10,
1858, James Kussell paid Fisk, Hull & Co. $650; Nov. 21,
1858, Fisk, Hull & Co. paid James Kussell $875. Now, since
F., H. & Co. had the use of $650 for 42 days, J. H. is entitled
to the use of $225 (the balance) until its interest equals the
interest of $650 for 42 days, which is 121 days. 121 days
from Nov. 21, 1858, is March 21, 1859.

Pr

Dr.
Due Nov. 21, . . $875
Int. to March 21, 1859, 17.65

90/*.

Or.
Due, Oct. 10, . . $650
Int. to March 21, 1859, 17.65
Balance, .... '225.

$892.65

$892.65

2. Suppose the debit and credit side of the above account,
when equated, to stand as follows :

Dr. Or.

Due, Nov. 21, 1858, $650. | Due, Oct. 10, 1858, $875.

220 EQUATION OF ACCOUNTS.

What is the equated time for the payment of the balance ?

Credits, .... $875 875

Debits, .... 650 _42

Balance, .... $225 225)36750(163 days.
Difference in time, 42 days. 225

1425

1350

750
675

Balance due 163 days previous to Nov. 21, 1858, which is
June 11, 1858.

Explanation. — Suppose the account settled Nov. 21. The
credit side is equal to $875, and its interest from Oct. 10 to
Nov. 21, or 42 days. That the debit side of the account may
be increased by an equal amount of interest, the balance of
the account must be regarded as due 163 days previous to
Nov. 21, or June 11.

Or tlius :

Oct. 10, 1858, James Kussell paid Fisk, Hull & Co. $875 ;
Nov. 21, 1858, F., H. & Co. paid J. K. $650. Since F., H. &
Co. had the use of $875 for 42 days, J. H. is entitled to the
interest of $225 (the balance) for 163 days. Hence, the bal-
ance must be regarded as due 163 days previous to Nov. 21.
The simple question is : How long must $225 be on interest
to equal the interest of $875 for 42 days ?

Note. — If Fisk, Hull & Co. should wish to give their note
for the balance, it is evident the note must be dated June 11,
1858.

First find the equated time 'for each side of the account
ivithout any reference to the other. Then 'multiply the side of
the account which falls due FIRST ~by the number of days between
the dates of equated time, and divide the product by the balance
of the account. The quotient ivill be the number of days to be
counted FORWARD from the LATEST DATE ivhen the SMALLER
side of the account falls due FIRST ; and BACKWARD when the
LARGER side falls due FIRST.

EQUATION OF ACCOUNTS. 221

NOTE. — Some authors give the following rule : — Multiply the smaller side of
the account by the number of days between the dates of equated time, and divide
the product by the balance of the account. The quotient will be the time for con-
sideration. From the equated date of the larger side, count FORWARD when, that
side becomes due last, but BACKWARD when it becomes due first.

ANOTHER METHOD.

ART. 145. The equated time for the payment of the bal-
ance of an account may be found directly without first aver-
aging the debit and credit items, by the following method :

Due,

July 3, 1853, $220 X 2= 440

oct. i, « 125 x 92= 11500

KOV.IS, •• 200x137= 27400

Feb. 24, 1853, 140x238= 33320

Aprn i, « 190x274= 52060

$875 124720

650 65700

Due,

July 1, 1858, $200 X 0=

. 150 x 94=14100
• 300x172=51600
$650 65700

262 days from July 1, 1858,
is March 21, 1858.

§225 59020

Explanation. — We assume July 1, 1858 (the earliest date
upon which any item becomes due), as the time upon which
all the items of the account becomes due. The interest of the
debit items, from this assumed date of maturity to the time
they respectively become due, equals the interest of $1 for
124720 days ; the interest of the credit items equals the inte-
rest of $1 for 65700 days. Hence, the balance of interest in
favor of the debit side equals the interest of $1 for 59020 days,
or $225 for ^ of 59020 days=262 days. Since the balance
of items is also in favor of the debit side, it is evident it can
remain unpaid 262 days without interest, or will become due
262 days from July 1, 1858, which is March 21, 1859. If the
balance of items had been on the credit side it would have
been due 262 days previous to July 1, 1858.

HTJILIE.

Assume the earliest date upon which any item of the ac-
count becomes due to be the time of maturity for all the items.

Multiply each item by the number of days intervening be-
tween this assumed date and the date upon ivhicli it becomes
due, and find the sum of these products on each side of the ac-

222 EQUATION OF ACCOUNTS.

count. Then divide the DIFFERENCE betiveen the sums of the
debit and credit products by the balance of the account; the
quotient ivill be the time for consideration.

When the difference of products and the balance of the ac-
count fall on the SAME side count FORWARD ; when on OPPOSITE
sides count BACKWARD.

Note. — The latest date may be used as a starting-point.
i

Examples.

3. A has with B an account, which, when each side is
equated, stands as follows :

Dr. Or.

Due, June 5, $1285. | Due, June 24, $1080.

What is the equated time of payment for the balance ?

Ans. Feb. 25.

4. C has with D an account, the debit and credit sides of
which, when equated, are as follows :

Dr. Or.

Due, Jan. 7, $325 | Due Jan. 11, $1090.

What must be the date of a note for the balance ?

Ans. Jan. 13.

5. What is the equated time for the payment of the bal-
ance of an account, which, when the two sides are equated,
stands as follows :

Dr. Or.

Due, July 12, $450. | Due, Sept. 1, $800.

Ans. Nov. 6.

6. At what time will the balance of the following account
commence drawing interest ?

Or. Dr.

Due, Oct. 15, $1260 | Due, Nov. 20, $900.

Ans. July 17.

7. What is the equated time for the payment of the bal-
ance of the following account, the merchandise items having a
credit of 4 mouths ?

EQUATION OF ACCOUNTS.

223

Dr. E. Bill & Co. in account with Orvil Blake.

Cr.

1858.

1859.

.

May 1

To Mdse. $850

70

Jan. 1 By Cash.

?500

00

June 6

it

340

75

Jan. 19

1C

440

00

July 3

a

180

25

Feb. 1

tt

100

00

Aug. 13

tt

500

00

Feb. 15

ft

980

00

20 "

340

40

30

80

00

Ans. 808 days back of Jan. 28, 1859.

Note. — In finding the equated time, when the cents are less
than 50 reject them ; when more, add $1. The work will be
sufficiently accurate.

8. When will the balance of the following account com-
mence drawing interest, allowing that each item was due from
date ? What will balance the account Oct. 1 ?

Dr.

A in account with B.

Cr.

1858.

July 10
" 30

Aug. 30
Sept. 9
" 30

To Mdse.
u

a
tt
tt

§120
450
380
560
400

00
00
00
00

oo ;

1858. |

Aug. 20 By Cash.
Sept. 25 ! " Mdse.
Oct. 3 " Cash.

1

$350
250
950

00
00
00

Ans. to first, Dec. 12.

Remark. — Since the balance of the above account com-
mences to draw interest at the equated time of the account, it
is evident that the cash value of this balance, at any date sub-
sequent to the equated time of the account, may be found
by adding to the balance its interest up to date; and at any
date previous to the equated time, by deducting from the bal-
ance its interest for the intervening time. By mercantile cus-
tom interest is deducted (as in the last case) instead of finding
the true present worthy when money is paid before it is due.

9. When will the balance of the following account com-
mence drawing interest ? What will be the cash value of the
balance, Jan. 1, 1859 ? Credit of 90 days on merchandise
items.

224

CASH BALANCE.

Dr.

B in account with C.

Or.

1858.

\

1858.

Aug. 18

To Mdse. $ 50| 00

Oct. 7 By Cash.

$200

00

Sept. 15

a

140 00

" 30

a

100

00

" 30

"

80 00

Dec. 1

n

400

00

Oct. 8

tt

200 00

Nov. 1

a

350 00

u

CASH BALANCE.

ART. 146. When an account current is settled by cash, it
is not necessary to find the equated time as in the preceding
article. The true or cash balance of an account at a particu-
lar date may be found directly as follows :

Ex. 1.
Dr. Dr. Murray & Co. in account with Jones & Sons. Or.

1859.

1859.

April 10

To Mdse.

§150

April 12

By Cash.

$250

" 30

a

400

May 1

a

180

May 16

it

90

June 7

a

400

'• 24

a

100

" 25

tt

564

June 1

a

300

" 10

a

340

" 26

it

200

What will be the true balance of the above account July
1, 1859, the time of settlement, allowing that each item draws
interest from its date, at 6 per cent. ?

Operation.
Debits.

.Lme, Days.

April 10, $150x82= 12300

30,
May 16,
" 24,
June 1,
" 10,
" 26,

62= 24800
90x46= 4140
100x38= 3800
300x30= 9000
340x21= 7140
200 x 5= 1000

§1580

6)62180
$ia364

Due,

Credits.

April 12, $250x80=20000

May 1, 180x61= 10980

June 7, 400x24= 9600

" 25, 564 x 6= 3384

$1394

6)43964
"7.327

CASH BALANCE. 225

Sum of debit items, $1580

" credit " 1394

Balance of items, $186

Int. of debit items, $10.364

" credit " 7.327

Balance of interest, $3.037

True balance, July 1, $186 + $3.04= §189.04.

Explanation — Since each item of the debit side of the ac-
count was on interest from its date to the time of settlement,
the total interest of the several debit items equals the interest
of $1 for 62180 days, which is $10.364. (The interest of $1 for
6 days is 1 mill ; hence, the interest of $1 for 62180 days is
found by dividing 62180 by 6, and pointing off three decimal
places.) The total interest of the several credit items equals
the interest of $1 for 43964 days, which is §7.327. Now, in-
stead of increasing each side of the account by its interest, and
then finding the balance, this same result may be obtained by
finding separately the balance of items and the balance of in-
terests. If the two balances fall on the same side of the ac-
count, it is evident the true balance will be their sum ; if on
different sides, their difference.

METHOD BY INTEREST.

Due, Davs. Int.

April 10, $150 for 82=f2.05

" 30, 400 for 62= 4.133
Mav 16, 90 for 46= .69
• " 24, 100 for 38= .634
June 1, 300 for 30= 1.50
" 10, 340 for 21= 1.19
" 26, 200 for 5= .17

Due, Days. Int

April 12, $250 for 80= $3.333
May 1, 180 for 61= 1.83
June 7, 400 for 24= 1.60
• " 25, 564 for 6= .564

$1394 $7.327

$1580 $10.367

Balance of items =$1580 -$1394 =$186.

" of interest=$10.367— $7.327= $3.04.
True balance, . =$186 +$3.04 =$189.04

Note. — The "method by interest'' will generally be found most convenient
either for finding the equated time for the payment of the balance of accounts, or
in finding the cash balance.

The above account, when balanced by interest, may be

presented as follows :

15

226

CASH BALANCE.

Dr. Murray & Co. in account with Jones & Sons. Cr.

1589. ,
April 10
" 30
May 16:
" 24
June 1
'• 10
26
]

To Mdse.

July

bal. by int.

Am't. Da

$150.0082

400.00 62

90.0046

100.0038

300.0030

340.0021

20000 5

3.04

$1583.04

Int
$2.05

4.133
.69
.634

1.50

1.19
.17

$10367

1853.

April 12 By Cash.

July

$250.00 U*.
180.00 80
400.00,6'-
564.0024

* 189.04 6

$3.333
1.83
1.60
.564

$7.327

$1583.04

Errors excepted. Portsmouth, July 1, 1859. Jones & Sou.

RULE.

Multiply each item of the account by the number of days
intervening betiveen the date on ivhicli it becomes due and the
time of settlement. Divide the sums of the debit and credit
products respectively by 6 : the quotient will be the interest of
the two sides of the account, at 6 per cent., expressed in MILLS.
Find the balance of items and also the balance of interests.

When the two balances fall on the SAME side of the account,
the cash balance will be their SUM ; when on opposite sides,
their DIFFERENCE.

Or,

Find the interest of each item from the date on ivhich it
becomes due to the time of settlement The difference between
the sums of interests on the debit and credit sides of the ac-
count ivill be the BALANCE OF INTEREST.

When the balance of interest falls on the same side as the
balance of items, the cash balance will be their SUM ; lohen on
opposite sides, their DIFFERENCE.

2. The following account was settled July 1, 1857. What
was the cash balance, interest being computed on each item
from date at *l% ?

Dr. James Kehoe in account with J. Smith. Cr.

1857. |

lint, or
Ds' prods.

1S5S.

Ds.

Int. or
prod&

Jan. 7 To bal. of acc't.

$120.00

April 1

By cash.

$140.00

" 15

' mdse.

96.75

" 30

u a

50.00

" 24

' bills payable

130.50

May 20 " order on T.S.

140.00

Feb. 27

' mdse.

200.80

" 31

" cash.

450.00

March 7

< <t

80.00

June 11

" Mdso. 500.00

May 10

« ii

300.00

June 9

u «

240.75

Ans.

ACCOUNT OF SALES.

227

3. What was due on the following account, Jan. 1, 1858,
interest 6 per cent., and a credit of 90 days being allowed on
each merchandise item ?

Dr. John Scott in account with Geo. Fields. Cr.

1557.

Days.

lot or

products.

1857 j j^'ys- Int-or
product

July 3ToMdse.$104

85

Aug. 12 By Mdse. $300 00

" 16 "

340

60

" 25

j. n

11680

" 31
Sept. 13; "

G7
236

80

Sept. 15
Oct. 13

II <(

" Cash.

33975
5000

« 20

9038

Xov. 1

u K

14875

*

" 27

6084

Oct. l| "

36040

Ans. $307.492.

4. What would have been the true balance of the above
account Jan. 1, 1858, at 7 per cent., no credit being allowed
on merchandise items ? Ans. §316.563.

ACCOUNT OF SALES.

ART. 147. An account of sales is a statement of the quan-
tity and price of goods sold, the charges incurred in the sales,
and the net proceeds, which a commission merchant or con-
signee makes to his employer or consignor.

The net proceeds is the . sum to which the employer is en-
titled after all charges are deducted. The net proceeds are
due as cash at the equated time of the different sales.

The following examples will give a fuller idea of an ac-
count of sales.

1. Account of sales of grain for Fisk, Cook & Co.

Data

Purchaser.

Description.

Bush. Price.

$

1858.

Jan. 30 M. B. Gilbert/Wheat,

white.

250 § .95

237.50

Feb. 3 Crest & Fisk. Wheat,

med.

1000 .88

880.00

" 16 Wheeler&Co. Corn.

'2000 .55

1100.00

" 28 C. A. Davis. Oats.

1500 .371

562.50

March 20 T. C. Skinner. Wheat,

Kv. white.

750 1.00"

750,00

April 9 Talcott & Co. Wheat,

red.

1450 .85

1232.50

" 28 J.B.Howard. Corn.

1300 .58

754.00

May 7T. Bentoa

1C

450 .60

270.00

" 30 F. Hart.

Wheat,

med.

9551 .90

859.50

1 §6646.00

228

CASH BALANCE.

Charges.

Commission 2| per cent, on $6646, $166.15

May 30— Freight on 955 bushels wheat, . 47.75

Drayage and sacks, . . . 51.00

Advertising in " Tribune/' . 7.50

, V . $272.40
Net proceeds to credit of F. C. & Co., $6373.60

Errors excepted.
New* York, June 1, 1858. SMITH & JONES.

2. Sales 544 barrels flour, for account of P. Rhodes & Son,
Navarre, 0., by Bryant & Stratton, Cleveland, 0.

1858.

S «?'S •

2 2 • g ,OT

o * £§
SHps

0

a
£

July 2

a tt

" 5

June 15

P. Anderson.

it

Morgan & Co.

Charges :
Trans. Boat
" Kent."
Less am't de
on boat.

Storage.
Insurance.
Commission

Proceeds to

400

125

19

=544bls.
damage

cash, Jul

§30

505

750

3,320
95
937

50

4,352

50

05

45

400125 19

400
due

on
ere

125

ted

43

dit

i

19

for

5250
as

16

3

*\%

y 10

8704

10
7704
1632
1088
10881

213
4,139

1858.
1

4,35250

Cleveland, 0.,
July 12, 1858.

(Signed) BRYANT & STEATTON.

3. What will be due P. Rhodes & Son on the above ac-
count January 1, 1859 ?

CASH BALANCE.

229

4. Sales, 100 barrels linseed oil, for account of Robert
Miller, Warren, 0., by Bryant & Stratton, Cleveland, 0.

1855.

Bis.

Gala.

May 14

a it

" 15

" 18

" 13

Cash.
Gaylord & Co.

Cash.
it

Charges :
Tr., Boat Cuyahoga.
Storage.
Fire Insurance.
Cooperage.
Com. on 365S28

Net proceeds due as

10
30
5
55

403
1,200
201i
2,200"

95
92
95
90

37s

8$

M*

z&

18,

38285
l,104j
19143
1,980!

3,658

148
3,5~09

28

60
68

100
100

cas

4,0041
h May

37

8
9
2
91

50

14

50
46

1855.

Cleveland, 0., (Signed) BRYANT & STRATTOX.

May 24, 1855.

5. Sales of provisions for account of M. Fisher & Co.,
Cincinnati, 0., by James & Co., St. Paul, Min.

1353.

Boxs
&
kegs

Bis.

Pieces.

Pounds.

•

Feb. 7

"Wheeler & Co.

29

Sams, plain.

1450

8£

" 22

M

42

" sugar cured.

2300

10i*

Mar. 6

U

18

Shoulders, plain.

846

7^

" 15 Altrara & Co.

|25

Mess pork, Xo. 2.

IP

Apr. 3 E. Miller.

15

i

Kegs butter. "W. R.

840

w

a a

ISO

[Cheese.

4200

6^

" 10 Wheeler & Co.

150 Bacon sides.

2432

7ic

May 2 Altram & Co.

15

Mess pork, Xo. 2.

16*

" 5.G-eo. Singer.

37 Shoulders (city).

2512

7ff

I

0.3

40

2761

14.580

Charges.

Feb. 1— Freight of 13,040, at 70$. per 100.
April 2^ " 5,040, " 68c. "

Storage, ff». Cooperage, 3-°r=SSO.
Fire Insurance, at ±% on §.
Commissions, " 2|^ " §.

Net proceeds as cash, due

St. Paul's, Minnesota, JANES & Co.

May 15, 1858.

230 ANNUITIES..

ANNUITIES.

ART. 148. An Annuity (L. annus, a year) is a fixed sum
of money payable annually, or at the end of equal periods of
time, to continue for a given number of years, for life, or for-
ever.

A certain Annuity, or an Annuity certain, is one that is
payable for a definite length of time.

A contingent Annuity is one that is payable for an uncer-
tain length of time ; as during the life of one or more persons.

A perpetual Annuity, or an Annuity in perpetuity, is one
that continues forever.

A deferred Annuity, or an Annuity in reversion (whether
certain, contingent, or perpetual) is one that begins at a future
time ; as at the death of a certain person.

An immediate Annuity, or an Annuity in possession, is one
that begins at once.

An Annuity forborne, or in arrears, is one whose pay-
ments have not been made when due.

The amount, or final value, of an annuity is the sum of
the amounts of all its payments, at compound interest, from
the time each is due, to the end of the annuity.

The present value of an annuity, at compound interest, is
the sum of the present values of all its payments ; or the pres-
ent worth of its final value. The present value, put out at
compound interest, will amount, at the time of the expiration
of the annuity, to its final value.

The subject of annuities is one of great practical import-
ance in the affairs of life. Its principal applications are leases,
life-estates, rents, dowers, reversions, life-insurance, etc. The
problems are readily solved by means of tables. which give the
present and final values of $1 for a given number of years at
the ordinary rates of interest. A complete discussion of the >
principles upon which these tables are computed would require
too much space.

ANNUITIES.

231

ART. 149. A TABLE,

Showing the present value, and also the amount, or final value,
of an annuity of $1, for any number of years not exceeding
fifty :

Present value of an Annuity of $1.

Final value of an Annuity of $1.

«? 4 per cent.

*

| !
5 per cent. 6 per cent 7 per cent

1

4 per cent

5 per cent.

6 per cent.

7 per cent.

1 0.961 533

0.952 331

0.943 39G

0.934 579

1

1 1.000 000

1.000 000

1.000 000

1.000 000

2 1.S36 095

1 1.S59 410

! 1.833 893

1.803 017

2

2.040 000

2.050 000

2 060 000

2.070 000

0 2.775 091

i 2.723 248

2.673 012

2.624 314

3

8.121 600

8.152 500 3.183 5-iO

3.214 900

1 4l &629 895

3.545 951

8.465 10G 3.387 207

4

4.246 464

4.310 125 4.374 616

4.439 943

5 4.451 822

4.329 477

4212 364

: 4.100 195

5

5.416 323

5.525 631

5.G37 093

5.750 739

6 5.242 137

5.075 692

4.917 824

4.766 537

G

6.632 975

6.801 913

6.975 319

7.153 291

7 6.602 055

5.736 373

5.5S2 381

5.339 286

7

7.893 294

8.142 003

8.393 833

8.654 021

8 6.732 745

6.463 213

6.209 744

5971 295

S

9.214 226

9.549 109

9.897 468

10.259 803

9 7.435 33-2

7.107 822

6.301 692

6.515 223 9

10.582 795

11.020 564

11.491 316

11.977 989

10 8.110 893

7.721 735

7.360 087

7.023 577

10

12.006 1C7

12.577 803

13.180 795

13.816 448

11 8.760 477

8.306 414

7.886 875

7.498 669

11

13.483 851

14.206 737

14.971 64=3

15.783 599

12 91385 074

8.863 252

8.383 844

7.942 671

12

15.025 805

15.917 127

16.869 941

17.888 451

13 9.935 613

9.393 573

8.852 683

8.357 635

Ifl

16.626 808

17.712 933

13.S82 138

20.140 643

14 li'.~>63 12-3

9 893 641 1 9.294 984

8.745 452 14

18.291 911

10.593 632

21.015 066

22.550 483

15 11.113 357 10.379 60S

0.712 249

9.107 898

15

20.023 5SS

21.573 564

23.275 970

25.129 022

16 11.652 296:10.837 770*10.105 895

9.446 632

16

21.824 5S1

23.657 492

25.670 528

27.888 054

17 12.105 G69

11.274 066

10.477 260

9.763 206

17

23.697 512 ! 25.840 366 28.212 830

30.840 217

IS 12.659 297

11.6*9 537

10.327 603 10.059 070' 18

25.645 413! 28.132 335 30 905 653

33.999 033

1!) 13.103 039

12.0S5 321

11.153 116

10.335 578

10

27.671 229

80.539 004

33.759 992

37.378 965

20 13.590 826

12.4C2 210 11.469 421

10.593 997

20

29.778 079

33.065 954

36.785 591

40.995 492

21 14.029 16)

12.821 153 11.764 077 10.835 527

21

31.969 202

35.719 252

39.992 727 i 44.865 177

22 14.451 115

13.163 Ot.3

12.041 532

11.061 24!

•22

34.247 970

38.505 214

43.392 200

49.005 739

23 14.856 842

13.433 514 12.303 379 11.272 187

23

36.617 839

41.430 475

46.995 823

53.436 141

•24 -15246 963
25 15.622 030

13.798 642 12.550 3." 8 11.469 8:34
14.093 945 12.783 856 11.653 5S3

24 39.1182 604
25| 41.645 908

44.501 909
47.727 099

50 815 577
54.864 512

5^.176 671
63.249 030

26 15.982 7G9

14.275 1S5

13.003 166

11.825 779

•26

44.311 745

51.113 454

59.156 383

63.676 470

27 16329 586 14.643 034

13.210 534 11.986 709

27

47.084 214

54.6J6 126

G0.7r.-> 76 i

74.483 823

28 16.653 063

14.893 127

13.406 164

12.137 111

23

49.967 583

53.402 533

68.528 112

80.697 691

29 16.933 715

15.141 074

13 590 721

12.277 674

•20

52.966 236

62.322 712

73.630 793

87.346 529

30 17.292 033

15.372 451

13.764 831

12.409 041

80

56.084 9:38

66.403 843

79 058 136

84.460 786

31 17.533 494

15592 811

13.929 086

12.531 814

•31

59.328 335

70.76D 790

84.801 677

102.073 041

32 17.873 552

15.302 66V

14.034 040 12.646 555

02

62.701 469

75.293 829

90.839 77.5

110.218 154

33 18.147 646

16.002 549

14.230 200

12.753 790

88

66.209 527

80.168 771

97.343 105

118.933 425

34 13.411 108

16.192 204

14.368 141

12.854 0;;9

04

69.857 909

85.066 950 104.183 "55

128.258 765

35 13.664 613^6.374 194 14.493 246

12.947 672

05

73.652 225

90.320 307 111.434 780 1G8.236 878

36 13.908 232

16.545 852

14620 987

13.C35 208

86

77.598814 95. S3G 323 119.120 867

148.913 460

37 19.142 579

167il 2>7

14.736 780

13.117 017

37

81.702 24GI101.623 109 127.263 119

1C0.337 400 :

3S 19367 864

16.S67 t93

14846 019

13.193 473

OS

85.970 336:K'7.709 646185.904 206

172.561 020

39 19.534 48i

17.017 041

14.949 075

13.264 928

89

90.4U9 150 114.095 0'23 145.058 45:.

135.640 292

4C 19.7U2 774

17.159 CS6 15.046 207

13.331 709

40

95.025 51C, 120.709 774 154.701 966 199.635 112

|

41 19993 052

17.294 363 15.133 016 13.394 120

41

90.826 536 127.839 763 165.047 CSi

214.609 570

42 ifl.lSS 627

17423 203

15.224 543

13.4:2 440

42

104. SI 9 593 155.201 751 175.950 645

230.632 24ti

43 -'0.370 795

17.545 912

15.306 173

13506 962

4:;

110.012 382 142.993 3391187.507 577

247.776 406

44 2)543 841

17.662 773

15.883 1-2

13.557 90S

44

115.412 877 151.143 006 109.753 <>02

266.120 851

45 20.72J 04) 17.774 070 15.455 832 13.605 522

45|l21.029 392 159.7uO 156 212.743 51-! 285.749 311

j

46 20 8?4 654

17.880 C67 15.524 870 13.650 020

46 126.870 563 163 685 164 226.508 125 S06.751 763

47.21.043 906

17.931 016

15.689 028

13.691 60S

47

132.945 890 173.119 422 241.098 612

829.224 386

4321 10.3 131

18.077 153

15.650 027

13.730 474

48

139.263 206 183.025 893 '256564 529

a53.270 093

4921.341 472

IS. 163 72215.707 572

13.766 799

49 145.833 734 193.426 6fi3 272.953 401 378.999 OOf

5021432 135

18.255 925 15.761 861

13.800 746

50 152.667 034 209.347 976 290.335 9.)5 406.523 929

232 ANNUITIES.

ART. 150. To find the amount, or final value, of an annuity
certain, at compound interest, in arrears, or forborne.

Ex. 1. Suppose a rental of $500 a year to remain unpaid 8
years ; what is the amount due, at 5 per cent, compound in-
terest ? Ans. $47745.545.

Operation.
$9.549109, amount of $1 for 8 years. (See Table).

500
$47.745.545 ; " $500 <

RULE. — Multiply the amount, or final value, of an annuity
of $1, for the given rate and time, by the given annuity.

Note. — When the annuity draws simple interest, the
amount is found as in annual interest.

Ex. 2. Find the final value of an annuity of §150, running
12 years at 4 per cent, compound interest.

Ans. $2253.87+.

Ex. 3. An annuity of $200 has been in arrears 15 years ;
what is the amount due, at 6 per cent, compound interest ?

Ans. $4655.194.

ART. 151. To find the present value of an annuity certain.

Ex. 1. What is the present value of an annuity of $120,
to continue 25 years, at 6 per cent. ? Ans. $1534.

Operation.

$12.783356, present value of $1. (See Table.)

120

$1534.002720 " §120.

EULE. — Multiply the present value of $1, as an annuity
for the given rate and time, ly the given annuity.

Note. — Since the present value of an annuity is the present
worth of its amount, or final value, the present value of an
annuity may also be found by first finding the amount, and
then the present worth of this amount.

Ex. 2. What is the present value of an annuity of §650, to
continue 15 years, at 5 per cent. ? Ans. $6746.7777.

ANNUITIES. 233

Ex. 3. What is the present worth of a leasehold of $1200,
payable annually for 50 years, at 6 per cent. ?

Ans. $18914.23.

Ex. 4. A widow is entitled to $140 a year, payable semi-
annua]Jy, for 18 years ; what is the present value of her inte-
rest, at 10 per cent compound interest ? Ans. $1158.80.

Ex. 5. I wish to purchase an annuity which shall secure to
my ward, at 4 per cent, compound interest, $250 a year for
14 years. What must I deposit in the annuity office ?

. Ans. $2640.78.

ART. 152. To find the present value of a perpetuity.

Ex. 1. What is the present value of a perpetual leasehold
of $1200 a year, at 5 per cent. ? Ans. $24000.

Operation.
$1200.00-^.05=:$24000, present value.

Explanation. — The present value must evidently be a prin-
cipal which yields an annual interest of $1200, at 5 per cent.

KULE. — Divide the given annuity l>y the interest of $l,/or
one year.

Ex. 2. What is the present value of the perpetual lease
of $4800 a year, at 8 per cent, interest ? Ans. $60000.

Ex. 3. What is the present value of a perpetual leasehold
of $1600 a year, payable semi-annually, at 6 per cent, interest
per annum ? Ans. $27066|.

Suggestion. — When an annuity is payable semi-annually,
or quarterly, interest must be allowed on the half-yearLy or
quarterly payments to the close of the year. The annuity in
the last example is $1624.

Ex. 4. The ground rent of an estate yields an annual in-
come of §2400, payable quarterly, at 4 per cent, per annum.
What is the value of the estate ? Ans. $60900.

ART. 153. To find the present value of a certain annuity
in reversion.

Ex. 1. What is the present value of an annuity of $250,
deferred 12 years and to continue 10 years, allowing 6 per
cent, compound interest ? Ans. $914.43+.

234 ANNUITIES.

Operation.

$12.041582— present worth of $1 for 22 yrs.
_8.383844 " 12 yrs.

"$37657738 " " 10 yrs. deferred 12 yrs.

250

$914.434500 " $250 " "

Explanation. — The present worth of an annuity of $1 for
22 years must be equal to its present worth for 12 years, plus
its present worth for the 10 succeeding years. Hence the pres-
ent worth of an annuity of $ 1 for 10 years deferred 12 years
must equal its present worth for 22 years, minus its present
worth for 12 years. The present worth of $250 is evidently
250 times the present worth of $1.

EULE, — Find from tlie table the present value of an annu-
ity of $1, commencing at once and continuing till the TEKMI-
NATION of the annuity, and also till the reversion COMMENCES.
Multiply the differences of these present values ~by the given
annuity.

Note. — If the annuity is perpetual, the present worth of
$1, commencing at once, is found according to the last article.

Ex. 2. What is the present value of a leasehold of $1800,
deferred 10 years and to run 20 years, at 5 per cent, compound
interest ? Ans. $13771.2888.

Ex. 3. A lease, whose rental is $1000 a year, is left to two
sons. The elder is to receive the rent for 9 years and the
youngest for the 12. years succeeding. What is the present
value of each son's interest, allowing 6 per cent, compound in-
terest ? Ans. to last, $4962.385.

Ex. 4. What is the present value of a perpetuity of $900,
to commence in 30 years, allowing 4 per cent, compound inte-
rest ? Ans. $6937.17.

ART. 154. To find the annuity, the present or final value,
time and rate being given.

Ex. 1. An annuity running 20 years, at 7 per cent, com-
pound interest, is worth $15,000 ; what is the annuity ?

Ans. $1415.89.

.ANNUITIES. 235

Operation.
$•15000 -^- $10.593997 = 1415.89.

Explanation. — Since §10.593997, at 7 per cent, compound
interest for 20 years, yields an annuity of $1, $15000 will
yield an annuity equal to $15000-^10.593997.

RULE. — Divide the present or final value of the given annu-
ity by the present or final value of an annuity of $1, for the
given rate and time.

Ex. 2. An annuity in arrears for 8 years, at 5 per cent,
compound interest, amounts to $47745.545 ; what, is the an-
nuity ? Ans. $500.

Ex. 3. A yearly pension, unpaid for 12 years, at 6 per
cent, compound interest, amounted to §1591.7127 ; what was
the pension ? Ans. $100.

Ex. 4. The present value of a lease, running 25 years, at 6
per cent, compound interest, is $15340.037 ; what is the an-
nual income ? Ans. §1200.

CONTINGENT ANNUITIES.

ART. 155. When the annuity is to cease with the life of a
certain person or persons, it becomes necessary to ascertain the
probability of the person or persons, upon the continuance of
whose life the annuity depends, surviving a given period. The
measure of this probability is called Expectation of Life, and
has already been noticed under Life Insurance.

In computing contingent annuities, the expectation of life
of the person or persons named, as shown in Bills of Mortality,
is taken as the time of the annuity. It can then be computed
as an annuity certain.

A table, showing the present value of an annuity of $1, to
continue during the life of an individual, is called a Table of
Life Annuities.

ART. 158. To find the present value of a life annuity.

ANNUITIES.

Ex. 1. What is the present value of a life pension of $150,
the age of the pensionary being 75 years ; interest, 5 per cent. ?

Ans. 8748.35.

Ans. $748.35.
Operation.

$4.989 — value of annuity of
150

$748.350 $150.

KULE. — Multiply the present value of a life annuity o/"$l,
as shown in the table, by the given annuity.

Ex. 2. Suppose a person 60 years of age is to receive an
annual salary of $600 during life. What is the present value
of such income, at 6 per cent.; compound interest ?

Ans. $4982.40.

Ex. 3. What must be paid for a life annuity of $560 a
year, by a person aged 55 years, at 5 per cent., compound in-
terest ? Ans. $5794.32.

ART. 157. To find how large a life annuity can be bought
for a given sum, by a person of a given age.

Ex. 1. How large a life annuity can be purchased for $2400,
by a person aged $65 years, at 7 per cent. Ans. $350.51.

Operation.

2400.000 ^ 6.847 = 350.51.

RULE. — Divide the given sum by the present value of an
annuity of $1 for the given age and rate.

Note. — This is the reverse of the preceding article.

Ex. 2. How large a pension, at 6 per cent., compound in-
terest, can be bought for $1600, the age of the pensionary
being 50 years ?

Ex. 3. How large an annuity can be bought for $3000, by
a person aged 25 ; interest, 5 per cent. ? Ans. 190.15.

ALLIGATION. 237

ALLIGATION.

ART. 158. In various kinds of business, it is sometimes
convenient or necessary to mix articles of different values or
qualities, thus forming a compound whose value or quality
differs from that of its ingredients. This process is called
ALLIGATION (L. ad, to, and ligatus, bound); a name sug-
gested by the method of solving some of its problems by join-
ing or binding together the terms.

The various problems in Alligation may be divided into
two classes, commonly called Alligation Medial and Alliga-
tion Alternate.

ALLIG-ATION MEDIAL.

ART. 169. Alligation Medial teaches the method of find-
ing the average value or quality of a mixture, the value or
quality, and also the quantity, of whose ingredients are known.
Ex. 1. A farmer mixed together 50 bushels of oats, at 40
cents per bushel ; 30 bushels of barley, at 50 cents per bushel ;
and 25 bushels of corn, at 60 cents per bushel. What was a
bushel of the mixture worth ?

Explanation. — Since the value of 50

OPERATION. bushels of oats, at 40 cents a bushel, is

cts. CK 2000 cents ; of 30 bushels of barley, at

50 cents a bushel, 1500 cents ; and 25
50x30=1500 ITT

60x95=1500 bushels of corn, at 60 cents a bushel,

105 )5000 1500 cents ; the value of the mixture is

—477| 2000 cents+1500 cents + 1500 cents=

5000 cents. But the mixture contains

50 bushels + 30 bushels +25 bushels =105 bushels. Hence, the
value of 1 bushel of the mixture is Tij of 5000 cents=47i£
cents.

Ex. 2. A goldsmith melted together 12 oz. of gold, 20

238 ALLIGATION.

carats fine ; 6 oz.} 18 carats fine ; and 10 oz., 16 carats fine.
What was the quality of the mixture ? Ans. 18| carats.

Explanation. — Since a carat of gold

OPERATION. is the twenty-fourth part of the mass

carats. Carats. regarded as a unit (here an oz.), 12

7o X g II -IQO oz. of gold, each oz. containing 20 carats

16 x 10 = 160 of pure gold, contain 12 times 20 carats

28 )508~ =240 carats ; 6 oz. of gold, each con-

~~18"i taining 18 carats, contain 108 carats ;

10 oz. of gold, each containing 16 carats,

contain 160 carats. Hence, 12 oz. + 6 oz.-f-lO oz.=28 oz. of
mixture contain 240 carats + 108 carats + 160 carats =508
carats, and 1 oz. of the mixture must, therefore, contain •£-§ of
508 carats=18| carats.

Note. — The regarding of a carat as a unit of measure of the
pure gold in a given mass is not essential to the explanation
of the above solution. For, suppose the comparative qualities
of the above varieties of gold, represented respectively by the
numbers 20, 18, and 16. Now, as these numbers represent
the comparative qualities of the three varieties of gold, it is
clear they must contain a common unit of quality. The num-
ber 20 denotes that the quality of the first variety contains
this common union of quality 20 times ; and, hence, 20 is the
measure of its quality. But the effect of 12 oz. in determining
the quality of a mixture is 12 times as great as the effect of
1 oz. ; hence, 12 x 20 or 240, is the effective quality of 12 oz.
of gold, if the quality of 1 oz. is 20.

RTJ3L.E.

Multiply the value or quality of each article by the number
of articles , and divide the sum of the products by the sum of
the articles. TJie quotient will be the average value or quality
of the mixture.

Ex. 3. A grocer mixed 15 Ibs. of coffee, at 18 cents a
pound ; 35 Ibs., at 16 cents a pound ; and 40 Ibs., at 14 cents a
pound. What is a pound of the mixture worth ? Ans. 15£ cents.

,Ex. 4. A grocer mixed 25 gallons of wine, at 90 cents a

ALLIGATION. 239

gallon ; 40 gallons of brandy, at 75 cents a gallon ; and 10
gallons of water without price. "What is a gallon of the mix-
ture worth ? Ans. 70 cents.

ALLIGATION ALTERNATE.

ART. 160. Alligation Alternate teaches the method of
finding in what proportion several simple ingredients, whose
values or qualities are known, must be taken to form a mix-
ture of a given mean value or quality.

Sometimes the quantity of one or more of the ingredients
is given, and it is required to find what amount of the other
ingredients must be taken.

Sometimes the quantity of the mixture is given, and the
relative amount of ingredients is required.

We shall give the solution of examples involving the last
two conditions, but omit special rules.

Ex. 1. A grocer has coffees worth 10 and 15 cents a pound.
In what proportion must they be taken that the mixture may
be sold for 13 cents a pound ?

Solution. — By selling the mixture for 13 cents a pound, he
will gain 3 cents on each pound of the coffee worth 10 cents,
and will lose 2 cents on each pound of the coffee worth 15
cents. Hence, to counterbalance the gain of 3 cents on 1
pound of the first kind, he must use l£ (3n-2) pounds of the
second kind. The proportion, therefore, must be 1 lb., worth
10 cents, to li Ibs., worth 15 cents.

Ex. 2. A grocer has sugars worth 7, 10, and 12 cents a
pound. In what proportion must they be taken to make a
mixture worth 9 cents a pound ?

Solution. — On each pound of sugar worth 7 cents there is
a gain of 2 cents, and on each pound of sugar worth 10 cents
there is a loss of 1 cent. He must, therefore, take 2 pounds of
the second that the loss may counterbalance the gain on 1 pound
of the first. On each pound of sugar worth 12 cents there is
a loss of 3 cents. To counterbalance this loss 1| (3-=-2) pounds

940 ALLIGATION.

more of the first kind must be taken. Hence, the proportion
is 1 + 1^—21 Ibs. worth 7 cents, to 2 Ibs. worth 10 cents, to 1
Ib. worth 12 cents.

Ex. 3. A grocer has four kinds of tea, worth respectively
50, 60, 70, and 90 cents a pound. In what proportion must
they be taken to make a mixture worth 80 cents a pound ?

Solution. — On a pound of the first kind there is a gain of
30 cents ; on a pound of the second, a gain of 20 cents ; on a
pound of the third, a gain of 10 cents ; and, hence, on a pound
of each of these three kinds a gain of 30+20+10—60 cents.
On 1 pound of the fourth kind there is a loss of 10 cents ; and,
hence, to counterbalance the 60 cents gain, 6 pounds of the
fourth kind must be taken. The proportion is, therefore, 1
Ib. of the first kind, to 1 Ib. of the second, to 1 Ib. of the third,
to 6 pounds of the fourth or multiples of these numbers.

Ex. 4. A farmer has oats worth 40 cents a bushel ; corn,
worth 50 cents ; rye, worth 70 cents ; and wheat, worth .90
cents. How must they be mixed that the mixture may be
worth 60 cents ?

Solution. — On each bushel of oats there is a gain of 20
cents ; on each bushel of wheat a loss, of 30 cents. Hence, he
must take \\ bushel of oats to 1 bushel of wheat. On each
bushel of corn there is a gain of 10 cents ; on each bushel of
rye, a loss of 10 cents. Hence, he must take 1 bushel of corn
to 1 of rye. Proportion, li, 1, 1, 1.

Note. — In the above solutions, it will be observed that the
ingredients are combined, two and two, in such quantities as
to make gains and losses EQUAL.

METHOD BY. LINKING.

3d Example above.

80

50x - - 10
60 \\ - - 10

70 0; - - 10

Ans., or Ans. Verifications.

4-10=

90' 30 + 20 + 10=60

10x50= 500 1x50= 50

10x60= 600 1x60= 60

10x70= 700 1x70= 70

60x90=5400 6x90=540

90 )7200 9 )720

~80" ~80~

'40
50

ALLIGATION. 241

4th Example.

Ans., or Ans. Verifications.

3 30x40=1200 3x40=120

1 10x50= 500 1x50= 50

1 10x70= 700 1x70= 70

2 120x90=1800 2x90=180
70 )420Q 7 )420

60 60

Or thus :

or Ans. Verifications.

10x40= 400 1x40= 40

30 x 50= 1500 3 x 50= 150

607(X) - - 20f~1~10 |2 J20x70=1400 2x70=140

|10 x 90= 900 1x90= 90

70 )4200 7 )42Q

60 60

RULE.

Write the values or qualities of the ingredients in a column,
and the value or quality of the mixture at the left hand. Link
each number in the column that is LESS than the value or qual-
ity of the mixture icith one that is GREATER, or the reverse.

Then find the difference between the value or quality of the
mixture and that of each ingredient, and place the same oppo-
site the number with which it is connected. The number, or
the sum of the numbers, opposite the value, or quality of each
ingredient, ivill denote the amount of the same to be taken.

Remark. — Since equi-multiples of quantities have the same
relation to each other as the quantities themselves, it follows
that any equi-multiples of these numbers will also satisfy the
conditions of the problem.

Ex. 5. A merchant has teas worth 60, 75, 80, and 100 cents
per Ib. How much of each kind must he take to make a mix-
ture worth 85 cents per Ib. ? " Ans. 1, 1, 1, 2.

Ex. 6. A wine-merchant wishes to mix wine worth $1.20
and $1.40 per gallon, with water. How much of each kind
must he use to make a mixture worth $1.00 per gallon ?

Ex. 7. A goldsmith wishes to combine gold 22 carats fine ;

19 carats fine ; 18 carats fine ; and 17 carats fine. In what

16

242

ALLIGATION.

proportion must they be united that the compound may be 20
carats fine ?

Ex. 8. A farmer wishes to mix 60 bushels of corn, at 60
cents a bushel, with rye, at 75 cents.; barley, at 50 cents ; and
oats at 45 cents. What quantity of rye, barley, and oats
must be taken that the mixture may be worth 65 cents a
bushel ?

Explanation. — Since
the amount of corn to
be taken is 6 times
the amount found — 10

[240

65

OPERATION.
45N - 10")

50\\ - - 10

eoO; - 10

75' 20+15 + 5=40

bushels — the quantity
of oats, barley, and
rye, must be increased in the same ration : i. e., be multi-
plied by 6.

Ex. 8. A grocer wishes to mix 100 pounds of coffee, worth
12 cents, with coffee worth 15, 10, and 8 cents. What quan-
tities must he take that the mixture may be worth 11 cents a
pound ?

10. A wine-merchant wishes to fill a cask containing 36
gallons with a mixture of wines worth $1.00, $1.20, $1.50,
and $1.60 per gallon. How many gallons of each kind must
he take that the mixture may be worth $1.40 per gallon ?

Operation.

Or thus

8

201

21

4

8

10 1

20 1

•M0=| >

16

40 I

4J

9

36^9=4

Ans.

8
4
8

I6
36

Explanation. — Since, in the first case, the amount required
— 36 gallons — is f of the amount obtained by mixing 20 gal-
lons of the first kind, 10 gallons of the second, 20 .gallons
of the third, and 40 of the fourth, it is evident that f of the
quantity of each ingredient must be taken. In the second
case, the amount required is 4 times the amount obtained ;

PARTNERSHIP. 243

and, hence, the quantity of each ingredient must be multi-
plied by 4.

Ex. 11. A trader wishes to fill 10 casks, each containing 28
gallons, with a mixture- of brandy, rum, and water. If the
brandy is worth 80 cents a gallon, and the rum 95 cents, how
many gallons of each must be taken that the mixture may be
worth 75 cents ?

PARTNERSHIP.

ART. 161. Partnership is the association of two or more
persons, for the purpose of carrying on business at their joint
expense.

Each person thus associated is called a partner ; and the
several partners, in their associated capacity, are called a com-
pany, firm, or house.

The money or property invested by such a company in
business is called their capital, or joint-stock, or stock in trade.

The profits and losses of the business are sometimes shared
by the several partners in proportion to their stock in trade ; or
more correctly, in proportion to the use or interest of their stock
in trade. When the stock of the several partners is invested for
the same length of time the interest of the stock is proportioned
to the stock itself] and, hence, the profits and losses in this
case are shared in proportion to the stock of the several partners.

Sometimes one or more of the partners furnish the capital,
and the other or others contribute their services.

The profit or loss to be shared is called a dividend.

The duration of a partnership is limited by contract, or is
left indefinite, subject to be dissolved by mutual consent and
agreement.

When a company is dissolved, either by the limitations of
the contract or by mutual agreement, the adjustment of the
accounts of the company, and the division of effects, is called
a partnership settlement.

244 PARTNERSHIP.

Note. — Although partnership settlements fall properly
within the province of book-keeping, we have added a few ex-
amples to illustrate the manner of closing such accounts.

ART 162. When the capital of the several partners is
invested for the same length of time, to find each partner's
share of the profit or loss.

Ex. 1. A, B, and C enter into partnership in the lumber
business for 3 years. A put in $2400 ; B, 3600; C, $600.€>
At the time of the dissolution of the firm the net profits were
$4000. What is each partner's share of the profits ?

FIRST METHOD.

A's stock, $2400=TVo0o°o = } of entire stock.

B's " 3600=TY¥Yo = r3o "

C's " 6000=^7^= \ " "

Entire stock, $12000

Hence, A's share of profits= } of $4000— $ 800
B's " " = y\rof $4000= 1200
C's " =1 of $4000= 2000

Entire profits, .... $4000

Explanation. — Since A's stock equals }, B's r3o , and G's j
of the entire stock, A would be entitled to }, B to T\, and C
to J of the entire profits.

SECOND METHOD.

A's stock, $2400

B's " 3600

C's " 6000

Entire stock, $12000

" profits, $4000

TVoVo = f Hence, profits= % of stock.

A's share of profits^ of $2400=$ 800

B's " " =1 of $3600= 1200

C's " " =iof$6000=_2000

Entire profits, .... $4000

Explanation. — Since the entire profits equal i of the entire
stock, each partner's share of the profits must equal i of his
stock.

PARTNERSHIP. 245

THIRD METHOD.

$4000-^$12000=.33i. Hence the profits=33j- per cent,
of the stock.

A's share of profits =$2400 x. 33 i=$ 800

B's " " = 3600 x. 33i= 1200

C's " " = 6000x.33j= 2000

Entire profits, . . $4000

FOURTH METHOD.

S 12000 : §2400 : : §4000 : 8 800, A's profits.
§12000 : $3600 : : $4000 : $1200, B's "
§12000 : $6000 : : §4000 : $2000, C's "

$4000, Entire profits.

EULE. — First find WHAT PART of the entire stock each
partner has contributed, then take the SAME PART of the total
profits or loss for each partner's share of the' same.
Or,

First find WHAT PART of the entire stock the total profits
or loss may be ; then take the SAME PART of each partner's
stock for his share of the profits or loss.
Or,

Find what per cent, of the entire stock the total profits or
loss may be ; then multiply each partner's stock by the rate
per cent, expressed decimally.
Or,

Form the proportion , as the ivhole stock is to each partner' s
stock, so is the whole profit or loss to each partner's profit or
loss.

Ex. 2. A, B, and C traded in company. A put in $8000 ;
B, $4500 ; and C, $3500. Their profits were $6400. What is
each partner's share of the profits ? Ans. C's $1400.

Ex. 3. A and B, in trading for three years, make a profit
of $4800. A invested f as much stock as B. What is each
man's share of profit ? Ans. B's $3000.

Ex. 4. Two drovers, A and B, have been operating in com-
pany in buying and selling sheep. A made purchases to the
amount of $6780, and paid expenses amounting to $274.12.
B made purchases to the amount of $3840, and paid expenses

246 PARTNERSHIP.

amounting to $312. The sheep were sold by A for $10,482.
How much was made or lost ? How will A and B settle, the
profits or losses to be shared equally ?

Ex. 5. C and D agree to perform a certain piece of work
for government, for which they are to receive $4680, provided
it passes inspection as No. 1. If it pass as No. 2, 15 per cent.
is to be deducted ; as No. 3, 20 per cent, is to be deducted.

The result of the inspection was as follows :

1st division, which is £ of contract, is No. 1.
2d " " i " No. 3.

2d " " J " No. 2.

C has advanced, for the prosecution of the work, $1328 ;
B has advanced $987.45. Neither has received anything from
government, and all the money advanced has been used. How
much have they gained, and what is each man's share ?

ART. 163. When the capital is invested for different periods
of time, to find each partner's share of the profits or loss.

Ex. 1. A, B, and C traded in company. When they com-
menced business, A put in $4000 ; B, $3000 ; and C, $5000.
At the close of the first year A put in $3000 more, and C took
out $1000. At the close of the second year B put in $2000.
At the close of the third year they dissolve partnership, and
the net profits of the firm are found to be $2100. What is
each partner's share of the gain ?

Operation.
fc SS «4000+«14000=?18000.

A, B, and C, together, had in $42000 for one year.

Hence, A's share of gam=}f Hf or •? of $2100=$900
" B's " ={i7fUor 11 of $2100=$550

" C's " =i|$n or i| of $2100=$650

Entire profits, . . . $2100

PA-RTNERSHIP. 247

Explanation.— Since A had in $4000 for 1 year, and $7000
for 2 years =$14000 for 1 year, A had in trade the same as
$4000 + $14000=§1SOOO for 1 year ; and, since B had in $3000
for 2 years=6000 for 1 year, and $5000 for 1 year, B had in
trade the same as $6000 + $5000= $11000 for 1 year; and
since C had in $5000 for 1 year, and §4000 for 2 years =$8000
for 1 year, C had in trade the same as $5000 +$8000= $13000
for 1 year. ' Hence, A, B, and C, together, had in trade the
same as $18000 +$1100 +$13000= $42000 for 1 year.

Note. — The remaining portion of the solution may be in
accordance with either of the four preceding rules ; for the
time the stock of the several partners is invested is now the
same— one year— A's stock being $18000 ; B's, $11000 ; and
C's, $13000.

BY INTEREST.

Years. Int. Int.

A had in $4000 for 1= §240.00 ) _
$7000 for 2=$840.00 \ -
B " §3000 for 2=$360.00 ) _
" $5000 for 1= $300.00 \ ~
C " §5000 for 1 = $300.00 ) _ft f-ftftm

§4000 for 2= $480.00 S~
Total interest of entire stock, at 6^= $2520.00

Hence, A's share of profits= 4^4 § or f of $2100=900
B's " =AVTor U of $2100=550

C's " =/5Vff or if of $2100=650

"

Note. — Since like parts of two numbers have the same ratio
as the numbers themselves, it is evident the interest may be
computed at any per cent. It is also evident, from the same
principle, that the interest of the stock may be regarded as the
stock itself; and, hence, when the interest is obtained, the
remaining portion of the solution may be in accordance with
either of the four preceding rules.

RULE. — Multiply each partner's stock by the time it was
invested, and regard the product as his stock in trade, and the
SUM of the products as the entire stock in trade, and then pro-
ceed according to either of the four preceding rules.

248 PARTNERSHIP.

Or,

Find the interest of each partner's stock for the time it ivas
invested, and regard the interest thus found as his stock in
trade, and the SUM of the interests as the entire stock in trade,
and then proceed ' in accordance with either of the four pre-
ceding rules.

Ex. 2. A and B entered into partnership Jan. 1, 1858. A
put in $4500, and B, $5500. July 1, 1858, B put in $1500
more. Oct. 1, 1858, A took out $500. Jan. 1, 1859, each put
in $1500. July 1, 1859, they dissolved partnership, and found
they had lost $846. What is each partner's share of the
loss ? Ans. A's $342.

B's $504.

Ex. 3. A, B, and C hired a pasture for 6 months, for $245.
A put in 40 sheep ; B, 50 sheep ; C, 80 sheep. At the close
of 3 months A put in 20 more ; at the close of 4 months B
took out 20 ; and at the close of 5 months C took out 60.
How much ought each to pay ? Ans. A $75.

B $65.
C $105.

Ex. 4. A and B enter into a partnership for 3 years. A
put in $10000, and B, $2500. B is to do the business, and
his services are to be regarded as worth the use of $7500, the
difference between his and A's stock. At the close of the first
year A increased his stock to $18000. At the close of the 3
years the partnership closed, and a net gain found of $9500.
What is each partner's share of the gain ? Ans. A's $5750.

Bs $3750.

DUODECIMALS. 249

DUODECIMALS.

ART. 164. A Duodecimal (Latin duodecim, twelve) is a
number whose scale is 12 ; hence, 12 units of any order make
one unit of the next higher order.

This system of numbers is used by artificers in finding the
contents of surfaces and solids. For this purpose the foot is
divided into 12 equal parts called inches or primes, marked ' ;
the inch or prime is divided into 12 equal parts called seconds,
marked ", &c. The accents used to mark the different orders
are called indices.

TABLE.

12 fourths ("") make 1 third ('")

12 thirds " 1 second (")

12 seconds " 1 inch or prime (')

12 inches or primes " 1 foot (ft.)

Note. — Duodecimals may be added and subtracted like
Denominate Numbers.

MULTIPLICATION OF DUODECIMALS.

ART. 165. To multiply one duodecimal by another.
Ex. 1. How many square feet in a board 9 ft. 5 in. long;
and 2 ft. 8 in. wide ?

Operation.

9 ft. 5' Explanation. — Since 8'= r\ of a foot,

2 ft. 8^ and 5'=T5T, 8' x5'= -fs x T^=TyT=40'=

;' 4" 3, g, ^yrjte 4* jn secon(is order. Again,

18 10' since 8'= fc, 9 ft, x 8'=9 ft. x I«7=f|=72/

25 sq.ft. 1 and 72'+ 3' (above) = 75'= 6 sq. ft. 3'.

Hence 9 ft. 5' x 8;=6 sq. ft. 3' 4". Again 5' or T\ x 2 ft.= | }

=10' and 9 ft.x2 ft.=18 sq. ft. Hence 9 ft. 5'x2 ft. = 18

250 MULTIPLICATION OF DUODECIMALS.

sq. ft. 10'.1 Adding these two products, the total product is
25 sq. ft. I' 4".

It will be observed that the denomination of the product
of any two denominations is denoted by the sum of their inj
dices; thus 5' xS"=40'", 6"x4"=24"", &c.

In the above process, the notations of feet, primes, &c., are
used for convenience. The multiplier is, however, really an
abstract number.

R.TJH.E.

Write the Multiplicand under the Multiplier, placing ft.
under ft., primes under primes, &c.

Beginning at the lowest order, multiply each order of the
multiplicand by each order of the multiplier, adding their in-
dices to ascertain the denomination of the product, and carrying
one for every twelve from a lower order to the next higher.

Add the several partial products for the product required.

!E x a m. pies.

2. Multiply 12 ft. 8' by 4 ft. 10'. Ans. 61 sq. ft. 2' 8".

3. Multiply 4 ft. 6' 4" by 8 ft. 8'. Ans. 39 sq. ft. 2' 10" 8'".

4. Multiply 10 ft. 6' 6" by 4' 8".

5. How many square feet in a board 12 ft. 9 in. long and
11' 4" wide ? Ans. 12 sq. ft. 2' 6".

6. How many cubic inches in a block 2 ft. 9' long, 1 ft. 8'
wide, and 2 ft. 4' high ?

7. Kequired the solid contents of a block 4 ft. 4' long, 2 ft.
3' wide, and 10' high.

8. How many square feet in GO boards, each board being
15 ft. 4' long, and 1 ft. 2' wide ?

9. Divide 10 sq. ft. 2' 10" by 5 ft. 7'. . Ans. 1 ft. 10'.

Remark. — By observing that division is the reverse of mul-
tiplication, the following process will be readily understood.
The divisor is placed at the right of the dividend for con-
venience.

INVOLUTION. 251

DIVIDEND. DIVISOR.

lOsq. ft. 2' 10" I 5ft. r

j> T 1 fr. 10', Quotient.

4— —?> 10"
4_ r 10"

10. Divide 62 sq. ft. 11" 3'" by 8 ft. 6' 9". Am. 7 ft. 3'.

INVOLUTION.

ART. 166. Involution is the method of finding the powers
of numbers or quantities.

The power of a number (except the^rsO is the product ob-
tained by multiplying the number by itself one or more times.

The first power of a number is the number itself. It is
also called the root.

The second power, or square, is the product of the number
multiplied by itself once.

The third power, or cube, is the product of the number
multiplied by itself twice.

The different powers derive their .names from the number
of times the number is taken as a factor. Thus, the first
power contains the number as a factor once ; the second
power, twice; the third power, three times, &c.

The index or exponent of a power is a small figure placed
at the right and a little above the number, to show the degree
of the power, or how many times the number is taken as a
factor.

The 0 power of any number or quantity results from di-
viding the number by itself and is equal to unity or 1. Thus,
6°=1, 25°=1, 50°= 1, &c.

The following table will illustrate the above definitions
and remarks.

5°(5-7-5)=l, the 0 power of 5.

51— 5, the first power or root of 5.

5- =5 x 5=25, the second power or square of 5.

252 INVOLUTION.

53=5 x 5 x 5=125, the third power or cube of 5.
54=5x5x5x 5=625, the fourth power of 5.
55=5 x 5 x 5 x 5 x 5=3125, the fifth power of 5.
Remark. — The second power of a number is called its
square , because the area of a geometrical square is obtained
by multiplying the number of linear units in one of its sides
by itself once. The third power is called the cube, because
the solid contents of a geometrical cube is obtained by multi-
plying the number of linear units in one of its sides by itself
twice.

Ex. 1. What is the cube or third power of 24 ?

Operation.
24, 1st power.
24

96 It is evident from the definition that

the cube of a number is obtained by inul-

576, 2d power. tiplying the number by itself twice, or by

taking it three times as a factor.
2304
1152
13824, 3d power.

RULE. — Multiply the number by itself as many times as
there are units in the exponent of the power, LESS ONE. The
last product will be the required power.

NOTE. — The power of a fraction, either common or decimal,
is found in the same manner.

Examples.

2. What is the square of 204 ? Ans. 41616.

3. What is the 4th power of 25 ?

4. What is the cube of ± ? Ans. 7Vj.

5. What is the square of 2.5 ?

6. What is the 4th power of .04 ? Ans. .00000256.

7. What is the 5th power of 1 ?

8. What is the 9th power of 12 ?

SUGGESTION. — Since the product of two or more powers of
a given number is the power denoted by the sum of their ex-

EVOLUTION. 253

ponents, the 9th power of 12 may be found by multiplying the
the 3d power by itself twice ; thus, 123 x 123 x 123=129.
9. What is the 4th power of 2j ? Ans. 39T'?

10. What is the 3d power of 2.04 ?

11. What is the value of 154 ?

12. What is the value of (f )' ? Ans. ^\.

13. What is the value of 201s ?

14. What is the value of .OOP ?

15. What is the square of 9 J ? Ans. 85TV

EVOLUTION.

ART. 167. Evolution is the method of finding the roots
of numbers or quantities.

Evolution is the reverse of involution. In the latter, the
root is given to find the power. In the former, the power is
given to find the root.

The root of a number is such a number as multiplied by
itself a certain number of times, will produce the given
number.

The first root of a number is the number itself. It is also
called the first power.

The second, or square root of a number is that number
which, multiplied by itself once, "411 produce the given
number.

The third, or cube root must be multiplied by itself twice
to produce the given number.

The different roots take their names from the number of
times they are taken as factors to produce the given number.
The first root is taken once as a factor ; the second or square
root, twice; the third or cube root, three times, &c.

A root of a number may be defined to be a factor
which taken a certain number of times, will produce the given
number.

The root of a number is usually indicated by the radical
sign 4/ placed before it, with the index of the root written
above it.

254 SQUARE BOOT.

Thus, 1/64 shows that the 3d root of 64 is to be taken ; V§T,
the 4th root of 81 ; V15, the 1st root of 15, &c.

The index is usually omitted in case of the second or
square root. Thus, v/64 or V64 equally indicates the square
root of 64.

The root of a number may also be indicated by a fractional
exponent, placed on the right of the number. Thus 16* indi-
cates the square root of 16 ; 81^, the fourth root of 81.

12^ denotes that the cube root of the square of 12 is to
be taken.

A number may be either the perfect or imperfect power of
a required root. 25 is a perfect square, but an imperfect cube.
The exact root of an imperfect power can not be extracted and
is called a surd. Prime numbers are imperfect powers of all
their roots, except the first.

SQUARE ROOT.

ART. 168. The Square Root of a number is a number
which multiplied by itself will produce the given number.
Thus the square root of 16 is 4, since 4 x 4=16.

The process of finding the square root of a number is best
understood by observing the manner in which the square of
a number is formed, and the relation which the orders of the
square bear to those of the root.

The first nine numbers are :

. 1, 2, 3, 4, 5, 6, 7, 8, 9,
and their squares

1, 4, . 9, 16, 25, 36, 49, 64, 81.
From which it is seen that the square of any number composed
of one order of figures, can not contain more than two orders.

Conversely, that the square root of any number composed
of one or two orders is composed of but one order.

It will further be seen that the numbers in the second line
above are the only perfect squares found below 100, and that

SQUARE BOOT. 255

the square root of any number between any two of these con-
secutive perfect squares is between the two corresponding roots
above. Thus, 75 is not a perfect square and its square root
is between 8 and 9.

The first nine numbers expressed by tens are,
10, 20, 30, 40, 50, 60, 70, 80, 90,
and their squares,

100, 400, 900, 1600, 2500, 3600, 4900, 6400, 8100.
From which it is seen that the square of tens gives no order
below hundreds or above thousands. In the same manner it
may be shown that the square of any number must contain at
least twice as many orders, less one, as the number squared.
If the left hand figure of the number squared is more than
three, the square will always contain just twice as many or-
ders as the root. Thus, the square of 456 contains six orders.

Again, every number may be regarded as composed of tens
and units. Thus, 65 is composed 6 tens and 5 units, that is
60+5=65 ; 365, of 36 tens and 5 units, that is 365=360+5.
Hence(65)2=(60)'+2 x 60 x 5 + (5) '=3600 +600 +25 =4225,
and (365)*= (360)2 + 2 x 360x5+ (5) 2= 129600+3600+25=
133225.

In like manner it may be shown that the square of any
number is equal to the square of the tens plus twice the product
of tens by units plus the square of units.

The two principles, above, determine the process of extract-
ing the square root of a number.

Ex. 1. What is the square root of 4225 ?

Operation. Explanation. — Since 4225 is composed

4225;65 of four orders, its root will be composed

of but two ; and since the square of units

6x2=12 5)625 is composed of units and tens, and" the

/^O •-• XT

square of tens, of hundreds and thousands,
we separate the number into periods of two figures each, by
placing a dot over units and another over hundreds.

Xow 42 must contain the square of the ten's figure of the
root. The greatest perfect square in 42 is 36, the square root
of which is 6. Hence 6 is the ten's figure of the root. Sub-

256 SQUARE BOOT.

trading the square of the ten's figure of the root from 42 hun-
dreds, we have 6 hundreds for a remainder, to which, if the
25 units be added, we shall have 625, which is composed of
twice the product of the tens of the root by the units (to be
found) plus the square of the units.

Now the product of tens by units gives no order below
tens, hence 62 tens must contain twice the product of the tens
by the units. It may contain more, since the square of units
may give tens.

If 62 tens be divided by 2 x 6 tens, or 12 tens, the quotient,
5, will be the unit figure of the root. By placing 5, the unit
figure, at the right of 12 tens, and multiplying the result, 125,
by 5, the product will be twice the tens by the units, plus the
square of the units.

Ex. 2. What is the square root of 133225 ?

133225(365, Ans.
3x3= 9
3x2=66)432
66x6= 396

36x2=725)3625
725x5= 3625.

RTJ L E.

1. Separate the given number into periods of two figures
each, commencing at units.

2. Find the greatest perfect square in the left hand period
and place its root on the right as the highest order of the root.

3. Subtract the square of the root figure from the left hand
period, and to the remainder annex the next period for a
dividend.

4. Double the part of the root already found for a trial
divisor, and see how many times it is contained in the divi-
dend, exclusive of the right hand figure, and write the quotient
as the next divisor of the root, and also at the right of the trial
divisor.

5. Multiply the divisor thus formed by the figure of the
root last found, and subtract the product from the dividend.

SQUARE BOOT. 257

6. To this remainder annex the next period for the next
^dividend, and divide the same by twice the root already found,

and continue in this manner until all the periods are used.

Notes. — 1. The left hand period often contains but one
figure.

2. Twice the root already found is called the trial divisor,
since the quotient may not be the next figure of the root.
The quotient may be too large, in which case it must be made
less. The true divisor is the trial divisor with the figure of
the root found annexed.

3. When any dividend exclusive of its right hand figure is
not large enough to contain its trial divisor, place a cipher for
the next figure of the root, and double the root thus formed
for a new trial divisor, and form a new dividend by bringing
down the next period.

4. When there is a remainder after all the periods are
used, annex a period of two ciphers, and thus continue the
operation until the requisite number of decimal places is ob-
tained. In this case, there will be a remainder, how far soever
the operation be continued, since the square of no one of the
nine digits ends with a cipher.

5. The square root of a common fraction may be found by
taking the root of both terms, when they are perfect squares.
When both terms of a fraction are not perfect squares, and
can not be changed to perfect squares, the root of the fraction
can not be exactly found. The approximate root, however,
may be found by multiplying the numerator of the fraction
by the denominator, and extracting the root of the product,
and dividing the result by the denominator. By extracting
the root to decimal places the error may be further lessened.

G. In finding the square root of a decimal or a mixed deci-
mal, commence separating into periods at the order of units
for the whole number, and at the order of tenths for the deci-
mal. If there be an odd number of 'decimal places, annex
a cipher.

7. Mixed numbers must first be reduced to improper frac-
tions or to mixed decimals.

258 THE RIGHT-ANGLED TRIANGLE.

3. What is the square root of 32041 ? Ans. 179.

4. What is the square root of 492804 ? .Ans. 702. -

5. What is the square root of 94249 ? Ans. 307.

6. What is the square root of 2 ? Ans. 1.414 + .

7. What is the square root of 62.8 ?

62.80(7.924, Ans.
7x7= ^9
7x2=14.9)13.80
14.9 x. 9= 13.41

7.9 x. 2= 15.82).3900
15.82 x. 02= _J3164

7.92 x 2= 15.844^073600

15.844 x. 004= .063376

.010224.

8. What is the square root of .0625 ? u4rcs. .25.

9. What is the square root of 57600 ? Ans. 240.

10. What is the square root of 176.89 ?

11. What is the square root of -/-/•$ ? Ans. 75F.

12. What is the square root of oW? ? Ans. f f.

13. What is the square root of 30 £ ? Ans. 51.

14. What is the square root of 69£ ? Ans. 8 J.

THE RIGHT-ANGLED TRIANGLE.

ART. 169. An angle is the divergence of two lines meeting
at a common point.

Angles are divided into three classes ; acute, obtuse, and
right.

The annexed figures illustrate the three kinds of angles.

Acute. Obtuse. Eight angle.

A triangle is a figure bounded by three straight lines. It
also contains, as its name indicates, three angles.

\

THE BIGHT-ANGLED TRIANGLE.

259

A rigfy-angled triangle contains a right angle.

The side opposite the right angle is called the hypotenuse,

The other two sides are called the base and perpendicular.

Perpendicular.^

Base.

It is an established theorem that the square of the hypot-
enuse of a right-angled triangle is equal to the sum of the
squares of the other two sides.

The annexed figure illustrates this theorem and the fol-

lowing rules.

KULE 1. — Extract the square root of the SUM of the square
of the base and the square of the perpendicular ; the result
be the HYPOTENUSE.

260 CUBE ROOT.

KULE 2. — Extract the square root of the DIFFERENCE 'be-
tween the square of the hypotenuse and the square of the
given side; the result will be the other side required.

E x a. m pies.

1. What is the hypotenuse of a right-angled triangle
whose base is 36 ft. and perpendicular 45 ft.? Ans. 57.6 ft.

2. If the hypotenuse of a right-angled triangle is 65 feet,
and the base 52 feet, what is the perpendicular ?

Ans. 39 feet.

3. The hypotenuse of a right-angled triangle is 80 feet,
and the perpendicular 48 feet, what is the base ?

Ans. 64 feet.

4. Two ships start from the same point at the same time.
In six days, one has sailed 500 miles due east, and the other
400 miles due north. What is their distance apart ?

5. How far from the base of a building must a ladder 100
feet in length be placed so as to reach a window 60 feet from
the ground ? Ans. 80 feet.

flS. A room is 32 feet long and 24 feet wide ; what is the
distance between the opposite corners ? Ans. 40 ft.

7. A boy in flying his kite let out 500 feet of string and
then found that the distance from where he stood to a point
directly under the kite was 400 feet ; how high was the kite ?

Ans. 300 feet.

CUBE ROOT.

ART. 170. The Cube Boot of a number is a number which
multiplied by itself twice, will produce the given number.
Thus, the cube root of 64 is 4, since 4 x 4 x 4=64.

The process of finding the cube root of a number is best
understood, as in square root, by involving a number, and thus
ascertaining the law of the formation of the power.

The first nine numbers are,

1, 2, 3, 4, 5, 6, 7, 8, 9,
and their cubes,

.1, 8, 27, 64, 125, 216, 343, 512, 729.

CUBE ROOT. 261

From which it is seen that the cube of any number composed of
one order of figures may contain one, two, or three orders.

Conversely, the cube root of any number composed of one,
two, or three orders, is composed of but one order.

The numbers in the second line above are the only perfect
cubes below 1000.

Again, 103=1000 and 903=729000. From which it is seen
that the cube of tens gives no order below thousands, or above
hundreds of thousands. In the same manner it may be shown
that the cube of any number must contain at least three times
as many orders, less two, as the number cubed. Thus the cube
of any number composed of four orders must contain either
ten, eleven, or twelve figures.

Let us now involve a number composed of two orders —
tens and units — to the third power, and observe the law of
formation.

54?= 503 + 3 x 50' x 4+3 x 50 x 42 + 43= 125000 + 30000+2400
+ 64=157464.

By using algebraic symbols, it may be rigidly shown that
what is true of the above number, is true of any number com-
posed of tens and units ; that is,

The cube of any number composed of tens and units is
equal to the cube of the tens, plus three times the product of
the square of the tens by the units, plus three times the product
of the tens by the square of the units, plus the cube of the units.

Let us now proceed to determine a process by which the
cube root of a number may be found.

Ex. 1. What is the cube root of 157465 ?

54 1574644154

>4 5'= 125 "

216 5s x 3=75 324

270 54' = 157464

2916
54

11664
14580
157464

262 CUBE ROOT.

Explanation. — Since 157464 is composed of six orders, the
root will be composed of two, and since the cube of tens give
no order below thousands, we separate the number into periods
of three figures each by placing a dot over units, and another
over thousands. Now, according to principles above explained,
157 must contain the cube of the ten's figure of the root. The
greatest cube in 157 is 125, the cube root of which is 5.
Place 5 for the ten's figure of the root. Subtract the cube of
5 from 157, and annex 4 of the next period to the remainder,
giving 324. Now three times the product of the square of the
tens by the units must be found in 324, since the square of tens
gives no order below hundreds.

Square 5 tens and multiply the result by 3 for a trial divi-
sor to find the next root figure. Place the quotient below the
order in the root. It may be too large, since three times the
product of the tens by the square of the units may give orders
above tens, thus forming a part of 324, cube 54, and since the
result is not greater than 157464, place 4 for the unit's figure
of the root.

Ex. 2. What is the cube root of 34328125 ?
33 32

33= 27
W "~64

34328125325
35

99 96 3'x3= 27)73__

iSr TOM 32- ^™-

32 32' x 3=3072)15601

3267" "2048 325°= 34328125.
3267 3072
"35937 32768

1. Separate the given numbers into periods of three figures
each, commencing at units.

2. Find the greatest perfect cube in the left hand period,
and place its root on the right as the highest order of the root.

3. Subtract the cube of the root figure from the left hand
period, and to the remainder annex the first figure of the next
period for a dividend.

CUBE BOOT. 263

4. Take three times the square of the root figure now found
for a trial divisor, and place the number of times it is con-
tained in the dividend, for the next figure of the root. Cube
the root now found, and if the result is less than the first tiuo
periods of the given number, bring down the first figure of the
next period for a neio dividend ; if, however, the cube is
greater than the first two periods, diminish the last root figure
by I.

5. Take three times the square of the root now found for
a new trial divisor, and place the number of times it is con-
tained in the new dividend for the third figure of the root.
Cube the three figures of the root, and subtract the result from
the first three periods of the given number. Continue the
operation in a similar manner until all the periods are used.

Notes. — 1. When any dividend is not large enough to con-
tain its trial divisor, place a cipher for the next figure of the
root, and take three times the square of the root thus formed
for a new trial divisor. Form a new dividend by bringing
down the remaining two figures of the period, and the first
figure of the next period.

2. When there is a remainder after all the periods are used,
annex periods of ciphers and continue the operation until the
requisite number* of decimal places is obtained.

3. Extract the cube root of both terms of a common frac-
tion, when they are perfect powers ; otherwise multiply the
numerator by the square of the denominator, and divide the
root of the product by the denominator. The result will be the
root with an error, less than one divided by the denominator.

4. In extracting the cube root of decimals or mixed deci-
mals, ciphers must be added, to fill the periods.

Kxamples.

1. What is the cube root of 912673 ? Ans. 97.

2. What is the cube root of 128024064 ? Ans. 504.

3. What is the cube root of 48228544 ? Ans. 364.

4. What is the cube root of 3048625 ? Ans. 145.

5. What is the cube root of 39TVj ? -4»«- 3|.

264 ARITHMETICAL PROGRESSION.

6. What is the cube root of .000097336 ? Ana. .046.

7. What is the cube root of llf f ? Ans. 2^ ?

8. What is the cube root of 7f H* ? ^s- aV

9. What is the cube root of 14 ? ^/is. 2.42 + .
10. What is the cube root of .015625 ? Ans. .25.

ARITHMETICAL PROG-RESSIO1ST.

ART. 171. When several numbers are so arranged as to
increase or decrease in regular order by a common difference,
they are said to be in arithmetical progression.

When they increase by the addition of a constant number,
•it is called an ascending series, e. g., 1, 3, 5, 7, 9, 11, 13, &c.

When they decrease by the subtraction of a constant num-
ber, it is called a descending series, e. g., 19, 16, 13, 10, &c.

The numbers are called terms, the first and last being
called extremes, and the intermediate terms the means.

In arithmetical progression there are five quantities so
related to each other, that any three of them being given, the
remaining two may be found. This fact gives rise to twenty
different cases or problems, only six of which will here be given.
These five quantities in the formulas expressing their rela-
tion, are represented as follows :

a = The first term.

I = The last term.

d = The common difference.

n = The number of terms.

s = The sum of all the terms.

FORMULAS.

(1), a, d and n being given, l=a±(n— Y)d.
(2), a,n ' I " " d=^.

(3), a. d " I " " n=t-a+l.
(4), a, n " I
(5), d,n " s

" "

, , .

(6), a, d ' n " " s=i«[2a±(»-l)d].

ARITHMETICAL PROGRESSION. 265

The interpretation of these formulas for those not familiar
with algebraic expressions, will furnish the following rules.
The student will be able to select the proper rule for any par-
ticular case by noting carefully which three of the five quan-
tities are given, and which is required.

(1). The first term, common difference, and number of
terms being given to find the last term.

EULE. — Multiply the common difference by the number of
terms, less one, and add the product to the first term, if the
series- be ASCENDING, but subtract it from it, if the series be

DESCENDING.

(2). The first term, number of terms, and last term being
given to find the common difference.

KULE. — Divide the difference of the extremes by the num-
ber of terms , less one.

(3). The first term, common difference, and last term being
given to find the number of terms.

KULE. — Divide the difference of the extremes by the com-
mon difference, and add 1 to the quotient.

(4). The first term, number of terms, and last term being
given to find the sum of all the terms.

KULE. — Multiply half the sum of the extremes by the num-
ber of terms.

(5). The common difference, number of terms, and sum of
all the terms being given to find the first term.

KULE. — Divide the sum of the terms by the number of
terms ; subtract from the quotient, if the series be ascending,
otherwise add to it half the product of the common difference
into the number of terms, less one.

(6). The first term, common difference, and number of
terms being given to find the sum of all the terms.

KULE. — Add to twice the first term, if the series be ascend-
ing; otherwise subtract from it the product of the common
difference into the number of terms, less one ; multiply the
sum or difference by half the number of terms.

266 ARITHMETICAL PROGRESSION.

Id 'x. a, m. pies.

1. A laborer agreed to dig a well 100 feet deep, for which
he was to receive 1 cent for the first foot, 5 cents for the second
and so on increasing the price 4 cents per foot for the entire
depth. What would he get for the last foot ?

Ans. $3.97.

2. If a man begin by lifting 200 Ibs., and make equal ad-
ditions to the weight daily for a year of 365 days, what must
be the daily additions to reach 800 Ibs. at the end of the year?

Ans. Iff- Ibs.

Secondly. With what weight must he begin, so that the
daily additions may be two pounds ? Ans. 72 Ibs.

Thirdly. If he begin with 200 Ibs., and add 1 J Ibs. daily,
how many days would it require to reach 800 Ibs.

Ans. 401 days.

3. How many strokes does the hammer of a clock make in
12 hours ? Ans. 78.

4. If 100 stakes bo set in a straight line 10 feet apart, how
much twine will it require to connect the first one in the line
with each of the others separately ? Ans. 49500 feet.

5. A man agreed to contribute for a benevolent object one
cent the first day, two cents the second day, three cents the
third day, and so on through the year of 365 days. What
was the amount of his donation ? Ans. $667.95.

6. A note was given for $1000, with interest payable an-
nually, at 7%. Nothing having been paid for ten years, how
much did the total amount of interest due exceed the simple
interest of the principal ? See Art. 100. Ans. $220.50.

7. If a note for §2000, drawing interest at 6^ per annum,
run 10 yrs. 3 mo. 9 d. with nothing paid, how much would
the condition of making the " interest payable semi-annually"
increase the amount due ? Ans. $361.80.

GEOMETRICAL PROGRESSION. 267

GEOMETRICAL PROGRESSION.

ART. 172. A geometrical progression is such a series of
numbers, that each term after the first shall be the product
of the preceding term and a constant multiplier, called the
common ratio.

The progression is ascending or descending, according as
the ratio is greater or less than unity.

In geometrical progression, as in arithmetical progression,
there are five quantities so related to each other, that any
three of them being given the remaining two may be found.
Of the twenty cases arising therefrom only four will here be
noticed.

In the formulas expressing the relation of the five quan-
tities referred to above, they are represented as follows :
a =• The first term.
I = The last term.
r = The common ratio.
n = The number of terms.
s = The sum of all the terms.

FORMULAS.

(1,) a, r and n being given, ?=arn~~1.

(2,) ?, r and n " " a=^.
; (3,) a, I and r « « s=^.

(4;) a, r and n " " s = *^-.

These formulas are equivalent to the following rules :
(1.) The first term, common ratio, and number of terms
being given to find the last term.

RULE. — JRaise the common ratio to a power whose degree
is one less than the number of terms, and multiply it by the
first term.

(2.) The last term, common ratio, and number of terms
being given to find the first term.

268 GEOMETRICAL PROGRESSION.

RULE. — Raise the common ratio to a power whose degree,
is one less than the number of terms, and divide the last term
by it.

(3.) The first term, last term, and common ratio being
given to find the sum of all the terms.

RULE. — From the product of the last term into the ratio,
subtract the first term; then divide the remainder by the ratio
less one.

(4.) The first term, common ratio, and number of terms
being given to find the sum of all the terms.

RULE. — From the power of the ratio whose degree is the
number of terms, subtract one; divide the remainder by the
common ratio less one, and multiply the quotient by the first
term.

REMARK. — It is sometimes convenient in working problems
to transpose a descending series so as to make it ascending, the
last term of the first series becoming the first term in the new.
In that case the new ratio would be the reciprocal of the old,
i. e., unity divided by that ratio, e. g., ± would become 3, |
would become 4, and so on.

Infinite Series.

ART. 173, If the number of terms in a descending geomet-
rical series be infinite, the last term will be 0.

It does not, however, follow that, because the number of
terms is infinite, the sum of those terms must be infinite, for
if we apply formula (3) making the last term 0, we shall find
the sum of an infinite decreasing series to be the first term
divided by the difference between the common ratio and unity,

Examples.

1. A man offered to purchase 10 cows, paying for the first
5 cents, for the second 15 cents, and so on tripling the amount
for each succeeding cow. What would the last one cost him,
and what would the whole cost him ?

Ans. The last would cost $984.15.
u " whole " $1476.20.

GEOMETRICAL PROGRESSION. 269

2. If the first term be 100, the common ratio 1.06, and the
number of terms 5, what is the last term ? Ans. 126.2477.

NOTE. — As the principles of arithmetical progression may
be applied with advantage to the computation of annual in-
terest, so may those of geometrical progression in computing
compound interest. When thus applied the principal is the
first term, the amount the last term, the number of regular
intervals, at the end of which the interest is to be com-
pounded, one less than the number of terms, and the amount
of one dollar for one of those intervals the common ratio. To
find the different powers of the ratio, the table on pages 132
and 133 may be used, the number in the column of years in-
dicating the degree of the power ; e. g., the 50th power of
1.03i is 5.58492686.

3. What is the amount of §100 for 50 years at 10 % com-
pound interest ? Ans. $11739.09.

4. If a man beginning at the age of 21, at the end of each
year pu's $100 at compound interest, what will these sums
amount to when he is 50 years old ? Ans. $7363.98.

5. A gentleman offered for sale a lot of ten acres on the
following terms : one mill for the first acre, one cent for the
second, one dime for the third, and so on in geometrical pro-
gression. What was his price for the whole ?

Ans. $1111111.111.

6. What is the sum of the series T37, T^, To3oo? &c-> or
.333, &c.j carried to infinity ? Ans. \.

7. What common fraction is equivalent to the repetend
.7777, &c. ? Ans. J.

8. At 12 o'clock the hour and minute hands of a clock are
together. In what time will they b3 together again ?

SOLUTION*. — When the minute hand has performed one entire revolution
around the face of the clock, the hour hand will be yV of a revolution in advance.
When the minute hand shall have gone over this rV, the hour hand will still be
yV of that twelfth in advance, or y^y of an entire revolution. When the minute
hand shall have reached that point, the hour hand will be y 2 of> TTT in advance,
and so the comparison of their relative position may be supposed to be made an
infinite number of times. It is evident that for the minute hand to overtake the
hour hand, it must perform as many revolutions (andl hence take as many hours)

270 MENSURATION.

as would be the sum of the series 1, yV, 74 T» TTaTi &c., continued to infinity
equal to ITT hours. "With the above reasoning one might almost believe that
the hour hand would always be ahead, bat as a matter of fact we know that the
minute hand does overtake and pass the hour hand, and therefore at some point
the distance between the two must be nothing. Farthermore, as the series above
represents the successive distances apart in their actual progress, we have from
this case conclusive proof that the last term of an infinite decreasing geometrical
series is absolutely nothing.

9. If an ivory ball is let fall upon a marble slab, from a
height of 10 feet, and it rebounds 9 feet, falling again it re-
bounds 8.1 feet, and so continues always rebounding T9¥ of the
distance through which it fell last, will it ever come to rest,
and if so, through what space will it have passed ?

Ans. It would pass through 190 feet.

10. If the banking law of Illinois allows the State Auditor
to issue to any banker depositing State Stocks, 90 per cent, of
the par value of those stocks in circulating bank notes, without
farther restriction, what is the amount of Stocks a banker
could so put on deposit with only $10000 Cash Capital, if he
continue to re-invest the bank notes for other Stocks both at
par, until he should have nothing to re-invest ? If the Stocks
draw 6 % interest, what dividend does he realize on his capital ?

Ans. to the first $100.000.

second 60 % per annum.

MENSURATION.

ART. 174, A point has neither length, breadth, nor thick-
ness, but position only.

A line has length without breadth or thickness, and may
be straight or curved.

A surface, has length and breadth without thickness, and
may be plain or curved.

A solid has length, breadth, and thickness.

An angle is the divergence of two straight lines from a
common point. When the divergence is equal to that made

MENSURATION. 271

by a straight line and one perpendicular to it, it is called a
right angle, and its measure is 90 degrees (90°). A less di-
vergence forms an acute angle, and a greater an obtuse angle.

The area of a figure is its quantity of surface, and is
measured by the product of the linear dimensions of length
and breadth, which will give the number of square units of the
same denomination covering an equivalent surface.

EEMARK. — The only difficulty then in computing the area of any figure is to
find the linear dimensions of its average length and breadth, or those of another
figure known to be of equal area. Take for example the " quadrature of the
circle." It can easily be proven that the area of a circle is equal to the area of a
rectilinear figure, with a length equal to the circumference of the circle, and a
breadth equal to half the radius ; but as our system of notation -will not express
the exact length of the radius for a given circumference, nor the exact length of
the circumference for a given radius, the problem will not admit of an exact solu-
tion, though the approximation may be carried to an indefinite extent.

The solidity or volume of a solid or body is the quantity
of space which it occupies, and is measured by the product of
the three linear dimensions of length, breadth, and thickness,
which will give the number of cubic units of the same deno-
mination occupying an equivalent space.

A rectilinear figure, or polygon, is a plane figure bounded
by straight lines. A polygon of three sides is called a triangle,
of four sides a quadrilateral, of five a pentagon, of six a hexa-
gon, and so on.

A regular polygon is one whose sides and angles are equal.

A trapezium is a quadrilateral which has no two sides
parallel.

A trapezoid is a quadrilateral which has only two sides
parallel.

A parallelogram is a quadrilateral whose opposite sides
are equal and parallel.

The altitude of a parallelogram or trapezoid is the perpen-
dicular distance between the parallel sides.
. A rectangle is a right-angled parallelogram.

A square is an equilateral rectangle.

A rhombus is an equilateral parallelogram with only its
opposite angles equal.

272 TRIANGLES.

A rhomboid is a parallelogram neither equilateral nor
equiangular.

Similar figures are those whose corresponding angles are
equal, and the sides about the equal angles proportional.

The areas of similar figures are to each other as the squares
of their corresponding linear dimensions, and the volumes of
similar solids are to each other as the cubes of their corre-
sponding linear dimensions.

TRIANGLES.

ART. 175- In computing the area of a triangle, either side
may he assumed as the base, and the altitude will be the per-
pendicular let fall from the vertex of the angle opposite upon
the base, or base produced if necessary.

To find the area of a triangle.

KULE. — Multiply the base by half the altitude, and the
product will be the area; or

Take half the sum of the three sides, and from this sub-
tract each side separately; then multiply together the half
sum and the three remainders, and the square root of the pro-
duct will be the area.

IE x a m pies.

1. How many square yards in a piece of ground of trian-
gular shape, one side measuring 50 yards, and the shortest
distance from this side to the opposite angle being 24 yards ?

Ans. 600 sq. yds.

2. The three sides of a triangle measure respectively 10,
12, and 14 feet ; what is the area ? Ans. 58.7878 sq, ft.

3. How much greater would be the area if we double the
linear dimensions in the last example ! Ans. Four times.

4. What should be the dimensions of a triangle similar to
the one proposed in example 1, to make the area 5400 s.q.
yards instead of GOO ? Ans. The base 150 yds.

The altitude 72 yds.

5. If one side of a field containing 50 acres is 50 rods,

&c. 273

•what must be the length of the corresponding side of a field
of similar shape to contain 112| acres ? Ans. 75 rods.

6. The area of a certain triangular field is 3f acres, and
one of its sides is 37 1 rods long ; what is the length of a per-
pendicular from the opposite corner ? Ans. 32 rods.

7. What is the side of a square containing the same area
as a triangle whose base is 36.1 feet, and altitude 5 feet ?

Ans. 9^ feet.

QUADRILATERALS, PENTAGONS, &c.

ART. 176. (1.) To find the area of any quadrilateral having
two sides parallel.

RULE. — Multiply half the sum of the two parallel sides by
the altitude, or perpendicular distance between those sides,
and the product ivill be the area. *

NOTE. — This rule is equally applicable to the square, rect-
angle, rhombus, rhomboid, and trapezoid. If the parallel sides
are equal, the half sum would be equal to one of them.

(2.) To find the area of a regular polygon.

RULE. — Multiply the sum of the sides or perimeter by half
the perpendicular let fall from the center upon one of its sides.

Or,

Multiply the square of one of the sides by the appropriate
number as given in the following

TABLE.

Triangle,

.433013

Octagon,

4.828427

Square,

1.000000

Nonagon,

6.181824

Pentagon,

1.720477

Decagon,

'- 7.694209

Hexagon,

2.598076

Undecagon,

9.365640

Heptagon,

3.633912

Dodecagon,

11.196152

(3.) To find the area of an irregular polygon of four or
more sides.

RULE. — Divide the figure into triangles by diagonals con-
necting some one angular point with each of the others; com-
pute the area of each triangle, and their sum will be the area

required.

IS

274 CIRCLES.

Examples.

1. How many square feet in a board 14 feet long and 10
inches wide ? Ans, 11 1 sq. ft.

2. How many square feet in a board 14 feet long, it being
15 inches wide at one end, and 9 inches at the other ?

Ans. 14 sq. ft.

3. If the same board be cut in two in the middle, making
each piece 7 feet long, how much more would one piece con-
tain than the other ? Ans. If sq. ft.

4. If the parallel sides of a trapezoid are 48 and 52 feet,
and the perpendicular breadth 17 feet, what is the area ?

Ans. 850 sq. ft.

5. What is the area of a regular decagon, one of its sides
being 10 feet, and the perpendicular let fall from the center
upon one of the sides being 15.3884 feet ?

Ans. 7G9.420 sq. ft.

6. What is the area of a regular pentagon, one of its sides
being 20 rods ? Ans. 688.191 sq. rods.

7. What must be the side of a regular octagonal field to
contain 3 acres, 2 roods, 14 rods, 19 yards ? Ans. 60 yards.

8. The sides of a certain trapezium measure 10, 12, 14;
and 16 rods respectively, and the diagonal which forms a tri-
angle with the first two sides named 18 rods, what is the area ?

Ans. 1 acre 3.9 rods.

9. How much more fencing will it require to enclose an
acre in the form of a square than in the form of a hexagon ?

Ans. 3.51 rods.

CIRCLES.

ART. 177. The ratio between the diameter and circum-
ference is an important number in problems relating to the
circle, and its approximate value should be retained in tlae
memory. That ratio is very nearly equivalent to the fraction
35 s? which may easily be remembered from its containing the
first three odd numbers each repeated, and found in their

CIRCLES. 275

natural order, if we read the denominator first. If expressed
decimally, and the approximation be earned to thirty places,
we have the following, 3.14159265358979323846264338328.

(1.) To find the circumference of a circle whose diameter
is known.

RULE. — Multiply the diameter by £ff or 3.1416.

(2.) To find the diameter, the circumference being known.

RULE. — Divide the circumference by fff or 3.1416.

(3.) To find the area of a circle, the diameter being known.

RULE. — Multiply the square of half the diameter by £f f
or 3.1416.

(4.) To find the area of a circle, the circumference being
known.

RUL"E. — Divide the square of half the circumference by
f f f or 3.1416.

(5.) To find the area of a circle, the circumference and
diameter both being known.

RULE. — Multiply the circumference by one fourth of the
diameter. See Art. 174, Remark.

(6.) To find the diameter or circumference of a circle, the
area being known.

RULE. — Divide the area by ff I or 3.1416, the square root
of the quotient will be equal to half the diameter; and the
diameter multiplied by f *-} or 3.1416, will equal the circum-
ference.

(7.) To find the side of the largest square that can be in-
scribed in a circle.

RULE. — Multiply the radius by the square root of two (^2).

(8.) To find the side of the largest equilateral triangle that
can be inscribed in a circle.

RULE.-— Multiply the radius by the square root of three (^3).

Note. — The side of an inscribed hexagon is equal to the
radius.

"Examples.

1. Suppose the earth to be distant from the sun 95 millions
of miles, and to revolve in a circular orbit, how far "does it
move in an hour ? Ans. 68093 miles.

276 ELLIPSE.

2. What is the diameter of a peach which measures 12
inches in circumference ? Ans. 3.82 inches.

3. What must be the inside measure of a square box to
exactly contain a globe 56 inches in circumference ?

Ans. 17.825+ in. sq.

4. If a horse be tied to a stake in a meadow, with a halter
20 feet long, upon how many square yards can he feed ?

Ans. 139.626 + .

5. If a circular fish pond is to be laid out containing just
half an acre, what must be the radius or length of the cord
needed to describe the circle ? Ans. 27.75 yds.

6. What is the area of a ring formed by two circles whose
diameters are 9 and 13 inches ? Ans. 69.1152 sq. in.

7. How large a square stick may be hewn from a piece of
round timber 109 inches in circumference ? Ans. 22.5 in. sq.

ELLIPSE.

ART. 178. To find the area of an ellipse the two diameters
being given.

RULE. — Multiply the two diameters together, then multiply
one fourth of this product by ^ff or 3.1416.

Examples.

1. What is the area of an ellipse whose two diameters are
18 and 24 feet ? Ans. 339.2928 sq. ft.

- 2. What is the area of an ellipse whose longest diameter is
20 feet, and shortest 15 feet ? Ans. 235.62 sq. ft.

MENSURATION OF SOLIDS.

PRISMS AND CYLINDERS.

ART. 179. A prism is a solid whose sides or faces are par-
allelograms and whose ends or bases are equal and parallel
polygons. A prism is triangular, quadrangular, pentagonal,
&c., according as its bases are triangles, squares, or penta-
gons, &c.

A parallelepiped is a prism whose bases are parallelograms.

PYRAMIDS AND CONES. 277

A cylinder is a solid resembling a prism, but having, in-
stead of polygons, for its bases, equal parallel circles or other
figures more or less elliptical ; its surface otherwise being uni-
formly curved instead of being made up of several plane faces.

The lateral or convex surface of a prism or cylinder does
not include the two ends or bases.

A solid is said to be right when its axis or general direc-
tion is at right angles with the base ; otherwise it is oblique.

To find the entire surface of a right prism or right cylinder.

RULE. — Multiply the perimeter or circumference of the base
by the height , and to the product add the area of the two bases.

To find the solidity of a prism or cylinder.

RULE. — Multiply the area of the base by the perpendicular
height.

NOTE. — In this case it matters not whether the solid be
right or oblique.

E x: a m pies.

1. What is the extent of surface of a rignt cylinder 10 feet
long, the diameter of the base being 2 feet ?

Ans. 69.1152 sq. ft.

2. What is the solidity of a triangular prism whose per-
pendicular height is 150 feet, the sides of the base being 60,
80, and 100 feet ? Ans. 360000 en. ft.

PYRAMIDS AND CONES.

ART. 180. A pyramid is a solid whose base is a polygon,
and whose sides are triangles meeting in a common point called
the vertex.

A right cone is a solid resembling a pyramid, but having a
curved surface, a circular base, and its vertex always equally
distant from all points in the circumference of the base.

A pyramid is regular when besides being right, its base is
a regular polygon.

The altitude or height of a pyramid, or of a cone, is the
perpendicular distance from the vertex to the plane of the base.

The slant height of a regular pyramid or cone is the shortest
distance from the vertex to the boundary of the base.

278 SPHERES.

The frustum of a pyramid or cone is that part that remains
after cutting off the top by a plane parallel to the base.

(1.) To find the entire surface of a regular pyramid, or of
a cone.

EULE. — Multiply the perimeter or the circumference of the
base by half of the slant height, and to the product add the
area of the base.

(2.) To find the solidity of any pyramid or cone.

EULE. — Multiply the area of the base by one third of the
altitude.

(3.) To find the entire surface of a frustum of a right py-
ramid, or of a cone.

EULE. — Multiply the sum of the perimeters, or of the cir-
cumferences of the two ends by half of the slant height, and to
the product add the areas of the two ends.

(4.) To find the solidity of the frustum of any pyramid,
or of a cone.

EULE. — Multiply the areas of the two bases together, and
extract the square root of the product. This root will be the
the area of a base which is a mean between the other two.
Take the sum of the areas of the three bases, and multiply it
by one third of the altitude; the product will be the solidity.

E x a m. pies.

1. What is the entire surface of a right cone, the diameter
of the base, and the slant height .being each 40 feet ? What
its solidity ? Ans. Entire surface 3769.92 sq. ft.

Solidity 14510.42 cu. ft.

2. What are the contents of a stick of round timber whose
length is 20 feet, the diameter of the larger end being 12
inches, and of the smaller end 6 inches ?

Ans. 9 1 cu. ft. nearly.

SPHERES.

ART. 181. A sphere is a solid bounded by a curved surface,
all the points of which are equally distant from a point within
called the center.

GAUGING. 279

The diameter or axis of a sphere is a line passing through
the center, and terminated each way by the surface.

The radius is a line extending from the center to the sur-
face, and is equal to half the diameter.

(1.) To find the surface of a sphere.

KULE. — Multiply the diameter by the circumference. Or,

Multiply the square of the diameter by fff or 3.1416.

(2.) To find the solidity of a sphere.

KULE. — Multiply the cube, of the diameter by £ ff or 3.1416,
and take, one, sixth of the product. Or,

Multiply the area of the surface by one sixth of the diameter.

E 3C a rn pies.

1. How many square miles on the surface of the earth, it
being 7912 miles in diameter ? Ans. 196663355.7504 sq. m.

2. What are the solid contents of a globe whose diameter
is 10 inches ? Ans. 523.6 cu. in.

3. The surface of a certain sphere is 1648 square feet ;
what is the surface of another whose diameter is three times
as great ? Ans. 14832 sq. ft.

4. What is the diameter of a sphere containing ^ of the
solidity of another sphere 7| feet in diameter ? Ans. 5 ft.

GAUGING.

ART. 182. Gauging is the art of measuring the capacity
of casks and vessels of any form. In commerce, most of the
gauging is done by the use of technical rules and instruments,
winch give only an approximate result ; perfect accuracy by a
long process being less desirable than a tolerable approxima-
tion requiring but little skill and labor.

To gauge accurately use the following general
RULE. — Having taken the necessary linear measurements,
compute by the rules under MENSURATION heretofore given, the
volume of the inside of the cask or vessel in cubic inches.
Divide this by 2150.42/0?* the measurement in bushels, by 282
for beer gallons, by 231 for wine gallons.

280 PARTNERSHIP SETTLEMENTS.

PARTNERSHIP SETTLEMENTS.

ART. 183. The true basis of all partnership settlements is
the original agreement or contract between the parties.

To avoid misapprehension and difficulty, such agreements
should be explicit and comprehensive on all essential points ;
for, although the legal construction of such instruments aims
at the " intent of the contracting parties/' it is best to save
the necessity of such construction, by putting the intent in the
plainest possible English.

The following points should be embraced in a partnership
contract :

1. The amount, time of investment, and continuation of
each partner's capital.

2. The proportionate amount to be drawn by each partner
for his private use.

3. The basis of gain or loss, and each partner's proportion
thereof.

4. The limitation of copartnership.

Other points may be added, according to the necessities of
the case ; but great care is necessary to avoid defeating the
purposes of the contract by verbosity and ambiguity of terms.
The object of a partnership settlement is to ascertain the
relations in which the partners stand to the business and each
other. Such settlements should be effected at least as often as
once every year.

The dissolution of a copartnership may be effected by the
expiration of the terms of copartnership — the decease of one
of the partners — the breaking out of a war between the two
countries of which the partners are citizens — or the mutual
consent of the partners themselves.

After a partnership has been dissolved, and proper notice
given, one member of the firm can not bind the others by
drawing or accepting drafts, or by making promissory notes,

PARTNERSHIP SETTLEMENTS. 281

even for previously existing debts of the firm ; and although
the partner drawing the same was authorized to settle the
partnership affairs.

If a partnership be formed for a single purpose or trans-
action, it ceases as soon as the business is completed, and
a settlement should be immediately effected between the
partners.

Either partner may dissolve the partnership at any time,
by giving notice to his copartners ; even though it was under-
stood and agreed at commencing, that the partnership should
continue for a longer and definite period. But the partner
thus dissolving his connection with the firm, will subject him-
self to a claim of damages for breach of contract.

When notice of dissolution is given, and also of the ap-
pointment of one of the partners to settle up the business, a
settlement made by a debtor of the firm with one of the other
partners, without the knowledge and consent of the partner
so appointed, would be fraudulent and void.

The almost endless variety of conditions which affect part-
nership settlement, renders it extremely difficult to give general
rules and illustrations, which will cover all cases. The follow-
ing examples, however, will be found both practical and im-
portant.

C A. S E I.

ART. 134. The investment and the resources and liabilities
at closing, being given to find the net gain or loss.

Subtract the sum of the liabilities (including the invest-
ment) from the sum of the resources , and the difference will
be the net gain; or (if the liabilities are the larger) subtract
the sum of the resources from the sum of the liabilities, and
the difference will be the net loss.

Ex. 1. A and B are partners. At the close of one year's
business, an inventory is taken showing the condition of affairs
to be as follows, viz. : Cash on hand $3278. Merchandise in
store valued at §1500. Five shares City Bank Stock $500.

282 PARTNERSHIP SETTLEMENTS.

House and lot valued at §4000. The firm owe on their notes
$2000, and to Wm. Brown on account, $1200. A invested
$2426, B invested $2872. What is the net gain ? Am. $780.

Operation.

Resources. Liabilities.

Cash $3278 Firms' Notes $2000

Merchandise 1500 Due Wm. Brown 1200

City Bank Stock 500 A invested 2426

House and Lot 4000 B do. 2872

9278 p498

_8498

Net Gain $780

Ex. 2. C, D, and E are partners. After conducting busi-
ness one year they have the following resources and liabilities :
Cash on hand f4S60. Mill and fixtures valued at $6924.
Bills Keceivable $896. Brown & Co. owe $2000. Ten shares
E. K. Stock $1000. The firm owe on notes outstanding $6400.
C invested $4500. D invested $3800. E invested $3600.
What is the net loss ? Ans. $2620.

C .A. S IE II.

ART. 185. The investment, the resources and liabilities at
closing, and the proportion in which the partners share the
gains or losses being given to find each partner's interest in
the concern at closin.

Find the net gain or net loss by Rule under Case I. Then,
if there is a gain, add each partner's share of gain to his in-
vestment and subtract the amount he owes the firm. Or, if
there is a loss, find each partner's share of loss and subtract
it from his investment; also subtract any amount that the part-
ner oives the firm, as before.

Ex. 1. A and B are partners. A is to share f of the gain
or loss, and B f . At the close of business the following is
shown to be the condition of their affairs, viz. : Cash on hand
$2680. Bills Keceivable on hand $3620. Five shares United
States Stock valued at $520. House and lot valued at $6000.

PARTNERSHIP* SETTLEMENTS.

283

Sturgis & Co. owe on account §1800. The firm owe on notes
outstanding §2840. They owe G. P. Carey on account §890.
A invested §4610. B invested §4860.

What is A's interest in the concern ? Ans. A $5178.
" " B's " " " B §5712.

Operation.

Resources.
Cash on hand
Bills Receivable
U. S. Stock
House and Lot
Sturgis & Co. owe

Liabilities.

§2680
3620
520
6000
1800
14620
13200

Notes unpaid §2840

Due G. P. Carey 890

A invested 4610

B do. 4860

Net Gain §1420

5)1420
* 284 i "
3

§852 B's | "
§568 A's f "

§13200
Net Gain,

Proof.

£ash §2680

Bills Receivable 3620

U. S. Stock 520

House and Lot 6000

Sturgis & Co. 1800

Total Resources §14620

Bills Payable

G. P. Carey

A invested 4610

" f Net Gain 568

" present interest in concern

B invested 4860

" Net Gain 852

§2840
890

5178

5712

" present interest in concern
Total Liabilities "§14620

Note. — In the following examples the resources are sup-
posed to be brought in at their actual cash value. No interest
is allowed on the partners' accounts unless so specified.

Ex. 2. C, D, and E are partners. To share the gains or
losses each one third. The resources and liabilities at the close
of the year are found to be as follows, viz. : Money deposited
in City Bank §8460. Copper Mine Stock valued at §10240.

284 PARTNERSHIP SETTLEMENTS.

Bills Receivable on hand $6420. Fulton Bank Stock on hand
valued at $3826. Block of buildings and Lot valued at
$35000. Hall & Co. owe on account $1344. L. M. Howard
owes on account $960. The firm owe on their notes unre-
deemed $5680. To Mason & Austin on account $1700. C
invested $18420. D invested $18460. E invested $18432.
What is each partner's present interest in the concern ?

Ans. C $19606, D $19646, E $19618.

Ex. 3. F, G, H, and I are partners. They share the gains
or losses as follows, viz. : F and G ^ each, H T42- and I T\.
At the close of business the resources are Cash $4628, Mer-
chandise $12620, Real Estate $5000, Bank Stock $3000,
Wheat and Corn $2800, Horses and Harness $500, Lumber
$520, Money deposited in Globe Bank $8620. F has drawn
from the business $450, H has drawn $180. The liabilities of
the concern are, Notes unredeemed $4600, Due Simon Good
on account $800, Due S. S. Packard on account $1200. F in-
vested $6682. G invested $6682. H invested $8908. I in-
vested $4454. What is each partner's interest in the concern?
Ans. F $7480, G $7930, H $10392, I $5286.

Ex. 4. J, K, L, M, and N are partners. The gain or loss is
to be divided as follows : J T53, K T4Tj L T\, M T2^, N JJ}
Upon examination the following is found to be the condition
of affairs at the close of business, viz. : Notes on hand against
other persons $12680, Ohio State Stocks $8420, New York
State Stock $6000, City Bank Stock $2800, Bonds and Mort-
gages $9460, Deposit in Ocean Bank $6742, Attica Bank
owes the firm $4286, Brown & Bros, owe $1520, Interest on
Notes, and Bonds and Mortgages in the hands of the firm
$688. Office Furniture on hand valued at $824. The liabili-
ties of the concern are as follows, viz. : Notes and Acceptances
outstanding $5486, Interest due on firm's Notes and Accept-
ances $280, Bal. favor Trader's Bank $2626, Bal. favor of
Fulton Bank $1500, N invested $2287, M invested $4575,
K invested $9150, L invested $6861, J invested $11455.
What has been the Net Gain ? What is J's interest in the
concern? K's ? L's ? M's? N's ?

PARTNERSHIP SETTLEMENTS. 285

A,is. Net Gain $10200. J's interest $14855. K's interest
$11870. L's interest $8901. M's interest 85935. N's in-
terest $2967. •

Ex. 5. There are four partners in a concern, 0, P, Q, and
K. Each partner to share | of the gains or losses. At disso-
lution there is Cash on hand $6820, Bills Keceivable $8922,
Croton Water Stock $4500, Deposit in Bank Commerce
$3860. 0 has drawn from the concern $860, P has drawn
$575, Q has drawn $630, K has drawn $452. The liabilities
are : Notes and Acceptances outstanding $3680, Bal. in favor
of Smith & Co. $1264, in favor of Hall & Keed $860, Geo.
Carey §575. 0 invested $5590, P invested $5322, Q invested
$5540, R invested $5228. What has been the net gain or
loss ? What is each partner's interest in the business ?

Ans. Net Loss $1440. O's interest $4370. P's $4387.
Q's $4550. R's $4416.

C A. S EJ III.

ART. 186. The resources, the liabilities (except the invest-
ment), and the net gain or loss being given, to find the net
capital at commencing.

RULE.

When the resources are larger than the liabilities, deduct
the given liabilities from the given resources (the difference
will be the present worth of firm), and from this remainder
deduct the net gain, or add the net loss. Or,

When the liabilities are greater than the resources, deduct
the resources from the liabilities (the difference will be the
net insolvency of firm), and deduct this remainder from the
net loss.

Note 1. — The liabilities can never exceed the resources at
closing when there is a capital at commencing and a net gain
during business,

Note 2. — In the following examples it is supposed that the
whole investment is made at the time of commencing business,
and that it remains undisturbed until the date of partnership
settlement.

286

PARTNERSHIP SETTLEMENTS.

Ex. 1. A and B are partners. A invested f and B |- of
the capital. They are to share equally in gains or losses. At
the close of business the resources are : Cash $6800, Bills
Keceivable $4700, Merchandise $6400, Real Estate $5000,
Bank Stock $900, Steamboat Stock $9000. A has drawn
from the business $365, B has drawn $526. The liabilities
are : Firm's Notes unredeemed $4680, Bal. favor of S. S.
Packard $620, J. T. Calkins $476, R. H. Hoadley $326. The
net gain during business has been $2644. What was the firm
worth at commencing ? What was each partner worth ?

Ana. Firm $24945. A §9978. B. $14967.

Cash

Bills Receiv.
Merchandise
Real Estate

$6800
4700
6400
5000

Bank Stock 900
Steam Bt. Stock 9000

A is charged 365
B " 526

$33691

Cash

Bills Receiv.
Merchandise
Real Estate
Bank Stock

$6800

4700

6400

5000

900

Steam Bt. Stock 9000

A is charged
B

365
526

$33691

Operation.

Bills Payable
S. S. Packard
J. T. Calkins
R. H. Hoadley

33691 Resources

6102 Liabilities
27589 Present worth of firm

2644 Net Gain

84680
620
476
326

$6102

5)24945 Net Cap. at com.

4989

2

9978 A's | of the Cap. at com.
14967 B's f

Proof.

Bills Payable

S. S. Packard

J. T. Calkins

R. H. Hoadley

A's Cap. at com. 9978
" i Net Gain 1322
" Present worth

B's Cap. at com. 14967
" J Net Gain 1322
" Present worth

?46SO
620
476
326

11300

_16289
$33691

PARTNERSHIP SETTLEMENTS. 287

Ex. 2. C, D, and E are partners. C invested {, D f , and
E |, to share the gain or losses equally. At the close of busi-
ness the resources are found to be : Wheat on hand valued at
§2600, Corn on hand $3200, Flour $1600, Mill and Fixtures
$8000. The firm owe Digby V. Bell $2600, to J. H. Gold-
smith $1500, and on their Notes unredeemed §949. The net
loss in the business has been $633. What was the net capital
of the firm at commencing ? What was each partner's net
capital ?

Ans. Firm §10984. C $1373. D §4119. E §5492.
Ex. 3. There are four partners engaged in business as a firm,
F, G, H, and I. They have been unfortunate, the net loss
being $15320. On examination the resources are found to be
as follows, viz. : Live Cattle on hand valued at $9680, Packed
Beef valued at $12600, Empty Barrels on hand valued at
$500, Deposit in Drov.ers' Bank $2500. The firm owe on
their Notes and Acceptances §22600, Warren P. Spencer on
account $4000, J. C. Bryant on account §6000. The partners
invested in equal amounts and are to share the gains or losses
in the same proportion. What was the investment of the
firm ? What was each partner's investment ?

Ans. Firm $8000. F §2000. G §2000. H. §2000. I $2000.

CA.SE IAT.

ART. 187. -When the firm commence insolvent.
The resources and liabilities at closing, and the net gain or
loss being given, to find the net insolvency at commencing.

R. TJH. IE.

Wlien the liabilities are greater than the resources at
closing , deduct the given resources from the given liabilities,
and to this remainder add the net gain or from it subtract the
net loss. Or,

When the resources are larger than the liabilities at
closing, deduct the liabilities from the resources, and deduct
this remainder from the net gain.

Ex. 1. A and B are partners. They commence business
insolvent. The proportion of their insolvency is A |, B j.

288 PARTNERSHIP SETTLEMENTS.

The gains or losses are to be equally divided. At the close of
business the resources are, Cash on hand $3246, Lumber on
hand valued at $6428, Timber and Logs valued at $3272,
Bills Receivable $1800. The firm owe on their Notes and
Acceptances $9400, to E. R. Felton on account $3684, to H.
W. Ellsworth on account $2160. The net gain during busi-
ness has been $1568. What was the net insolvency of the
firm at commencing ? What was each partner's net insolvency
at commencing ?

Ans. Finn's $2066. A's $1549.50. B's $516 50.

Operation.

Cash on hand $3246 Bills Payable $9400

Lumber " 6428 E. R. Felton 3684

Timber and Logs on h. 3272 H. W. Ellsworth 2160

Bills Receivable " 1800

$"14746 $15244

$15244 Liabilities

4)2066 Net Insolv. at com. 14746 Resources

516.50 B's i " « ~^98~Pres. Net Insolv. of firm

3_ 1568 Net Gain

$1549.50 A's | " " 2066 Insolv. of firm at com.

Proof.

Cash $3246 Bills Payable $9400.00

Lumber 6428 E. R. Felton 3684.00

Timber and Logs 3272 H. W. Ellsworth 2160.00

Bills Receivable 1800 B's £ Net Gain 784.00

A's Insolv. at com. 1549.50 " Ins, at com. 516.50

" J Net Gain 784 " Net Capital ~ ~26750.00

" Net Insolvency . . 765.50
Tot. Resources of firm $1551150 Tot. Liab. of firm"|l5511~50

Eemarlc. — In the foregoing example the partners were both
insolvent at commencing business. The business was profit-
able, and B's share of the gain was more than his insolvency
at commencing, so that he ends with a net capital. A is still
insolvent, but to a less amount than when he commenced.

PARTNERSHIP SETTLEMENTS. 289

Ex. 2. C, D, E, and F are partners, commencing with
equal insolvency, the gains or losses to be shared as follows,
viz. : C T3o, D T42? E T22> & T32' Two years having passed an
inventory is taken, showing the following condition of affairs :
20000 Ibs. Cheese on hand @ 8 cents, $1600 ; 40000 Ibs. But-
ter @ 18 cents, $7200 ; 2000 bush. Potatoes @ 40 cents, $800 ;
3000 bush. Wheat @ 90 cents, $2700. The firm owe on their
Notes and Acceptances $8628. They owe E. B. Kockwell
on account $3242. They owe W. H. Clark on account $4563.
There has been a net loss during the business of $528. What
was the net insolvency of the firm at commencing ? What
was the net insolvency of each partner ? What is the net in-
solvency of each partner at closing ?

Ans. Insolvency of firm at com. $3605. Insolvency of each

partner $901.25. Insolvency of firm at closing $4133.

C $769.25. D $725.25. E $813.25. F $769.25.

Ex. 3. G, H, I, J, and K formed themselves into a co-
partnership for the purpose of carrying on the building and
masonry business. The firm to assume the liabilities of the
partners. The proportion in which the partners are insolvent
at commencing is as follows, viz. : Gr -f-g, H ^ I ^ J ^
and K ^V The gains or losses are to be divided in the pro-
portion of their insolvency. At the close of business the fol-
lowing is the condition of affairs : Deposit in City Bank
$5428, Bonds and Mortgages Kec. $3826, Notes and Drafts
$6294. J. C. Bryant owes on account $4466, Brick and
Stone on hand valued at $3688. The firm owe on their Notes
and Acceptances $18000. They owe Baldwin & Co. $3620.
The Net Gain has been $5622. What was the net insolvency
of firm at commencing ? What was the insolvency of each
partner ? What is the net capital of firm at closing ? Of
each partner ?

Ans. Insolvency of firm at commencing $3540. Of
G $354, H $531, I $708, J $885, K $1062.
Net capital of firm at closing
H$ ,I8^

19

290 PARTNERSHIP SETTLEMENTS.

MISCELLANEOUS.

1. D. Y. Bell, J. H. Goldsmith, E. G-. Folsom, and J. C.
Bryant, are partners. The two former furnish the capital, and
the two latter are to bear the expenses of conducting the busi-
ness, each one half. The profits or losses are to be distributed
as follows : Bell ^ Goldsmith Yflu? Folsom ^, and Bryant ^.
Bell advanced at commencing business $18423. Goldsmith
advanced $13142. At the close of the year it is ascertained
that the profits have exceeded the losses (not including ex-
penses) $6823.80. The expense account has an excess of
debits of $2412.08. Bell has drawn out during business $426.
Folsom has drawn but $2342.13. What is each partner's in-
terest in the concern at the close of the year ?

Note. — In the above example Mr. Goldsmith was allowed
to draw a large amount from the business, and by consent of
the other partners was not to pay interest upon it. Interest
is not to be taken into account in solving this and the follow-
ing examples unless it is so specified.

2. S. S. Packard, J. T. Calkins, and E. B. Rockwell are
partners, to share the gains or losses equally. At the close of
one year the following is the result of the business : Cash on
hand $8920, Bills Receiv. $6273, Merchandise $5682, Bank ]/
Stock $896, Mr. Packard has drawn from the concern $672.43,

Mr. Calkins $2471.04, Mr. Rockwell $1896.06. Bills Payable
outstanding §5957.95. Packard invested $7420, Calkins in-
vested $6812, Rockwell invested $4635. What has been the
gain or loss ? What is each partner's present interest in the
concern ?

3. R. W. Hoadley, H. W. Ellsworth, and H. C. Spencer
are partners. They invest in equal amounts, and share gains
and losses equally. At the expiration of two years they" have
Cash on hand $7242, R. R. Stock $4860, Real Estate $4673,
Produce $2921. They have Bills Payable outstanding
$2326.41. During business Mr. Ellsworth has withdrawn
from the concern $924, and Mr. Spencer has advanced to the

PARTNERSHIP SETTLEMENTS. 291

concern $1138. The total losses have been $754.25, the total
gains §3269.54. What is each partner's share of gain or loss ?
What was each worth at commencing ? What is each part-
ner's" interest in the concern at closing ?

4. R. C. Spencer, W. H. Clark, L. Fairbanks, and C. E.
Wilber have been associated in business during the past three
years. The books have remained unclosed to this date.

R. C. S. invested at commencement of business $6824.00

W. H. C. " " " 5982.00

L. F. " " " 7126.00

C. E. W. " " " 4998.00.

They are to share equally in gains or losses. Since the books

were opened the partners have made the following additional

investments : R. C. S. $2128.40, W. H. C. $684.12, L. F.

81242.78, C. E. W. §946.64. The partners have each drawn

from the concern the following amounts : R. C. S. $8126.42,

W. H. C. $5274.18, L. F. §8232.64, C. E. W. $3178.26.

There are no resources or liabilities at this date except such as

are shown by the partners' accounts. Has the business been

prosperous or adverse ? If a dissolution now take place, how

shall the partners settle with each other ?

5. G. B. Collins, A. H. Redington, and Alonzo Gaston
were partners in a manufacturing business, commencing July
1st, 1856. At that date G. B. C. put into the concern $1600,
A. H. R. put in §4000, A. G. made no investment, but was to
superintend the business. They were to share equally in gains
or losses. Six per cent, interest to be allowed on each side of
the partners' accounts. The books are not closed until July 1st,
1858, when the following statement is rendered by the book-
keeper : G. B. C. has drawn from the concern at different
times to the amount of $14760, the average date at which it
was drawn, being September 12th, 1857. A. H. R. has drawn
$11380, average date January 22d, 1858. A. G. has drawn
§16240, average date May 16th, 1857. G. B. C.'s total invest-
ment has been $2982, average date August 17th, 1857. A. H.
R/s total investment $6824, average date October 9th, 1856.
A. G.'s total investment $1528, average date April 24th, 1858.

292 PARTNERSHIP SETTLEMENTS.

Cash on hand $628, Cash in Bank $2892, Bills Keceivable on
hand $5462, Real Estate $7586, Manufactured Articles $4327,
Personal Accounts $1523, R. E. Stocks $837, Bills Payable
unredeemed $6248, Balance due on personal accounts $4895.

What has been the net gain or loss of the firm ? What
is each partner's present interest in the concern ?

A. H. R. proposes to retire from the business, and the other
partners agree to give him $900 more than the books show to
be due him. How much will he receive ?

6. A of New York, and B of Ohio, enter into an arrange-
ment to buy and sell Cattle, and share equally in gains and
losses ; B to make the purchases, and A to effect most of the
sales. A forwarded to B a draft of $8000, B made purchases
to the amount of $13682.24. B has forwarded cattle to A
during the season, from which he has made sales to the amount
of $9241.18. B has made sales to the amount of $2836.24.
A has paid out for expenses $364.16. B has paid out for ex-
penses $239.14. At the close of the season B has on hand
a number of cattle the cost of which was $2327.34. A has a
quantity on hand which are estimated to be worth, in the New
York market, $3123.42. The parties now propose to dissolve
the copartnership, each taking the stock he has in his posses-
sion at the figures given above, and the balance in their ac-
counts, if any, to be paid in cash. What has been the gain or
loss ? What is each partner's share of gain or loss ? What is
the cash balance to be paid, and which partner is to receive it ?

7. C and D make a contract with government to do a cer-
tain piece of work, which is divided into three sections, for
which they are to receive as follows, provided the work all
pass as No. 1 on being inspected : for Section 1, $1842, for y
Section 2, $1275, for Section 3, $1563. If any portion of
the work pass as No. 2 on inspection, 15 per cent, will be de-
ducted from the original estimate ; if any portion as No. 3,
20 per cent, will be deducted. The following is the result of
the inspection :

Section 1, passes as No. 1. Section 2, as No. 3, and Sec-
tion 3, as No. 2.

PARTNERSHIP SETTLEMENTS. 293

0 has drawn from government $728.42. D has drawn
§1226.14. D has made disbursements to the amount of
$1342.25. C has made disbursements on the work to the
amount of §987.45. What has been the gain or loss ? How
much is due C ? How much is due D ?

8. Two persons, E and F, enter into business under an
agreement that E shall draw from the concern weekly $5 more
than F. Subsequently F lends E $260 from his private funds,
with the understanding that they were then to draw an equal
sum weekly until the loan be liquidated. How long will
it take ?

9. Three mechanics are partners. They agree that each
shall pay $2.25 per day for all working days that he is absent
from the business. At the close of the year it is found that
A has lost 44 days, B 28 days, C 12 days. How will the
partners adjust the matter between them ?

10. A, B, and C enter into a copartnership, each in-
vesting $5000. A is worth to the business $1500 a year ; B
$1200 ; C §1000. At the end of two months B draws out
$500, and A adds to his capital $1000. At the end of five
months, C withdraws §300. They close up their business at
the end of a year, and find that a net profit has been realized
of $3500. What proportion of this gain belongs to each
partner, if money is worth 7 per cent, per annum ?

11. Again : A, B, and C are partners, each investing at
the commencement of business $5000, and each being of equal
value to the business. They draw from and add to the capital,
as before, and at the end of the year ascertain their gain to be,
as before, $3500. How will the gain be equitably divided ?
And should the value of money, as in the former case, have
any efiect on the adjustment of gains ?

12. Again : A, B, and C are partners, investing as in the
former two instances, with the understanding that C shall con-
duct the business, for which he is to receive a commission of
25 per cent, on the net gain. The additions and withdrawals
the same as above, and also the gain. How much of the gain
should each have ?

294 PARTNERSHIP SETTLEMENTS.

13. There are five partners in a concern, sharing the gains
or losses equally. The liabilities of the firm have been can-
celed, after which the remaining effects were appropriated by
the partners without regard to the proper proportion that
each should take. The following is the condition of the part-
ners' accounts, as they now stand. A invested $5680, and
has drawn from the concern §4700. B invested $4780, and
has drawn $4400. C invested $4980, and has drawn $4600.
D invested $3984, and has drawn $3300. E invested $5600,
and has drawn $5346. How will the partners settle with
each other ?

14. A and B are partners. They have Cash and Collect-
able Paper on hand to the amount of $5280.11. A has drawn
from the concern $2446.80, B has drawn $905.98. A put
into the concern $3127.25, B put in $448.75. The firm owe
on Paper and Book Debts $4005.48. What is each partner's
present interest in the concern, if they share equally in gains
and losses ?

15. S. S. Guthrie and H. C. Walker purchased a vessel on
joint account, for which they paid $8400, Mr. G. taking one
third interest and Mr. W. two thirds.

During the season G. paid for supplies, repairs and

sundry expenses $956.00

And received Cash from freight and passage receipts 2686.40

W. paid for repairs, supplies, &c. . . . 1548.26

And received Cash from freight and passage receipts 4862.48

At the close of the season they sell the vessel for $9000,

receiving one half in Cash, and the purchaser's Note for one

half.

W. agrees to take this Note, to apply on his account, at
^% discount, which G. assents to ; and then the $4500 Cash
is properly divided between the two partners ; how much is
taken by each ?

16. Alonzo Gaston and G. B. Collins take a contract of
A. H. Kedington to sink an aqueduct of a certain width 50
rods in length, and if it average 10 feet deep, they are to
receive for constructing the same $26 per rod. If on measure-

PARTNERSHIP SETTLEMENTS. 295

ment it average less than 10 feet, 3$ will be deducted for the
first 6 inches, 6% for the second 6 inches, 9$ for the third 6
inches.

A. G. has paid out for wages and material $158
G. B. C. " " " $536

A. H. R. has advanced $488, of which A. G. received $242.18,
G. B. C. received $245.82. The average depth was to he ascer-
tained by measurement at the end of every five rods, which
resulted as follows :

ft. in. ft. in.

End of 1st five rods 10 4 End of 6th five rods 7 10

" 2d " 10 9 " 7th " 84

" 3d « 98 " 8th " 79

" 4th "94 " 9th " 9 7

" 5th "83 " 10th " 88

What has been the gain or loss ? How much is due from A.

H. R. ? How will Mr. Gaston and Mr. Collins settle with

each other ?

17. A and B contracted with Kussell & Co. to erect a
Steam Flouring Mill for $11000. Not wishing to be burdened
with the salary of a bookkeeper, it was arranged that each
partner should keep a strict account of all his receipts and ex-
penditures, and report at the completion of the contract, at
which time they would have a general settlement. On the
fulfillment of the contract they find their affairs standing as
follows, viz. : A has paid out for building material and wages
$2862.48. He has received from Russell & Co. at different
times to the amount of $1324.08. B has paid out for building
material and wages $4788.04. He has received from Eussell
& Co. ?5024.44. There is due the hands for wages $410.

What has been the1 profit ? How much is due from Russell
& Co. ? And how much of it should be paid to A ? How
much to B ?

18. E. C. Bradford, Joseph Dawson, and E. Young have
been doing business together as partners, with the understand-
ing that Mr. B. should receive a salary of $1200, for managing
the concern, the other partners' time not to be required in the
business. Interest to be allowed on both sides of each part-

296 PARTNERSHIP SETTLEMENTS.

ner's account. The profits or losses to be divided equally be-
tween them. Mr. B. invested January 1, I860, $6000, May 2,
$350, October 12, $500. He drew out February 8, $250,
April 4, $380, July 5, $620, November 20, $782. Mr. D.
invested January 1, $5400, June 12, 860, $280, October 3,
$365, December 18, $428. He drew out March 2, $468, May
21, $428, August 3, $542, September 15, $247, December 19,
$388. Mr. Y. invested January 1, $4896, May 9, $356, July 2,
$428. He drew out March 13, $355, June 3, $126, August 9,
$281, October 6, $126, December 24, $43£. On December 31,
I860, one year from the day of commencing business, the re-
sources and liabilities (not including the partners' accounts)
are as follows, viz. :

Cash on hand .... $5680
Bills Keceivable on hand . . . 4366
Heal Estate "... 5200

Bank Stock " ... 5388

$20634

Bills Payable unredeemed . . $1298.40
What is the net capital of the firm at closing ? What is
each partner's interest in the concern at closing ?

19. The following " Statement/' taken from a single entry
ledger, in part, the balance being made up from inventories
and estimates shows the present condition of the affairs of the
firm of A & B.

RESOURCES TAKEN FROM THE LEDGER.

John Smith owes $460.00

Wm. Brown " 680.00

Geo. Carey " 1260.00

Wm. Dudley " 870.00

Geo. Bryant " 260.00

Amos Dean " 890.00

A has drawn from the concern ! 2400.00

B " " " 1261.00

LIABILITIES TAKEN FROM THE LEDGER.

Due Baldwin & Co., on account .... $546.00

A invested 11600.00

B " . 13742.00

PARTNERSHIP SETTLEMENTS. 297

RESOURCES NOT SHOWN ON LEDGER, TAKEN FROM
INVENTORIES AND ESTIMATES.

Merchandise on hand, per Inv. . . . $9685.00

Notes and Drafts on hand, per B. B. (Face) . . 5672.00

Store Fixtures on hand 384.00

Horses, Carriages, and Harnesses .... 865.00

Stable and Feed 1262.00

City Bank Stock 892.00

House and Lot valued at 6000.00

C. C. & C. R. R. Stock valued at .... 1820.00

Bent paid in advance 600.00

LIABILITIES NOT SHOWN ON LEDGER.

Firm's Notes and Acceptances outstanding (Face) $3826.00
Mortgage on House and Lot 500.00

ADDITIONAL ITEMS OF RESOURCE AND LIABILITY.

The interest upon the Notes and Drafts that are on

hand, computed up to this date, is ... $694.00
The interest upon the Notes and Drafts that the firm

owe, computed to this date, is ... 148.00

A was to share f of the gain or loss, and B f . What was
the firm worth at commencing business ? What is the firm
worth at the close of business ? What has been the net gain
or net loss of firm ? What is each partner's interest in the
concern at closing ?

20. Wrn. H. Kinne and Edward Rice are partners in the
Stone business. They have a Stone Yard, and buy and sell
that material. Their books are kept by single entry. The
books run four years before they are closed. An Inventory is
taken and a Statement made up at the close of the first year.
At the close of the second year, the party having charge of
the books neglects to do this. At the close of the third year,
the Inventory and Statement are made up, showing the result
of two years' business. The Statement and Inventory are
made up again at the close of the fourth year.

The profits or losses of the first year are to be divided as
follows, viz. : Wm. H. Kinne |, Edward Rice £.

298

PARTNERSHIP SETTLEMENTS.

At the commencement of the second year J. G. Kanney is
admitted as a partner, the three partners to be equally in-
terested in gains or losses.

The following Statements were made out at the close of
the first, third, and fourth years.

1856 to 1857. 1st year's business.

Cash on hand

W. H. Kinne — paid him .
Stone on hand
Balances on Ledger .
Edward Eice — advanced by him
Gains

Resources.

$1260.11

786.49

430.66

6945.00

$9422.26

Liabilities.

$2675.44

6746.82

$9422^6

1857—1858 to 1859. 2d and 3d years' business.

Edward Kice — paid him . $2675.44

" advanced last year
" " paid him . . 829.58
W. H. Kinne " " . 2947.73

J. G. Kanney " " 1535.39

Balances on Ledger . . 7039.67

" " " last year

Gains ......

$15027.81

1859 to 1860. 4th years' business.

$2675.44

6945.00
. 5407.37
$15027.81

Edward Kice — paid him

Win. H. Kinne " " .

J. £. Kanney " "

Balances on Ledger .

" " " last year
Stone on hand .
Gains

$1014.47

1543.16

. 557.95

10137.06

981.49

$14234.13

$7039.67

_ 7194.46
$14234.13

The above Statements are given precisely as they were
made up by one of the partners who handed them to us for

P A R T N BOl SHIP -SETTLEMENTS. 299

^adjustment. The student will please exercise his skill in pro-
ducing the best form of Statement for showing clearly and
conclusively each of the answers to the following questions.

How much is the firm worth at the close of each year, and
what does the property consist of ? What is each partner's
nterest in the concern at the close of each year ?

SUPPLEMENT.

RATES OF INTEREST ASTD STATUTE LIMITATIONS
IN THE UNITED STATES.

STATES.

1

!

Allowed
by contract.

PENALTY FO2 USURY.

Statute
Limitations.

«
\

1
£

Judgments.

c
S
6
10
G
6
G
7
6
G
G
G
5
G
G
G
7
7

G

6

G
6

7

6

G
G
6
7
G
8
6
G
7

%

10
18

8
10
10
8

10
Free

10
10

10
12

12

Forfeiture of entire interest

yrs.
3
3
1
6
3
5
4
5
6

1
3
6
3
6
6

3
5
6
6

6
3
6
6
6
4
3
2
6
5
6

yrs.
6
5
4
6
6
5
6
5
20
5
5
5
6
3
6
6
6
6
10
6
16

6
3
15
6
6
4
6
4
6
5
6

yrs.
20
10
5
17

20
20
20
20

15

20
12

10
7
20
20
16

20

20
20

16

8
20

Arkansas

California

Forfeiture of entire interest

Connecticut

Delaware

principal

Florida
Georffi0

Forfeiture entire interest.

" excess of interest

Illinois

" entire interest

Usurious interest recoverable. . . .

Iowa

ti U . ((

Kentucky
Louisiana

" excess void. .

Forfeiture of entire interest

Usurious excess void.

Maryland

Forfeit of usur v

Massachusetts. . .
Michigan

Forfeit 3 fold usurious interest taken
Usurious excess void

Minnesota

Forfeiture of interest

Mississippi.

Missouri

Forfeit entire interest

New Hampshire. .
New Jersey
New York

Forft. 3 fold usurious interest taken
Contract void

f Con. void. Fine not over $100, and im-
prisonment not over 6 mos., or both. . .
Forfeit double the debt . . .

North Carolina. . .
Ohio

Usurious excess void

Pennsylvania ....
Ehode Island ....
South Carolina. . .
Tennessee

Forfeit entire principal and interest

Usurious excess void . .

Forfeit entire interest

Fine at least $10

Texas . . .

Forfeit entire interest • . -t .

Vermont

"Virginia >

Contract void . . .

Wisconsin . .

Forfeit entire debt..

* Corporations excepted.

302 SUPPLEMENT.

EXCHANGE TABLES.

[COMPILED MAINLY FROM TATE'S MODERN CAMBIST,
AND THE BANKERS' MAGAZINE.]

GREAT BRITAIN.

MONEY OF ACCOUNT. — 1 pound =12 shillings =2 40 pence, called
Sterling money, to distinguish it from Colonial money, and
other moneys of the Continent having the same denomina-
tions.

PAR OF EXCHANGE. — 1 sovereign =£1= $4. 86 1.*

FRANCE.

MONEY OF ACCOUNT.— 1 franc =100 centimes. Formerly livres
and sous were used; 81 livres=80 frcs., and 1 sou=5 centimes.

PAR OF EXCHANGE. — 20 francs gold=15s. lO^d. sterling=$3.84.
Or, $1=5 frcs. 21 centimes, or £1=25 frcs. 22 centimes.

AMSTERDAM.

MONEY OF ACCOUNT. — 6 florins or guilders =600 centimes =120
stivers=240 grotes Flemish=20 schillings Flemish=2f rix
dollars.

PAR OF EXCHANGE. — 12 florins 9 centimes =£1= $4. 86 f. Or, 1
florin =$0.40. In the U. S. the quotations of exchange on
Amsterdam are so many cents per florin or guilder.

BELGIUM.

MONEY OF ACCOUNT. — The official money of account is kept in
francs and centimes the same as in France. But in mercantile
accounts and exchange it is generally in florins and centimes,
as in Amsterdam — the denominations of schillings and grotes
being sometimes used in London Exchange.

* This value of the pound sterling is TV of a cent lower than that given on
page 164, as here the weight of the sovereign is taken to be 123£££ grains in-
stead of 123^ grains, as assumed there.

S U P P L,E M E N T . 303

PAR OF EXCHANGE. — The fixed relative value of the franc to the
florin is 47| centimes of a florin =1 franc. 25 frcs. 22 cen-
times=12 florins 9 centimes=40 schillings 3 grotes=£l =

$4.86f.

HAMBURG.

MONEY OP ACCOUNT. — There are two standards in Hamburg, the
one Banco and the other currency — the former being from 20
to 26^ higher than the latter, varying with the market price
of fine silver. The former is used in wholesale business and
in exchanges, and is nominal ; while the latter is used in the
smaller trade, and is represented by corns in circulation. The
Cologne mark weight, of the Hamburg standard, is 3608 grains
Troy ; and this weight of fine silver is assumed to be divided
into 27f marks banco, but is coined into 34 marks current.
The denominations in the two valuations being the same, the
terms banco and current are used to distinguish the standard.
1 mark=16 schillings =192 pfennings. 3 marks, or 48 schil-
lings, are called in exchange a rix dollar.

PAR OF EXCHANGE. — 13 marks 10| schil. banco =£l=$4.86|.
16 " 12~ " cwm?w*=£l=$4.86*.
Or, 1 mark banco = 3 5 ^ cents. In the U. S. the quotations of
exchange on Hamburg are so many cents per mark banco.

PRUSSIA.

MONEY OF ACCOUNT. — 1 Prussian dollar =30 silver groschen.

PAR OF EXCHANGE. — 1 Cologne mark weight of fine silver is
coined into 14 dollars ; hence, 6 Prussian dollars 27 silver
groschen = £l = $4.86f.

RUSSIA.

MONEY OF ACCOUNT. — 1 ruble =100 copecs. 100 silver rubles =
350 paper or bank rubles — the latter being the money of ac-
count, previously to July, 1839.

PAR OF EXCHANGE. — 1 silver ruble=37^d. sterling. At Odessa
the rate of exchange on London is still generally made in paper
rubles, in which the par of exchange is 2240 paper rubles^
£100 sterling.

304 SUPPLEMENT.

•

FRANKFORT-ON-THE-MAINE.

MONEY OF ACCOUNT. — 1 rix dollar— 90 krenzeT8=l| florins =
22£ batzen = 360 hellers. The Prussian money is used for the
payment of duties in Frankfort, and in all the States of the
German Customs-Union — the value of 1 Prussian dollar being
fixed at 105 kreuzers. There are two moneys of account at
Frankfort, viz., Reichsgeld or 24 Guldenfuss, and "Wechselzah-
lung. Reichsgeld is called 24 Guldenfuss or florin-foot, from
the Cologne mark weight of fine silver being valued at 24 of
these florins. WechselzaKlung, or exchange reckoning, is de-
duced from the estimation of the carolin at 9 florins 12 kreuz-
ers in Wechselzahlung, the value of the same being 11 florins in
24 Guldenfuss, from which 46 rix-dollars W. Z.=55 rix dollars
in24G.F.

PAK OF EXCHANGE.— 148.2 batzeu W.Z. = £l=$4.86f.

1 rix-dollar in 24 Guldenfuss =30. 4 7 pence sterling.
" Wechselzahlung=36.43 "

AUSTRIA.

MONEY OF ACCOUNT. — 1 florin =60 kreuzers. A rix-dollar is 1^
florins or 90 kreuzers, and is a nominal money used in ex-
changes but not in accounts. The value of the money of
account is that called Convention, or 20 Guldenfuss, in which
the Cologne mark weight of fine silver is supposed to bo
coined into 20 florins, a standard only T4T$ above the Wechsel-
zahlung of Frankfort. The currency of Austria is of both
paper and metal. The paper money, called Wiener-wahrung,
or Vienna value, is at a fixed discount of 60$: by which 100
florins in cash are equal to 250 florins in W. "W. Bills upon
Vienna are generally directed to be paid in effective — that is,
in cash — sometimes mentioning the kind (as 20 kreuzer-pieces,
for example), to guard against their being paid in paper money
of the depreciated value.

PAR OF EXCHANGE. — 9 florins 50 kreuzers =£1=84.86=-.
1 rix-dollar in 20 Guldenfuss = 3 6. 5 6 pence sterling.

VENICE AND MILAN.

MONEY OF ACCOUNT. — 1 lira Austriaca=100 centisimi=20 soldi
Austriaci. The lira has the same value as the 20 kreuzer-piece,
or the third of an Austrian florin.

PAR OF EXCHANGE. — 29 lire 52 cent.=£l, or 1 lira=8id.

SUPPLEMENT. 305

TUSCANY.

MONEY OP ACCOUNT. — 1 lira Toscana=100 centisimi=20 soldi
di Lira, a little below the Venetian standard.

PAR OF EXCHANGE. — 30.69 lire =£1, or 1 lira=

BREMEN.

MONEY OF ACCOUNT. — 5 schwaren— 1 grote ; 72 grotes=l rix-
dollar. The rix-dollar is valued, in gold, from the old French
and German Louis d'or, at the rate of 5 rix-dollars to 1 Louis
d'or.

PAR OF EXCHANGE. — 1 rix-dollar = 3s. 3.4d. sterling=S0.79£. In
the U. S. the quotations of exchange on Bremen are so many
cents per rix-dollar.

CANADA.

MONEY OP ACCOUNT. — 1 pound =20 shillings =240 pence =4 dol-
lars =400 cents. The decimal system of dollars and cents has
been recently introduced.

PAR OF EXCHANGE. — The Canadian pound (£), as represented
by their paper currency, has been considered equivalent to four
dollars U. S. currency. But the recent silver coinage, fur-
nished that province by England, is 3f$ below the silver coin-
age of the U. S. in value, their 20 cent-piece being worth only
$0.1927; and as the U. S. silver coinage is somewhat below
par, taking the gold coinage for the standard, we may con-
clude that the par of exchange between Canada and the United
States will soon be 104 cents Canada currency = 6 1, or 100
cents U. S. currency.

UNITED STATES.

PAR OF EXCHANGE. — Gold, or its equivalent, being the cur-
rency of New York city, and paper money being extensively
used throughout the States, the par of exchange on New York
city, for the year 1860, is very nearly as follows:

New England States, \% prem. \ Ohio, Ky., and Ind.,

New York State, £$ '" j Detroit/

Baltimore, - - Par. Interior Michigan, \\%

Philadelphia,

Pit tsburg" par funds," "

""

currency

20

Iowa, 111., and Wis., \\% "
Missouri, - - \~ % "
New Orleans, - Par.

306

SUPPLEMENT

FOREIGN COINS.

Their Weight, Fineness, and Value, as Assayed at the United States Mint.

Remark. — The basis of valuation of the silver coins is $1.21
per ounce of standard fineness, which is the present mint price.

GOLD COINS.

CouNTar.

DENOMINATION.

Weight.

Fineness.

Value.

Australia

Pound of 1852

Oz. dec.
0.281

Thous.
916.5

D. C. 3f.

532 0

Australia . . . .

Pound of 1855

0 257

9165

4 85 0

Austria

Ducat

0.112

986

2 28 0

0.3G3

900

6 V7.0

Belgium . .

Twenty-five francs.

0 254

899

4 72 0

Bolivia

Doubloon

O.S67

870

15 58 0

Brazil

20,000 reis

0.575

917.5

1090 5

Central America. .

Two escudors

0 209

853 5

3 66 0

Chili

Old doubloon

0 867

870

15 57 0

Chiii

0.492

900

9 15.3

Denmark

Ten thaler

0 427

895

7 900

Ecuador. . ...

Four escudors

0433

844

7 60 0

England

Pound or sovereign, new. . .

0.256 7

916.5

4 86.3

England

Pound average .

0 256

915 5

4848

France

Twenty francs new .

0.207 5

899 5

3 86 0

France

Twenty francs, average

0 207

899

3 84.5

Germany North

Ten thaler .

0 427

895

7 900

Germany North

Ten thaler. Prussian.

0497

(03

8 00 0

Germany, South
Greece

Ducat..

0.112
0.185

986
900

2.28.3
3.45.0

Hindostan

Mohur ... .

0 374

916

7 08.0

Mexico

Doubloon, average ....

0 867 5

866

15,53.4

Naples

0.245

996

5.04.0

Ten guilders

0.215

899

3.99.0

New Grenada

Old doubloon Bogota

0 8G8

870

15 61.7

New Grenada.. . .

Old doubloon, Popayan.

0 867

858

15.39.0

New Grenada,

0.525

891.5

9.67.5

Peru

Old doubloon

0 867

868

15.56.0

Portugal

Gold crown

0 308

912

5.81.3

Rome

2-J- Scudi, new

0.140

900

2.60.0

Russia

Five roubles

0.210

916

3.97.6

Sardinia

Spam

100 reals

0 268

896

4.96.3

Sweden

Ducat .

0 111

975

2.26.7

Turkey

100 piastres

O.°31

915

4.37.4

Tuscan\-. . .

Sequin. .

0.112

999

2.30.0

The above shows the intrinsic relative value, as compared with
the amount of fine gold in the U. S. coin. The price paid at the
mint would be \% less.

SUPPLEMENT.

307

SILVER COINS.

COUNTRY.

DENOMINATION.

Weight.

Fineness.

Value.

Austria,

Rix-dollar

Oz. dec.
0902

Thous.
833

D.C.M.
1013

Scudo of six lire

0 836

902

1 01 5

Austria . . .

20 kreutzer

0 915

582

16 8

Five francs. ....

0.803

897

96 8

Bolivia

Dollar

0.871

900.5

1.05 4

Bolivia

Half dollar 1830

0433

670

38 5

Bolivia

Quarter dollar 1830.

0.216

670

19 2

Brazil

2 000 reis

0 890

918 5

1 01 3

Central A.merica . .

Dollar

0866

850

97 3

Chili

Old dollar. .

0.864

908

1 047

Chili

New dollar

0.801

900.5

97 0

Denmark . .

Two ri<rsdaler

0 927

877

1 09 4

England

Shilling, new

0.182.5

924.5

22 7

England

Shilling average

0 178

995

22 2

France

Five francs, average . .

0.800

900

96 8

Germany, North

Thaler

0 712

750

71.7

Germany South

Gulden, or florin

0340

900

41 2

Germany, North & South .
Greece rf

2 thaler, or 3^ guld
Five drachms

1.192
0.719

900
900

1.44.3

869

Hindostan . .

Rupee . .

0374

916

46 0

Japan

Itzebu

0.279

991

37 0

Mexico

Dollar average

0 866

901

1 04 9

Naples

Scudo ....

0 884

830

98 8

Netherlands

2i guilder

0.804

944

1 023

Norway

Specie-daler

C 927

877

1 09 4

New Grenada

Dollar of 1357

0803

896

968

Peru

Old dollar

0 866

901

1 04 9

Peru

Old dollar of 1855

0 766

909

93 6

Peru

Half dollar, 1835-'38..

0.433

650

377

Portugal

Silver crown

0 950

912

1166

Rome . .

Scudo

0864

900

1 04.7

Russia

Rouble

0 667

875

78 4

Sardinia. . . ....

Five lire . .

0800

900

96 8

New pistareen

0.166

899

20 1

Sweden

Rix-dollar

1 092

750

1101

Switzerland

Two francs

Oo23

899

39 0

Turkey

Twenty piastres

0 770

830

86 5

Tuscany.. .

Florin. . .

0.220

925

27.4

308

SUPPLEMENT.

LINEAR, OR LONG MEASURE.

This measure is used to define distances in any direction.

12 inches

3 feet
5^ yards
40 rods

8 furlongs

TABLE.

(in.) make 1 foot ft.

" 1 yard yd.

" 1 rod rd.

" 1 furlong fur.

" 1 statute mile. . mi.

EQUIVALENTS.

mi. fur. rd. yd.

1 = 8 = 320 = 1760

1 = 40 = 220

1 = 5

1

ft.

= 5280
— 660
= 16
= 3
1

in.

= 63360
— 7920
= 198
= 36
= 12

SCALE OF UNITS:— 12, 3,

3 Jbarleycorns

4 inches
6 feet

1.15 statute miles
3 geographic miles

60

69^ statute "
360 degrees

40, 8.

ALSO:

make 1 inch
" 1 hand
" 1 fathom

" 1 geographic mile . . "
" 1 league.

" )

„ j- 1 degree.

" the circumference of the earth.

.used by shoemakers.
. " to measure horses.
. " to measure depths at sea.
. " " distances "

SQUARE MEASURE.

This measure is used to compute surfaces or areas.

TABLE.
144 square inches (sq. in.) make 1 square foot

9 square feet

30£ square yards

40 square rods

4 roods
640 acres

1 square yard. ..

1 square rod

1 rood

1 aero

1 square mile

EQUIVALENTS.

eq. mi. A. R. eg. rd. sq. yd. sq. ft.
I = 640 = 2560 = 102400 = 3097600 = 27878400

1 = 4 = 160 = 4840 =
1 = 40 = 1210 =

1 =

43560
10890

SCALE or UNITS :— 144, 9, 30£, 40, 4, 640.

. sq.ft.
. sq. yd.
. sq. rd.
. E.
. A.
. sq. mi.

sq. in.

= 4014489600

= 6272640

= 1568160

39204

= 1296
= 144

SUPPLEMENT. 309

SURVEYORS' MEASURE.

This measure is used to compute land distances and areas. A Gunter's chain,
which is the measure used by surveyors, is four rods in length, and consists of 100
links.

TABLE OF LINEAR DISTANCES.

7.92 inches (in.) make 1 link I

25 links " 1 rod. rd.

4 rods, or 66 feet, " 1 chain.. . ch.
80 chains " 1 mile.. . . mi.

EQUIVALENTS.

mi.

ch.

rd.

I

in.

1 =

80

= 320 =

8000

=

63360

1

= 4 =

100

=

792

1 =

25

—

198

1

—

7.92

SCALE OP TT^ITS: — 7.92, 25, 4, 80.

TABLE OF AREAS.

625 square links (sq. I) make 1 pole P.

16 poles " 1 square chain, sq. ch.

10 square chains " 1 acre A.

640 acres " 1 square mile. . sq. mi.

36 square miles (6 miles square) " 1 township. . . . Tp.

EQUIVALENTS.

Tp. sq. mi, A. sq. ch. P. sq. 1.

1 = 36 = 23040 = 230400 = 3686400 = 2304000000

1 = 640 = 6400 =± 102400 = 64000000

1 = 10 = 160 = 10000

1 = 16 = 1000

1 = 625
SCALE or UNITS:— 625, 16, 10, 640, 36.

CUBIC MEASURE.

This measure is used to compute the contents of solid substances ; it is sometimes
called "solid" measure.

TABLE.

1728 cubic inches (cu. in.) make 1 cubic foot cu.fl.

27 cubic feet " 1 cubic yard. . . cu. yd.
16 cord feet " 1 cord foot cd.fi.

8 cord feet, or )

••no *-•?*. 1 cord of wood., cd

128 cubic feet )

24f- cubic feet " 1 perch Pch.

310 SUPPLEMENT.

LIQUID MEASURE.

This measure is used for measuring liquids ; such as liquors, molasses, water, etc,

TABLE.

4 gills (gi.) make 1 pint pt.

2 pints " 1 quart qt.

4 quarts " 1 gallon gal.

31 } gallons " 1 barrel bbL

2 barrels " 1 hogshead MuL

EQUIVALENTS.

hhd. III. gal. qt. pt. gi.

1 = 2 = 63 = 252 — 504 = 2016

1 = 31 J = 126 — 252 = 1008

1 = 4= 8 = 32
1=2= 8

1 = 4

SCALE or UNITS: — 4, 2, 4, 31£, 2.

ALSO,

36 gallons make 1 barrel of ale, beer, or milk.
54 " " 1 hogshead " "

42 " " 1 tierce.

2 hogsheads " 1 pipe, or butt.

2 pipes " 1 tun.

DRY MEASURE.

Used for measuring articles not liquid; as grain, fruit, salt, etc.
TABLE.

2 pints (pt.) make 1 quart qt.

8 quarts " 1 peck ' pk.

4 pecks " 1 bushel bu.

36 bushels " 1 chaldron. . . ch.
EQUIVALENTS.

ch.

^

bu.

36 =

pk.
144

ft

= 1152

pt.
= 2304

1 =

4

= 32

= 64

1

= 8

= 16

1

= 2

SCALE OF UNITS: — 2, 8, 4, 36.

AVOIRDUPOIS WEIGHT.

Used to weigh all coarse articles ; as hay, grain, groceries, wares, etc., and aU
metals, except gold and silver.

TABLE.

16 drams (dr.) make 1 ounce oz.

16 ounces " 1 pound Ib.

25 pounds " 1 quarter qr.

4 quarters " 1 hundred weight, cwt.
20 hundred weight " 1 Ton T.

S U P P L E M E N T. 311

EQUIVALENTS.

T.

1

ewt.
= 20

gr.

= 80

W.
= 2000 =

oz.
32000

dr.
= 512000

1

= 4

— 100 =

1600

= 25600

1

= 25 =

400

= 6400

1 =

16

= 256

1

= 16

£CALE OP UNITS:— 16, 16, 25, 4, 20.

TROY WEIGHT.

For weighing gold, silver, jewels, and liquors.

TABLE.

24 grains (gr.) make 1 pennyweight . . pwt.
20 pennyweights , " 1 ounce — . . . . . oz.

12 ounces " 1 pound Ib.

EQUIVALENTS.
II. oz. pwt. gr.

1 = 12 = 240 = 5760
1 as 20 = 480
1 = 24
SCALE OP UNITS: — 24, 20, 12.

APOTHECARIES' WEIGHT.

Used by apothecaries and physicians in mixing medicines.

TABLE.
20 grains (gr.) make 1 scruple. ... 3

3 scruples " 1 dram 3

8 drams " 1 ounce §

12 ounces " 1 pound 5>

EQUI VALEN TS.

fc § S » I*

1 = 12 = 96 = 288 = 5760

1 = 8 = 24 = 480

1 = 3 = 60

1 = 20

SCALE OP UNITS: — 20, 3, 8, 12.

TIME MEASURE.

Used to denote the passage of time.

TABLE.
60 seconds (sec.) make 1 minute .... m.

60 minutes " 1 hour hr.

24 hours " 1 day da.

7 days " 1 week wk.

365^ days " 1 year yr.

100 years " 1 century C.

312 SUPPLEMENT.

EQUIVALENTS.

I =

1 = 60

Note. — It is customary to reckon 4 weeks to the month, and 1 2 months to thd
year, but as this only approximates the truth we have omitted it. Twelve
calendar months make a year, but, these months are not of regular length, as the
following table will show: —

wk.

da.

hr.

min.

sec.

52 =

365^ =

8766

—

525960

=

31557600

1 —

7 =

168

=

10080

=

604800

1 =

24

—

1440

—

86400

1

=

60

=

3600

1. January has 31 days.

2. February " 28 "

3. March "31 "

4. April " 30 "

5. May " 31 "

6. June " 30 "

7. July has 31 days.

8. August "31 "

9. September " 30 "

10. October " 31 "

11. November " 30 "

12. December "31 "

The year, as indicated above, would consist of 365 days. This is the length
of the common year. Once in four years, however, one day is added to Febru-
ary, making 366 days ; and thus, each year averages 365^ days. The longest
year is called Bissextile, or Leap year. The leap years are all exactly divisible
by 4.

CIRCULAR MEASURE

Is used to determine localities, by estimating latitude and longitude; also, to
measure the motions of the heavenly bodies, and computing differences of time.
All circles, of whatever dimensions, are supposed to be divided into the same num-
ber of parts — as quadrants, signs, degrees, etc. It witt, therefore, be evident, that
there can be no "fixed " dimensions of the units named.

TABLE.

60 seconds (") make 1 minute. . . . '

60 minutes " 1 degree. . . . °

30 degrees " 1 sign. ..... S.

12 signs, or 360 degrees " 1 circle 0.

EQUIVALENTS.

C. S. ° "

1 = 12 = 360 = 21600 = 1296000
1 = 30 = 1800 = 108000
1 = 60 = 3600

1 = 60

SCALE OF UNITS: — 60, 60, 30, 12.

SUPPLEMENT.

313

MISCELLANEOUS TABLE.

12 units

make

1 dozen.

12 dozen

<(

1 gross.

12 gross

«

1 great gross.

20 things

it

1 score

100 pounds

a

1 quintal offish.

196 pounds

«

1 barrel of flour.

200 pounds

ll

1 barrel of pork.

18 inches

II

1 cubit.

22 inches (nearly)

i;

1 sacred cubit.

14 pounds of iron or lead

"

1 stone.

2H stones

((

1 Pig.

8 pigs

a

1 fother.

BOOKS AXD PAPER,

Barnes of different sizes of paper made by macJiinery.

Double imperial, 32 by 44 inches. Imperial,

22 by 32 inches.

Double Super Royal, 27 by 42 "

Super Royal,

21 by 27

Double medium, 23 by 26 "

Royal,

19 by 24 "

" 24 by 37 £ "

Medium,

18J by 23£ "

" 25 by 38 "

Demy,

17 by 22

Royal and Half, 25 by 29 "

Folio Post,

16 by 21

Imperial and Half, 26 by 32 "

Foolscap,

14 by W "

Crown, 15 by 20 inches.
A sheet folded in 2 leaves is called a folio.

12
18
24
32

a quarto, or 4to.
an Octavo, or 8vo.

a 12mo.
an 18mo.
an 24mo.

a 32mo.

In estimating the size of the leaves, as above, the double medium sheet is
taken as a standard,

24 sheets

20 quires

2 reams

6 bundles

make

quire.
ream.
bundle.
bale.

314

SUPPLEM ENT.

PRACTICAL HINTS FOR FARMERS.

1. MEASURING GRAIN.— By the United States
standard, 2150 cubic inches make a bushel. Now,
as a cubic foot contains 1728 cubic inches, a bushel
Is to a cubic foot as 2150 to 1723 ; or, for practical
purposes, as 4 to 5. Therefore, to convert cubic
feet to bushels, it is necessary only to multiply

by |. EXAMPLE. — IIovv much grain will a bin hold
which is 10 fe»-t Ions, 4 feet wide, and 4 feet deep?
Solution.— 10 x 4 x 4=160 cubic feet. 160 x f =128,

the number of bushels.

To measure grain on the, floor. — Make the pile
in form of a pyramid or cone, and multiply tho
area of the base by one-third the height. To find
the area of the base, multiply the square of its di-
ameter by the decimal .7854. EXAMPLE.— A coni-
cal pile of grain is 8 feet in diameter, and 4 feet high,
how many bushels does it contain ? Solution.— The
square of 8 is 64; and 64 x. 7854 x J =83.776, the
number of cubic feet. Therefore,

83.776 x 4 =67.02 bushels. Answer.

2. To ASCERTAIN THE QUANTITY OF LU.MBER IN A
Loo. — Multiply the diameter in inches at the small
end by one-half the number of inches, and this
product by the length of the log in feet, which last
product divide by jl2. EXAMPLE.— How many
feet of lumber can bf made from a log which is 36
inches in diameter and 10 feet long? Solution. —
36 x 18=643; 648x10=6480; 64SO-f 12=540. Am.

3. To ASCERTAIN TIIB CAPACITY OP A CISTERN
OR WELL.— Multiply the square of the diameter
in inches by the decimal .7854, and this product by
the depth in inches; divide this product by 231,
and the quotient will be the contents in gallons.
EXAMPLE. — What is the capacity of a cistern which
is 12 feet deep and 6 feet in diameter > Solution.—
The square of 72, the diameter in inches, is 5184;
51S4 x .7854=4071.51 ; 4071.51 x 144=586297.44, the
number of cubic inches in the cistern. There are
231 cubic inches in a gallon, therefore, 586297.44

-•-231=2538+, gallons. To reduce the number of
gallons to barrels, divide, by 31£.

4. To ASCERTAIN THE WEIGHT OK CATTLH BY
MEASUREMENT. — Multiply the girth in feet, by the
distance from the bone of the tail immediately over
the hinder part of the buttock, to the fore part of
the shoulder-blade ; and this product by 31, when
the animal measures more titan 7 and lean than 9
feet in girth; by 23, when less than 1 and more
man 5; by 16, when leafs than 5 and more than
3 ; and by 11, when lens than 3. EXAMPLE.— What
is the weight of an ox whose measurements are
as follows; girth, 7 feet 5 inches; length, 5 feet
6 inches?

Solution.— 5i.x7T82=405i; 40-^x81 = 1264 + . AM.
A deduction of one pound in 20 must be made for
half-fatted cattle, and also for cows that have had
calves. It is understood, of course, that such
standard will at best, give only the approximate
weight.

5. MEASURING LAND.— To find the number of
acres of land in a rectangular field, multiply the
length by the breadth, and divide the product by
160^ if the measurement is made in rods, or by
43560 if made in fret. EXAMPLE.— How many
acres in a field which is 100 rods in length, by 75
rods in width? Solution.— 100x75=7500 ; 7500
-*-160=46fi. Answer. To find the contents of a
triangular piece ot land, having a rectangular cor-
ner, multiply the two shorter sides together, and
take one-half the product.

6. MEASUREMENT OF HAY.— 10 cubic yards of
meadow hay, weigh a ton. When the hay is taken
out of old, or the lower part of large stacks, 8 or 9
cubic yards will make a ton. 10 or 12 cubic yards
of clover, when dry, make a ton.

Hay stored in barns, requires from 3M to 400
cubic feet to make a ton. if it be of medium coarse-
ness, and greater or less quantity, varying from
300 to 500 solid feet, according to its quality.

OF

MONEY, WEIGHT, AND MEASURE,

PRINCIPAL COMMERCIAL COUNTRIES IN THE WORLD.

WE are indebted to the Publishers of " WEB-
BTEK'S COUNTING HOUSE DICTIONARY" for the use
of the following admirably arranged Tables, which
will be found of great value for reference. The
tables have been prepared with much care and
may be relied upon as correct

GREAT BRITAIN.

(Principal Commercial City, LONDON.)

Money.

The national Currency of Great Britain is called
Sterling Money — thus we say, so many pounds

sterling. The Pound Sterling is represented by a
gold coin called :\ Sovereign, and its custom-house
value in the United States is fixed by law at $4.84.
The intrinsic value of the Sovereign varies some-
what, depending on the date of the coinage. Vic-
toria sovereigns are worth the most, as being of the
latest coinage; those of William IV. or Goorge III.
less, as more worn. The commercial value of the
pound sterling varies, like merchandise, according
to demand; $4.84 is that on which duties are
charged. Thus if you buy a bill of goods in Lon-
don of £100, on which the duty in this country is
25 per cent., and import them, you pay at tho
Custom house 25 per cent, on $484, or $121. What

STTPPLEM ENT,

315

Is called the par value of the pound sterling in
the United States is $4.44 4-9. The par value of
the pound in London, in American currency, is
$4.Sd. The difference between the par value of
the pound sterling in this country ($4.44 4-9) and
the actual value to us here, at the time, of a pound
sterling in London, is called the Exchange. Thus,
if exchange on London, ia New York, is 9 per cent.,
a pound sterling is worth $4.44 4-9, and 9 per cent.
added, or $4.84. If 7 per cent., of course, less; if
lj per cent., more.

freight bills for goods by ehip are payable at
f4.80 the pound, which is 8 per cent on $4.44 4-9.
Exchange on London is usually 7 to 10 per cent, in
New York, i. e. a pound sterling in London is
worth $4.44 4-9 and 7 to 10 per cent, additional, in
New York, nearly.

In the following Tables we give the pound at
f4.S4, it being understood that its commercial
Value ia sometimes higher and sometimes lower.

4 farthings, qr. = 1 penny, d.

12 pence = 1 shilling, «.

20 shillings = 1 pound, £.

A sovereign, = 2) shillings.

A guinea = 21 "

A crown = 5 * "

A groat = 4 pence.

The farthing is an imaginary coin ; the penny,
copper; the sixpence, shilling, and crown, silver;
Eovcreiprnand guinea, gold.

The EnglislTTables of Weights, Measures, Time,
Ac., are the same essentially as the American.

The value of the Pound Sterling ia the following
Tables ia put at $4.84.

AUSTF.IA.
(Chief 'Commercial City, YICX
Money. In Silver.

fl. krt.
10 0

0 30

0 2*

70

4 40 or ducat

£ s. d. $ c. m.

= 1 0 0 = 4 II 0

= 010 = 0242

= 0 0 1 = 0 C2 02-13

= 0 13 6 = 3 26 7

= 094 = 2 25 8 8-12

1 0 silver florin =020 = 0434

2 0 or 1 dollar = 040 = 09(38

0 20 or 1 zwanzigcr = 008 = 0131 4-12
1 florin is equal to CO kreutzers.

Taper currency is depreciated now from 25 to C5
per cent.

"Weights and Measures.
AUSTRIAN*. ENGLISH.

100 commercial Ibs. = 123.6 Ibs. avoirdp.

1 staro .. .. = 2.34 Winch, bush.

IpoloHick .. = 0.861 ditto

1 cimer .. .. = 15 wine gallons

Ibarilc .. .. = 173| ditto

1 ell woolen measure = 26.6 in.

1 ell silk.. .. = 25.2 ia.

Or njore particularly —

Weight.

ENGLISH.
123.6 Ibs. avoirdp.
= 4 vindlinge
= 4 unzen
= 2 loth
= 4 quintl.
= 20 Ihs.
= 275 Ibs.

AUSTRIAN*.

100 commercial Ibs. =

lib.

1 vindlingo

1 unzen .".

lloth ..

1 stone ..

1 sanae . .

Measure.

1 foot = 12i inches
1 nult = •

Grain.

C4 moasel = 1 metz
SJmetz = 1 muta
1 muth = 5o£ bush. Eng.

EAVAEIA AND BADIIT.
(Principal Commercial City, AUGSBTTBG.)

Honey.

fl. krt £ 8. d. $ c. m.

12 »at par .. .. = 1 0 0 = 4 84 0
036 .. .. =010 = 0242

03 .. .. =001=0 02 0 2-12

10 0 gold 10 guildr. piece = 0 16 8 = 4 08 34-12
5 0 gold 5 do. do. =0 8 4 = 2 01 6 8-12
3 30 silver 3f flor. piece = 0 5 10 = 1 41 1 S-12
5 35 or ducat .. =09 3 = 2 23 8 6-12
2 42 or crown thaler =0 4 4 = 1048 8-12
10 .. .. =018 = 0 40 3 4-12

1 florin is equal to CO kreutzers.

Books are kept in Gulden a CO krentzer of the 20
grulden fuss, so called because the Cologne mark of
line silver is worth only 2 ) fl. Augsburg currency,
while all other South German States reckon on thd
24 gulden fuss.

Coix.— Gold (old). 1 Caroline=li>. <kZ. En-

glish =$4.44.

i caroline=9s. 8*7. English = $2.22.
1 double max d'or=24*. 4d. English = $5.84.
1 max d'or=12s. 2d. English = $2.92.
1 ducat (new)=9s. 4d. English =$2.24.

Silver pieces of S| gulden, 1 gulden. $ pnlden, 1
kreuUer, 3 kreutzer, all in the 24 gulde

1 ponnd=5GO grammes French=lJ pound avoir-

dupois.

1 cwt.=100 pounds=3,200 loth=12.8nO qnent
1 Ausrsburg marc=16 loth =64 quent=25G pfen-

ning=3,643 grains troy English.

Measure.

The foot =11 1 inches English.
1 ruthe=U feet=120 zoll or inches=1440 lines.
1 ell=2 41-48 feet =83!- inches English.
1 klafter=6 feet=5= feet English.

FOR COBS.— 1 6cheffel=6 bushels 1 gallon En-
glish.

1 scheffel=6metz=12 viertel=48 maas.
FOB LIQUOES.— Wine, 1 eymer=6o inaaa.
Beer, 1 " =6^ ••
1 maas=lj pints English.

BELGIUM.

(Principal Commercial City,
Money (at par).

fr. cts.

25 0

1 25

0 10

£ s. d. $ c. m.

= 1 0 0=^4840

=0 1 0 =: 0 24 2

0 0 1 = 0 02 0 2-12

25 Oorl gull Leopold = 0 19 1) = 4 79 98-12
10 0 or Id Irane piece =0 7 10 = 1 8958-12
5 Oor 5 franc piece =0 3 11 = 094710-12
10 .. .. =00 9|= 0 19 17-12

1 franc is equal to 100 centimes.
"Weights and measures the same as in Franc*.

816

SUPPLEMENT.

BRAZILS.
(Principal Commercial City, Eio DE JANEIRO.)

Money.

reis. £ s. d. $ c. m.

6400 or gold piece = 1 15 9 = 8 65 1 6-12

4000 or gold piece of =100 = 4 84 0
1200 or silver piece of =04 2 = 1 00 8 4-12
960 " = 0 4 1 = 0 98 0 4-12

640 " = 0 2 9 = 0 66 5 6-12

820 " = 0 1 4 = 0 32 2 8-12

200 " = 0 0 8 = 0 16 1 4-12

1 mil reis is equal to 1000 reis.
The unit is the reis, as in Portugal.
Com.— Gold dobra a 12,800 reis= $18.00.
Meia dobra a 6,400 reis =$9.00.
Moeda a 4oOO reis=$5.75.

Silver.— Pieces of 1200 reis=$1.00. ; 400 reis=$0.83.
Pieces of 1«0 rcb=$o.v/8.

Bank Notes are worth less than specie "by about
one third.

Exchange on London, SOd. sterling per milrea in
bank notes.

Exchange on Paris, fr. 3.15 to fr. 3.20 per 1000
reis.

Weight

1 quintal =4 arrobas a 82 arratels, (pounds.)
1 arratel (lb.) = ll^- oz. avdp.
1 quintal=9H lb. avdp.
Gold and silver weight is the arratel a 2.
Marcos a 8 oncas a 8 oitavas a 72 granos.
1 ma'rco=7 oz. 7 4-7 dwts. troy.
Diamonds, emeralds, rubies, pearls, &c. are sold
by the quilate. Topazes by the oitava a 3 escrupu-
losa 3 quilates a 4 granos.

1 oitava=l"oz. 19 9-10 dwts. troy.
1 quilate=4 13-30 dwts. troy.

Measure.

1 pe (foot) 1= foot Eng.
1 paltno=9i inches Eng.
1 braca=2 varas=8£ covades=10 palmas,
1 braca=2; yards Eng.

1 legoa(mile)=4| miles Eng.
CORN, EICE, Corn

)FFEE, &c.—l mayo=15 fanegas,
each i'anega=4 alqueires.

1 mayo=22i bushels Eng.
1 fanega=ll ; gall.
WINE. — The same as in Portugal.

BREMEN.

(One of the, four Free Cities of Germany?)

Money.

rigdl. grosch. £ B. d. $ c. m.

66 .. .. =100=4 84 0

024 .. .. =010 = 0 24 2

1 0 or gold rigxd.nl. =0 3 4 = 0 80 6 8-12
0 86 or 36 groat piece =0 1 6 = 0 86 3
5 24 or Louis-d'or = 0 16 0 = 3 87 2
1 thaler is equal to 72 groten.

BRUNSWICK AND HANOVER.

(Principal Commercial Cities, BRUNSWICK and
HANOVER.)

Money.

tl. grs. pfci. £ B. d. $ c. m.

6 16 0 .. .. = 1 0 0 = 4 84 0
080 .. .. =010 = 0 24 2
0 0 10 .. .. = 0 0 1 = 0 d2 02-12

10 0 0 dble. Georged'or = 1 12 4 = 7 72 48-12

6 0 0 or single " = 0 16 2 = 8 91 24-12

100 .. .. =080 =

0 1 0 or 12 pfennings =00 1±= 0 02 5 5-24

1 thalur is equal to 24 groschen.

CB3NA.

(Principal Commercial City, CANTON.}
Money.

The Chinese reckon in taels, a 10 mace, a 10 can-
darin, a 10 cash.

1 tael = 6s. 6rf. = $1.56.

COIN.— They only have the cash or li. All other
are imaginary. They use the piasters of Spain at
72 candarins. The East India Company take the
tael only at 6s. 720 taels= 1,000 dollars of Spain.

The exchange on London is 4s. 8d., more or less,
for one Spanish dollar.

Weight.

1 pecul=100 cattys (gin), a 16 taels (lyang), a 10 mazas

(tachen), or lo candarins (tv/in), a 10 cash (li).
1 pecul = 133} pounds avoirdupois.
1 catty = li pound
1 tael = lj ounce "

1 catty (also the weight for gold and silver) =1

pound 7 3-5 ounces troy English ; 1 tael=579 4-5

grains troy English.

The assay of gold and silver is done by 100 parta
called toques. Silver must be 80-100 pure.

Pleasure.

The covid=14| inches English.
1 covid=10 punts.

The Chinese use four different feet:
Tor mathematics = 13^ inches English.
For builders = 121-15

For engineers = 12| "

For trade = 18j "

1 li=180 fathoms of 10 feet of the engineers=2-5

of an English mile.

DENMARK

(Principal Commercial City, COPENHAGEN.)

Money.

rigsd. ekil. £ s. d.

9 16 .. .. =1

44 .. .. =0

8J .. .. = 0

50 or 1 Christian d'or= 0 16 3
0 or \ species silver =0 44
0 .. .. = 0 2 2

00
10
0 1

$. c. m.
=4840
=0 24 2
= 0 02 02-12
= 3 93 2 6-12
=1048 8-12
= 0 52 44-12

0
0
7
2
1

0 16 or 1 mark .. =0 0 4} = 0 09 1

1 rigsb. diilor is equal to 96 skillings.

2 rigsbank daler=l hpecie-daler=3 mark banco in

Hamburg.

1 rigsbank daler =2*. Sd. English.
1 skilling=l farthing=half a cent American.

Bank notes in specie daler are freely taken — 100
specie daler for 200 rigsbank daler.

They draw generally on Hamburg at sight or 14
days after date, and the exchange on London is 9J
rigsbank daler for £1 sterling. Exchange on Pa-
ris (rarely) from fr. 2.60 to fr. 2.70 per rigsbank
duler.

Weight.

1 pound =1 pound If oz. avoirdupois.
1 pound=16 ounces=82 loth=128 quenta-
1 ship-pound =320 pounds.
1 last=16i do. or 52 cwt. of 100 pounds.
Gold and silver are sold by the pound=2 marks
=16 ozs.=512 orts=8192 es. 1 mark =7 ozs. 4 1-5
dwts. Troy.

Measure.

1 foot=12* inches English.
ell =24 j inches English.
mile=4* miles English.
FOR CORN.— 1 toende=8 skieps=S2 viertels.
toende=80 gallons 4^ pints English.
skiep=3 gallons 6 \ pints English.
last =22 toendes.

STIPPLE MENT.

317

EAST INDIES.

(Principal Commercial Cities, BOMBAY, BEXGAL,

CALCUTTA, and MADRAS.)
Tup's, ann. \>\. £ s. d. $ c. m.

10 8 0 .. =100=4840

0 8 4 .. =010=0242

0 0 8 .. =001=0 02 0 2-12

1C 0 0 gold mohur= 1 9 0=7018
100 rupee sicca =0 1 10£ = 0 45 3 9-12

0 8 0 half rupee =0 011^=022621-24

1 rupee is equal to S annas or 90 pice.

More particularly —

CALCUTTA. Money.
The Company's rupee=15-16 sicca rupee=ls. lid.

=$0.40.
1 rupee=16 anas; 1 ana=12 pice.

COIN— Gold : 1 mohur=15 rupees=33*. 2d. En-
glish=$3."2.6 4-12. Silver : 1 sicca rupee=2*. En-
glish = $0.43.4

Weight

1 mannd (factory maund), a 49 seers, a 16 chattacks.
1 maund=74 pounds 10 ounces avoirdupois.
1 seer=29j ounces avoirdupois. The bazaar weight

is 10 p. ct. heavier.

1 sicca=10 massa a 32 grains, or 4 punkhos.
1 sieca=173j grains troy Engl.

Measure.

1 cubit=13 inches English. 1 guz=l yard English.
1 coss=4,000 cubits=lV mile English.

Corn is sold by the khahoon of 40 maunds or 16
soallis a 20 pallies. 1 pallie=9^ pounds avoirdupois.

MADRAS. Money.
The same as Calcutta.

Weight

1 can<lv=2r> mrrinds=16J vis — 6,400 pollams.
1 candy =500 Ibs. avdp.

Measure.

Long measure the same as Calcutta.

FOR CORX — 1 garee=400 mercals a 8 puddys or
84 allocks.
1 garee=135 bushels.

BOMBAY. Money.

1 rupee=100 reas. Value as in Calcutta.
Exchange on London, 2s., more or less, i'or 1 Com-
pany's rupee.

Weight

1 candy=20 maunds a 43 seers a 30 pice.
1 candy =560 Ibs. avdp.

Measure.

1 covid=18 inches English.
FOB Coax— 1 candy =8 parahas a 16 adowlies.
1 candy=24^ bushels.

EGYPT.

(Principal Commercial City, ALEXAITDBIA.)

Money (at par.)

piast. par. £ s. d. $ e. m.

97 20 . . . . = 1 0 0 = 4 84 0

50 .. .. =010=0242

017 .. .. =001=0 02 0 2-12

5) 0 gold new sequin = 0 10 4 = 2 50 0 8-12
13 0 silver new piast =0 3 4 = 0 8:-) 6 8-12
4 0 silver grush =0 1 2=0 23 2 4-12

1 0 piastre .. =00 21=00505-12
Wholesale payments are made in purses of 500
current piasters, chiefly in Span, dollars or piasters.
1 Sp. dollar =20 Egypt, piust.

1 piaster in Alexandria has 40 medinis or paras, or

100 good or 12J current aspers.
In Cairo 1 piaster=8o aspers or 33 paras.

COIN.— Ducatillo a 10, griscio a 30, piaster a 40,
mahouib a 90, and zumabob a 120 paras. Also,
zenzerli a 107, and mecchini a 146 zedinis.
Cotton is sold by cantaros. 1 cantaro=115 Ib. Eng.
Coffee and Cotton are invoiced in Span, dollars.
Other goods in Egyptian Piasters.

Exchange on London, 80 piasters, more or less,
for $1 sterlg.
Exchange on Paris, 315 a 320 per fr. ICO.

Weight

1 cantaro a 100 rotoli.

The rotoli differ. There are rotolo forforo =
15 oz. ; rotolo zauro = 33V oz. ; rotolo zadino =•-
21 5-16. ; rotolo mina=26 5-7 oz.

The quintal of coffee in Cairo=1033-5 Ib. Eng.
1 oka=400 drachmas a 16 carat a 4 grain.
1 oka=3 Ib. 2 oz. 17 2-5 dwt. troy.
1 drachma =1 dwt 22£ grs.

Measure.

lpik=264-5in. En?.
FOB COBX.— 1 rebebe=36 galls. Eng.
1 kisloz=39 galls. Eng.

FRANCE.

(Principal Commercial City, PAEIS.)

Money (at par.)

frs. cts. . £ s. d. $ c. m.

25 0 .. .. =100=4840

1 25 .. .. = 0 1 0 =024 2

0 10 . . . . =001=0620 2-12

20 0 or gold Napoleon = 0 16 0 = 3 87 2
5 0 or silver do. = 0 4 0 = 0 96 8
10 do. . . =00 9^= 0 19 1 7-12
0 10 . . . . =00 l"= 0 02 0 2-12

1 franc weighs 5 grammes=100 centimes.
Coix.— Gold pieces of 100, 40, 20 and 10 francs.

Silver pieces of 5, 2, 1, £ and £ francs.
Bank notes of 500 and 1000 francs.
Exchange on London, fr. 25.50 for £1 sterlg.
Exchange on New York, fr. 5.25 to 5.30 for"$l.

Weights.

Milligramme = 0.0154 grs.

Centigramme = 0.1543

Decigramme = 1.5434

Gramme .. = 15.4340

Decagramme = 154.3420

or 5-64 drams avoirdupois.
Hectogramme . . = 32.154 oz. troy,

or 3-527 oz. avoirdupois.
Kilogramme =2 Ibs. 8 oz. 3 dwt. 2 grs. troy,
or 2 Ibs. 3 oz. 4652 drams avoirdupois.
Myriogramme . . = 26.795 Ibs. troy,

or" 22-0485 Ibs. avoirdupois.
Qnintal=l cwt. 3 qrs. 25 Ibs. nearly.
Millier or bar =9 tons 16 cwt. 3 qrs. 12 Ibs.
The weight of 1 cubic centimetre of pure water
is taken as the foundation. It is called gramme.
1 myriagramme-10 kilogr.=100 hectogr.=1000de-

cagr.= 10,000 grammes.
1 gramme=10 decigr.=100 centigr.=1000 milligr.

1 eramme=152-5 grains troy,
or the kilogr. =15434 grains troy.
873J gramrnes=l Ib. troy.
453 3-5 grammes=l Ib. avdp.
1 kilogr. =2 Ib. 3* oz. avdp.
1 quintal=100 kilogr. =22Ci Ib. avdp.

318

SUPPLEMENT.

Measures.

Long Measure,

FRENCH. ENGLISH.

Millimetre .. = 0.08937 in.
Cenliuietre = 0.89371

Decimetre = 8.93710

Jleti-t* .. = 89.37100

Decametre = 32.S(i9l6 feet

Hectometre = 828.09167

Kilometre = 11,93.63890 yds.

Myriometre . = 10936.3S900

or 6 miles, 1 furlong, 28 poles.
1 myriametre=10 kilometres=lUOhectoinetres=
1000 Decam= 10,000 Metres.

1 metre=10 decimetres=100 centimetres =1000
millimetres.

The metre is the 10,000,000th part of the north-
ern meridian quadrant.

1 metre=39 7-25 in. En?.
1 lieue=l myriametre=6? Eng. miles.
1 auue=l 1-5=47 l-6=in Eng.

Measures of Capacity.

Millitre .. .. = 0.06103 cub. in.

Centilitre . . = 0 61023

Decilitre .. = 6.1028;)

Litre* .. .. = 61.02Su3
or 21135 wine pints.

Decalitre .. = 610.28028 cub. in.

or 2-642 vino gallons.

Hectolitre .. = 8.531T cub. ft.
or 26.419 wine gallons, 22 imperial gal-
lons, or 2.839 Winchester bushels.

Kilolitre . . . . = 85.3171 cub. ft.
or 1 tun and 12 wine gallons.

Myriolitre .. = 353.17146 cub. ft.
FOR WINE, &c. — 1 litre =1 cubic decimetre.
1 myrialitre=10 kilol.=100 hectol.=1000 decal.=
10,000 litres.

1 litre=10 decil.=100 centil.=1000 millit.'

1 litre=lf pint Eng.

1 hectolitre =22 gallons Eng.

Superficial Measure.

Centiare .. .. = 1 -I960 sq. yds.

Are (a sq. decametre) = 119-6C46
Decare .. .. = 1196-0460
Hectare .. .. . = 11960-46C4
or 2 acres, 1 rood, 85 perches.

Solid Measure.

D6cistere

Stere (a cubic metre)

Decastere

3-5317 cub. ft.
&5-3174
353-1741

FRANKFORT ON THE HATH".
AND THE SOUTHERN PARTS OF GERMANY.

Money.

1 gulden a 63 kreuzers a 4 pfennigc.

1 gulden=$0.40=3 kreutzere=0.o2.
COIN.— Ducats a $2.20.

Pieces of 8* gulden = $1.40; 1 guld. = $0.40,

and half gulden = $0.20.
Old pieces of 2 2-5 gulden = $0.96 ; i=$0.4S.
Exchange on London, 12") fl., m. or 1., for £10 stg.

" Paris, fr. 2.10 a 2.15 per fl.

* Metre Is the fundamental nnit of -weights and
measures ; it is the ten-millionth part of the one-
fourth of the terrestrial meridian.

t A cubic decimetre.

Money (at par).

florins, kr. £ s. <j. $ c. m.

12 0 . . . . = 1 0 0 = 4 84 0-

0 36 .. .. =0 1 0 = 0242

9 4s or g. Louis-d'or = 016 1 = 3 89 2 2-12
5 85 or gold ducat =0 9 3 = 2 23 8 6-12

42 or silver crown = 0 4 4 = 1 04 8 8-12

10 •• -. =018 = 0 40 3 4-12
1 florin is equal to 60 kreutzers.

Weight.

1 cwt.= 100 great or heavy pds.= 108 small or light

1 Ib. heavy=17jj oz. avdp.
1 Ib. light=2 mark=321oth=12S quent=
512 pfennig=15 1-20 oz. troy.
1 mark=7 oz. 1C* dwts. troy.
1 cwt. of 100 heavy or 1C8 light Ibs. = 111

Ibs. avdp.

Gold and silver are sold by the mark.
1 curat of jewels=l dwt. 7 5-7 gr. troy.

Measure.

1 foot=ll} in. Engl.
1 foot =12 zoll=144 lines.
1 ell=21 5-9 in. Engl.
1 Francfort Brabant ell =2Tj in. Engl.
FOR CORN. — 1 maker a 4 simmer a 4 sechter a 4

gescheide.

1 malter=3 bnsh. 1} gall. Eng.
1 simmer=6 5-16 galls. Eng.
FOR LIQUORS. — 1 ohm a 80 maas a 4 schoppen.
1 maas=l gescheid=3 5-32 pints Eng.
1 ohm =31 5-16 galls.
1 fuder=6 ohms; 1 stuck =8 ohm.

GERMANY.

Thrre can be properly no classification under thig
general head. See Frankfort on the Main, which
is the principal commercial town of Germany.

GREECE.

(Principal Commercial Cities, ATHENS, NAUPLIA,

ETC.)
Money.

clrarhm. lept. £ s. d. $ c. m.

23 15 .. .. = 1 0 0 = 4 840

1 30 .. .. =0 1 0 = 0 242

0 11 ... .. =0 0 1 = 0 020 2-12
43 Oorgoldpieco = 1 10 6 = 7 38 1

5 0 or silv. piece =0 3 9 = 0 90 7 6-12

1 0 .. .. =00 8;= 0 IV 611-24
1 drachme is equal to 100 leptas.

HAMBURG AND LTJBECK

(Commercial Cities of GERMAN Y).
Money.

mk. c. schil. pfen. £ 8. d. $ c. m.

lo 8 0 .. =100 = 4 84 0

0 13J 0 . . = 0 1 0 = 0 24 2

0 1 8 .. =001 = 0 02 0 2-12
8 0 0 or 1 ducat =093 = 22386-12
3 0 Oorldol.cur.= 0 4 4 = 10488-12

1 0 0 .. =01 2i= 0 29 26-12
0 1 0 .. =00 0}=00153-24

1 mark current is equal to 16 schillings.
1 thaler=3 marks =48 schillinge; but they have
two different values.

1st — According to the coin, called current ;
2d — Imagined, used in trade, and called banco,
generally 25 per cent, better than current.

1 murk currency = $0.26.
Exchange on London, 14 marks banco, m. or 1., for

£1 sterling.

" on Paris, fr. 1.50 to fr. 1.70 per mark
banco.

SUPPLEMENT.

3J9

Weight.

1 pound=16£ oz. avdp. Engl.
1 pound=32 loth a 4 quent
1 centner=lll lbs. = 119i Ibs. Engl.
1 ship pound =2^ cwts.=20 lies pound.
1 lies pound for shipping=14 Ib.
1 " " land carriage =16 Ibs.

1 stone flax, " =20 "

1 '• wood, etc. " " =10 "

For jewels the weight is the same as Berlin.

Measure.

HAMBURG. ENGLISH.

1 foot .. .. = 11.2S9 in.

100 commercial Ibs. . . = 106.833 Ibs.
100 feet .. .. = 94.021 feet.

100 ells . . . . = 62.681 yds.

100 viertels =159-39 imperial gallons.

lOOfass .. =18-135 imperial qurs.

1 last .. =11 imperial qrs.

1 ship last .. = 3 tons.

1 foot=f2 zoll=9G achtelzoll.
1 Ehineland foot in Hainbro'=12i in. Engl.
1 Hambro' ell=22| in. Eng.
1 Brabunt ell in Hambro' =2T in. Engl.
1 Hauibro' mile =4 3-5 Engl. miles.

Grain.
CORN— Is sold by the last a 3 -wispel a 10 scheffel

a 2 wispel a 10 scheffel a 2 lass.
BAJOJET — Is sold by the stock a 3 wispel a 10

scheffel a 3 fass.

1 fass=l bush. 3 galls. 4* rints Engl.

1 scheffel=2 bush. 7 gall. 1 pint.

1 wispel =29 bush.

1 last=10 quarters 7i, bush.

EOLLAin).

A part of the Netherlands.

(Principal Commercial OVtVs.AMSTERDAM. HAAR-
LEM, THE II AGUE, ROTTERDAM, LEYDEN, «fcc.)

Money (at par.)

.guilder, cts. £ s. d. $ c. m.

12 0 .. .. =100 = 4840

0 63 .. .. =010 = 0242

0 5 .. .. =001 = 0 02 0 2-12
10 0 gold 10 fl. piece = 016 6 = 3 99 3

5 55 or ducat . . = 0 9 3 = 2 23 8 6-12

1 0 or silver florin =0 1 8 = 0 43 34-12
1 guilder is equal to 100 cents.

Weights and Measures.
DUTCH. ENGLISH.

1 foot . . . . =11 1-7 in.
lell .. .. = 27 1-12 in.

1 last for corn . . =10 qrs. 5£ bush. Win-
chester measure.

1 aam . . . . =41 wine gallons.
1 hoed . . . . =5 chaldr. Newcastle.
1 last for freight = 4000 Ibs.

1 last for ballast = 2000 Ibs.

LOMBA.RDY.

(Principal Commercial Cities, VENICE and MI-
LAN.)
Money.
1 lira Anstriaca = 100 centesimi or 20 soldi a 5

centesiini.
1 lira Austriaca = $0.16 cents.

The Austrian is the current coin, under other
names.

2 gulden = 1 scudo nuovo = $0.96.
1 gulden = £ scudo ntiovo = $0.48.
I gulden = | scudo nuovo = $0.24.
1 gulden = 1 lira Austriaca = $0.16.

Exchange on London, 30 lira Anstriache m. or
1. for £1 sterlg.

Exchange on Paris, fr. 85.00 m. or 1. per L Aust.
100*

Weight.

1 libbra=l kilogramme=2 Ib Sioz. avd.
1 libbra =10 oncie=100 grossi=looo denari.
1 quintale=100 libbre.
1 rubbo=10 libbre.

Measure.

Equal to the French.
1 metro=10 pal mi = 100 diti=100o adomi.
1 miglia=1000 metri.

CORN.— 1 soma=l hectolitre, French.

lsoma=10 mine=lOOpinta=1000 coppi.

MEXICO AND MONTE VIDEO.

MEXICO, Capital of Republic of Mexico.

MONTE VIDEO, Capital of Repi&lic of Uraguay

(or Banda, Oriental), S. A.

MEXICO.

Money.
£

s. d.
0

$ c. m.
= 15 73 0
= 7865
= 3 93 2 6-12
= 0 96 8
= 1 00 8 4-12
= 0 50 4 2-12
= 0 25 2 1-12
= 0 12 6 1-24

d-->ls. rea?s.

Iti 0 or gold doubloon =35
8 0 or i do. =112

0 or i do. =0 16

0 or 1-16 do. =04

0 silv. dol. (8 reals) = 04
4 do. * dol. =02
2 do. i dol. =01

1 do. k dol. =00
1 dollar is eqnal to S reals.

1 peso a 8 reales de plata a 4 cuartos.
1 peso=l dollar U. 8. currency.
The piaster or duros of 1S33 and 1834 are about
6 per cent, less value.
COIN.— Gold doblones a 16 duros.

i, i and 5 do.

Silver duros or dollars, i, i and g.
Reales and £ reales.

MONTE VIDEO. Mcnej.

The peso or dnro a 8 reales de plata a 100 cen-
tesimos.

This peso is not eqnal with the Spanish or Mex»
ic.'.n, and is generally called the peso corriente.

1 peso corriente = $!'.SO, or 5 pesos corrientes =
4 pesos duro (Spanish silver dollar).

Exchange on London = 52 d. sterling for 1 peso
duro.

Msasure and Weight.

108 varas=100 yards English.

For the rest, see Spam.

NAPLES.

(Principal Commercial City, NAPLES, the capital.)

Money,
ducat, grani. • £ s. d. $ c. m.

6
0
0
SO

1

0

3
30
2,
0
0
120

piece of . .
silver ducat
or dollar . .

1
0
0
5
0
0

0

1

0
0
3
4

0
0
1
0
4
0

=

4 84
0 24
002
24 20
0 80
096

0
2
02-12
0
68-12
8

0 20 piece of.. =008=0161 4-12
9 10 piece of.. =004=0030 8-12

1 ducat is equal to 100 grani.
Ducati di regno a 10 carlini a 10 grani.
1 ducato=$0.90.

320

SUPPLEMENT.

COIN.— Gold pieces of 6, 4 and 2 ducati, and
pieces of 3 ducati or 1 oncia, and pieces of 2, 5 and

Silver pieces of 12, 10, 6, &c. carlini.
Scudi of 12 carlini and ducati in silver of 10
carlini.

Exchange on London, 575 grani per £1 sterlg.
Exchange on Paris, 22 a 25 grani per 1 fr.

Weight

1 cantaro=100 rotoli a 83} oncie.
1 rotolo=l Ib. 15 3-7 oz. avdp.

The libbra for gold, silver, &c., has 12 oz.
860 trappesie, 7200 acini.

1 libbra=10 oz, 1£ dwts. troy.

Measure.

1 palmo=12 oncie=60 minuti=120 punti.

1 palmo= 10 10-27 in. Eng.

1 canna=8 paliui=2£ yards Eng.

CORN.— 1 carro a 36 tompli a 24 mass or 1 to-
molo a 2 mezzetti a 4 quarti a 8 stoppeli=12 galls
li pints Eng.

WIN-E.— 1 carro=2 batti=24 bamli=1440 caraffi,
in the country 15S4 carafli.
1 barile=9; galls., 1 caraffo=l 5-22 pints.

Oil is sold by the salma a 16 staji a 256 quarti or
1536 inisurelle, and weighs about 350 Ibs. Ens.

The salma of Bari about 312 and of Gallipoli only
295 Ibs. Eng.

1 quarto in measure =5-6 pint.
1 staja in measure =27 galls.

THE NETHERLANDS.

{Principal Commercial City, AMSTERDAM.)
Money.

1 gulden=100 cents=l*. Sd. English =$0.40.3 4-12
5 cents=l stuiver=lrf. English =$0.02.0 2-12.
?iguilders=$1.00.

COIN.— Gold pieces of 10 and 5 gulden. Silver
pieces of 3 and 1 gulden, 50, 25, 10 and 5 cents.

Old gold coin.— Ducats weighing 52 4-5 grains
English, double ducats, ryders=14 gulden.

Butter is sold by the ton, which differs from the
common ton=336 pounds Holl. 1 pound=15-12
avoirdupois. 1 ship-pound =300 pounds.

Exchange on London, 11 g. 80 cts., more or less,
for £1 sterlg.

Exchange on Paris, 2 fr. 10 cts., more or less,
per gulden.

Weight.

lood.
10
1

wl-tj.
100
10

1

korrels.
1000
100
10

1 lb.=l Ib. 1£ oz. Avdp.

Measure.

The Ell^l French metre=391 inches English.

roede. ell. palm duim. streep.

1 =10 =100 = 1,000 = 10,000

1 = 10 = 100 = 1,000

1 = 10 = 100

1 = 10

1 myl (mile) =1,000 ells=| mile English.
FOB CORN.— 1 mudde=2 bushels 61- gallons.
1 mud=10 schepel=100 kop=l,000 maajtes.
1 last=80 mudden.

FOR LTQPORS.— 1 vat=22 1-10 gallons English.
1 vat=100 kann=l,000 maatj.= 10,000 vingerh.

NORWAY.

(Principal Commercial City, CHRISTIANA.)

Money.

sp. dol. skil. £ s. d. $ c. m.

4 75 .. .. =100=4840
0 28 .. .. =010=0 24 2
0 2i .. .. = 0 0 1 = 0 02 02-T2

0 24 or 1 mark.. =00 9^=01917-12

1 0 specie dollar =0 4 4=1 01 8 8-12
0 60 orlrigsbankdol= 0 2 2=05244-12
0 1 nearly .. =00 C*= 0 01 0 1-12

1 specie dollar is equal to 120 skillings.

POLAND.

(Principal Commerical City, "WARSAW.)

Money.

flor. grosch. £ s. d. $ c. m.

42 0 .. . =100=4 84 0

2 3 ... .. =010=0 24 2

0 5 .. .. =001=0 02 0 2-12
18 15 or 1 gold ducat =0 9 3=2 23 8 6-12

8 0 or 1 rix dollar =0 4 0=0 96 8

1 0 or 1 silver florin = 0 0 5|= 0 11 5 23-24

1 florin is equal to 30 groschen.
Formerly, the gulden a 30 graschm Polish.
1 gulden = $0.11£ cents.

At present the Russian coin is the only legal
tender.

Bank notes of the Polish National Bank of 5,50
and 100 guilders.

Exchange on London, 82 Polish gulden M. or L.
for £1 Sterling.

Exchange o'n Paris, fr. 60.50 a fr. 60.75 per 100
gulden.

Weight.

1 funt (lb.)=14 7-16 ounces avdp.

1 funt (lb.)=13.| ounces troy.

1 lb.=16 oz.=32 loth =128 drams a 3 scruples a 24

grains.

1 centner=3 stones=100 lbs. = 87 7-8 Ibs. avdp.
Wool is sold by the stone of 82 Ibs.

Measure.

1 foot (stopa)=lli in. Eng.
1 ell (lokiee)=25 in. Eng.
1 mile=8 wersts=5 miles Eng.
CORN.— 1 kwart=2 litre=l? pint Eng.

1 korzek=128 kwarts=28 gall. Eng.

PORTUGAL.

(Principal Commercial City, LISBON.)

Money,
reis. £ s. d. $ c. m.

4120 =100 =4 84 0

206 =0 1 0 =0 24 2

20orlvintem .. =00 1,1=002233-48
6400 or gold Joannose =1 16 0 =8 71 2
1 000 silver crwn. or mil reis=0 4 8 =1 12 94-12
400 or crusado .. =02 3=05446-12
1 mil rcis is equal to 1000 reis.

Accounts are kept in rois.
1 milrei (or 1000 reis)=2 1-12 new=2£ old cruza-

dos=10 testons=25 reales ; 1 rei=6 ceitis.
1 conto de reis (1 million reis) =£270 sterling
= $1,296 (the dollar at the rate of 50 pence
English).

1 milree=$1.25.
1 crusado velho=about $0.50.
1 crusado no vo= about $0.60.
COIN.— Gold pieces of 24 and 12 thousand reis
=$16.80 and $33.60.

SUPPLEMENT.

321

Silver pieces, 1, |. i, J cruzado.

Exchange on London, 1 milrei for 59 pence.

on Paris, fr. 6.2J a fr. 6.3J per milrei.

Weight

1 quintal a 4 arrobes a 32 libras a 2 marcas.
llibra=llb. avdp. Eng.

GOLD AND SILVER. — 1 marco=S oncas=64 outa-
va3=4tiOS grainos.

1 inarca=i lb.=8 8-29 oz. troy.
1D1 carats of jewels = 1 oz. Eng. troy.

ROME.

(Capital of the PAPAL STATES.)

Money.

pioli.baj. £ s. d. $ c. m.

4ii 0 .. .. =1 0 0= 4 84 0

25 .. .. =0 1 0= 0 24 2

02 .. .. =0 0 1= 0 02 02-12

100 0 gold 10 scudi piece =2 2 6=10285
10 0 silver scudo .. =04 2=10084-12
10 .. .. =0 0 5= 0 10 010-1J

1 paoli is equal to 10 bajochi.

Msasure.

Thepe=12J- in. Eng.

BTJSSIA.

The vara=43 4-5 in. Eng.
The covado=26 7-10 in. Eng.

(Principal Commercial City, ST. PETEESBTTRO.)

The passo geometrico=li vara.
1 inile=4 miles Eng.

Money.

CORN is sold by the moyo a 15 fanegas a 4

rouble, hop. £ s. d. $ c. m.

alqueiras a 4 quartos a 8 selamis.
1 moyo=23 bushels Eng.
1 fanega=ll^ galls. Eng.
TVrvE AXD OIL. — 1 tonelada a 2 pipas or botas=52
almudas=lU4 alquires or potes and 624 canadas.
1 alrnude of Lisbon =3 galls. 5 pints Eng.
1 " of Oporto =5 galls. 5 pints Eng.
1 canada=13 1-16 pints Eng.

6 33 .. .. =100 = 4840
0 32 . . . . = 0 1 0 = 0 24 2
0 21 .. =001 = 0 02 02-12
5 15 gold half imper. = 0 16 3 = 3»93 26-12
3 0 ducat .. =0 92 = 22184-12
1 0 silver rouble =0 3 2 = 0 76 64-12
1 rouble is equal to 100 kopeks.
COIN*. — Gold imperials of 10 and 5 roubles (silver).
Silver, rouble, and pieces of 75, 50, 40, 3 ',

&c., to 5 kopeks silver.

PBTJSSIA.

Bank notes from 1 to 1000 roubles silver.

(Principal Commercial City, EERLIX.)

Exchange on London, from 39d. to 42d. for 1
rouble silver.

Honey.

Exchange on Paris, from fr. 4.10 to fr. 420 per

rouble silver.

thai. per. pf. £ s. d. $ c. m.

6 20 0 .. .. = 1 0 0 = 4 84 0
099.. .. =010 = 0 24 2

Weight and Measure.

0 0 10 .. .. = 0 0 1 = 0 C2 02-12

RUSSIA*. ENGLISH,

5 2J OgoldFrederick= 0 16 9 = 4 05 36-13

1 arsheeu* . . =28 in.

100 silver thaler =0 3 1 = 0 74 6 2-13

1 sashent . . =7 feet

0 1 Osilbergroschen= 0 0 li=00255-24

100 feet . . . . = 114i ft.

1 thaler=33 silver groschcn a 12 pfenning.

1 werst . . . =5 furl. 12 poles.

11X — A3"! ft *t trr«

COINS.— Friedrichs d'or=16*. 6<7. English =$3.96.
Double do. 33*. =$7.92. Half do. 8*. 3d. =$1.93.
In silver pieces of 2, 1, |, ±, £, 1-12 thaler. Do of 2,

10. . . . — Oolo.U £T"S.

100 Ibs. . . . = 90.26 Ibs. avdp.
1 pood . . . =36 Ibs. 1 oz. 11 dr.
1 chetwert . = 5.952 Wine. bush.

1, i groschen.

100 do = 74.4 quarters.

Bank notes of 1, 5, 5\ IfH, 5^0 thaler freely taken
in the whole of Germany for their nominal value.
Wool is sold by the stein of 22 pounds =22}

1 wedro .. *. = 3J wine gallons.
More particularly —

pounds avoirdupois.
Exchange on London, 6 thalers 25 gr., more or
IP<V<L for £1 sterling. Do. Paris, fr. 3.75. innr« nr

Weight.

1 r»ATiTirl ffnnt^=14-l or. ftvdn.

less, per tnaler.

1 pound =467

Weight
'•10 grammes French=l 1-52 pound

avoirdupois.

1 cwt. = 110 pounds Pr.=113 7-1G Ibs. avoirdupois.
1 last (shipping) is 4,000 pounds.

Gold and silver are sold by the mark=^ pound
=7 oz. 10\ dwts. troy English.

The mark is=233 grains.

For assay of silver the mark is divided into 16
loth a 13 grs. ; and of gold into 24 carats a 12 grs
1 carat of jewels is=9-160 quent=l dwt. 7 5-7
grains troy.

Measure.

The foot=12', inches English.

1 ruthe = 12 feet=144 zoll = 1723 linien.

1 ell =254 zoli=26i inches English.

1 faden=6 feet. 1 mile=4 2-5 miles English.

FOR CORN.— 1 schefiel=H bushel.

1 scheffel=16 metz ; 24 scheffel=l wispeL

1 pood=40 lb.=36i Ibs. avdp.
1 bercowitz=10 poods =362^ Ibs. avdp.
1 bruttolast=6 chetwerts.
(The funt is=95 solotnick. 1 sol.=96 doll.)

Measure.

1 foot =1 foot Enrr.

1 arsheen = 28 in. Eng.

1 sashen = 3 arsheens.
1 sashen=3 arsheens=7 feet=43 worschecks=84

inches=1008 lines.
1 werst=500 sashen=f mile Eng.

CORN; &c. — 1 chotwert=4 pajok.
8 tschetwerick=32 tschewerka=64 garner.
1 chetwert=5 bushels. 6 galls., 2 pints, Eng.
1 tschetwerick=57-9 sails. Ens.
1 kuhl or sark=10 tschetwericki.
1 wedro =2 1 galls. Eng.
1 fass=40 wedroja.

21

* 1 arsheen=28 in. Eng.
t 1 sashen =3 arsheens.

322

S tJP PL EM E NT.

SARDINIA.

(Principal Commercial Cities, GENOA and TURIN.)

Money.
The lira nuova=l franc a 100 centesimi=9i<?. Eng.

COIN.— Gold: Pieces a 20, 40, 80, and 100 lire
nuove or $3.75, $7.50, $15.00, and $18.75. Silver
scudi d'argento a 5 lire nuove. Pieces of 2 and 1
lire and 51) and 25 centesimi.

Bank notes of 5, 10, and 20 scudi.

Exchange on London, 25.50 lire, more or less, for
£1 sterlg.

Exchange on Paris, 21 lire per fr. 20.

Weight

IN GENOA. 1 peso grosso=121-6 oz. avdp.

1 peso sottile=l Ib. dwt. 18 gr. troy.
IX TURIN. 1 libbra=13 oz. avdp.

The Custolns use the French kilogramme.
'Gold and silver weight is the marco=8 uneio a 24
denari a 24 grani.

1 rnarco=S oz. troy.

Measure.
IN GENOA. 1 palmo=9J in. Eng.

FOB CORN— 1 inina=8 bush. 2i gall. Eng.

1 mina=8 quarti=96 gombette,
FOB WISE— 1 barile=16£ galls. Eng.

1 mezzarola=2 barili = 100 pinte.
FOR OIL— 1 barile = 14J- galls. Eng.
IN TURIN. 1 piede liprando=l foot 8* in. Eng.
1 picde manelle=12r in. Eng.
1 r^y (ell)=23i in. Eng.
FOB COEX — 1 sacco=5 emine a 8 copi a 24 cuc-

chiari.

1 sacco=25i; galls. Eng.
FOB WINE— 1 brenta-10 4-5 galls.

1 carro=10 brenta, a 86 pinte a 2 boc-
cali.

SAXONY.

(Principal Commercial Cities, DUESDEN and
LEIPSIC.)

Money.

rd. gn. pf. £ s. d. $ c. m.

6150 .. .. =100=4840
099 .. .. =010=0 24 2

0 0 10 .. .. =001 =00202-12
5 12^ 0 or Augnst.-d'or = 0 16 2 = 3 91 2 4-12

1 10 0 or specie thaler = 0 311 = 0 94 7 10-12
1 0 0 currency .. = 0 8 1 = 0 74 62-12
010 . .. = 0 0 1J= 0 02 OC-'i4

1 thaler a 80 groschen a 10 pfenninge.

1 thaler = 2s. llrf. Eng. = $0.70.5 10-12.

COIN.— August d'or=16*. Eng. = $3.87.2.

Silver pieces of 2, 1, £, 1-6, and 1-12 thaler.
Paper money is issued by the Government in notes

of 10, 5, and 1 thaler.
By the Bank of Leipsic in cotes of 20, 100, 200, 500,

and 1000 thalers.

Also 1 thaler notes by the Leipsic Dresden Railway
Company.

Exchange on London, 6 thaler 25 groschen, more
or less, per £1.
Exchange on Paris, fr. 8.50 a fr. 8.75 per thaler,

Weight

llb.=llb. l^oz. avdp. Eng.
1 cwt.=100 lbs.=1000 millas.
For the retail trade the Ib. ia divided into 82 loths,
a 4 quenta.

Measure.

1 foot=ll£ in. Ens.
1 ell =3-5 French metre =24 in. Eng.
FOB CORN— 1 schaffel = 100 litres French = 22
galls, nearly.

12 schaffels=lmalter, 2 malters=l wispel.

1 wispel = 66 bushels Eng.

FOB LIQUIDS — 1 oxhooft=l| ohm=3 eimer=210
kanns.

1 fuder=4 oxhoofts.

1 kanue=l litre=l| pints Eng.

EMTSNA AND THE LEVANT.
Money.

Like Constantinople. In the Levant are like-
wise used to a great extent, Spanish dollars and
Dutch, Hungarian and Venetian ducats. Likewise
German Conventions thaler =$0.96 to $1.00, bein:j
subject to variation.

Exchange on London, 1C5 piasters, more or less,
for £1.

Exchange on Paris, fr. 4.75 to fr. 5 per piaster.

Weight

1 cantaro=7| battman=22£ chequis=45 okes=100
rotoli a 18J drachms.

The oka, as a gold and silver weight, has 400
drachms, and is equal to 3| Ibs. Troy.
1 cantaro = 127| Ibs. Troy.
1 rotolo = 1 Ib. 4| oz.

Goat's hair is sold by the chequi a 800 drachmas.
Silk is sold by the teffei a 610 drachmas.
Opium is sold by the teffei a 250 drachmas.
1 drachm =49 3-5 grains troy weight.

Measure.

1 pik = 27 in. Eng.
COEN.— The killo\v=llf gall. Eng.

SPAIN.

(Principal Commercial City, MADRID.)

Money.

dols.rls. £ s. d. $ c. m.

4 14 barley .. =1 0 0 = 4 84 0

0 5 .'. .. =0 1 0 = 0 24 2
16 0 or gohl doubloon=3 6 0=15972

4 0 or gold pistole =016 6 = 3 99 3

1 0 or silver dollar =0 4 8 = 1 02 8 6-12
0 1 or real vellon -0 0 2jj= 0 05 3 45-48

\ dollar is equal to twenty re:ils.

They use eight different sorts of money : — 1.
Castilian. 2. Mexican. 3. Catalonian. 4. Ma-
jorcan. 5. Valencian. 6. Arragon. 7. Navarre,
and 8. The Canarian money.

The Castilian is the chief, and is 1 real de plate
antigua=l 15-17 real de vellon=16 cuartos=34
maravedis de plata antigua=64 marav. de vellon
=640 Castil. dineros.

10| reales de plata antigna=l piaster.

1 piaster or duro=4s. 4d. Enff. = $1.04 8 8-12.

1 real de plata =5d. Eng. = $0.10.0 10-12.

COIN. — Gold, 1 quadrupel pistole=8 eseudos=
$16 to $15.60=doblon or onza de Oro=$16 subdi-
vided into |, }, f, and 1-16. Peso duro or dollar
need not be described.

Exchange on London, 4fld. sterling, more or less,
per peso de plata antigua=48d. to 52d. Eag. per
dollar.

Exchange on Paris, fr. 5.10 a fr. 5.30 per peso duro.

Weights and Measures.
SPANISH. ENGLISH.

1 cana = 21 inch, nearly.

100 " = 58.514 yards.

100 qnarteras = 23.536 Win. qrs-

100 Ibs. = 88.215 Ibs. avdp.
More particularly —

SUPPLE ME XT.

323

Weight.

1 Castilian marca=S 1-7 oz. avdp. or 7 oz. 3 4-25

dwts. troy, Eng.

1 marca=8"onzas=64 octaves =46r>8 granos.
1 quintal uiacho=6 arrobas=150 libras.
800 marcas = 152± Ibs. avdp.
1 quintal=4 arrobas=100 libras=101£ Ibs. avdp.

Jewels and pearls are weighed by the CasUlian

ounce a 14 ) quilates, a 4 granos.
1 oz.=43H grains troy.

1 pie =11 } in. Eng.
1 estado=2 varas=6 pies=5 ft. 6^ in. Eng.
1 league =4J miles Eng.
FOR CORN. — 1 cahir=12 fanegasa!2 celeminesor

almudos a 4 quartillos.
1 fanega=12j- galls. Eng.
FOR LIQUIDS. — 1 cantaroorarrobamayor=Sazum-

bres=32 quartillos.
1 arrobamayor=3 galls. 3} pints Ens:.
1 arrobamenor for oil=2 galls. 5J pints Eng.
1 moyo=16 cantaros. 1 pipa=27 canturos.
1 bota=3J caataros.

SWEDEN.

(Principal Commercial City, STOCKHOLM.)

Money.

rd. skil. £ s. d. $ c. m.

12 0 in banco .. =10 0=4840

0 23 .. ..=01 0=0 24 2
02} .. ..=00 1=0 (12 0 2-12
5 25 or 1 gold ducat.. =09 2=2 21 8 4-12
2 25 or 1 specie silver =04 4=1 04 8 8-12

1 0 banco .. .. =01 8=04034-12
1 12* or half specie silver = 02 2=0 52 4 4-12
1 rd. banco is equal to 43 skillin<rs.

1 silver species is equal to 96 skillings.
1 riksdaler specie a 43 skillings=$1.05.
Payments are however made chiefly in bank
notes of 8, 10, 12, 14, and 16 skillings, and 2, 3, 5, 6,
9, up to 53 riksdalers.

Banco=l riksdaler specie.

Exchange on London, 12 dalers banco for £1 sterlir.
Exchange on Paris, fr. 2.10 to fr. 2.15 for 1 riksdal.

Weight.

1 skal pound. = 15 oz. avdp.

1 schip pound = 4M) skal Ibs.

Icwt. =12) Ibs.

1 scale of spelter = 165 Ibs.

1 stone wool = 32 Ibs.

1 mark (for gold) = 6 oz. 10 dwt troy.

Measure.

1 foot =1 foot Eng.
1 faam=3 alnar=6 feet=17 rerthum.
1 alnar=2 feet Eng.
CORN.— 1 tonn=4 bush. Eng.
1 toun=8 quarts=32 kappar=56 cans=44S quarr-
tiera,

WINE.— 2 pipes=l fuder=4 oxhoofte=12 eimer
= 7iJ stop.

SWITZERLAND.

(Principal Commercial Cities, GENEVA,

BERN, BASLE.)
Money. Old System.

fr. batz. rap. £ s. d. $ c. m.

17 7 5 .. =100 = 4840

087 .. =010 = 0 24 2

007 .. =001 = 0 02 0 2-12

4 0 0 piece of = 048 = 1129 4-12
10 0 or 10 batz = 0 1 1| = 0 27 2 3-12
01 0 .. =001£=002G 32-36

1 franc is equal to 10 batzen.

New System— as in Franca

1 frane=10 batzen a 10 rappen or 1 livre a 20 sols a
12 deniers.

1 franc=l livre=$0.27.
COIN.— Gold pistoles a 32 francs ^$3.63.

les a 16 francs- $432i.

Silver pieces of 40, 20, 10. and 5 batzen.
| N. B.— Each Canton has besides these its own
currency.

Exchange of Basle on London, 17 francs 5 rappes,
more or less, for £1 sterling.

Exchange on Paris, fr. 1.50 per fr. 1, or 50 per cent,
premium, more or less, in favor of liasie.

Waight
1 cwt.=100 lbs.=50 kilogr amines =110i Ibs. avdp.

Eng.
1 lb.=^ kilogramme=l Ib. If oz avdp. Eng.

Measure.

The basis is the Helvetian foot.

1 foot=3-10 French meter=ll 17-20 in. Eng.

2 feet=l ell ; 4 feet=l stab or staff.
16,000 feet=l hour (mile)=3 Eng. mil- •<.

FOB CORN.— 1 malter=10 viertel^l" :-:ur.
1 malter=4 bushels 1 j;a:i. Eng
1 immir=3| pints.

WINE. — 1 ohm =100 inaas (or measures).
1 ohm =33 galls. Eng.
1 maas =3$ pints Eng.

TURKEY.

(Principal Commercial City, CONSTANTINOPLE.)

Money.

pias. par. £ s. d. $ c. m.

109 0 .. =1 0 0 =4 84 0

5?- 0
0 13

0 =0 24 2

1 =0 02 0 2-12
0 =7 50 2

0 =3 35 6
2J=0 04 5 9-24

2 =1 00 8 4-12

200 0 gold new dble. seq. =111
100 0 " 1 seq. =0 18

10 .. =00

22 0 or 1 Spanish dollar =0 4
Piaster a 40 paras a 3 aspers.
Also piaster (grush) a 100 aspers.

1 piaster=2irf. English =$0.05.
1 purse silver is 500 piasters.
1 purse gold is 30,000 piasters.
1 juk is 100,000 coined aspers.

The government or bank notes bear 8 per cent,
interest.

Exchange on London, 104 piasters, more or less,
for £1 sterling.

Exchange on Paris, from 400 to 410 piasters for
100 francs.

Weight.

1 pound, chequi=llj oz. avo:rdupois.

1 oka=2 Ibs. 12 oz. avoirdupois.

1 oka =4 chequi=400 drachmas.

1 taffee=610 drachmas.

1 batman =6 okas.

1 cantaro=44 a 45 okas.
Gold and silver weight like Alexandria.

1 chequi opium =250 drachmas.

1 chequi goat-hair=800 drachmas.
PIECE GOODS. — 1 mazzee=50 pieces.

Measure.

The large pikhalebi,archim=27 9-10 inche? Eng.

The small pik andassa=27 1-16 inches Enelish.
FOR CORN.- The killow=7| gallons English.

1 fortin=4 killows=30 gallons English.

1 killow of rice should weigh 10 okas.
FOR LIQUORS. — 1 almud=l 2-5 gallon English.

1 almud of oil should weigh 22 5-S pounds avoir-
dupois.

324

SUPPLEMENT.

TUSCANY.

(Principal Commercial Cities, FLOBBNCB and
LBGHOBN.)

Money.

1 lira Toscana=100 centesimi=7 4-5cL Eng.=
$0.15 3-5.

1 lira Toscaua=20 soldi=240 denari.

25 lire Toscane=21 francs.

COIN.— Gold: Kusponi a 3 zecchini = $6 25

Zecchini gigliati, = 2 05

Half " = 1 03

Silver : Francesconi a Leopoldinl = 0 96

Half " = 0 48

Tallari = 0 92

Testoni = 0 80
Lire a 12 crazie, about 15

Exchange on London, 30 lire, m. or 1., per £1.
Paris, 80 to 85 centimes per lira.

Weights and Measures.

LEGHORN.

1 braccio
155 bracci

1 sacco

4 sacci
100 Ibs.

1 centinajo

1 rottolo

ENGLISH.

= 22.93 in.

r= 100 yards.

= 2.0739 Winchester bushels.
= 1 imperial quarter nearly.

= 74.864 Ibs. avoirdupois.

= 100 Ibs.
= 3 Ibs.

More particularly—

Weight

1 quintal =100 Ibs. =1200 uncie a 24 denari
1 Ib. = 12 oz. avoirdupois.
1 quintal=74& Ibs. avoirdupois.
FOE GOLD.— 1 Ib. = 10 11-12 oz. troy, and Is
divided into 24 carati a 8 ottavi.
FOR SILVER, into 12 uncie a 24 denari.
Jewels are weighed by the carat a 4 grant

Measure.

1 braccio = 23 in. English
1 mile = 1 mile, 48 yards, English.
The braccio used by builders=21 3-5 in. English.
FOB CORN. — 1 sacco=3 Btaja=6 mines;

100 sacchi=201 bushels.

FOR WINE— 1 barile=20 fiaschi=80 mezzette=
160 quartuzzi = 10 1-30 galls. Eng.
1 barile of oil=7f galls English.

SHIPPING MEASUREMENT.
FOB GRAIN. — 42 cubic feet=l ton shipping meas-
urement.

1 bushel = 60 Ibs.
1 bushel = 2218| cubic inches.
8 bushels = 1 quarter.

1 quarter = 17745 cub. in. or 10.27 ft.
Therefore 1 ton will take 4 quarters and one -tenth
1 bushel being equal to 60 Ibs.,
1 quarter will be equal to 480 Ibs.,
1 ton=1968 Ibs. or 17 cwt. 2 qrs. 0 Ibs. fully.
1 ship of 200 tons measurement can therefore
carry 820 quarters, but it generally can carry much
more.

MISCELLANEOUS TABLE

FOREIGN WEIGHTS AND MEASURES.

Arroba of Bnenos Ayres .. =
Amir, or Emir, of Stuttgard . . =
Balsam Copaiva, 8 Ibs. . . =

Butt of wine =

Canado of Balsam Copaiva .. =

Chaldron coal, British Provinces =

do. do. Cumberland .. =

Cheki of opium (from Smyrna) =

Coal, a railway wason load, Pictou =

Flax, head of, about . . . . ;

Foot, 100 feet St. Domingo . . =

Honey, 1 gallon . . . . =

Linseed, one bushel . . . . =

Mudd, or maud, of Rotterdam :

Moyo of salt (Spain) .. .. :

Modius of salt (from Ivica, Spain):

do. do. (Oporto & St. Ubes):

Mass (of Antwerp) ith of ohm :

Ohm do. .. .. ;

Pou nds of A ustria, . . 100 Ibs. :

do. Antwerp, .. do. :

do. Bavaria, .. do. -

25-36 Ibs. U. S. Pounds of Beldum.

100 Ibs. =103 35-1-00

78 gallons.

do. Brussels,

do.

=10835-100

1 do.

do. Bremen,

do.

=109 80-100

130 do.

do. Berlin,

do.

=103 11-100

30 pounds.

do. Hamburg,

do.

=106 80-100

36 bushels.

do. Malaga,

do.

=101 44-100

53 do.

do. Netherlands, . .

do.

=108 98-100

If pound.

do. Portugal,

do.

=101 19-100

62 cwt.

do. Prussia,

do.

=103 11-100

6|-pounds.

do. Eotterdam, . .

do.

=108 93-100

106 60-100 feet.

do. Spain,

do.

=101 44-100

12 pounds.
47 do.

do. St. Domingo, . .
do. Trieste,

do.
do.

=107 93-100
=123 60-100

143 do.

do. Vienna,

do.

=123 60-100

70 bushels.

Palm of Italy, of marble

= 6 inches.

40 do.

Quintal of France

=220 54 -100 Ibs.

23 do.

10 gallons.

Skippond of Gottenburg
do. Gefle

=300 pounds.
=314 1-10 Ibs.

40 do.

Salt, one barrel

=5| bushels.

: 123 60-1 00

Vara, Spanish

=8 feet

103 35-100

Yara of Baracoa . . . .

=20 feet.

123

SUPPLEMENT.

325

RATES OF FOREIGN MONEY OR CURRENCY, FIXED BY LAW.

The following condensed presentation of the United States value of Foreign Currencies, "Weights and
Measures, is to a considerable extent a repetition of what may be found in the foregoing Tables. It is
here thus given, first, for the greater convenience of this condensed form; and secondly, as giving the
specific values established by law in the United States, while that presented in the foregoing is the one
recognized in London, estimated in Sterling Currency, and that reduced to Federal Currency, putting
the pound at $t.Si. The slight discrepancies between the two are thus accounted for, and the reader will
hear in mind that the following are the popular values or rates at which these foreign coins pass in the U. S.

The Editor acknowledges his essential indebtedness for these to a volume, entitled " United States
Tariff," &c., published by'Messrs. Rich & Loutrel, New York, to whose courtesy we are indebted for the
use of these Tables. In it may be found a great amount of valuable information to commercial men,
respecting the Rates of Duties on foreign merchandise and other matters. The volume is compiled by E.
D. O^ len~ Esq., Entry Clerk i*i the New York Custom House, and is made the text book in all the Cus-
tom Houses throughout the United States and by the Departments at Washington.

$ eta.

8)

136-10
40
4}

Ducat of Naples, ..

Franc of France and Belgium,

Florin of the Netherlan is,

Florin of the Southern States of Germany,

Florin of Austria and Trieste, 4?*

Florin of Nuremburg and Frankfort, .. .. 4)

Florin of Bohemia, 43*

Guilder of Netherlands, &c. — same as Florins.

Lira of the Lombardo and Venetian Kingdom, 1")

Livre of Leghorn, 15

Lira of Tuscany, 15

Lira of Sardinia, 136-10

Livre of Genoa, 136-10

Milrea of Portusral, 113

Milrea of Ma leira, 103

Milrea of Azores 8-3}

Marc Banco of Hamburg, 35

Ounce of Sicily, 240

Pouni sterling of Great Britain, .. .. 4^4

Pound sterling of Jamaica, 484

Poun 1 sterling of British Prov. of Nova Scotia,

New Brunswick, Newfoundland and Canada, 4 00

Payola of In lia, 184

Real vellon of Spain, 5

Real plate of Spun, .. .. .. .. 10

Rupee Company and British In lia, .. .. 44*

Eix dollar (or thaler) of Prussia and the

Northern States of Germany €9

Rix dollar (or thaler) of Bremen, .. .. 73|
Eix dollar (or thale -) of Berlin, Saxony & Leipsic, 69

Rouble, silver, of R.issia, 75

Specie dollar of Denm irk, 105

Specie dollar of Norway, 1 06

Specie dollar of Sweden, .. 106

TaleofC.iini 1 43

Banco rix dollar of Sweden and Norway, .. 39}

Bano rix dollar of Denmark, .. .". .. 53

Curacoag-jilder,
Leghorn dollar or pezzo, .
Livre of Catalonia, ..
Livre of Neufchatel,
Swiss livre, ..
Scudi of Malta,
Scudi, Roman,
St. Gall guilder,

40
90 76-100

: P

40
99 a 99*
40 36-100

Rix dollar of Batavia,
Eoman dollar,

75
. 1 05

Rouble, paper, of Russia, . .

Turkish piastre,
Current mark,
Florin of Prussia, ..
Florin of Basle,

Genoa livre,

Livre tournois of France, . .

21
18*

100 grani
100 centimes
100 do.

60 kreutzera

60 do.

60 do.

60 do.

100 centisimi

20 soldi

2U soldi
4 reali

20 soldi
1000 reas
1000 do.
1000 do.

16 shillings

SOtari

20 shillings

20 do.
36 fanams
34 maravedis
84 do.
16 annas

80 groschen
72 grotes
80 groschen
10) kopecks

6 marks

6 do.
43skillings
10 mace

20 soldi
2) stivers
20 sol.-li
20 sueldos
20 sols
100 centimes
12 tair

60 krentzers

43 stivers

of

4 pfennings
4 do.
4 do.
4 do.

100 millesemi
12 -lenari
12 denari
20 soldi
12 'denari

12 pfennings
20 grani
12 pence

12 do.
43jittas

12 pice

12 pfennings

5 swares

12 pfennings

16skillings
16 do.
12 'ore
100 candarem*

12 denari
12 pfennings
12 denari
12 dineros
12 deniers

20 grani
4 pfennings

f Varies from 4 roubles

i n<\ v v J 65 copecks to 4 rou-
100 kopecks j b]es £j Ck8 to

[ the dollar.
100 aspers

SUPPLEME NT.

A TABLE OF FOREIGN WEIGHTS AND MEASURES,

EEDUCED TO THE STANDARD OF THE UNITED STATES, AND AS RECEIVED AT THE
UNITED STATES CUSTOM HOUSES.

ALEXANDRIA (Egypt).

Cantaro of 100 rottoli farlbro

of 15 oz. (avoirdupois) . . = 9"4 Ibs.

300 rottoli zaydino of 2Hoz. = 18o| "

100 " zauraof83oz. .. = 2 '7 "

100 " minaof 26} oz... = 167 "
1 oke 400 drams of 16 carats

each . = 43 "

Stone of flax. .
Stone of wool
Lispund

100 Ibs.

= 20 Ibs.

= 10 "

= 14 "

= 1C9.8 "

ALICANT (Spain).

CADIZ (Spain).

Quintal of 4 arrobas .. = ICO Ibs.

1 lb., 2 marcs, 16 oz., or 256

adarins.
100 Ibs. . = 101.43 Ibs.

Arroba = 27 Ibs. 6 oz.
Quintal = 109J Ibs.

CAIRO (E^ypt).
Cantaro, 100 rottoli. . . . = 93 Ibs.

AHSTERDAH.
100 Ibs. 1 centner . . . . = 10S.<T, Ibs.

1 rottoli =144 drams.
r»n«<i J ^OO drams, or
ucca — -j 26.39 Ibs.

Last of grain = 85.25 bush.

86 occas . . . . = 1 cantaro.

Ahmofwine .. .. = 41.00 gall.

Amsterdam foot . . . . = 0.93 foot.

cinxTA,

Antwerp foot . . . . = 0.94 "

Tail . . — 1\oz

Rhinlandfoot .'.' '.'. = 1.03 "

16 tails =1 catty .. .. = l.llb.

Amsterdam ell .. .. = 2.26 feet.

100catties=l picul .. = 133 i Ibs.

Ell of the Hague . . . . = 2.28 "

Ell of Brabant .. .. = 2.30 «

CONSTANTINOPLE.

Medden or measure of coal = 2$ bush.

Quintal = IPO rottolis.

do. . . . . . . = 45 okes.

ANCONA (Italy).

do. = 176 cheques.

100 Ibs. Roman . . . . = 102.75 Ancona.

do. =127 Ibs.

100 " Ancona . . = 73.75 Ibs.

One oko = -j 2 JJ*?' 13 oz> ~

ARRAGON (Spain).

CALCUTTA.

Libras of 100 Ibs = 77.01 Ibs.

Maund = 40 seers.

Quintal, 4 arrobas of 36 Ibs. = 112.00 "
BA330RA. (Persian Gulf).

Seer = 16 chattacks.
English factory maund . . = 74 Ibs. 10 oz.
Seer = 1 lb. 13 oz.

Maund attary, 25 vakias tary = 23.05 Ibs.

Chattack = 1 oz.

One vakia = 19 oz.

BATAVIA (E. Indies).

Bengal bezar maund is 10 per
cent, heavier than the fac-
tory maund.

Large bahar . . . . . = 4£ peculs.

Small " = 8

ijczar maunu . . . . •< drains

1 pecul . . . . . = 100 catties.

Seer = 2 Ibs. 1 3 | drams.

1 catty = 16 tales.

Chattack = 2 oz. 5-6 drams.

1 pecul =135 Ibs. 10 oz.

IEH~I!T (ZTorway).
Bhippond of 20 lisnonds .. = 820 Ibs.
Centner of 6^ lispomls .. = 100 "
Lispond = 16 "
Waag. 8 bismar Ibs. .. = 8G "
1 lb., 2 marcs, 1G oz., 32 loths.
100 Norway Ibs = 110.23 Ibs.

DENMARK.

100 Ibs. =1 centner .. .. = 110.23 Ibs.
Barrel or toende of corn .. = 3.95 bush.
Viertel of wine .. . . = 2.04 galls.
Copenhagen, or Rhineland ft.= 1.08 foot.
Centner or 100 Ibs. Denmark = 110.28 lb.
Shipfund=20 lispunds .. = 820 Ibs.
1 lispund = 16 "

CHRISTIANA (ITorway).
Shippond = 352 Ibs.

1 bismerpund . . . . = 12 "
1 waag=3 bismerpunds . . = 86 "

LAURWIQ a:orx7a7).

ENGLAND.

Bhippond = 852 Ibs.

Old ale gallon .. .. = 1.22 galls.

BOMBAY.

Imperial gallon . . . . = 1.20 "
Old wine " .. .. = 1.00 "

Ccindv.. . = 26^ Ibs.

Quarter of grain, or 8 imperial

Maurid = 28 "

bushels = 8.25 bush.

Beer *= lll-5oz.

Imperial corn bushel, or 8 im-

Candy = 20 maunds.

perial gallons . . . . = 1.03 "

Maund = 4 ) seers.

Old Winchester bushel .. = l.CO "

Beer = 3J pice.

Imperial yard .. .. = 36 inches.

rp , ( 144- 175th sofa Ih,

BBhEXESt

Troy pound = -J nvoirdnpoi8.

Shlpfund = 2J centners.

Newcastle chaldron . . = 86 bushels.

Centner =116 Ibs.

Stone = 16 Ibs.

VTaagofiron = 120 "

Tun of wine = 250 Imp. galls.

SUPPLEMENT.

327

FRANCE.

PORTUGAL.

Metro = 3.28 feet.

100 pounds =

101.19 Ibs.

. Decimetre (l-10tli mutre) = 8.94 inches.
Velt = 2.00 galls.

22 pounds (1 arroba) . . =
4 arrobas of 32 Ibs. (1 quintal) =

82.00 «
1.28 "

Hectolitre = 26.42 "

Alquiere =

4.75 bush.

Decalitre = 2.64 "

Mojo of grain .. .. =

23.03 "

Litre .. .. •• .. = 2.11 pints.

Last of salt =

70.00 «

Kilolitre = 35.32 feet

Almade of wino . . . . =

437 galls.

Hectolitre = 2.34 bush.
Decalitre = 9.'US quarts.

PRUSSIA.

Millier = 22.U5 Ibs.

103 Ibs. of 2 Cologne marks

Quintal = 220.54 "

each =

103.11 Ibs.

Killogramma .. .. = 2.21 "

Quintal, of 110 Ibs =

113.42 "

100 pounds = 107.93 "

Sheffel of grain . . . . =

1.56 bush.

100 feet = lJ6.60feet

Eiimr of wine . . . . =

13. 14 galls.

Tun (of wine) . . . . = 240.00 galls.

Ell of cloth =

2.19 feet.

Foot =

1.03 foot

FLORENCE AND LEGHORN.

"ROME

100 Ibs. or 1 cantaro . . = 74.86 Ibs.
Moggio of grain . . . . = 16.59 bush.
Barileofwino .. .. = 12.04 galls.

JfcW Ifl • 1.

Rubbio of grain . . . . =
Barile of wine . . . . =
100 Koman Ibs. . . . . =

8.36 bush.
15.31 galls.
74.77 Iba.

GENOA.

RUSSIA.

100 Ibs. or peso grosso . . = 76.87 Ibs.
100 " or peso sottilo . . = 63.89 "
Mina of grain .. .. = 3.43 bush.
Mezzarola of wine . . . . = 39.22 galls.

100 Ibs. of 32 loths each . . =
Chertwert of grain . . . . =
Vedro of wine . . . . =
Petersburg foot . . . . =

90.26 Ibs.
5.95 bush.
3.25 galls.
1.18 foot

HAMBURG.

Moscow foot. . . . =

1.10 "

Last of grain = 8D. 64 bush.

Pood =

36. 00 Ibs.

Ahmofwine .. .. = 33.25 galls.

STCT7Y

Hamburg foot .. .. = 0.96 foot.

Vll 1 oo u

DJLvJ-ij i «

Cantaro grosso . . . =

192.50 Ibs.

Ji-il . . . . . . . . — l._li

*. sottilo =

175 Ibs.

Jihipfund, equal to 2^ cent-
ners, or 230 Ibs. Hamburg = 299 Ibs.
{8 lispunds, or
112 Ibs. Ham-
burg.

lf)0 pounds =
Salma grossa of grain . =
" generale . . . =
" of wine . . . . =

70 "
9.77 bush.
7.85 "
23.06 galls.

1 lispund = 14 Ibs. Hamburg.
1 stone of flax .. .. = 23 " "

SPAIN.
Quintal, or 4 arrobas . . =

131.44 Ibs.

1 stone of wool .. .. = 10 " "

Arroba =

25.36 "

1 stone of feathers . . . . = 13" "

" of wine .. . . =

4.43 galls.

DO ibs. Hamburg .. .. = 106.8 Ibs.

Paaega of grain . . =

1.GO bush.

ITALY.

ST. GALL.

100 rottoli of 31 3-7 oz. each = 19G4 Ibs.
1 cantaro grosso . . . . = 19G4. "

109 heavy Ibs. .. .. =

100 light " .. .. =

128 Ibs.
102 "

MADRAS.

Candy = 503 Ibs.
" = 20 maunds.
Maund = 8 bis.

SURAT.

20 Surat maunds, or 10 Ben-
gal factory maunds. . . =
1 candy =

1 candy.
746 Ibs. 10 oz.

Bis = 8 seers.

SWSDZIT.

MALACCA.
Pecul =135 Ibs.

r.Q Ibs. or 5 lispunds . . =
Kan of corn =
Last . . . . =

73.76 Ibs.
7.42 bush.
75 00 "

^ pecul — J 10° catties» or !COO

Cann of wine . . =

69.09 galls.

\ talcs.

Ell of cloth =

1.95 foot

MALTA.

2 ) commercial Ibs =

1 lispund.

100 Ibs. 1 cantaro .. .. = 174.50 Ibs.
Salma of grain .. .. = 8.22 bush.

20 lispunds =

1 skeppund.

Cantaro =103 rottoli.

SMYRNA.

Kottoli = 33 oz.

100 Ibs. (1 quintal) . . . . =

129.43 Ibs.

1 cantaro (mercantile usage) = 175 Ibs.

Oke .. .. .. =
Qtiillot of grain .. .. =

2.83 "
1 .46 bush.

_ , NAPLES.
Cantaro grosso .. .. = 196.50 Ibs.
picolo . . . . = 106.00 "

Quillot of wine . . . . =
TRIESTE.

13.50 galls.

Carro of grain .. .. - 52.24 bush,
wine .. .. = 264.00 galls.

100 pounds =
Stajo of grain .. .. =
Orna or eimer of wine . . =

123.60 Ibs.
2.34 bush.
14.94 galls.

NETHERLANDS.

Ell for woolens . . . . =
" for silk =

2.22 feet
2.10 "

MuddeofZak .. .. =.- 284.00 bush.
V at hectolitre . . . . = 26.42 galls.

VENICE.
100 Ibs. peso grosso. . . =

105.1 8 Ibs.

f>an1li.tr® = 2.11 pints.
Pond killogram™ . . .. = 2.21 Ibs.
100 pounds - 108.93 "

100 " " sottile.. .. =
Mo<r<rio of grain .. .. =
Anifora of wine . . . . =

66.04 "
9.08 bush.
137.00 galls.

328

SUPPLEMENT.

TABLE

GIVING TUB

CUMENCY, EATE OF INTEREST,

PENALTY FOR USURY,

AND LAWS IS REGARD TO COLLECTION OF DEBTS, &c.,

IX THE SEVERAL UNITED STATES.

THE following items of information, it is believed, will be found convenient for business men, and
useful in the "Counting-house and Family." They have been collected with much care, and original
sources resorted to in the respective localities, for the most part. Yet, as the legislation in regard to
some of these matters is changing, and what is true this year, in a given State, may not be entirely so the
next, some caution will be required in relying too implicitly upon present statements, hereafter. They
will serve, however, as a general guide, and are as valuable as any thing of the sort, from the nature of
the case, can well be.

Although the Federal Currency is that established by law for tho whole country, and that in common
use in all the btates, yet, as previous to its adoption tho different States had different usages in these
respects, that ancient usage, to some extent, continues. Thus, in Massachusetts, six shillings make a
dollar, in ^e\v York, eight shillings, &c.

MAINE.

Currency. — The dollar is 6s. ; Is. is lG"c. ; 6J. is
&£c. ; 9d., 12|c., &c.

Interest. — Six per cent.

Penalty for Usury, — Usurious excess void. For
debts contracted out of the State, the rates of in-
terest in that State aro supported by our laws ; i. e.
a debt contracted in California, interest 12 per
cent., both parties remove here and note still due,
interest continues the same as where it began.

Collection of Debts. — He.tl estate, and goods and
chattels, may be attached and held as security to
satisfy a judgment, which must be rendered by the
appropriate court. Property possessed by a woman
before marriage, remains hers after marriage, and
not liable for husband's debts. Arrest for debt
allowed if party about to leave the State, but if he
disclose he is discharged, if he has not wherewithal
to pay the debt. Certain specified property, for
current support, exempt from attachment. There
is a homestead exemption and mechanics' lien law.

NEW HAMPSHIRE.

Currency. — Same as Maine.

Interest. — Six per cent.

Penalty for Usury.— Forfeiture of threo times
the usury.

Collection of Dfl>U.— There is a mechanics1 lien
and homestead exemption law. Certain specified
property is also exempted from attachment Other
real and personal estate may be attached. Mort-
gages of personal property must be recorded in
town clerk's office.

VERMONT.

Currency. — Same as Maine.

Interest.— Six per cent. Unusual interest legal
when contracted for.

Penalty for Usury. — Excess not collectable, and
when paid may be recovered back and costs.

Collection of Debts.— Heal and personal property
may be attached on mesne process, and persons
jesiding in tho State owing debtor exceeding $10

may be trusteed. Xo imprisonment on contract,
except on affidavit that debtor is about to remove
from the State and has money or property secreted
Mechanics have a lien for a limited time. Home-
stead exemption, $500. Household furniture, cloth-
ing, and tools, exempt from attachment.

MASSACHUSETTS.

Currency. — Some as Maine.

Interest. — Six per cent.

Penalty for Usury.— Three times the unlawful
interest taken. A Lank taking unlawful interest
forfeits the debt.

Collection of Debts.— A mechanics' lien and home-
stead exemption law. Other specified property for
fumily use and carrying on trade, exempt from at-
tachment. Mortgages of personal property to bo
recorded by town clerk. Keal and personal prop-
erty not exempted, attachable. Imprisonment for
debt not allowed except for fraud. Two thirds in
value of the creditors may put a debtor into insolv-
ency, when all his property shall be applied ibr
equal benefit of all creditors in proportion to claims
proved ; or any creditor of $100 and upwards may,
for specified causes, compel debtor to insolvency.
Debtor complying with certain conditions and giv-
ing up all property, not further liable for any debts
thereafter in the State. Married women have in-
dependent rights of property.

RHODE ISLAND

Currency. — Same ns Maine.

Legal Interest. — Six per cent.

Penalty for Usury. — Forfeiture of excess.

Collection of Debts. — Mechanics' lien law. Speci-
fied property exempt from attachment ; other prop-
erty may be attached. Mortgages of personal prop-
erty must Jfce recorded in town clerk's office. Im-
prisonment for debt allowed, but the jail limit.3
extend to the county. Here, as in most of tho
States, unwitnessed notes and ordinary book ac-
counts can not be sued for after six years, unless 9-
formal judgment of court shall have been had.

SUPJ'LEM ENT,

32

CONNECTICUT.

Currency. — Same as Maine.

Interest.— Six per cent.

Usury. — Forfeiture of all interest.

Collection of Debts. — A mechanics1 lien law.
Other specified property exempted from attach-
ment. Mortgager of personal property may retain
possession of it. Goods, chattels, and real estate of
debtor may be attached, subject to be defeated by
insolvency within sixty days. Person of debtor
not liable to arrest Wife's property at time of
marriage, or subsequently acquired by devise or
inheritance, not liable for husband's debts.

NEW YORK.

Currency.— T)o\\*r, 8 shillings; Is., 12*0.; 6d., GJc.

Legal Interest.— Seven per cent.

Penalty for Usury. — Voids the contract, but
corporations can not set up usury as defense. Per-
sons who take usury deemed guilty of a misde-
meanor and liable to a flue not exceeding $100, or
imprisonment not exceeding six months, or both.

Collection of Debts.— Certain specified property
exempt from attachment; also a homestead ex-
emption to value of $1000, and continued for benefit
of widow and children until youngest child 21.
But the deed conveying the property must show it
intended to be held as such homestead, or a precise
notice given and recorded to that effect. Mechan-
ics, laborers, &c., in all cities and certain counties,
have a lien on buildinss. <fcc., for pay for labor, ma-
terials, Ac., on such buildings. Chattel mortgages
void unless filed with town or county clerks, or
goods delivered. Personal arrest allowed in case
of fraud, concealment, &c. Property owned by
female at marriage not liable for husband's debts.
Married woman may hold separate property, taken
by inheritance, or by gift or bequest from any per-
son other than the husband, and the same shall not
be liable for the debts of the husband, nor subject
to his disposal.

NEW J3E3ET.

Currency. — 7s. 6d. to the dollar.

Interest. — Six per cent.

Paltry. — Forfeiture of whole amount.

Collection of Debts.— Homestead exemption to
amount of $1000. Other specified property ex-
empt from attachment. A mechanics' lien law.
Ordinary debts outlawed in six years. Females
exempt" from arrest for debt. Widows1 right of
dower, one third husband's real estate.

PENNSYLVANIA.

Currency.— Is. 6d. to the dollar ; 121 cts. called a
levy, an abbreviation of eleven pence ; 6£ cts.
an abbreviation of five pence orjippenny bit.

Legal Interest. — Six per cent.

Penalty for Usury. — Forfeiture of usurious in-
terest in action on the contract, and of the money
lent in a penal action.

Collection of Debt*.— Property to amount of $300,
and clothing, school books, &c., exempt from at-
tachment. Mechanics have lien on buildings for
labor an I materials in their construction in most of
the coanties. Arrest of person of debto^ not al-
lowed except for fraud or concealment. Six years
voids debts by simple contract. Women's individ-
ual right in property continues after marriage, as
before.

DELAWARE.

Currency.— -7s. 6d. to the dollar.

Rate of Interest. — Six per cent.

Penalty for Usury. — i orfeiture of debt.

Collection of Debts.— Specified property, not ex-
ceeding $100, exempted from attachment. Person
of debtor may not be arrested, except for fraud,
concealment, <fec. Limitation of debts, not of rec-
ord, three years; for recovery of land, twenty
years; note of hand, six years.

MARYLAND.

Currency. — 7s. 6d. to the dollar, but shillings and
pence are abolished in law and obsolete in popular
use.

Interest. — Six per cent.

Usury. — Forfeiture of usury.

Collection of Debts. — Mechanics and men supply-
ing material have a lien in Baltimore city and most
of the counties for work done and materials furnished
on and for the construction of buildings. Property
belonging to a woman not liable for payment of
husband's debts. Wearing apparel and bedding of
debtor and family exempt from execution. Mort-
gages of personal property must be in writing,
acknowledged, and recorded within twenty days of
their date. Actions for debt, not on a seale'd instru-
ment, must be brought within three years; on
sealed instruments within twelve years. Xo im-
prisonment for debt.

VIRGINIA.

Currency. — 6s. to the dollar.

Interest. — Six per cent.

Usury. — Renders contract void, and in criminal
action forfeits double the value of money lent.

Collection of Debts. — Mechanics have lien on
land upon which they erect buildings, provided
they build by contract in writing and recorded.
Growing crops, not severed, not liable to distress
or levy, except Indian corn, which may be taken
after 15th October. Specified articles also exempt-
ed. Slaves not to be distrained or levied upo*a
without debtor's consent, where other effects suffi-
cient are shown to o.licer, and in his power to take.
Mechanics1 tools exempt to value of twenty-five
dollars. Actions on unsealed instruments barred
generally in five years; on sealed instruments in
ten and twenty years. Imprisonment for debt
abolished. In certain cases, debtor, when sued,
maybe held to bail; ani in default of giving bail
may be imprisoned. Married women may hold
property separate from their husbands. Widow's
dower, one third of real estate for life, and of per-
sonal estate absolutely after payment of debts, ex-
cept only life estate in slaves.

Judgments sive lien on real estate from first day
of the term of the court at which they are rendered.
Executions bind all the personalty which tb.3
debtor possesses, or to which he is entitled, from
the moment they are in the hands of an officer
who can by law levy them ; and jtidsment debtor
may be compelled, by interrogatories filed before a
commissioner in chancery, to disclose upon oath
all his effects, real, personal, and mixed, in his pos-
session or under his control. If he answer said
interrogatories fraudulently, or evasively, the com-
missioner may attach and commit him. Any ona
indebted to a judgment debtor may be garnished
by the judsment Creditor, and made to pay such
creditor. Elegits now extend to all debtor's real
estate. Judgment creditors may sue, at law or in
equity, at their own costs, in name of sheriff or
other officer, to recover any property of their debt-
ors, on which they obtain a lien.

330

SUPPLEMENT.

NORTH CAROLINA,

Currency. ~- 10s. to the dollar.

Interest—Six per cent.

Usury.— Voids the contract; lender forfeits
double the amount of money lent.

Collection of Debts. — Specified property exempt
from attachment. Actions on simple contract
must be brought within three years; for land,
eeven years ; by infants, feme coverts, or non com-
pos mentis, within three years after disability re-
moved; persons beyond seas, within eight years
after title accrues. Possession for twenty-one
years, under color of title, a bar to the State.
Three years' possession of personal property gives
title. Wife's real estate at time of marriage can
not be sold or leased by husband without consent
of wife. Deeds, mortgages, marriage settlements,
&c., must be recorded, or are void as to creditors.

SOUTH CAROLINA.

Currency. — 4s. 8d. to the dollar.

Interest. — Seven per cent.

Usury. — Forfeiture of interest with costs.

Collection of Debts.— Attachment holds against
the property of a non-resident or absconding debt-
or, and the person of a debtor about to abscond.
Actions for debt must be brought within four years ;
to recover possession of land, within ten years.
Deeds of marriage settlement must be recorded.
Mechanics have lien on building. Chattel mortga-
ges void as against subsequent purchasers, unless
recorded. Specified property, and a house and fifty
acres of land, exempted from attachment, to $500.

GEORGIA.

Currency. — 4s. 8d. to the dollar.

Interest. — Seven per cent.

Usury. — Usurious interest only void, principal
and legal interest recoverable.

Collection of Debts.— AM actions under the com-
mon law of England in force in this State. Me-
chanics have a lien on buildings they have built or
repaired. Liens on river steam-boats for wages,
provisions, supplies, and repairs; the same lien
extends over mills for lumber, wages, provisions
furnished, and repairs. There is a homestead ex-
emption from levy and sale, but the property must
not exceed in value $230. All conveyances of land
must be recorded within six months ; all mortga-
ges, both of real and personal estate, must be re-
corded within ninety days. Actions on open ae-
count3»mu3t be brought within four years; on
promissory notes, unsealed, six years; for recovery
of land, seven years ; on bonds ami other sealed
instruments, twenty years. All property of what-
ever kind subject to attachment. Honest debtors'
act in force; its operation is to release the debtor's
person from arrest, but not his present or any
future property from levy. Wives and widows are
not exempt from the operation of the attachment
law; but the persons of all women in Georgia are
exampt from arrest under any civil process.

ALABAMA,

Currency.— Federal money only.

Interest.— Eisrht per cent.

Usury.— Forfeits all interest.

Collection of Debt*.— Specified articles and home-
stead to value of $500 exempt from execution and
sale. Mechanics' lien law. Actions on liquidated
demands must be brought within six years; on
open account, in three years. Mortgages of real
and personal property must be recorded. Sale of
goods over $200 must be evidenced by transfer of

some portion of the goods, or payment of somo
portion of purchase money, or written contract
Attachment lies for debts, whether now due or
not, in case of fraud in the debtor and non-resi-
dence. Arrest of person allowed, if fraud or con-
cealment. Husband acquires no right to wife's
property by marriage, so as to make it liable for
his debts, but is entitled to its management and
control during coverture ; and husband and wife
are jointly liable for family supplies.

MISSISSIPPI.

Currency. — 8 bits (12£ cents) to the dollar.

Interest.— Six per cent., or by contract in writ-
ingfor money lent, any rate of interest not exceed-
ing ten per cent.

Usury.— Forfeiture of interest.

Collection of Debts.— No imprisonment of debtor.
Mortgages and deeds of trust must be acknowl-
edged and recorded. Specified property and a
homestead exempted from execution and attach-
ment. A mechanics' lien law. Actions on notes
and bills, limited to six years ; open accounts for
goods sold, three years; bonds and sealed instru-
ments, seven years ; possession of land, ten years.
Property of wife only sold by joint deed of herself
and husband.

LOUISIANA.

Currency. — Federal money, only in New Orleans
a picayune is 6 lr cents.

Interest. — Five per cent; by agreement of parties,
ten per cent. Bank interest, five to eight per cent

Usury.— Forfeiture of interest.

Collection of Debts. — A mechanics' lien law.
Specified property exempt from attachment. "Wo-
men not subject to arrest for debt Property owned
by either party before marriage remaining such
afterward. No imprisonment for debt

FLORIDA.

Currency. — Federal money only.

Interest. — Six per cent, or by agreement, eight.

Usury. — Forfeits interest.

Collection of Debts. — Imprisonment for debt
abolished. Specified property and forty acres of
land exempt from attachment, not exceeding $200 ;
also dwelling house to same amount by city or
town resident. A mechanics' lien law. Mortgages
of personal property must be recorded. Widow's
dower, life interest in one third of real estate.
Wife's property at marriage continues hers, and not
liable for husband's debts.

TEXAS.

Currency. — Federal money.

Interest. — Eight per cent, or higher to twelve per
cent., by agreement.

Usury. — Forfeits interest.

Collection of Debts. — Mortgages of personal prop-
erty must be recorded, and may be set aside for
valuable consideration, or possession given to mort-
gagee. Actions for debt on account must be brought
within two years; on contract, four years; real
estate, varying with circumstances. A homestead
exemption; specified personal property r.lso ex-
empted from attachment. A mechanics' lien law.
No imprisonment for debt. Property attachable
of debtor non est. Widow's dower, life interest in
one third real estate. Property of feme sole fit mar-
riage, if registered, remains hers independently.

SUPPLEMENT.

331

TENNESSEE.

Currency. — 6s. to the dollar.

Interest.— Six per cent,

Usury— Fine at least $10.

Collection of Debts.— Specified property exempt
from attachment. A mechanics' lien law. Mort-
gages of personal property must be recorded. ><'o
imprisonment for debt. Property of concealing or
absconding debtor attachable. Actions for dubU
of account must be brought within three years.
Widow's dower, one third of husband's estate at
death. Married women, the twain are not one as
to wife's property, in which she has an independent
ri^ut A hoineoteal exemption.

KENTUCKY.

Currency. — 6s. to tho dollar.

Interest. — Six per cent.

Usury. — Forfeiture of usury and costs.

Collection of Debts.— Mortgages of personal and
real property must be recorded. A mechanics'
lien law in certain towns. Specified property ex-
empt from attachment. Debtor is held to bail on
specified conditions. Property attachable in case
of concealment, proposed removal, absence, &c.
Feme covert has independent rights in property,
but husband not liable for wife's debts before mar-
riage. Actions limited, on account, to one year.

OHIO.

Currency.— -Ss. to the dollar.

Interest.— Sis. per cent As high as ten per cent,
if stipulated in written instrument. Banks allowed
only six per cent.

Usury.— Forfeiture of usury.

Collection of Debts.— Mecuanics' lien. Specified
property exempt from execution. A homestead
exemption. Mortgages of personal property valid
for one year if recorded. Lands not to be sold for
Jess than two thirds of the appraised value. Attach-
ments allowed in specified cases. First attachment
of prior validity. Limitation laws: real estate,
twenty-one year's; written contracts, fifteen years;
not written, six years. Widow's dower, one third
of real estate.

INDIANA.

Currency. — 63. to the dollar.

Interest.— Six per cent

Usury.— Forfeiture of nsnrions interest.

Collection of Debts. — Mechanics' lien law. Home-
stead exemption law. Specified property exempt
from attachment. Mortgages of personal property
must be acknowledged and recorded unless prop-
erty transferred. Ordinary debts outlawed in six
years ; contracts in writing and real estate. Real
and personal property not specially exempted may
be taken on execution. Wife's real estate at or
after coverture, not liable for husband's debts.

ILLINOIS.

Currency.— Federal money.
Interest. — Six per cent. ; by agreement, as high
as ten per cent

Usury. — Forfeits entire interest.

Collection of Debt*.— Widow's dower, one third
of real estate. A mechanics' lien law. Homestead
exemption law. Specified articles not attachable.
Chattel mortgages must be acknowledged and re-
corded or property delivered. Body of debtor may
be arrested for fraud or concealment.

MICHIGAN.

Currency. — Ss. to the dollar.

Interest.— Seven per cent., yet as high as ten per
cent by agreement of parties.

Usury. — Voids the excess.

Collection of Debts.— There is a mechanics' lien
law, and a homestead exemption law. Mortgages
of personal property must be recorded, and then
are void, as against other creditors or mortgagees,
after one year, unless within thirty days preceding
an authenticated certificate is attached to the in-
strument or record setting forth mortgagee's inter-
est Contracts for sale of goods invalid above $50,
unless part of goods delivered, or something given
to bind the bargain. Actions for ordinary debts
must be brought within six years. Person of
debtor may be arrested, if debtor about to remove

Eroperty from State, or fraudulent concealment or
itent to defraud. Feme- coverfs right to property
possessed before marriage, or to which she becomes
entitled subsequently, continues her separate
property, and not liable for husband's debts, and
she may alienate it as if unmarried.

MISSOTJBL

Currency.— -6s. to the dollar ; bit, 12J cts. ; pica-
yune, 6'f cts.

Interest.— Six per cent ; by agreement, as high
as ten.

Usury. — Forfeits usury and interest

Collection of Debts.— Wife's dower, life estate in
one third real, and specified personal property ab-
solutely. Wife's property at marriage not liable
for husband's old debts. No imprisonment for
debt. Attachment of property in case of fraud,
concealment, or removal of property, or non-resi-
dence. Property not specially exempt may be
taken on execution. Mortgages of personal prop-
erty must be recorded. Suits on open account
debts must be brought within five years ; on store
accounts, two years; on notes, bonds, bills. &c..
ten years. Specified property exempt from sale on
execution. A mechanics' lien law.

IOWA.

Currency. — Federal money.
Interest.— Sis. per cent., and up to ten by agree-
ment.

Usury.— Usurious interest recoverable.

Collection of Debts. — A mechanics' lien law. A
household exemption law. Specified property ex-
empt from attachment Mortgages of personal
property must be recorded. Ordinary indebted-
ness outlawed in five years ; written contracts, as
notes, <fec., ten years. Person of debtor exempt
from arrest Married woman has rights in prop-
erty independent of husband.

WISCONSIN.

Currency. — Federal money.

Interest.— Seven per cent. ; as high as twelve bj
agreement

Utsury. — Forfeiture of entire debt

Collection of Debts.— A. mechanics' lien law. A
homestead exemption. Mortgages of personal prop-
erty must be filed or recorded. Actions for recov-
ery of ordinary debts must be commenced within
six years. No imprisonment for debt, but property
of debtor attachable under certain circumstances.
Real and personal estate of feme sole not liable for
husband's debts.

332

SUPPLEMENT.

MINNESOTA.

Currency. — Federal money.

Interest.— Seven per cent., or any higher rate if
agreed in writing.

Usury. — No usury law.

Collection of Debts. — A mechanics' lien. A
homestead exemption law. Specified property ex-
empt from attachment. Mortgages of personal
property, a copy must be filed with or recorded
by county register. Imprisonment for debt abol-
ished. Contracts for sale of goods must be in writ-
ing for amounts over $50, unless part of goods
delivered, or part of purchase money or considera-
tion paid. Keal and personal estate of feme sole
not liable for husband's debts after marriage.
"Widow's dower, life interest in ono third real es-
tate.

CALIFORNIA.

Currency. — Federal money, but usage not wholly
established.

Interest. — Ten per cent. ; any higher rate by
contract not exceeding 18.

Usury. — Forfeiture of excess.

Collection of Debts.— Mechanics' lion law. Home-
stead exemption law. Specified property exempt
from attachment Mortgages of personal property,
property must bp transferred. Contracts void if
over $200, unless in writing, or part payment made,
or part goods delivered. Property may be at-
tached, although debt not due. if fraud, conceal-
ment, or absconding. Wife holds in separate right
property owned by her before marriage.

DISTRICT Oj1 COLUHI3IA.

Currency.— Federr.l money.

Interest. — Six per cent.

Usury.— Voids contracts at laxr, but a complain-
ant in equity is relieved only as to the excess.

Collection of Debts. — Debts of $50 or less are re-
coverable speedily before a justice; above that, in
Circuit Court. Where matter in controversy is
$1000, appeal lies to Supreme Court. Money in the
treasury cannot be attached, but a party having tho
apparent right to receive money from the treasury,
may be enjoined from receiving the same by his
assignee or otiiar person Laving tiie substantial

equitable title to that very fund. No bail in civil
cases ; no imprisonment for debt.

NOVA SCOTIA.

Currency.— 5s. or J pound to the dollar.

Interest.— Six. per cent.

J'enaliy for Usury.— Forfeiture of treble tho
amount ; does not extend to any hypothecation or
agreement in writing entered into for money ad-
vanced upon the bottom of a ship or vessel, her
cargo or freight.

Collection of Debts.— In tho Supreme Court,
major's and magistrate's courts by civil summons;
capias where parties are about to quit the province.
Limitation laws ; written contracts under seal,
twenty years ; ordinary contracts, six years. Mort-
gages of personality, same as under the English law.
Widow's dower, ono third of real estate and one
third of personality.

CANADA.

Currency. — 4s. sterling equals 4s. IP^d. currency
at the banks. Elsewhere, 4s. sterling equals 5s.
currency. Is. currency, 20 cents. 5s. currency to
the dollar. $4 to the pound.

Interest.— Six per cent, at banks. Elsewhere, any
rate of interest agreed upon ; but no more than six
per cent, can bo recovered at la^c, even where a
higher rate may have been stipulated.

Usury — Penalties for usury abolished, except as
regards banks.

Collection of Debts. — No homestead exemption.
Specified articles not seizablc. "When married here,
without a marriage contract, the wife's dower is
the half of the real estate the husband has at the
time of tho marriage, or which he may acquire by
inheritance during the marriage. Mortgages on
real estate obtain precedence of payment according
to the date of their registration. No mortgages
obtainable on personal property. No seizure of
estate for debt before judgment, except where a
creditor swears his debtor is fraudulently conceal-
ing or disposing of it. No imprisonment for debt,
except when a debtor is leaving the province of
Canada with a fraudulent intent. Limitation laws:
possession for thirty years creates a title ; when
proprietor is in a foreign country, twenty years.

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