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734 BROADWAY, NEW YORK.
A TREATISE ON PHYSIOLOGY AND HYGIENE.
FOR EDUCATIONAL INSTITUTIONS AND THE GENERAL READER.
By Joseph C. Hutchison, M.D.,
President of the New York Pathological Society; Vice-President of the New York
Academy of Medicine; Surgeon to the Brooklyn City Hospital; and late
President of the Medical Society of the State of New Yo/k.
Fully Illustrated with Numerous Elegant Engravings. 12mo. 300 pages.
1. Tlie Plan of tlie Work is to present the leading facts and principles
of human Physiology and Hygiene in language so clear and concise as
to be readily comprehended by pupils in schools and colleges, as well as
by general readers not familar with the subject. 2. The Style is terse
and concise, yet intelligible and clear; and ail useless technicalities have
been avoided. 3. The Range of Subjects Treated includes those on which
it is believed all persons should be informed, and that are proper in a
work of this class. 4. Ihe Subject-matter. — The attempt has been made
to bring the subject-matter up to date, and to include the results of the
most valuable of recent researches to the exclusion of exploded notions
and theories. Neither subject— Physiology or Hygiene— has been elabo-
rated at the expense of the other, but each rather has been accorded its
due weight, consideration, and space. The subject of Anatomy is in-
cidentally treated with all the fullness the author believes necessary in a
work of this class. 5. The Engravings are numerous, of great artistic
merit, and are far superior to those in any other work of the kind,
among them being two elegant colored plates, one showing the Viscera
in Position, the other, the Circulation of the Blood. 6. The Size of the
work will commend itself to teachers. It contains about 300 pages, and
can therefore be easily completed in one or two school terms.
The publishers are confident that teachers will find this work full of valuable
matter, much of which cannot be found elsewhere in a class manual, and so pre-
sented and arranged that the book can be used both with pleasure and success in
the schoolroom.
" Many of the popular works on Physiology now in use in schools, academies, and
colleges, do not reflect the present state of the science, and some of them abound
in absolute errors. The work which Dr. Hutchison has given to the public is free
from these objectionable features. I give it my hearty commendation." — Samuel
Q. Armor, M.D., late Professor in Michigan University.
"This book is one of the very few school books on these subjects which can be
unconditionally recommended. It is accurate, free from needless technicalities,
and judicious m the practical advice it gives on Hygienic topics. The illustrations
are excellent, and the book is well printed and bound. "—Boston Journal of
Chemistry.
"just the thing for schools, and I sincerely hope that it may be appreciated for
what it is worth, for we are certainly in need of books of this kind."— Prof. Austin
Flint, Jr., Professor of Physiology in Bellevne Hosspital Medical College, Neto York
City, and author of " Physiology of Man,'''' etc., etc.
"I have read it from preface to colophon, and find it a most desirable text-book
for schools. Its matter is judiciously selected, lucidly presented, attractively
treated, and pointedly illustrated by memorable facts; and, as to the plates and
diagrams, they are not only clear and intelligible to beginners, but beautiful speci-
mens of engraving. I do not see that any better presentation of the subject of
?hysiology could be given within the same compass." — Prof. John Ordronaux,
*rofessor of Physiology in the University of Vermont, and also in the National
Medical College, Washington, D. C.
The above work is the most popular work on the above subjects yet published. It is
used in thousands of schools with marked success.
Published by CLARK & MAYNARD, New York.
Digitized by the Internet Archive
in 2007 with funding from
Microsoft Corporation
http://www.archive.org/details/commercialarithmOOthomrich
THOMSON'S MATHEMATICAL SERIES.
tyv Qt^e^l
A
COMMERCIAL
ARITHMETIC;
Academies, Hioii Schools, Counting Rooms ;
EMIES, t^fGHtfeCHO^LS, CoUN*T\
>\^ BUSINESSK.O
G \*
LLEGES
James B. Thomson, LL. D.,
AUTHOR OF MATHEMATICAL SERIES.
NEW YORK:
Clark & Maynard, Publishers,
734 Broadway,
THOMSON'S NEW ARITHMETICAL SERIES
IN TWO BOOKS.
I. First Lessons in Arithmetic,
Oral and Written. Illustrated.
(For Primary Schools.)
II. Complete Graded Arithmetic,
Oral and Written. In one Volume.
(For Schools and Academies.)
Key to Complete Graded Arithmetic.
(For Teachers only.)
THOMSON'S MATHEMATICAL SERIES
illustrated table-book.
new rudiments of arithmetic.
complete intellectual arithmetic,
new practical arithmetic.
KEY TO PRACTICAL ARITHMETIC. (For Teachers only.)
HIGHER ARITHMETIC.
PRACTICAL ALGEBRA.
KEY TO PRACTICAL ALGEBRA. (For Teachers only.)
COLLEGIATE ALGEBRA.
KEY TO COLLEGIATE ALGEBRA. (For Teachers only.)
COMMERCIAL ARITHMETIC.
Copyright, 1884, by M, C. Thomson.
Smith & McDougal, Electrotypees.
82 Beekman St., N. Y.
o=>
I
o Teachers.
" o ^ =^»
TF1HE present work has been prepared with sole reference to a business
education in its higher departments. To this end, subjects which
have been fully explained in the author's elementary works, or an
equivalent, and with which the student is supposed to be familiar, are
omitted, and he is introduced at once to the subject in hand. All
irrelevant matter is rejected, and that which helps towards the accomplish-
ment of the object is adopted.
A large amount of valuable business information is embodied in a
concise form, and presented in a manner to be easily understood. In the
fundamental rules, many labor-saving methods of operation are given under
the appropriate name " Counting Room Methods," so called from the
fact that rapid computations are so generally practiced by expert account-
ants. These methods may be applied, not only to the examples given
for illustration and practice, but to every operation involving the simple
rules, and will often greatly facilitate arithmetical calculations.
A variety of business forms are introduced, and their nature and uses
explained, in order to assist the student to an understanding of what
constitutes an important part of a practical business life. The manner
of keeping Book Accounts, Averaging Payments, Partnership Settle-
ments, etc., are fully explained and illustrated by examples from actual
business transactions.
The chapter on the Metric System of Weights and Measures is
made prominent in the body of the book, and includes all the latest
recommendations of the Metric Bureau. Examples involving a knowledge
of its applications are freely scattered through the book.
The subject of Analysis, the business man's specialty, enters largely
into the elucidation of every subject, and has an entire chapter devoted to
its various applications.
The facts and methods given on many commercial subjects, have been
procured from reliable persons who are thoroughly versed in their several
IV
To Teachers.
departments. They are therefore authentic business facts, and in accord-
ance with present usage.
Special care has been devoted to the chapter on Stocks and Bonds, and
to Stock Exchange business, which is a full and reliable summary of
affairs as now conducted on the New York Stock Exchange. The
examples embrace true specimens of daily operations in Wall Street.
The chapters on Banking, Clearing Houses, and Custom House busi-
ness have also been subjected to the most careful scrutiny, as also, Life
Insurance, Annuities, Sinking Funds, etc.
The Commercial Arithmetic is intended to follow the author's Com-
plete Graded, or the Practical Arithmetic, taking up some subjects and
carrying them forward to their higher applications, and treating of others
which are beyond the limits of the more elementary works. In subjects
which are identical with the Complete Graded, the same definitions and
principles are retained. In the discussion of new topics, the same clear-
ness, conciseness, and accuracy of style have been strictly adhered to.
The examples are all new, and have been selected with a special view
to their practical application to business, and not as a trial of the
mathematical skill of the learner.
Many thanks are due to the gentlemen of the Stock and Produce
Exchanges ; to the Collector of the Port of New York and his associates ;
to the Bankers, Brokers, and Lawyers who have so kindly given valuable
information and suggestions.
It is hoped the Commercial Arithmetic will creditably fill the niche for
which it was designed, and that it will commend itself to the good judg-
ment of teachers, the understanding of learners, and the approval of busi-
ness men.
The kindly criticisms of all will be gratefully accepted, and their
continued favor highly appreciated.
New York, March 1, 188k.
CONTENTS
PAGE
Counting-Room Exer-
cises 7
Addition 8
Subtraction 9
Multiplication (Short Methods) 11
Division, Contractions 16
Divisibility of Numbers 18
Factoring 18
Cancellation 20
Greatest Common Divisor 21
Common Multiples 23
Weights and Measures. . . 26
Weight per bushel of Grain
and Seeds 31
To Change Dates from 0. S. to
N. S 37
United States Money 38
Canada Money 39
English Money, French Money. 40
German Money 41
Metric System 42
Metric Reduction 50
Foreign Weights and
Measures 53
Reduction 55
Denominate Fractions 57
Reduced to Lower Denomina-
tions 57
Reduced to Higher Denomina-
tions 58
Addition of Compound Num-
bers 59
Subtraction of Compound
Numbers. 60
Exact Time between Two
Dates 61
Compound Multiplication 62
Compound Division 63
Longitude 63
Time and Longitude 65
•PAGE
Applications of Weights
and Measures 66
Measurement of Rectangular
Bodies 69
Cisterns, Bins, etc 70
Measurement of Lumber 71
Masonry 73
Applications of IT. S.
Money 73
Methods by Aliquot Parts. . . 74
Bills of Merchandise 78
Entry Clerk's Drill 80
Percentage 81
Applications of Percentage. . . 88
Profit and Loss 88
Trade Discount 89
Commission and Brokerage. . 91
Insurance. 94
Adjustment of Losses 98
Taxes 100
Interest 103
General Method 104
Six per cent Method 107
Method bv Days 108
Banker's Method 109
Accurate Interest Ill
Annual Interest 112
Partial Payments 116
U. S. Rule 117
Mercantile Method 118
Connecticut Rule 119
Vermont Rule 121
New Hampshire Rule 122
Interest on Sterling Money . . 123
Compound Interest 124
True Discount 127
Bank Discount. 128
Commercial Paper 130
Forms of Notes and Drafts.. . 133
VI
Contents.
PAGE
Averaging Accounts 137
Rules. — Product Method, ) * .^
Interest Method )" 140
Cash Balance 149
Rule for Product Method 150
Rule for Interest Method 151
Account Sales 154
To Find Due Date 156
Partnership 158
Bankruptcy 169
General Average 170
General Analysis 172
Ratio 178
Proportion 180
By Cause and Effect 182
Compound Proportion 184
Partitive Proportion 187
Exchange 189
Domestic Exchange 190
Foreign Moneys of Account. 192
Quotations of Foreign Bills. . 193
Foreign Exchange 194
Duties or Customs 199
Custom House Business 200
Import Entries 203
Course of Import Entry in
N. Y. Custom House 204
Banks and Banking 206
Bank Account Current 208
Bank Checks 209
Clearing Houses 211
Savings Banks 212
Stocks 216
United States Bonds 218
National Debt of U. S 219
Funded Debt of Foreign
Countries 220
Stock Exchanges 220
Quotations. — Seller's Option, ) 9Q „
Buyer's Option ]
Stock Investments 223
PAGE
Produce Exchanges 232
Storage 234
Life Insurance 236
Table of Rates 238
Annuities 241
Annuities at Compound Inter-
est 243
Sinking Funds 248
Powers and Roots 251
Square Root 253
Cube Root 256
Similar Surfaces and Solids . . 258
Mensuration 261
Area of Plane Figures 262
Area of Triangles 264
Circles 265
Solids 268
Gauging of Casks 273
Tonnage of Vessels 275
Grain Measurement 275
Lumber, Doyle's Rule 276
Test Questions 278
Appendix 286
Drill in Percentage 287
Metric Drill 289
G. c. d. of Fractions 290
L. c. in. of Fractions 291
Table of Prime Numbers 292
Property of the No. 9 293
Contractions in Mult 293
Table of Time, in days 295
Mortality Table 297
Life Estates 298
Northampton Table 299
Business Information 300
Letters of Credit 304
Instruments under Seal 304
Book Accounts 305
Statute of Limitations 306
Stock Clearing Houses 307
Abbreviations (Stocks) 308
Miscellaneous Examples 309
Commercial Arithmetic
Art. 1. The student of Commercial Arithmetic is presumed
to be familiar with the ordinary operations of Common Arith-
metic. For this reason, the four fundamental rules, fractions,
decimals, etc., are omitted in this work.
COUNTING ROOM METHODS.
2. Facility in adding is of the first importance in commer-
cial life. It can be acquired only by constant practice, and a
thorough acquaintance with the simple combinations of num-
bers.
3. In adding ledger columns, accountants frequently use the
following methods :
(Ex. 1.)
(Ex. 2.)
$784,306
$346.82
9.348
204.36
751.675
56.07
0.384
207.00 814.25
95.832
862.741
2204.206
26.35
460.48
1.76
$4708.492, Ans.
763.48 1252.07
232 323
Ans. $2066.32
Explanation. — Ex. 1. Write the units' figure of the sum of each col-
umn under the column added, and the tens, or figures carried, below as in
the example. In adding, name only results.
Ex. 2. The second method divides the columns into parts, adding each
part separately to find their sum.
8
Counting Rooyn Metlwds.
4. Principles of Addition.— 1°. Only like numbers and
like orders of units can be added one to another.
2°. The sum is the same in whatever order numbers may be
added.
3. Add the numbers from 1 to 29 in a column. From 29
to 109. From 109 to 199 inclusive.
5. Adding two or more columns at a time.
4. Find- the sum of 29, 48, 37, and 56.
Explanation.— To the number at the bottom add the
tens, then the unitsaLthe next number above it. Thus,
5G and ^0 are KG, ,n < 7 arc 93, and 40 are 133, and 8 are
14jS Bo afVilifflrand 9 are 170, Ans.
527, 432, and 245,
at the bottom, 245,
the units of the next
are 645, and 30 are
, and 20 are 1197, and
30 are 1834, and 9 are
OPERATION.
29
48
37
56
170
Ans.
S£pJ
ind the sum
Kins at a time
EXPLANATIO
add the hundreds,
pfPfoer above it ; thus,
675, and 2 are
?»rol204, and
Ine following, in like manner
24
32
27
23
42
91
26
34
12
67
21
53
26
78
25
82
93
54
62
58
53
24
66
J 2
26
87
72
65
(8.)
46
32
17
81
28
52
23
20
71
39
18
42
73
24
519
271
436
587
333
745
52
158
232
464
643
27
235
103
(10.)
607
232
211
380
578
231
145
605
760
357
544
276
803
725
adding three
OPERATION.
639
527
432
245
Ans. 1843
(n.)
253
12
849
436
551
349
763
37
155
676
844
232
383
918
Counting Room Methods.
6. To Add Numbers Horizontally.
It is sometimes convenient to add numbers, when written
horizontally, instead of under each other.
12. Find the sum of 428 + 253 + 647 + 926 + 425.
Explanation. — Beginning at the right, add the units of all the num-
bers, then the tens, then the hundreds ; the sum is 2679. Arts.
13. Find the sum of 2345 + 621 + 2417 + 385 -f- 6457.
14. Find the sum of 325, 4623, 435, 2843, 7546.
Note.— To insure accuracy, the addition should be performed by differ-
ent methods, or in different directions, in order that mistakes made by one
method may be detected by another.
7. Principles of Subtraction. — 1°. Only like numbers
and like orders of units can be subtracted one from the other.
2°. The difference and subtrahend are equal to the minuend.
3°. If two numbers are equally increased, their difference is
not altered.
15. From 3427 subtract 1235. Ans. 2192.
16. A has 8268 more than B and $150 less than C, who has
$4580; D has as much as A and B together; how much
hasD?
8. When the Sum and Difference of Two Numbers are given, to
find the Numbers.
17. The sum of two numbers is 283, and their difference is
35 ; what are the numbers ?
Analysis. — The difference subtracted from the sum will leave twice
the smaller number, and 283-35 = 248 ; half of 248 is 124. the less num-
ber. Again, the difference added to the less must be equal to the greater
number, and 124 + 35 = 159, the greater number. Hence, the
Koxe. — From the sum subtract the difference ; half the
remainder will be the less number.
TJie difference added to the less will be the greater
number.
10 Short Methods in Multiplication.
18. The whole number of votes cast for the two candidates at
an election was 15564, and the successful candidate was elected
by a majority of 1708 ; how many votes did each receive ?
19. A lady paid $350 for her watch and chain ; the former
being valued $52 higher than the latter ; what was the price
of each ?
20. A and B found a pocket-book, and returning it to the
owner, received a reward of $500, of which A took $138 more
than B ; what was the share of each ?
21. The sum of two numbers is 4487, and the greater is 653
more than the less ; what are the numbers ?
9. The Complement of a number is the difference between
the number and the next higher order.
Thus, 2 is the complement of 8, also of 98 ; for 10—8 = 2, and
100-98 = 2.
22. What is the complement of 87 ? Of 125 ? Of 3284 ?
23. By how much does the sum of 6 and 4 exceed their
difference ?
24. By how much does their complement exceed their dif-
ference ?
25. Victoria was bom in 1819, the Prince of Wales in 1841 ;
how old was each in 1882 ?
26. A poor-house had 133 inmates, consisting of infirm and
able-bodied 70 ; able-bodied and children 105 ; children and
officers 63 ; officers 5 ; what number of each class ?
27. A basket held oranges, nuts, and eggs ; in all 1769 arti-
cles; there were 1696 oranges and nuts, and 1262 nuts and
eggs ; how many more nuts were there than oranges ?
Short Methods in Multiplication. n
SHORT METHODS IN MULTIPLICATION.
10. Peikciples. — 1°. The multiplicand may be either ab-
stract or concrete.
£°. TJie multiplier must be considered an abstract number.
3°. The multiplicand and product are like numbers.
4°. TJie product is the same in whatever order the factors are
taken.
11. To multiply by I with a significant figure annexed.
1. If one city lot costs $3245, what will 17 lots cost ?
Explanation.— Multiply the multiplicand by the operation.
7 units, and setting each figure of the product one place oZ<kO X 1 (
to the right of the order multiplied, add the partial 22715
product to the multiplicand. The result is,$55165. $55165 Ans.
Note. — This method may be applied when the multiplier has one or
more ciphers between the two figures, by writing the product two or more
places to the right. (Ex. 6.)
2. 78465 x 16. 4. 84769 x 17.
3. 86794 x 18. 5. 79876 x 19.
6. Multiply 4584 by 106. Ans. 485904.
7. Multiply 64358 by 108.
12. To multiply by I with any significant figure prefixed to it.
8. Multiply 6347 by 41.
6347 x 41
Explanation.— Multiply by the tens and set the 25388
first product figure in tens place, etc.
* F 260227, Ans.
9. 63758 x 71. 11. 74656 x 81.
10. 85459 x 61. 12. 87435 x 91.
13. 73648 x 601. Ans. 44262448.
14. Multiply 84325 by 801.
12 Short Methods in Multiplication.
13. To multiply by the actors of a number.
15. What will 21 writing-desks cost at $72 apiece ?
$72
Explanation.— The factors of 21 are 7 and 3. As 7
1 desk costs $72, 7 desks will cost 7 times $72, or $504 ; - ~
and 21 desks will cost 3 times as much as 7 desks, or
504 x 3 = $1512, Ansi 3
$1512, Ans.
16. Multiply 7389 by 63. 17. Multiply 8479 by 84.
14. Moving a figure one place .to the left, or annexing a
cipher, multiplies a number by 10 ; moving it two places, or
annexing two ciphers, multiplies by 100, etc.
18. Multiply 276 by 100. 20. Multiply 8760 by 2000.
19. Multiply 3458 by 1000. 21. Multiply 3897 by 32000.
15. If a number having two figures is multiplied by 11, the
product will be the first figure of the number, the sum of the
two figures, and the last figure.
Thus, 43 x 11 = 473, or 4, (4 + 3), and 3.
Note. — If the sum of the two figures exceeds 9, the first or left-hand
figure must be increased by 1. Thus, 48 x 11 = 528.
22. Multiply 45 by 11. 23. Multiply 67 by 11.
16. To multiply by 9, 99, or any number of 9's.
24. What is the product of 2736 multiplied by 99 ?
Explanation.— Annexing two ciphers operation.
to the multiplicand, multiplies it by 100; 273600 Prod, by 100.
but 99 is 1 less than 100, and subtracting 2736 " 1.
the multiplicand from the result will give
the true product. Hence, the 270864 99.
Rule. — Annex as many ciphers to the multiplicand
as there are 9's ' in the multiplier, and from the result
subtract the multiplicand.
25. Multiply 62743 by 999. 26. Multiply 843625 by 9999.
Short Methods in Multiplication. 13
17. To multiply by any number which ends with 9.
27. Multiply 67 by 49.
Explanation. — The next number higher than 49 operation.
is 50. Multiplying the multiplicand by 5 and annex- 67 X 50 = 3350
ing one cipher, the product is 3850. But 49 is 1 less 67 X 1 = 67
than 50, and subtracting once the multiplicand from
the result gives the true product. ^ns. 3283
28. Multiply 73 by 699.
Solution.— The next number above 699 is 700, and (73x700)-73
= 51027, Ans. Hence, the
Rule. — Multiply by the next higher number, and from
the result subtract tlte multiplicand.
29. Multiply 642 by 39. 31. Multiply 423 by 599.
30. Multiply 724 by 79. 32. Multiply 648 by 499.
18. To multiply by any number that is a little less or a little
greater than 100, 1000, etc.
33. What is the product of 53172 multiplied by 993 ?
Explanation. — The complement of operation.
993 is 7. Annexing 3 ciphers to the 53172 X 1000 = 53172000
multiplicand gives the product by 1000, 53172 X 7 = 372204
and subtracting 7 times the multiplicand
from the result gives the true product. Ans * ^7yJ79b
34. Multiply 63147 by 108.
Explanation. — The excess of the mul- operation.
tiplier above 100 is 8. Therefore annexing 63147 X 100 = 6314700
2 ciphers to the multiplicand, and adding 63147x8 5051 7P
to the result its product by 8, gives the true
product. Hence, the Ans. 6819876
Ktjle.— Assume 100, 1000, etc., as the multiplier ; this
product plus or minus the product of the multiplicand
by the difference between the true and assumed mul-
tiplier, will be the true product.
35. 56836x96. 37. 915236x9907.
36. 864532x995. 38, 520316x9904,
14 Short Methods in Multiplication.
19. When one part of the multiplier is a factor of the other part.
39. Multiply 436 by 248.
OPERATION
436
Analysis. — Since 8 is a factor of 24, the other fac- 248
tor of which is 3, the product by 24 will be 3 times
the product by 8. The partial product by 8 is 3488,
and 3488 x 3 = 10464.
3488
10464
40. Required the product of 6453 by 742.
Analysis — Since 7 is a factor of 42, the other
factor of which is 6, the partial product of 7, multi-
plied by C, equals the product by 42. The partial
product by 7 is 45171, the first figure of which being
hundreds, is placed under the multiplying figure.
(Art. 4, 1°.) This partial product multiplied by 6 gives
the product by 42. The sum of the two results is the
true product. Hence, the
108128, Ans.
OPERATION.
6453
742
x6
45171
27102 6
4788126, A ns.
Rule. — Multiply by the part of the multiplier which
is a factor of the other part, and this result by the other
factor, setting the first figure of each partial product
under the right-hand figure of the part of the multi-
plier which produced it. TJie sum of the partial prod-
ucts will be the true product. (Art. 10, 4°.)
Note. — When the multiplier has figures which are not factors of
another part, multiply by them in the usual way.
41. Multiply 4378 by 428.
42. Multiply 6253 by 357.
43. Multiply 38674 by 856.
44. Multiply 63942 by 639.
20. To multiply by two op more figures, without setting down
the partial products.
45. Multiply 68 by 43.
Explanation. — The product of units (3x8) — 24, or
2 tens and 4 units. The product of tens (3x6 tens) = 18
tens, and (4 tens x 8) = 32 tens. Now 18 + 32 = 50 tens,
and 2 to carry make 52 tens, or 5 hundred and 2 tens.
Set the 2 in tens place. Again, (4 tens x 6 tens) = 24
hundreds and 5 are 29 hundreds, or 2 thousands and
OPERATION.
68
43
Ans. 2924
) hundreds,
which aro written in their proper places (Art, 4, 1°.) The product is
2924.
Short Methods in Multiplication.
15
46. Multiply 357 by 245.
Explanation. — The product of the units is 35. Set operation.
down the units and carry tens. The product of tens is
(5 x 5) + (7 x 4) + 3, (carried) = 56 tens, or 5 hundreds and
6 tens. Next the product of hundreds is (3 x 5) + (5 x 4) +
(7 x 2) + 5 = 54 hundreds, or 5 thousands and 4 hundreds.
Again, the product of thousands is (3 x 4) + (5 x 2) + 5 = 27
thousands, or 2 ten-thousands and 7 thousands. Finally the product of
ten-thousands is (3 x 2) + 2 = 8 ten -thousands. The result 87465 is the
product. Hence, the
357
245
Ans. 874G5
Eule. — I. Multiply the units, setting down the result
and carrying as usual.
II. Multiplij the orders which produce tens, and add-
ing the tens carried, set down the result as before.
III. Proceed in this manner till all the orders of the
multiplicand are multiplied by each order of the mul-
tiplier.
Note. — With practice the products may be written without placing
the numbers under each other, thus saving time in entering sales, etc.
47. What is the product of 23456789 into 54321 ?
ANALYTIC SOLUTION.
2x5
2x4
3x5
2x3
3x4
4x5
2x2
3x3
4x4
5x5
2x1
3x2
4x3
5x4
6x5
3x1
4x2
5x3
6x4
7x5
4x1
5x2
6x3
7x4
8x5
5x1
6x2
7x3
8x4
9x5
6x1
7x2
8x3
9x4
7x1
8x2
9x3
8x1
9x2
9x1
12
1
9
2
6
9
Note. — In the solution above, the multiplications which produce the
order are placed in the same column, that the results may be
readily seen.
48. Multiply 87 by 54.
49. Multiply 256 by 85.
50. Multiply 563 by 325.
51. Multiply 3754 by 537.
16 Contractions in Division,
General Principles of Division.
21. 1°. Multiplying the
dividend, or dividing the
divisor, multiplies the quo-
tient.
Thus, 24-^-4 = 6,
Then, (24x2)-j-4 = 6x2,
And, 24-=- (4-^-2) = 6x2.
2°. Dividing the dividend, 1 rpi lug (24-^-2)— 4 = 6—2
or multiplying the divisor, \ An ^ 24-j-(4x2) =6-5-2!
divides the quotient. J
3°. Multiplying or dividing ~1 Thug ( 2 4^-2)-*-(4— 2) = 6
both by the same number, [ And ' (u ' \_ ^ = ^
does not chatige the quotient. J
Ji°. When the divisor and dividend are like numbers, the
quotient is an abstract number.
5°. When the divisor is an abstract nun^er, the quotient and
dividend are like numbers.
6°. The product of the divisor and quotient is equal to the
dividend.
CONTRACTIONS IN DIVISION.
22. To divide by 5, 25, or 125.
1. Divide 678 by 5.
Analysis.— By Prin. 3°, 5 is contained in 678, operation.
as many times as 10 {twice 5) is contained in twice 5 ) 678
678. Thus, 678x2 = 1356, and 1356 -i-10 = 135 £ 2
and 6 over; cutting off one figure divides by 10. —
The true remainder is 6-r-2 = 3, which placed over M^ ) loo|o
the true divisor 5 (10-^-2) becomes f. Ans. 135, 3 rem.
2. Eequired the quotient of 4364 divided by 25.
Analysis. — Reasoning as before, 25 is con- operation.
tained in 4364 as many times as 100 (25 x 4) is 25 ) 4364
contained in 4 times 4364, or 17456. Cutting off 4 4
2 figures from the right divides by 100. The -\iyA\ 7r
figures cut off divided by 4 gives a true remain- -M*-^ ) 174|oo
der of 14, or |f Hence, the Ans. 174, 14 rem.
Contractions in Division. 17
Eule. — I. To divide by 5. — Multiply the dividend by 2
and cat off one figure.
II. To divide by 25. — Multiply the dividend by 4 ati d
cut off two figures.
III. To divide by 125. Multiply by 8 and cut off three
figures. #
Notes. — 1. The true remainder is found by dividing the figures cut off
by the number used as the multiplier.
2. The same principle applies to any power of 5, the multiplier being a
like power of 2.
3. Divide 240653 by 25. 6. Divide 820345 by 625.
4. Divide 963438 by 125. 7. Divide 579600 by 125.
5. Divide 44800 by 25. 8. Divide 8065227 by 3125.
23. To divide when all the figures of the divisor, except the first
on the left, can be changed to ciphers.
9. Divide 35273 by 15.
Analysis.— The divisor 15 is changed to 30 by operation.
multiplying it by 2 ; the dividend being also niulti- 15 ) 35273
plied by 2, the quotient is not altered. (Prin. 2 2
3°.) Cutting off the cipher and dividing by 3, SiO ^7054lf
there is 1 remainder, which prefixed to the 6 cut off ' I L_
makes 16. This divided by 2 is the true remainder. Quot. 2351, 8 rem.
10. What is the quotient of 42653 divided by 75 ?
Explanation.— Multiplying by 4, cutting 75 ) 42653
off two figures and dividing as before, there is 4. 4.
a remainder 2, which prefixed to the figures
cut off gives 212 ; this divided by 4 makes 53,
3|00)1706|12
the true remainder. Hence, the 568, 53 rem.
Rule. — Multiply both the divisor and dividend by
such a number as will change all the figures of the
divisor into ciphers except the first ; then divide as
usual.
Note. — If a remainder occurs, it must be annexed to the figure cut off,
and this number, divided by the multiplier used, is the true remainder.
11. Divide 38643 by 35. 13. Divide 624395 by 75.
12. Divide 406891 by 45. 14. Divide 2345062 by 175.
2
18 Factoring,
DIVISIBILITY OF NUMBERS.
24. An Exact Divisor or Measure of a number is one which
will divide it without a remainder.
One number is said to be divisible by another when there
is no remainder.
All numbers are divisible
1°. By 2, which end with a cipher, or a digit divisible by 2.
2°. By 3, when the sum of the digits is divisible by 3.
3°. By 4, when the number expressed by the two right-hand
figures is divisible by 4.
Jf°. By 5, which end with a cipher or 5.
5°. By 6, when divisible by 2 and 3.
6°. By 8, when the three right-hand figures are ciphers, or
when the number expressed by them is divisible by 8.
7°. By 9, when the sum of the digits is divisible by 9.
Notes. — 1. This principle of the number 9 affords a concise method of
proving Multiplication and Division. (See Appendix, Art. 699.)
2. The preceding is not a necessary but an incidental property of the
number 9. It arises from the Jaw of increase in the decimal notation. If
the radix of the system were 8, it would belong to 7 ; if the radix were 12,
it would belong to 11 ; and universally, it belongs to the number that is
one less thnn the radix of tbe system of notation.
FACTORING.
25. The Factors of a number are the numbers whose
product is equal to that number. Thus, 6 and 9 are factors of 54.
26. A Composite Number is a product of two or more factors.
27. A Prime Factor is a prime number used as a factor.
28. A Common Factor is an exact divisor of two or more
numbers.
Note.— Numbers are Prime to each, Qther, which have no common
divisor greater than 1.
Factoring. 19
29. Factoring a number is separating it into factors.
Note. — It is not customary to consider the unit 1 and the number
itself as factors ; if they were, all numbers would be composite. (Art. 26.)
30. Principles. — 1°. If one number is a factor of another,
the former is also a factor of any Product or Multiple of the
latter.
2°. A factor common to two or more numbers, is also a factor
of their Sum, their Difference, and their Product.
3°. Every composite number is divisible by each of its Prime
factors ; and by the Product of any tivo or more of them.
31. To find the Prime Factors of a number,
l. What are the prime factors of 2780 ?
Explanation. — Any prime number operation.
which will exactly divide a' given num- 2
ber is a prime factor of it. The prime
numbers 2, 2, and 5, exactly divide the
gfiven number and the successive quo- 5
tients. The last quotient, 139, is a
prime number, which with the several
divisors are the prime factors required. For, 139 x 2 x 2 x 5 = 2780.
Hence, the
2780 Given Number.
1390 1st Quotient.
695 2d
139 3d
Rule. — Divide the given number by any prime factor ;
then divide this quotient by another prime factor ; and
so on until the quotient obtained is a prime number.
The several divisors, with the last quotient, are the prime
factors required.
2. What is the only even prime number ? When are two
numbers prime to each other ?
Find the prime f J^tors of
3. 286. 5. 2460. 7. 3225. 9. 2572.
4. 48831. 6. 2810. 8. 3840. 10. 8964.
20 Factoring.
32. To find the Prime Factors common to two or more numbers.
11. What are the prime factors common to 264, 84, and 450 ?
Explanation.— Since the prime numbers 2, ^ ) 264, 84 , 450
2, and 3, divide the given numbers and succes- 2 ) 132 42 225
sive quotients, and the last quotients are prime
to each other, the several divisors are the prime ^ ) 66, 21, 22 5
factors required. Hence, the 22 7 75
Bule. — Divide the given numbers by any common
prime factor, and the quotients thence arising in like
manner, till they have no common factor ; the several
divisors will be the prime factors required.
12. Find the prime factors common to 326, 452, and 450.
13. 240, 96, 684. 14. 264, 640, 456. 15. 325, 650, 875.
CANCELLATION.
33. Cancellation is the method of shortening operations hy
rejecting equal factors from the divisor and dividend.
The Sign of Cancellation is an oblique mark drawn across
the face of a figure ; as, $, 0, $, etc.
34. Principles.— 1°. Cancelling a factor of a number di-
vides the number by that factor.
2°. Cancelling equal factors of the divisor and dividend does
not change the quotient. (Art. 21, 3°.)
35. Cancellation may be applied to all examples in which
the divisor and dividend have one or more common factors.
l. Divide the product of 18 x 16 x 28 by the product of
12 x 7 x 14.
SOLUTION.
3 X
X$xl6xn 3x16
XtxlxW 7
Or,
= 6-|, Ans.
7
U
1$ 3
16
&
7
48 = 6|, Ans
Greatest Common Divisor. 21
Explanation. — The division may be represented in the form of a frac-
tion, or with the dividend on the right and ihe divisor on the left of a
vertical line. Cancelling the factors common to both, it becomes
— — — = 6f. Hence, the
Eule.— Cancel the factors common to the divisor and
dividend, and divide the product of those remaining in
the dividend by the product of those remaining in the
divisor.
Note. — When a factor cancelled is equal to the number itself, the unit
1 always remains. If the 1 is in the dividend it must be retained ; if in
the divisor, it may be disregarded.
2. Multiply 74 x 12 by 14 x 6, and divide the product by
28x72x24.
3. Divide 112 x 27 x 163 by 54 x 63 x 89.
4. 128 x 16 x72-f-44x 32x18.
5. 135 x 12 x 29-^27 x 18 x 154.
6. 45x63x144^72x24.
7. 28x42x96^-7x21x12.
8. If 24 pieces of cloth, containing 32 yards each, cost $384,
what will 48 yards cost ?
9. Bought 48 tons of coal at $9 a ton ; how many barrels of
flour, at $12 a barrel, will pay for it ?
10. If 26 bushels of wheat make 6 barrels of flour, how many
bushels will be required to make 156 barrels ?
11. If 500 copies of a book of 210 pages require 12 reams of
paper, how much will 1200 copies of a book of 280 pages
require ?
12. If 9 men cut 150 acres of grass in 18 days, how many
men will do the same work in 27 days ?
GREATEST COMMON DIVISOR.
36. A Common Divisor or Measure is a number that will
divide two or more numbers without a remainder.
37. The Greatest Common Divisor or Measure of two or
more numbers is the greatest number that will divide each of
them without a remainder.
Thus, the greatest common divisor of 18 and 30 is 6.
Note. — The letters a. c, d. stand for greatest common divisor.
22 Greatest Common Divisor,
38. Principles. — 1°. An exact divisor of a number is a
divisor of any multiple of that number.
2°. A common divisor of two numbers is a divisor of their
sum and of their difference.
3°. The greatest common divisor of two or more numbers is
the product of all their common prime factors.
39. To find the Greatest. Common Divisor by Factoring.
1. What is the g. c. d. of 84, 96, 276 ?
OPERATION.
2 ) 84, 96, 2 76 84 = 2x2x3x7
2 ) 42, 487~l 38 96 = 2x2x3x8
3 ) 21, 24, 69 276 = 2 x 2 x 3 x 23
7, 8, 23 Ans. 2 x 2 x 3 = 12, g. c. d. Hence, the
Kule. — Separate the numbers into their prime factors ;
the product of those that are common to each is the
greatest common divisor.
What is the greatest common divisor of
2. 144 and 288. 4. 46 and 322. 6. 475 and 589.
3. 112 and 254. 5. 84 and 268. 7. 516 and 898.
8. What is the greatest length of boards that may be used
without cutting to fence two sides of a lot, one 80 ft., the
other 144 ft. long ?
9. The g. c. d. of 896, 254 ? 10. Of 324, 816 ?
40. To find the g. c. d. by continued division,
li. What is the g. c. d. of 96 and 876 ?
OPERATION.
Explanation. — When the greater number is qp x „„„ , ~
divided by the less,*the quotient is 9 and 12 remain- ' ^
der. The divisor 96, divided by the remainder 12,
has no remainder ; therefore, 12 is tlie greatest com- 12 ) 96 (
mon divisor. Hence, the 9@
Common Multiples. 23
Rule. — Divide the greater number by the less; then
divide the first divisor by the first remainder, and so
on, until nothing remains ; the last divisor will be the
greatest coimnon divisor.
If there are more than two numbers, find the greatest
common divisor of two of them; then of this divisor
and a third number, and so on, until all the numbers
have been taken.
Note. — The greatest common divisor of two or more 'prime numbers,
or numbers 'prime to each other is 1. (Art. 28, N.)
12. A man has 3 farms containing respectively 128, 236, and
344 acres ; what is the largest number of acres that he can put
into fields of equal size in all the farms ?
13. What is the greatest width of matting that may be used
without cutting, to cover the floors* of 3 rooms of 15, 18, and
24 feet wide respectively ?
14. The four sides of a garden are 168, 280, 182, and 252 ft.
respectively ; what is the greatest length of boards that may
be used in fencing it without cutting any of them ?
15. A merchant wished to cut equal dress-patterns from
3 pieces of silk containing respectively 48, 32, and 64 yds. ;
what is the greatest length of the patterns ?
COMMON MULTIPLES.
41. A Multiple of a number is one which is exactly divisi-
ble by that number.
Thus, 12 is a multiple of 4 ; 18 of 6.
42. A Common Multiple is a number that is exactly divisible
by two or more numbers.
Thus, 18 is a common multiple of 2, 3, 6, and 9.
43. The Least Common Multiple (I. c. fit.) of two or more
numbers, is the least number exactly divisible by each of them.
Thus, 15 is the least common multiple of 3 and 5.
2 ) 20,
24,
36
2 ) 10,
12,
18
3 ) 5,
6,
9
5,
2,
3
24 Common Multiples.
44. Principles. — i°. A multiple of a number must contain
all the prime factors of that number.
2°. A common multiple of two or more numbers must contain
all the prime factors of each of the given numbers.
3°. Tlie least common multiple of two or more numbers is the
least number which contains all their prime factors, each factor
being taken the greatest number of times it occurs in either of
the given numbers,
45. To find the Least Common Multiple of two or more numbers.
1. What is the I. c. m. of 20, 24, and 36 ?
Explanation. —A rrange the
numbers in a line and divide by
any prime number, as 2, that will
exactly divide two or more of them,
setting the quotients and undivided
numbers below. Continue dividing
till no two of the numbers have a
common factor. The continued 2x2x3x5x2x3 = 360, A ns.
product of the divisors 2, 2, 3, and
the prime numbers 5, 2, and 3, is 360, the least common multiple
required. Hence, the
Rule. — Write the numbers in a line, and divide by
any prime number that will divide two or more of them
without a remainder, placing the quotients and, undi-
vided numbers in a line below.
Repeat the operation till no two numbers are divisible
by any number greater than 1. The continued product
of the divisors and numbers in the last line is the
answer.
Notes.— 1. The operation may often be shortened by cancelling any
number which is a factor of another number in the same line.
2. When the given numbers are prime or prime to each other, their con-
tinued product will be the least common multiple.
3. The I. c. m. of fractions equals the 1. c. m. of the numerators
divided by the a. c. d. of the denominators. The result may be expressed^
as a fraction, a mixed number, or an integer, as the case may be. Thus,
the 1. <', m. of |, f , rnd £ is the integer 12, the denominators being prime
to each other.
Common Multiples. 25
2. What is the I. c. m. of 21, 35, 42 ?
3. 21, 36, 50, 64 ? 7. 189, 153, 144 ?
4. 48, 98, 21, 27 ? 8. 3150, 2310 ?
5. 16, 40, 96, 105? 9. 43T00, 9430?
6. 25, 36, 33, 12 ? 10. 729, 336, 1836 ?
n. Find the I. c. m. of the 9 digits.
12. Of the even numbers from 1 to 21.
13. Of what is the I, c. fit. of several numbers the product ?
14. Find the least common multiple of §, J, f , and f .
15. A bookseller ordered boxes in which to pack books 3, 4,
and 6 inches long ; what is the shortest box in which these
books could exactly fill the space ?
16. What is the least number of peaches that can be exactly
divided among 3 classes of children containing 15, 18, and 24
pupils respectively?
17. Find the least number of weeks in which a man who
earns $18 a week can earn an exact number of double- eagles.
18. Find the I. c. m. of f , &, and |f
19. The price of Histories is 44 cents, of Arithmetics 32
cents, and of Grammars 36 cents each ; what is the least equal
sum a teacher could expend on each? How many of each
could he buy ?
^eights and Measures
LINEAR MEASURE.
46. A Measure is a standard unit established by law or
custom, by which the length, surface, capacity, and weight of
things are estimated.
47. Linear Measure is used in measuring lines and dis-
tances.
48. A Line is that which has length only.
Table.
12 inches (in.) = 1 foot, . . . ft.
3 feet = 1 yard, . . . yd.
5| yds., or 16| ft. = 1 rod, . . . rd.
40 rods = 1 furlong, . . fur.
320 rods, or)
5280 fee. I = * mi,e ' • ■ ■ "*
3 miles = 1 league, . . I.
Note. — The yard for common use is divided into halves, quarters,
eighths, and sixteenths. At the U. S. Custom Houses it is divided into
tenths and hundredths.
49. The Standard Unit of length in the United States and
England is the Yard of 3 feet.
Note. — The Standard Yard is determined by the pendulum, which
vibrates seconds in a vacuum at the level of the sea, in the latitude of
London, and the temperature of 62" Fahrenheit. This pendulum is
divided into 391393 equal parts, and 360000 of these parts constitute
a yard.
^ inch
Square Measure. 27
Special Linear Measures.
~ -11* [ Applied to pendulums.
3^ inch
i inch = 1 size, applied to shoes.
18 inches = 1 cubit.
3.3 feet s= 1 pace.
5 paces = 1 rod.
6 feet =1 fathom.
20 fathoms s 1 cable length.
120 knots, or
1.16 statute miles
= 1 Nautical or Geographical mile.
00 geog., or ) j 1 Degree of Long, on the Equator, or
69.16 statute miles ( ~ ( 1 Degree of a Meridian.
360 degrees = Circumference of the Earth.
SQUARE MEASURE.
50. Square Measure is used in measuring surfaces; as,
flooring, land, etc.
51. A Surface is that which has length and breadth only.
Table.
144 square inches (sq. in.) = 1 square foot, . . sq. ft.
9 square feet = 1 square yard, . . sq. yd.
SOI SQ- yards, or ) j 1 sq. rod, perch
272^ sq. feet, ) ) or pole, . . . sq. r.
160 square rods = 1 acre, . . . .A.
640 acres = 1 square mile, . . sq. m.
52. The measuring unit of surfaces is a Square, each side
of which is a linear unit.
53. A Square is a rectilinear figure which has/o&r equal
sides, and four right angles.
54. The Area of a figure is the quantity of surface it con-
tains.
* The progress of sailing vessels is determined by a half-mmvte. glass and a log line,
"'hich is divided into knots, bearing the same ratio to a mile that a half -minute has to
**\ hour.
28 Weights and Measures.
SURVEYOR'S MEASURE.
55. Surveyor's Measure is used in measuring land, etc.
56. The Linear Unit commonly employed by surveyors is
Guntefs Chain, which is 4 rods or 60 feet long, and divided
into 100 links.
Table.
7.92 inches {in.) — 1 link, J.
25 links = 1 rod or pole, . . . r.
4 rods, or 100 links = 1 chain, . ... eh.
80 chains = 1 mile m.
Notes. — 1. Surveyors usually record distances in chains and hun-
dredths of a chain. Thus, 45 ch. 37 1. is written 45.37.
2. In measuring roads, etc., engineers use a chain, or measuring tape,
100 feet long, each foot being divided into tenths and hundredths.
57. The Measuring Unit of Land is the Acre.
Table.
625 sq. links = 1 sq. rod or pole, . sg. rd.
16 sq. rods = 1 sq. chain, . . . sq. c.
10 sq. chains, or ) .,
-«/v , > = 1 acre, A.
160 sq. rods \
640 acres = 1 sq. mile, . . . sq. mi.
Notes. — 1. The Rood of 40 sq. rods has fallen into disuse.
2. A Square, in Architecture, is 100 square feet.
58. In Surveying Government Lands a parallel of latitude
called the Base Line, and a meridian called the Principal Meri-
dian are first established. From these other lines are run at
right angles, six miles apart, which divide the territory into
rectangular tracts six miles square.
These tracts are called Townships.
Since the surface of the Earth is convex, all Meridians
converge as the latitude increases. Hence, the Townships and
Sections are not exactly rectangular, which creates a necessity
for occasional offsets called Correction Lines.
59. Townships are designated by their number N. or S. of
the base line.
Cubic Meastire.
29
60. A line of townships running N. and S. is called a
Range, and is designated by its number E. or W. of the prin-
cipal meridian. Thus,
T. 39 N., R. 14 E. 3d P. M., describes a township in the 39th tier North
of base line, and 14th range East of the 3d A sectkjn.
principal meridian.
61. A Township is divided into
Sections each 1 mile square and con-
tains 640 acres. Thus,
1 Sec.
= 1 mi. x 1 mi. = 640 A.
\ Sec.
= 1 " x|" =320 "
\ Sec.
= 1 « x i " =160 "
jx J Sec.
.-= 1 " x I " = 80 "
\*\ Sec.
= 1" x T V " = 40 *
The sections are numbered commencing
at the N. E. corner, and running W. in
the North tier, E. in the second, etc.
Each section is divided into 4 quarter
sections, called N. E., S. E., N. W., and
S. W. quarters, each containing 160 acres.
Thus, S.E. \, sec. 10, T. 39 N., R. 14 E.
3d., P. M., is read, " Southeast quarter of
sec. 16, tier 39 north, range 14 east of
third principal meridian."
1 MILE SQUARE.
A TOWNSHIP.
N
W
6
5
4
3
2
1
7
8
9
10
11
12
18
17
18
15
14
13
19
20
21
89
23
21
30
20
2S
~7
26
25
31
32
33
34
35
36
6 MILES SQUARE.
CUBIC MEASURE.
62. Cubic Measure is used in measuring solids or volume.
63. A Solid is that which has length, breadth, and thickness ;
as, timber, boxes of goods, etc.
64. A Cube is a regular solid bounded by six equal squares
called its faces. Hence, its length, breadth, and thickness are
equal to each other.
65. The measuring unit of solids is a Cube the edge of
which is a linear unit.
30 Weights and Measures.
Table.
1728 cubic inches {cu. in.) = 1 cubic foot, . . cu.ft.
27 cubic feet = 1 cubic yard, . . cu. yd.
128 cubic feet = 1 cord of wood, . C.
66. A Cord of wood is a pile 8 ft. long, 4 ft. wide, and 4 ft.
high; for 8x4x4 = 128.
67. A Cord Foot is one foot in length of such a pile ; hence,
1 cord foot = 16 cu. feet; 8 cord ft. = 1 cord.
Special Cubic Measures.
100 cu. ft. = 1 register ton (shipping.)
40 cu. ft. in U. S., or, ) . .. . ■
42cu.ft.inEng. \= 1 fre ^ ht ton -
Note. — A cu. foot of distilled water maximum density weighs 62| lbs.
avoirdupois.
LIQUID MEASURE.
68. Liquid Measure is used in measuring milk, oil,
wine, etc.
Ta ble.
4 gills (gi.) = 1 pint . . . pt.
2 pints = 1 quart . . qt.
4 quarts = 1 gallon, . . gal.
31 J gallons = 1 barrel, . . bar. or bbl.
63 gallons == 1 hogshead, . hhd.
69. The Standard Unit of Liquid Measure is the gallon,
which contains 231 cubic inches.
The British Imperial Gallon contains 277.274 cu. inches.
Notes. — 1. The barrel and hogshead, as units of measure, are chiefly
used in estimating the contents of cisterns, reservoirs, etc.
2. Casks varying in capacity are often used in commerce, called tierces,
pipes, butts, tuns, etc. Their capacity is determined by gauging or
measurement, and the number of gallons each contains is usually marked
upon it.
3. A Carboy holding about 12 gallons, is sometimes used for corrosive
and other liquids.
4. Beer Measure is practically obsolete in this country. The old beer
gallon contained 282 cubic inches ; the barrel 36 gallons ; the hogshead
51 gallons.
Dry Measivre.
31
DRY MEASURE.
70. Dry
salt, etc.
Measure is used in measuring grain, fruity
Table.
2 pints (pt.) = 1 quart, .
8 quarts = 1 peck,
4 pecks, or 32 qts. = 1 bushel, .
36 bushels = 1 chaldron,
qt.
pk.
bu.
ch.
71. The Standard Unit of Dry Measure is the bushel, which
contains 2150.42 cu. inches.
The British Imperial bushel contains 2218.192 cu. inches.
Notes. — 1. The Eng. Quarter seen in, prices current, is equal to 8 bu.
of 70 lb. each, or to 560 lb. = \ of a long ton.
2. Stricken or Even Measure is used in measuring grain, seeds, etc.,
the article measured being scraped off level by a straight instrument
called a strike, or strickle.
3. Heaped Measure is used in measuring vegetables and fruit, as
potatoes, apples, etc.
4. A heaped bushel is equivalent to a Winchester bushel, heaped in
the form of a cone, the height of which is 6 inches.
Four heaped measures are about equal to five stricken measures.
72. The standard weight, Avoirdupois, of a Bushel of different
kinds of grain and seeds, as fixed by law in the several States named.
Table.
commodities.
Wheat
Indian Corn
Oats
Barley
Buckwheat
Rye...
Clover Seed
Timothy Seed . . .
Blue Grass Seed
Flax Seed
Hemp Seed
60 56
52|56
32
50
1
i |
IN
60
5(^52
| i
60 60 60
50 56
33
- 1
i 1
60| 60 GO 60 60 60
66 56 56| 56 52 56
32 30
! 46
32 35 30
48 48
52 50 48
56 56 56
60 64
45
14'
56 5Dj5£
44
60 60
54 56
.32
is
5C,
CO 60
56 56
861 32
45 48
42 42
56 56
60 60
46
!56
I
32 Weights and Measures.
Notes.— 1. Beans, peas, and potatoes v.re usually estimated at 60 lb. to
the bu., but the laws of N. Y. make 62 lo. of Leans to a bushel.
In Illinois, 50 lb. of common salt, or 55 lb. fine, are 1 bu. In N. J.,
56 lb. of salt are 1 bu. In Ind., Ky., and Iowa, 50 lb. are 1 bu. In Penn.,
80 lb. coarse, 70 lb. ground, or 62 lb. fine salt are 1 bu.
In Maine, 30 lb. oats, and 64 lb. beets or of rutabaga turnips = 1 bu.
In New Hampshire, 30 lb. of oats are 1 bu.
2. Grains, seeds, and small fruit are sold by the bushel, stricken or
level measure.
Large fruit, potatoes, and all coarse vegetables by heaped measure.
TROY WEIGHT.
73. Troy Weight is used in weighing gold, silver, jewels, and
in philosophical experiments.
Table.
24 grains (gr.) = 1 pennyweight, . pwt.
20 pennyweights = 1 ounce, . . . . oz.
12 ounces = 1 pound, . ... lb.
74. The Standard Unit of weight in the United States, is
the Troy pound, which contains 5760 grains and is equal to
the Imperial Troy pound of England.
75. The Value of Diamonds and other jewels is estimated
by carats, grains, and quarters. Thus,
4 quarters = 1 grain, . . gr.
4 grains = 1 carat, . . . car.
AVOIRDUPOIS WEIGHT.
76. Avoirdupois Weight is used in weighing coarse articles;
as hay, cotton, groceries, etc., and all metals except gold and
silver.
Table.
16 ounces {oz) = 1 pound, . . . lb.
_ j cental, or . . ctl.
^ 1 hundredweight, cwt.
2000 lb., or 20 cwt. = 1 ton, . . . . T.
Note. — The long ton of 2240 lbs. is used in calculating duties, in
weighing coal at the mines, and in a few other cases.
Apothecaries Weight 33
77. Comparison of Avoirdupois and Troy Weight.
7000 grains Troy = 1 lb. Avoirdupois.
5760 grains " = 1 lb. Troy.
437^ grains " = 1 oz. Avoirdupois.
480 grains " = 1 oz. Troy.
Special Avoirdupois
Weights.
100
lbs. Nails
= 1 Keg.
100
lbs. Dry Fish
= 1 Quintal.
196
lbs. Flour
= 1 Barrel.
200
lbs. Beef or Pork
= 1 Barrel.
240
lbs. Lime
= 1 Cask.
280
lbs. Salt, N. Y. Salt Works
= 1 Barrel.
150
lbs. Potatoes, as freight
= 1 Barrel.
6| lbs. Crude or Refined Petroleum = 1 Gallon.
A ton (2000 lbs.) of Lehigh white ash coal, egg size = 34| cu. ft.
A ion of white ash Schuylkill, " =35 cu. ft.
A ton of pink, gray, and red ash, " =36 cu. ft.
A ton of hay upon a scaffold measures about 500 cu. ft. ; when in a
mow, 400 cu. ft. ; and in well-settled stacks, 10 cu. yards.
APOTHECARIES WEIGHT.
78. Apothecaries Weight is used by apothecaries in mixing
medicines.
Table.
20 grains (gr.) = 1 scruple, . . sc, or B.
3 scruples = 1 dram, . . . dr., or 3 .
8 drams = 1 ounce, . . . oz. t or § .
12 ounces = 1 pound, . . . lb., or lb.
Notes. — 1. The pound, ounce, and grain are the same as Troy
weight. The only difference between them is in the subdivisions of the
ounce.
2. Drugs and Medicines are sold at wholesale by Avoirdupois
weight.
3
34 Weights and Measures.
APOTHECARIES FLUID MEASURE.
79. Apothecaries Fluid Measure is used in mixing liquid
medicines.
Table.
60 minims, or drops (TR. or git.) = 1 fluid drachm, . fl .
8 fluid drachms = 1 fluid ounce. . . /§ .
16 fluid ounces = 1 pint 0.
8 pints = 1 gallon, .... Cong.
Notes.— 1. Ott. for guttoa, Latin, signifying drops ; O,iovoctarias, Latin
for one-eighth ; and Cong., congiarium, Latin for gallon.
2. The symbols of this measure precede the numbers to which they
refer. Thus, O. 2 "f §6, is 2 pints 6 fluid ounces.
80. The following approximate measures, though not
strictly accurate, are often useful in practical life :
Table.
45 drops of water, or a common teaspocnful = 1 fluid drachm.
A common tablespoonful = -| fluid ounce.
A small teacupful, or 1 gill = 4 fluid ounces.
A pint of pure water = 1 pound.
4 tablespoonful s, or a wine-glass = £ gill.
A common-sized tumbler = \ pint.
4 teaspoonfuls = 1 tablespoonful.
Abbreviations.—^, recipe, or take; a, aa, equal quantities; j, 1;
ij, 2 ; ss, semi, half; P, particula, little part ; P. aeq., equal parts ; q. p.,
as much as you please.
CIRCULAR MEASURE.
81. Circular Measure is used in measuring angles, latitude,
longitude, etc.
82. A Circle is a plane figure bounded by a curve line,
every part of which is equally distant from a point within,
called the center.
Time. 35
Table.
60 seconds (") = 1 minute, . . '.
60 minutes = 1 degree, . . °, or deg.
30 degrees = 1 sign, . . . S.
12 signs, or 360' = 1 circumference, Gir.
The Standard Unit for measuring angles is the Degree.
83. A Degree is the angle measured by the arc of -jj-g- part
of the circumference of a circle.
A degree at the equator, also the average degree of latitude,
adopted by the U. S. Coast Survey, is equal 69.16 miles, or
69| miles, nearly.
TIME.
84. Time is a measured portion of duration.
Table.
60 seconds (sec.) = 1 minute, . . rain.
60 minutes = 1 hour, . . . hr.
24 hours == 1 day, . . . d.
7 days -- 1 week, . . . wk.
365 days = 1 common year, c. yr.
366 days = 1 leap year, . I. yr.
12 calendar months (mo.) = 1 civil year, . yr.
100 years = 1 century, . . 0.
Note. — In most business transactions 30 days are considered a month.
85. Time is naturally divided into days and years. The
former are measured by the revolution of the earth on its axis ;
the latter by its revolution around the sun.
86. Days are divided into Apparent Solar, Mean Solar, and
Civil days.
An Apparent Solar Day is the time between the apparent
departure of the sun from a given meridian and his return to
it, and is shown by sun dials.
A Mean Solar Day is the average length of apparent solar
36
Weights and Measures.
days, and is the Standard Unit for measuring Time. It is
divided into 24 equal parts, called hoars, as shown by a per-
fect clock.
A Civil Day is the day adopted by government for business
purposes. It begins and ends at midnight, and is divided into
two part^ of 12 hours each ; the former are designated A. M.,
the latter p. m.
Notes. — 1. The difference between the apparent and mean solar day
is called the Equation of Time, and varies from 16£ min. to nothing.
This difference is owing to the obliquity of the ecliptic, and the unequal
velocity of the Earth in its orbit.
2. The Astronomical Day begins at noon and is counted on through
24 hours to the next noon, and corresponds to the apparent solar day.
3. We have seen that the pendulum which vibrates seconds, is the
standard of the English and American measures of extension, capacity,
and weight. But the length of the pendulum is determined by the mean
solar day ; hence, the mean solar day is the ultimate standard of all our
weights and measures.
87. Years are divided into Civil and Solar years.
88. The Solar Year is equal to 365 d. 5 hr. 48 min. 49.7 sec,
or 365J d. nearly.* *In 4 years this fraction amounts to about
1 day. To provide for this excess, 1 day is added to the mo.
of Feb. every 4th year, which is called Leap Year.
Note. — Every year that is exactly divisible by 4, except centennial
years, is a leap year ; the others are common years. Thus, 1876, '80, etc.,
were leap years ; 1879, '81, were common. Every centennial year exactly
divisible by 400 is a leap year ; the other centennial years are common. .
Thus, 1600 and 2000 are leap years ; 1700, 1800, and 1900 are common.
89. The Civil Year includes both common and leap years,
and is divided into 12 Calendar months, viz :
January
(Jan.)
31 days.
July
(July)
31 days.
February
(Feb.)
28 "
August
(Aug.)
31 "
March
(Mar.)
31 "
September
(Sept.)
30 "
April
(Apr.)
30 "
October
(Oct.)
31 "
May
(May)
31 "
November
(Nov.)
30 "
June
(June)
30 "
December
(Dec.)
31 "
Laplace, Somerville, Baily's Tables.
Miscellaneous Tables.
37
90. A Calendar is a division of time into different periods,
adapted to the wants of society.
91. The first Civil Calendar worthy of notice was estab-
lished by Julms Caesar 46 years before Christ, and continued
in use until the adoption of the Gregorian Calendar in 1582.
Dates prior to the adoption of the Gregorian Calendar are called old
style, and are marked 0. S. ; those since are called new style, and are
marked N. S.
92. To change dates from Old Style to New.
From 1582 to 1700 (1600 being leap year) add 10 days to
Old Style.
From 1700 to 1800 add 11 days ; from 1800 to 1900 add
12 dajss ; and from 1900 to 2100 (2000 being leap year) add
13 days.
Note. — Russia continues to use the Julian calendar, or Old Style ;
hence., Russian dates are now 12 days behind ours.
MISCELLANEOUS TABLES.
12 things = 1 dozen.
12 dozen = 1 gross.
12 gross = 1 great gross.
20 things = 1 score.
Paper.
24 sheets
= 1 quire of
paper. 2 reams = 1 bundle.
20 quires
= 1 ream.
5 bundles = 1 bale.
Books.
2 leaves
= 1 folio.
8 leaves rs 1 octavo, or 8vo.
4 leaves
= 1 quarto,
or 4to. 12 leaves = 1 duodecimo, or 12mo.
Notes. — 1. The terms folio, quarto, octavo, etc., denote the number of
leaves into which a sheet of paper is folded in making books.
2. In copying legal papers, recording deeds, etc., clerks are usually paid
by the folio. Thus,
100 words make 1 folio in New York.
72 words " 1 folio in com. law in England.
90 words " 1 folio in chancery in England.
3. In printing books, 250 impressions or 125 sheets printed on both
sides, make 1 token.
38 United States Money.
UNITED STATES MONEY.
93. Money is the measure of value.
94. Moneys of Account are those in which accounts are kept.
95. Currency is the money employed in trade.
96. Coins or Specie are pieces of metal of known purity and
weight, stamped at the Mint, and authorized by Government
to be used as money at fixed values.
97. Bullion is uncoined gold or silver, and includes bars,
gold-dust, etc. c -
98. Paper Money is a substitute for metallic currency. It
consists of Treasury Notes issued by the Government known
as Greenbacks, and Bank Notes issued by banks.
99. U. S. Money is the legal currency of the United States,
and is often called Federal Money. Its denominations are
Eagles, Dollars, Dimes, Cents, and Mills, which increase and
decrease by the scale of ten, and it is thence called Decimal
Currency.
Table.
10 mills = ' 1 cent, . . ct.
10 cents = 1 dime, . . d.
10 dimes, or 100 cts. = 1 dollar, . . dot., or $.
10 dollars = 1 eagle, . . E.
100. The U. S. coins are gold, silver, nickel, ana bronze.
101. The Gold coins are. the double eagle, eagle, half eagle,
quarter eagle, three-dollar piece, and dollar.
102. The Silver coins are the dollar, half dollar, quarter
dollar, and dime.
103. The Nickel coins are the 5-cent and S-cent pieces.
104. The Bronze coin is the 1-cent piece.
United States Money. 39
105. The weight and purity of the coins of the United
States are regulated by the laws of Congress.*
Notes. — 1. The gold dollar is the Unit of Value. Its standard weight
is 25.8 gr. ; that of the quarter eagle, 64.5 gr. ; of the 3-dollar piece, 77.4
gr. ; of the half eagle, 129 gr. ; the eagle, 258 gr. ; the double-eagle, 516 gr.
2. When pure, gold is said to be 24 carats fine. If it contains 18 parts
of pure gold and 6 parts of alloy, it is 18 carats fine, etc.- Gold for
manufacturing purposes varies from 14 to 18 carats fine.
3. The weight of the standard silver dollar is 412| grains ; the half dol-
lar, 12| grams or 192.9 grains ; the quarter dollar, 6^ grams, or 96.45 gr. ;
the dime, 2£ grams or 38.58 grains.
4. The weight of the nickel 5-cent piece is 77.16 grains, or 5 grams;
of the 3-cent nickel, 30 grains; of the cent, bronze, 48 grains.
5. The standard purity of the gold and silver coins is by weight nine-
tenths pure metal, and one-tenth alloy. The alloy of gold coins is silver
and copper; the silver, by law, is not to exceed one-tenth of the whole
alloy. The alloy of silver coins is pure copper. f
6. The 5-cent and 3-cent pieces are composed of one-fourth nickel and
three-fourths copper ; the cent, of 95 parts copper and 5 parts of tin and
zinc. They are known as nickel and bronze coins. The diameter of the
nickel 5-cent piece is two centimeters, and its weight 5 grams.
7. The Trade Dollar of 420 grains is no longer coined.
106. Legal Tender is money which, if offered, legally satis-
fies a debt.
Notes. — 1. All the gold coins, and the silver coins of $1 and upwards,
except the trade dollar, are legal tender for all payments.
2. Silver coins less than $1 are legal tender to the amount of $10 ;
nickel and bronze pieces to the ambunt of 25 cents.
CANADA MONEY.
107. Canada Money is the legal currency of the Dominion
of Canada. It is founded on the Decimal Notation, and its
denominations, Dollars, Gents, and Mills, have the same
nominal value as the corresponding denominations of U. S.
Money. Hence, all the operations in it are the same as those
in U. S. Money.
* The United States adopted the decimal system of currency in 1789. Since then it
has been adopted by France, Belgium, Brazil, Bolivia, Canada, Chili, Denmark, Ecuador,
Greece, Germany, Italy, Japan, Mexico, Norway, Peru, Portugal, Spain, Sweden, Switz-
erland, Sandwich Islands, Turkey, U. S. of Colombia, and Venezuela.
t Report of Director of the Mint.
40 Weights and Measures.
ENGLISH MONEY.
108. English or Sterling Money is the currency of Great
Britain.
Table.
4 farthings (qr. or far.) = 1 penny, . . . . d.
12 pence = 1 shilling, ....*.
20 shillings, or i
10 florins W , = 1 Pound or sovereign, £. ^ __
21 shillings = 1 guinea, . . . . g.
109. The Unit of English Money is the Pound Sterling,
which is represented by a gold Sovereign equal in value to
$4.8665. The guinea is no longer coined.
Notes. — 1. The standard purity of the gold coins of Great Britain is
22 carats fine ; that is, \^ pure gold and -fa alloy. That of the silver coins
is 1 1 pure silver and -fa alloy.
2. The silver coins are the crown (5s.) ; half crown (2s. 6d.) ; florin (2s.) ;
shilling (12d.) ; the six-penny, four-penny, and three-penny pieces.
3. The copper coins are the penny, half-penny, and farthing.
4. Farthings are commonly expressed as fractions of a penny, as 7|d.
FRENCH MONEY.
110. French Money is the national currency of France.
The system is founded upon the decimal notation ; hence, all
the operations in it are the same as those in U. S. money. The
denominations are the franc, decime, and centime.
Table.
10 centimes (c.) = 1 decime, . . d.
10 declines = 1 franc, . . fr.
111. The Unit of French money is the Franc. Decimes are
tenths of a franc, and centimes are hundredths.
French Money. 41
Notes. — 1. Centimes by contraction are commonly called cents.
2. Decimes, like our dimes, are not used in business calculations ; they
are expressed by tens of centimes. Thus, 5 decimes are expressed by
50 centimes ; 63 fr., 5 d., and 4 c. are written, 63.54 francs.
3. The legal value of the franc in estimating duties, is 19.3 cents; its
intrinsic value is a trifle more.
112. The Coins of France are of gold, silver, and bronze.
The Gold coins are the hundred > forty, twenty, ten, and/ve
franc pieces.
The Silver coins are the five, tivo, and one franc pieces, the
fifty and twenty-five centime pieces.
Bronze coins are the ten, five, two, and one centime pieces.
The gold and silver coins of France, like those of the U. S., are ^ pure
metal and ^ alloy.
GERMAN MONEY.
100 pfennigs = 1 reischmark.
113. The Coins of the New German Empire consist of gold,
silver, and nickel.
The Gold coins are the 5-mark piece called half krone (half
crown), the 10-mark piece called krone (crown), and the 20-
mark piece called doppel krone (double crown).
The Silver coins are the 2 and 1 mark pieces.
The Nickel coins are 10 and 5 pfennigs (pennies).
114. Reischmark {Royal Mark) is the Standard Unit. It
is equal to 23.85 cts. U. S. money, and is divided into 100 equal
parts, one of which is called a pfennig.
Note. — The coins most frequently referred to in the United States are
the Silver Thaler which equals 74.6 cents, and the Silver Groschen equal
eteio System.*
[&
Definitions.
115. Metric Weights and Measures increase and decrease
regularly by the Decimal Scale.
116. The Meter is the Base of the System, and is one ten-
millionth part of the distance from the Equator to the Pole, or
39.37 inches, nearly.
Note. — The term Meter is from the Greek metron, a measure.
117. The Metric System has three principal units, the
Me'ter (meeter), Li'ter (leeter), and Gram. To these are
added the Ar and Ster,\ for square and cubic measure. Each
of these units has its multiples and subdivisions.
118. The names of the higher metric denominations are
formed by prefixing to the name of the unit, the Greek
numerals, Dele' a, Hek'to, Kil'o, and Myr'ia.
Thus, from Dek'a, 10, we have Dek'ame'ter, 10 meters.
" Hek'to, 100, " Hek'tome'ter, 100
" Kil'o, 1000, " Kil'ome'ter, 1000
* Myr'ia, 10000, " Myr'iame'ter, 10000 "
* This system had its origin in France near the close of the last century. Its sim-
plicity and comprehensiveness have secured its adoption in nearly all the countries of
Europe and South America.
Rs use was legalized in Great Britain in 1864, and in the United States in 1866.
It Is adopted hy the TJ. S. Coast Survey, and is extensively used in the Arts and
Sciences, and partially in the Mint and Post Office.
t The spelling, pronunciation, and abbreviation of metric terms in this work, are the
same as adopted by the American Metric Bureau, Boston, and the Metrological Soc, N.Y.
Metric System. 43
119. The lower denominations are formed by prefixing to
the name of the unit the Latin numerals, Dec'i, Certti, and
Mil'li.
Thus, from Dec'i, y 1 ^, we have Dec'ime'ter, T ^ meter.
" Cen'ti, yi^, * Cen'time'ter, T £ 7
« Mil'li, T ^, " Mil'lime'ter, ^ "
Note. — The numeral prefixes are the Key to the whole system, and
should be thoroughly committed to memory.
METRIC LINEAR MEASURE.
Tab le.
10 mtt'li-me'ters {mm.) — 1 cen'ti-me'ter,
10 cen'ti-me'ters = 1 dec'i-me'ter, .
10 dec'i-me'ters = 1 METER, . .
10 me'ters = 1 dek'a-me'ter,
10 dek'a-me'ters — 1 hek'to-me'ter,
10 hek'to-me'ters = 1 kil'o-me'ter,
10 kiVo-me'ters = 1 myr'ia-me'ter,
em. (jU »»•)
dm. ( T V m.)
m.
Dm. (10 m.)
Hm. (100 m.)
Km. (1000 m.)
Mm. (10000 m.)
Notes. — 1. The principal unit of each table is printed in capital
letters ; those in common use in full-faced Roman.
2. The Accent of each unit and prefix is on the first syllable, and
remains so in the compound words.
3. Abbreviations of the higher denominations begin with a capital,
those of the lower begin with a small letter.
Common Equivalents.
1 cen'timeter = 0.3937 inches.
1 dec'imeter = 3.937 "
1 me'ter = 39.37* "
1 kil'ometer = 0.6214 mile.
4. — Merchants usually reckon the meter as 1 T V yard.
ONE DECIMETER.
i t 1 1 1 T 1 1 1 1 1 1 1 1 f 1 1 1 1 1 1 1 1 1 1 T 1 1 1 1 1 « 1 1 1 1 i f I II i il 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ii 1 1 1 1 1 Li 1 1 1 1 1 1 f 1 1 ■ 1 1 H 1 1 Ti 1 1 1 1 1 1 1 1 1 1
100 Millimeters.
* Established by Act of Congress in 1866.
44 Weights and Measures.
120. The Meter is the Standard Unit of length, and, like
the yard, is used in measuring cloths, laces, short distances, etc.
121. The Kilometer, like the mile, is used in measuring
long distances. *
>.
122. The Centimeter and Millimeter are used for minute
measurements, as the thickness of glass, paper, etc.
Note. — The compound words may be abbreviated by using only the
prefix and the first syllable or letter of the unit , thus, centimeter, milli-
meter, centiliter, milliliter, centigram, decigram, may be called centim,
millim, centil, decig, etc.
123. The approximate length of 1 meter is 40 in.; of 1
decim., 4 in.; of 5 meters, 1 rod; of 1 kilom., § mile.
Note. — Decimeters, dekameters, hektometers, like dimes and eagles, are
seldom used.
124. Since meters, centimeters, and millimeters, correspond
to dollars, cents, and mills, it follows that metric numbers may
be read like U. S. Money. Thus, 28.375 meters are read 28
and 375 thousandths meters, or 28 m. 3 dm. 7 cm. 5 mm., or
28 m. 37 cm. 5 mm.
1. Read in meters 15 'Dm.; 78 Hm.; 355 Km.; 49.237 dm.;
3.54 Mm.
125. To write Metric Numbers decimally in terms of a given Unit.
2. Write 9 Hm. 4 m. 6 dm. 8 cm. in terms of a meter.
Explanation. — We write meters in units place, operation.
on the left of the decimal point, the Dm. in tens 904.68 m., Ans.
place, the Hm. in hundreds place, etc., and the
decims. in tenths place, centims. in hundredths, etc., as we write the orders
of integers and decimals in simple numbers. Hence, the
Kule. — Write the given unit and the higher denomi-
nations in their order, on the left of a decimal point, as
integers, and those below the unit, on the right, as
decimals.
Note. — If any intervening denominations are omitted in the given
number, their places must be supplied by ciphers.
Metric System, 45
3. Write in terms of a meter 15 Dm. Ans. 150 m.
4. Write in meters 254 Dm. 42 cm.
5. Write 385 Hm. 24 mm.
6. Write 172 Hm. 32 Dm. in meters.
7. Write 8 Km. 9 Hm. 6 Dm. 8 mm.
8. Write in meters and decimals 4 Mm. 15f Dm. 7 cm.
5 mm.
9. Write in Km. 37 Mm. 64 Dm. 37£ m. 8 dm. 7 mm.
126. To reduce Metric Numbers from higher denominations to
lower, and from lower to higher.
10. Reduce 352 meters to millimeters.
OPERATION.
Solution. — Since 1 m. = 1000 mm., 352 ^52 m.
meters = 352 x 1000, or 352000 mm., Ana. 1000
Ans. 352000 mm.
n. Change 843000 millimeters to meters.
Solution. — Since 1000 mm. = im. 843000 mm. = as many meters as
1000 is contained times in 843000. Pointing off three decimal places
divides a number by 1000. Ans. 843.000 m. Hence, the
Rule. — Move the decimal -point one place to the right
or left, as the case may require, for each denomination
to which the given number is to be reduced.
12. Change 75.25 Km. to meters. Ans. 75250 m.
13. Change 8427.83 meters to Hm. Am. 84.2783 Hm.
14. Change 9723.8 m. to Km. Ans. 9.7238 Km.
15. Change 83605.24 cm. to meters and decimals. To Dm.
16. Change 75842 mm. to meters and decimals. To cm.
17. Reduce 187.62 dm. to meters. To cm.
18. Reduce 61.75 Km. to cm. To mm.
19. Reduce 158364 mm. to Hm.
20. Reduce 28.53 Km. to dm.
21. Reduce 153 Mm. to Dm. To cm.
46
Weights and Measures.
METRIC SQUARE MEASURE.
127. The Measuring Unit of Surfaces is a Square, each side
of which is a Linear Unit.
Table.
100 sq.
milli-me'ters (sq. mm
) = 1 sq. cen'ti-me'ter,
sq. em.
100 sq.
cen'ti-me'ters
= 1 sq. dec'i-me'ter,
sq. dm.
100 sq.
dec'i-me'ters
_ jl SQ. METER, .
( or cent/ar, . .
sq. m.
ca.
100 sq.
me'ters
j 1 sq. dek'a-me'ter,
( or Ar, . . .
sq. Dm.
A.
_ ( 1 sq. hek'to-me'ter,
( or hek'tar, . .
sq. Hm.
100 sq.
dek'a-me'ters
Ha.
100 sq.
hek'to-me'ters
= 1 sq. kil'o-me'ter,
sq. Km.
Common
EQU 1 VALE NTS.
1 sq. centim.
=a 0.1550 sq. in.
1 sq. decim.
= 0.1076 sq. ft.
1 sq. meter
= 1.196 sq. yd.
1 ar
= 3.954 sq. rods.
1 hektar
= 2.471 acres.
1 sq. kilo
= 0.3861 sq. mile.
128. The sq. meter is used- in measuring ordinary surfaces,
as floors, ceilings, etc. ; the ar and hektar in measuring land ;
and the sq. kilometer in measuring States and Territories.
Note. — The term ar is from the Latin area, a surface.
129. The approximate area of a sq. meter is lOf sq. ft., or
H S( l- jd- > ai *d- °^ ^ ne hektar about 2 J acres.
130. The scale of surface measure is 100 (10 x 10).
That is, 100 units of a lower denomination make a
unit of the next higher ; hence, each denomination
must have two places of figures.
Sq. Centim.
Thus, 23 Ha. 19 A. 25 ca., written as ars, is 2319.25 A., and may he read
"2319 ars and 25 centars" If written as hektars, it is 23.1925 Ha., and
may he read "23 hektars and 1925 centars,"
Metric System. 47
22. Express 86.34 A. as centars. As Hektars.
23. Write 75 sq. m. as sq. mm. As sq. dm.
24. In 8234 ca. how many A.?
25. In 184.38 A. how many Ha. ?
METRIC CUBIC MEASURE.
131. The Measuring Unit of solids is a Cube, the edge of
which is a Linear Unit.
Table.
1000 cu. mil'li-me'ters {cu. mm.) = 1 cu. cen'ti-me'ter, cu. cm.
1000 cu. cen'ti-me'ters = 1 cu. dec'i-me'ter, cu. dm.
1000 cu. dec'i-me'ters = 1 CU. METER, . . cu. m.
10 dec'i-sters = 1 STER, . . . . st.
10 sters = 1 dek'a-ster, . . Dst.
Common Equivalents.
1 cu. centimeter = 0.061 cu. in.
1 cu. decimeter = 61.022 cu. in.
1 cu. meter = 1.308 cu. yds.
Note.— The ster = .2759 cord is seldom used.
132. The cubic meter is used in measuring ordinary solids,
as timber, excavations, embankments, etc.
When applied to fire-wood, it is sometimes called a Ster, and
is equal to about 35J cubic feet.
Note. — The cubic decimeter, when used as a unit of dry or liquid
measure, is called a Liter,
133. The scale of cubic measure is 1000 (10 x 10
x 10) ; hence, each denomination must have three
places of figures.
Cu. Cm.
26. Express 18000 cu. mm. as en. cm. Ans. 18.000 cu. cm.
27. Write 28 cu. m. and 15 cu. dm. as cu. meters.
Ans. 28.015 cu. m.
28. Write in centimeters 256 cu. dm, 34 cu, cm. 89 cu, mm.
48
Weights and Measures.
29. In 38450 cu. dm. how many meters ?
30. In 253 cu. m. how many cu. mm.? Cu.-em.?
METRIC DRY AND LIQUID MEASURE.
134. The Liter is the principal unit of Dry and Liquid
Measure, and is equal in volume to a cubic decimeter.
Table.
10 mirii-li'ters (ml.)
= 1 cen'ti-li'ter, .
. . cl.
(ikO
10 cen'ti-li'ters
= 1 dec'i-li'ter, . .
. . dl.
(tV *0
10 dec'i-li'ters
= 1 LITER, . . .
. . 1.
10 li'ters
sb 1 dek'a-li'ter, .
. . Dl
(101)
10 dek'a-li'ter
= 1 hek'to-li'ter, .
. . El.
(100 I.)
10 hek'to-li'ters
= 1 kil'o-li'ter, . .
. . Kl.
(1000 I)
10 kil'o-li'ters
ss 1 myr'ia-li'ter, .
. . Ml.
(10000 I.)
1 cubic centimeter = 1 milliliter of water.
Common E
QUI VA LENTS.
1 liter bb
61.022 cu. inches.
1 liter =
1.0567 liquid quarts
1 liter =
0.908 dry quarts.
1 hektoliter =
3.531 cu. feet.
1 hektoliter =
26.417 gallons.
1 hektoliter ss
2.837 bushels.
Notes. — 1. The Centiliter is a little less than | gill, and is used for
measuring liquids in small quantities.
2. The Liter is used in measuring milk, wine, and small fruits, and is
about equal to a quart.
3. The Hektoliter is used in measuring grain and liquids in casks, and
is equal to about 26| gal., or 2f bushels.
• 31. In 128.653 ml. how many dl.? How many cl.?
32. Write 35 1. as cl. As ml. As Dl.
33. How many liters in a cistern measuring 2 cu. meters ?
34. How many Dekaliters in such a cistern ? How many HI.?
Metric System.
49
METRIC WEIGHT.
135. The Gram is the principal unit of weight, and is equal
to a cubic centimeter of distilled water at its greatest density,
viz., at 4° Centigrade, or 39.2° Fahrenheit.
10 milli-grams (rng.) =
10 cen'ti-grams =
10 dec'i-granis =
10 grams ==
10 dek'a-grams =
10 hek'to-grams =
10 kil'o grams =
Table.
1 cen'ti-gram,
1 dec'i-gram, .
1 GRAM, . .
1 dek'a-gram
1 hek'to-gram,
1 kil'o-gram,
dg.
9-
Dg.
Hg.
Kg.
(tV <h)
(10 g.)
(100 g.)
(1000 g.)
1 myrla-gram, . Mg. (10000 </.)
100 myr'ia-grams = 1 tonneau or Ton, T.
i
lDg.
Idg.
ldg.
leg.
©
lmg.
Common Equivalents.
1 gram
1 kilogram
1 metric ton
gram
gram
kilogram
metric ton
= 11
cu. centim., or
millil. of water,
cu. decim., or
liter of water,
cu. meter, or
kiloliter of water.
= 15.432 grs. Troy.
= 0.03527 oz. Av.
= 2.2046 lbs. Av.
= 1.1023 tons.
50 Weights and Measures.
136. The Gram is used in weighing gold, silver, jewels, and
letters, and in mixing medicines.
137. The Kilogram (often called kilo) = %\ lb. nearly, is
used in weighing common articles ; as sugar, tea, butter, etc.
Note. — The Quintal = 10 Mg., or 100 Kilos, is seldom used.
The Metric ton of about 2200 lb. is used in weighing heavy
articles ; as hay, coal, etc.
Note. — The nickel 5 -cent piece weighs 1 gram. The weight of a letter
for single postage must not exceed 15 grams, or 3 nickels.
35. Write 23.847 g. as dg.; as eg.; as Dg.; as mg.
36. In 2.5384 mg. how many dg.? How many grams ?
37. In 2.158 Kg. how many grams ? How many eg.?
38. What decimal of a Kg. will be equal to 1 gram ?
39. Express in grams, 31.0006 Tons.
138. Metric weights and measures are added, subtracted,
multiplied, and divided in the same manner as decimals or
U. 8. Money, and therefore require no special rules. (Complete
Graded Arith., Arts. 252-261.)
139. To Reduce Metric to Common Weights and Measures.
1. In 387 cm. how many feet ?
Explanation. — Since 1 meter (the 1 meter r= 39.37 in.
principal metric unit) is equal to 39.37 337 cm< _ 3,87 m.
in., 3.87 meters are equal to 39.37 x 3.87, — — .
or 152.3619 inches. These reduced to ** ) 15^.3619 inches,
feet are 12.69+ ft. Hence, the A)IS. 12. 6968 J ft.
Kule. — Multiply the value of the principal metric unit
of the Table by the given metric number expressed in the
same unit, and reduce the product to the denomination
required, (Art. 148.)
2. Describe the standard unit of weight m the Metric
System.
3. How many pounds in 84 kilograms f 4ws. 185,1864 lbs.
Metric System. 51
4. Change 25 HI. into bushels.
5. Express 85 liters in gals.
6. Reduce 360 Km. to miles.
7. Change 864 eg. to ounces.
8. In 84 ars how many sq. rods ?
Solution. — One ar. = 3.954 sq. r. ; hence, 84 ars s 3.954 x 84, or
332.136 square rods, Am.
9. In 80. 75 Ha. how many acres ?
10. Change 250 cu. m. to cu. feet.
140. To reduce Common to Metric Weights and Measures.
11. How many Km. in 3758 yds. 2 ft. 6 in.?
Explanation. -The given com- 3758 ? d ' 2 ft * 6 in '
pound number reduced to inches £
= 135318 in. Dividing this number 11276
by 39.37, the number of inches in a in
meter, reduces the given number to
meters. Removing the decimal point o9.o7 ) lo5ol 8 inches.
3 places to the left gives the number 3437.084+ m.
of kilometers. Hence, the . , 0WA0 , , -^
Ans. 3.437084+ Km.
Rule. — Divide the given number by the value of the
principal metric unit of the Table, and reduce the quo-
tient to the denomination required.
Note. — Before dividing, the given number should be reduced to the
denomination in which the value of the principal metric unit is expressed.
12. Reduce 2J yd. to cm.
13. Change 24 lbs. 3 oz. to grams.
14. Reduce 28 qts. 1 pt. to centiliters.
15. In 84.326 acres how many ars ?
16. Express an acre as the decimal of a hectar. (Art. 130 )
17. In a farm containing 150 A. 19 sq. r. how many
hectars ?
18. How many lb. Av. in a quintal, if 1 Dg. =: .3527 oz.?
19. How many 5-Qent pieces may be coined from 3 lb, § og t
Of meta] ?
52 Weights and Measures.
Examples.
1. Express the sum of 325.6 dm., 2064.3 cm., 17.654 m.,
23.8 Dm., and 2.583 Km., in terms of a meter.
32.56
Explanation. — The numbers are first reduced 20.643
to meters, the principal unit of the table, by 17 P^A
removing the decimal point to the right or left as
in the margin ; they are then added as in deci-
238.000
mals. ^583.000
Am. 2891.857 m.
2. Add 238 cm., 438.4 dm., 52 m., 82 Hm, and 2.5 Km.
3. What is the difference between 128.6 dl. and 34.5 HI. ?
Solution.— 3450 liters- 12. 86 liters = 3437.14 liters, Am.
4. By how much is 35 m. 7 cm. less than the average of
34 m. 2 dm., 37 m. 8 dm., 36 m. 9 dm., 35 m. 7 dm., 36 m.
6 dm., and 34 m. 8 dm. ?
5. The circumference of a circular court is 48 m. 4 dm. ;
how many Km. should I walk by going 8 times around it ?
6. A service of plate weighed respectively 4 Kg. 9 Dg.,
15 Hg. 5 dg., 1 Kg. 560 g., and 35947 eg. ; what is its value at
%\\ an ounce ?
7. How much does its weight fall short of 8J Kg. ?
8. From Paris to Madrid is 1450 Km. ; how many miles per
hour does a train go which makes the trip in 36 hours ?
9. What cost a pile of wood 42.5 m. long, 2 m. wide, and
1.9 m. high, at $2 per ster ?
10. If 35 Kg. of beef cost 50 fr. 40 c, what is the cost of
1 Kg. ? Of 23£ Kg. ? Of 9 Kg. 5 dg. in IT. S. Money ?
n. A merchant buys 2f Hm. of silk for $480, and sells it at
$1.95 a yard ; how much does he gain or lose ?
12. Bought 454 bu. of wheat at $3 a bu., and sold it for
$8.75 a HI. ; what is the gain ?
13. In a public office, 35 fires consume 336 sters of wood ;
what is the average consumed by each, and what its cost at
75 centimes a ster?
Foreign Weights and Measures. 53
FOREIGN WEIGHTS AND MEASURES.
141. The Metric System is in general use in the following
countries :
Argentine Confederacy, Austria, Belgium, Chili, Colombia,
Ecuador, Egypt, France, Germany, Greece, Italy, Japan,
Mexico, Netherlands, Peru, Spain, Switzerland, Turkey, Uru-
guay, and Venezuela.
142. The Metric System is permissive, and in partial use :
In Great Britain, United States, India, Norway, Sweden,
Denmark, and Kussia.
143. In Bolivia, though the Metric is the legal system, the
old Spanish weights and measures are used to some extent.
In Brazil the freight of ships is estimated by the English ton
of 2240 lbs.
Canada, Cape of Good Hope, Liberia, and Ceylon use the
same as Great Britain. The following are often met in
Market reports :
144. In China and Hong Kong.
1 tael = 1£ oz. Av.
1 catty = li lb. "
1 picul = 133i lb. "
1 chili = 14.1 in.
1 chang = 11.75 ft.
In Denmark.
1 pound = 1.102 lb. Av.
1 centner = 110.23 lb. "
1 tonde, grain = 3.948 U. S. bu.
1 " coal = 4.825 " "
1 fod(foot) = 1.03 " ft.
1 viertel = 2.04 * gal.
1 alen (Ell) = .684 " yds.
Note. — In coinage the metric system is used.
54 Weights and Measures.
145. In Siam, 1 tael = 1-J oz. Av. The Picul, Catty, and
Chang, are like Java.
In Java.
1 Ams. pond = 1.09 lb. Av. 1 catty = 1* lb. Av.
1 picul = 133£ lb. " 1 chang = 4 yd.
In Russia.
1 pound = ^ lb. Av.
1 pood (63 to a ton) = 36 lb. "
1 berkowitz = 360 lb. "
1 chetvert — 5.956 U. S. bu.
1 vedro = 3.25 " gal.
1 arsheen = 28 in.
1 ship last = 2 tons.
In India.
1 Bombay maund of 40 seers = 28 lb. Av.
1 "42 "
=
29.4 lb. M
1 Bombay candy of 20 maunds
560 lb. «
1 Surat maund of 40 seers
=
3U i b . -
1 "42 "
r=
39^ lb. "
! "44 "
=
41 T Vlb. -
1 Bengal factory maund
r=
74| lb. "
1 Bengal bazaar maund
—
82| lb. Av.
1 Madras maund
=
25 lb. "
1 " candy (20 maunds)
=
500 lb. "
1 Travancore " "
=
660 lb. -
1 tola
=
180 gr.
1 guz, Bengal
=
1 yd. Eng.
1 Corge pound
=
2 lbs. Av.
146." In Spain and many South American States and in
Cuba:
1 libra = 1.0141b. Av. 1 quintal (100 lib.) = 101.44 lb. Av.
1 arroba = 25.36 lb. " 1 vara = .914 yd.
IK*
m EDUCTION
147. Reduction is changing Compound Numbers from one
denomination to another without altering their vaZt/e. It is
of two kinds, Descending and Ascending.
148. Reduction Descending is changing higher denomina-
tions to loiver ; as, yards to feet, etc.
149. To reduce Higher denominations to Lower,
1. Eeduce 23 bbl. 4 gal. 3 qt. to quarts.
Explanation.— Since 31| gal. make 1 bbl. 23 bbl. 4 gal. 3 qt.
there are 3H times as many gallons as 31 J
barrels, and 7241+4 = 728| gallons. Like- "toqjl l
wise, there are 4 times as many quarts as gal- 2 °
Ions, and (728J x 4) + 3 = 2917 quarts. Hence, Z
the 2917 qt., A?is.
Rule. — Multiply the highest denomination by the
number required of the next lower to make a unit of the
higher, and to the product add the loiver denomination.
Proceed in this manner with the successive denomina-
tions, till the one required is reached.
2. In 17 days, 18 hours, 27 minutes, how many seconds ?
3. How many sec. in the circumference of a circle?
4. Change 12 mi. 8 rd. 3 yd. 2 ft. to inches.
5. Reduce 83 cu. yd. to en. in.
6. Reduce 243 lb. 3 oz. 6 pwt. to grains.
7. Reduce 16 T. 8 cwt. 29 lb. to pounds.
8. Reduce 18 A. 22 sq. r. 25 sq. yd. to sq. ft.
9. How many feet and inches would a man go in walking
2J miles ?
56 Compound Numbers.
10. What cost 250 miles of telegraph wire, at 3 cents a foot ?
11. What cost 253 lb. 6 oz. of silver, at 6 J cts. a penny-
weight ?
12. A school feast for 73 children cost £3 2s. 4Jd.; how many
farthings each did it cost ?
13. What cost 27 T. 3 cwt. 15 lb. of potash, at $3.87£ per
cwt. ?
150. Reduction Ascending is changing lower denominations
to higher ; as, feet to yards, etc.
151. To reduce Lower denominations to Higher.
14. Eednce 67031 far. to pounds, shillings, and pence.
Explanation. — Since 4 far. = Id., 67031 4 ) 67Q31 far -
far. = as many pence as 4 is contained times 12 ) 16757d. 3 far.
in 67031 far., or 16757d. and 3 far. over. So, 20^ 139Ps 51
dividing the pence by 12 reduces them to I
shillings, and dividing the shillings by 20 £69 16s.
reduces them to pounds. Hence, the Ans. £69 16s. 52 d.
Eule. — Divide the given denomination by the number
required to make one of the next higher.
Proceed in this manner with the successive denomina-
tions, till the one requireol is reached. The last quotient,
with the several remainders, will be the answer.
Note. — The remainders are the same denomination as the respective
dividends from which they arise.
15. Reduce 2690 inches to rods, yards, etc.
Ans. 13 r. 2£ yd. 2 ft. 2 in., or 13 r. 3 yd. 8 in.
16. Reduce 642518 gr. to pounds.
17. Reduce 24748 pt. to bushels.
18. Reduce 384634 sec. to days.
19. Reduce 748490 cu. ft. to cords.
20. Reduce 864138 gi. to barrels.
21. Reduce 3187463 sq. yd. to acres.
22. Reduce 2835468 sheets to reams.
Reduction. 57
23. Eeduce 160750 links to miles.
24. What cost 12760 lb. of hay, at $9.50 per ton ?
25. What will 350 rd. of stone wall cost, at 31 cents a foot?
26. How many acres in 350 city lots, each 25 by 100 ft.
27. A jewel weighing 2 oz. 16 pwt. 14 gr. was sold for $1.38
per grain ; what was the amount paid for it ?
DENOMINATE FRACTIONS.
152. Denominate Fractions are fractions of denominate
Integers, and may be common or decimal.
153. To reduce Denominate Fractions, Common or Decimal, of
higher denominations, to Integers of lower denominations.
28. Reduce -fa A. to lower denominations.
BY COM. PKACTIONS. BY DECIMALS.
_^Xl60 = 1440 15 A = -36 acres.
25 25 ' ° r 25 sq " r ' 160 sq.r. mi a.
15 x 30}= 453J 1Q 3| 57.60 sq.r.
25 25 25 oOf sq. yd. in 1 r.
3f x 9 = j53£ 8| 18.15 sq.yd.
25 25 ,0r 25 Sq ' ft 9 sq.ft. in 1 sq.yd.
8}xl44 = 1260 KA 2 1.35 sq.ft.
25 "25" ' ° r 5 °5 "* * _144 sq. m. m 1 sq . ft.
Ans. 57 sq.r. 18 sq.yd. 1 sq.ft. 50f sq.in. 50.40 sq. in.
Ans. 57 sq. r. 18 sq. yd. 1 sq. ft. 50.4 sq. in.
Note. — Only the fractional or decimal parts are multiplied. Pointing
off 2 decimals in the several products is equivalent to dividing them by
100, the denominator of the given decimal. Hence, the
Eule. — Multiply the given fraction or decimal by the
successive numbers which will reduce a unit of the given
fraction to the denomination required, and divide each
■product by the given denominator.
Or, Cancel, multiply, and reduce the result.
58 Compound Numbers.
29. Reduce -J bu. to integers of lower denominations.
SOLUTION.
J X f x f = 28 qt., or 3 pk. 4 qt., Ans.
30. Reduce |- mi. to integers.
31. Reduce -f bu. to pecks, etc.
32. Reduce ^-f-g- gal. to lower denominations.
33. Reduce .458 cwt. to lb., etc.
34. Reduce .8975 wk. to days, etc.
35. Reduce -§- lb. Troy to pwt.
36. Reduce .815625 lb. to Troy oz., etc.
37. Reduce .3945 day to hr., etc.
38. Reduce .845 mi. to fur., rods, etc.
39. How many sq. ft. in a lot lof r. long and 12f r. wide ?
40. How many cu. J- in. are contained in 1 cu. inch ?
154. To reduce Denominate Integers or Fractions of lower, to
Fractions (either Common or Decimal) of higher denominations.
41. Reduce 4s. 5d. to the common fraction of a pound.
Solution.— 4s. 5d. = 53d. £1 = 240d. Ans. ££fc.
42. Change 7 fur. 29 r. to the fraction of a mile.
7 fur. 29 r. = 309 r.
40)29.00 rods.
1 mile = 320 r.
8)7.725 far.
Ans. Mini. = .965625.
Ans. .965625 m.
Rule. — Reduce the given compound number to the
lowest denomination mentioned for the numerator, and
a unit of the required fraction to the same denomina-
tion for the denominator.
For decimals, divide the given numbers as in reducing
integers to higher denominations. (Art. 151. )
Note. — If the lowest denomination of the given number contains a
fraction, the number must be reduced to the parts indicated by the
denominator of the fraction.
Addition. 59
43. Reduce f pwt. to the fraction of a pound Troy. (Com-
plete Graded Arith., Art. 179, 2°.)
SOLUTION.
3 3 1 ,, ,
= -7-j— lb., Ans.
8x20x12 8x20x*2 640
4
44. Reduce 8 oz. 5 pwt. 3 gr. to the decimal of a pound.
45. Reduce 14s. 8d. to the decimal of £1.
46. Reduce 0.87259 yd. to the decimal of 1 m.
47. Reduce \% pwt. to the fraction of 1 lb. Troy.
48. Reduce .45 pt. to the decimal of 1 gal.
49. Reduce 9f hr. to fraction of 1 week.
50. Reduce -^ cwt. to fraction of 1 ton.
51. What cost 2 bales 3 bun. 1 rm. 4 qr. 21 sheets of paper,
at $46.87| a bundle ?
52. How much will it cost to dig a cellar 40 ft. long, 32 ft.
wide, and 5 ft. deep ; at $0.25 a cu. yard.
155. To find what part one Compound Number is of another.
Reduce the numbers to the same denomination, and make the
number denoting the part the numerator, and that tvith which
it is compared the denominator. (0. G. Arith., Arts. 226, 249.)
53. What decimal of 4s. is 3 pence ?
54. Of 3 gal. 3 qt. 1 pt. is 1-J gal. ?
55. Of 1 wk. 3 da. is 4 da. 4J hr.?
56. Of 16 m. is 6 miles 30 rods?
57. What decimal part of 20 bu. is 2 pk. 3 qt. 1.2 pt. ?
58. What decimal part of a fathom is 3f feet?
ADDITION.
156. Compound Numbers are added, subtracted, multiplied,
and divided in the same manner essentially as simple numbers,
and require no special rules.
Note. — 1. The apparent difference arises from their different scales of
increase, one being variable, the other decimal.
lb.
oz.
pwt.
gr.
12
1
19
8
6
10
3
18
19
8
14
6
60 Compound Numbers.
1. Add 12 lb. 1 oz. 19 pwt. 8 gr., 6 lb. 10 oz. 3 pwt. 18 gr.,
19 lb. 8 oz. 14 pwt. 6 gr.
Note. — 2. The sum of the first column
is 32 gr. = 1 pwt. 8 gr. Adding the 1 pwt.
to the next column, its sum is 37 pwt.
= 1 oz. 17 pwt. The next column is 20 oz.
= 1 lb. 8 oz. Setting like denominations
in the same column, the sum is 38 lb. 8 oz. 38 8 17 8, Ans.
17 pwt. 8 gr.
2. Add 78 A. 84 sq. rd., 64 A. 32 sq. rd., and 98 A. 45 sq. rd.
3. Add 96 bu. 3 pk. 2 qt. 1 pt., 46 bu. 3 pk. 1 qt. 1 pi, 2 pk.
1 qt. 1 pt., and 23 bu. 3 pk. 4 qt. 1 pt.
4. Add 2 mi. 3 fur. 8 rd. 2 ft, 4 mi. 7 fur. 6 rd. 4 ft., 12 mi.
5 fur. 17 rd. 11 ft., and 18 mi. 6 fur. 7 rd. 2 ft.
5. Add together -^fas hhd. and f gill.
Note.— 3. Denominate Fractions should *iiW nn( *' = foil S]-
be reduced to integers and fractions of lower f o 32> or Y S 1, — IT 8 1,
denominations, and to a common denomina- -| gi. = T 4 ^ gi.
tor, then added. Am ^ gi>
6. Find the sum of £J f s. Jd. in integers.
7. Add f lb. |- oz. f pwt. 9. Add f wk. { d. If hr.
8. Add J gal. f qt. 2£ pt. 10. Add £| |s. 4|d.
SUBTRACTION.
11. From 18s. 8d. take 13s. lOd.
Note. — Since lOd. cannot be taken from 8d., it be- 18s. 8d.
comes necessary to add Is. = 12d. to 8d., making 20d., jcj iq
and 10 from 20 leaves lOd. Then 17s. - 13s. = 4s. -—
The remainder is 4s. lOd. ^ *-®> Ans.
12. From 24 mi. 7 fur. 8 rd. 12| ft. take 15 mi. 6 fur. 30 rd.
4| feet.
13. From 1 lb. take 10 oz. 17 pwt. 18 gr.
14. From £2$ take 7f shillings.
15. A barrel (31^ gal.) is £ full ; if 7 gal. are drawn off, what
part of the contents will remain ?
Subtraction. 61
157. To find the Exact Number of Years, Months, and Days,
between two dates.
16. What is the difference of time between Sept. 12, 1882,
and Dec. 25, 1884 ?
Analysis.— The time from Sept. 12, 1882, to Sept. 12, 1884 = 2 yr.
The time from Sept. 12th to Dec. 12th = 3 mo.
The time from Dec. 12th to Dec. 25th =13 d.
Ans. 2 yr. 3 mo. 13 d. Hence, the
Eule. — First find the number of entire years, next the
number of entire months remaining, then the days in
the parts of a month.
Note. — 1. The day on which a note or draft is dated, and that on
which it becomes due, must not both be reckoned. It is customary to omit
the former and count the latter.
17. How much time between Nov. 10, 1876, and May 15,
1883?
18. A note dated Dec. 12, 1871, was paid Oct. 1, 1884 ; how
long did it run ?
19. Wellington was born May 1, 1769 ; how old was he at
the date of the battle of Waterloo, which occurred June 18,
1815?
20. Find the exact number of days between Apr. 10, 1879,
and Aug. 25, 1880.
Note.— 2. In finding the operation.
exact time by days, write Apr. 10, '79 to Apr. 10, '80 = 365 d.
down 365 d. as the time Apr. 30-10 = 20 d.
May has - 31 d.
June <•' 30 d.
days remaining in the first " u ty «H ".
and each succeeding month ; Aug. " 25 d.
the sum is the number of An S 502 d
days required.
21. How many days did a note run dated June 1, 1879, and
paid Sept. 28, 1880 ?
22. How many days from June 13, 1869, to Sept. 30 fol-
lowing ?
from the first date to the
same date the next year
then write in a column the
62 Compound Numbers.
23. From May 6, '81, to Aug. 11, '82 ?
24. From Apr. 24, '82, to July 4, '83 ?
25. From Jan. 28, '75, to Feb. 6, '76 ?
26. From Dec. 25, '82, to Jan. 31, '83 ?
27. The latitude .of Cape Cod is 42° 1' 57" N., that of New
York is 40° 42' 43"; what is the difference of their latitude?
Note. — 3. When two places are on opposite sides of the Equator, the
difference of latitude is found by adding their latitudes.
28. The latitude of Havana is 23° 9' N., that of Cape Horn
is 55° 59' S. ; what is the difference ?
29. The latitude of Valparaiso is 33° 2' S., that of St. Au-
gustine is 29° 48' 30" N. ; what is the difference ?
MULTIPLICATION.
158. l. Multiply 2 lb. 8 oz. 5| pwt. 4 gr. by 8.
Explanation.— Multiply each 2 lb. 8 oz. 5| pwt. 4 gr.
denomination separately and unite % g
like denominations as in addition.
Or the multiplicand may be reduced Ans - 21 lb - 6 oz - 5 P wt - 8 g r -
to the decimal of a pound by Art. 154.
Note. — If a fraction occurs in the product of any denomination except
the lowest, it should be reduced to lower denominations, and be united to
those of the same name as in Compound Addition. (Art. 156.)
2. Multiply £12 8s. 6d. by 6.
3. Multiply 17 gal. 3 qt. 1 pt. 2 gi. by 8.
4. Multiply 48 mi. 3 fur. 10 rd. by 12.
5. Multiply 2 hr. 45 min. 17 sec. by 25.
6. Multiply 48° 25' 17" by 28.
7. Multiply 28 bu. 6 pk. 5 qt. by 13.
8. Of 36 persons visiting the Crystal Palace, London, 17
spent 16s. lfd. apiece; each of the rest spent 8s. 10-Jd, more
than each of the 17 5 how much did they all spend ?
Longitude. 63
DIVISION.
159. 9. A man paid £15 12s. 6^d. for 8 chests of tea ;
what was that a chest ?
Note.— Since 8 chests cost £15 12s. operation.
6Jd., 1 chest will cost j as much, and 8 ) £15 12s. 6^d .
£15+8 = £1, and £7 over. Reducing An§ £± 19g Q(L g, far>
£7 to shillings and adding the 12s. gives
152s., which divided by 8 is 19s. The pence cannot he divided by 8, but
6£ d. = 25 far., which +8 = 3^ far. Am. £1 19s. 3± far.
10. Divide 12 gal. 3^ qt. by 5. 12. 18s. 3£d.-r-5 == ?
11. Divide 24 bu. 3| pk. by 7. 13. 83° 19' 9"-f-15 = ?
14. How many cords in a pile of wood 196 ft. long, 7 ft.
6 in. high, and 8 ft. wide ?
15. Paid £1 7s. 7Jd. for a boy's coat and vest ; the price of
the coat was double that of the vest ; what price was the vest ?
16. If a franc is $.193, how many francs equal $1500 ?
17. An importer paid £48 7s. 3d. for English files, at £1
6s. 6d. per dozen ; how many dozen did he import ?
18. If a rail-car goes 17 mi. in 45 min., how far will it go in
5 hr. at the same rate ? •
19. In 4 mi. 3 fur. 28 rd. 4 yd., how many kilometers ?
LONGITUDE.
160. The Longitude of a place is the number of deg., min.,
and sec, reckoned on the equator, between a standard meridian
(marked 0°) and the meridian of the given place.
All places are in East or West longitude, according as they
are East or West of the Standard Meridian, until 180°, or half
the circumference of the Earth is reached.
Notes. — 1. The English reckon longitude from the meridian of Green-
wich ; the French from that of Paris. Americans generally reckon it from
the meridian of Greenwich ; sometimes from that of Washington.
2. When two places are on opposite sides of the Standard Meridian,
the difference of Ion. is found by adding their longitudes. (Art. 157, N ( . 3.)
64 Compound Numbers.
161. Comparison of Longitude and Time.
162. The Earth turns on its axis once in 24 hours ; hence,
■fa part of 360°, or 15° of longitude, passes under the sun in
1 hour.
Again, -fa of 15° Ion., or 15', passes under the sun in 1 min.
of time. And -fa of 15', or 15" Ion., passes under the sun in
1 sec. of time, as seen in the following
Table.
360° Ion. make a difference of 24 hrs. of time.
15° « " « lhr.
" 4 mm.
1' " " " 4 sec.
1" " " " T Vsec.
163. To find the difference of Longitude between two places,
the difference of Time being known.
1. The difference of time between St. Petersburg and Wash-
ington is 7 hr. 9 min. 19£ sec. What is the difference of
longitude ?
Explanation. — Every 15' of Ion. operation.
makes a difference of 1 min. of time ; 7 hr. 9 mill. 19 J sec.
hence there must be 15 times as many 15
min. of Ion. as there are min. and „
seconds of time, and (7 hr. 9 min. 19£ sec.) Ans ' iU7 iy 4y *
x 15 = 107° 19' 48f". Hence, the
Kule. — Multiply the difference of time, ex-pressed in
hours, minutes, and seconds, by 15 ; the product will be
the difference of longitude in degrees, minutes, and
seconds. (Art. 162.)
2. A ship sailing westward reached a point where its chro-
nometer at noon showed the time at Greenwich to be 6 hr.
45 min. 28 sec, p. M. ; what was its longitude ?
3. If the difference of time between two places is 19 min.
12 sec, what is the difference of longitude ?
4. The difference of time between New York and Chicago is
54 min, 30J- sec What is the difference of longitude ?
Longitude. 65
5. If the time at Greenwich is 4 hr. 56 min. 4^ sec. when
it is noon at New York, what is the difference of longitude ?
164. To find the Difference of Time between two places, the
Difference of Longitude being known.
6. When it is 2 hr. 36 min., A. m., at Cape of Good Hope, Ion.
18° 24' E., what is the time at Cape Horn, Ion. 67° 21' AY. ?
Explanation.— The difference of longitude 18° 24' E.
between two places on opposite sides of the g^° 21' W.
standard meridian is found by adding their Ion- — •
gitudes. As there are ^ as many hrs., etc., as -^ / "^ ^ ^ l ^
there are deg., the difference of time is 5 hr. 43 min. Ans. 5 hr. 43 min.
Again, 12 hr.— 5 hr. 43 min. = 6 hr. 17 min.
Adding to this the time before 12, 2 36
Gives the hour before midnight. 8 hr. 53 min., Ans.
Hence, the
Eule. — Divide the difference of longitude, in degrees,
minutes, and seconds, by 15 ; the quotient will be the
difference of time in hours, minutes, and seconds.
Note. — Add the difference of time for places east, and subtract it for
places icest of a given meridian.
7. New York being 3° E. from Washington, and San Fran-
cisco 45° 25' W., what time will it be at New York when it is
noon at San Francisco ?
8. The difference of Ion. between Albany and San Fran-
cisco is 48° 41' 55" ; what is the difference of time ?
9. Constantinople is in Ion. 28° 49' E., St. Paul 93° 4' 55"
W. ; when it is 2 o'clock p. m. at St. Paul, what time is it at the
former place ?
io. Mobile, Ala., is 88° 1' 29" W. Ion. ; Cambridge, Eng., is
5' 2" E. Ion. When it is noon at Mobile, what time is it at
Cambridge ?
n. How much earlier does the sun rise in Boston, Ion. 71°
3' 30", than in New Orleans, Ion. 90° 2' 30" ?
12. Than in Astoria, Ion. 124° ? St, Louis, 90° 15' 15"?
13. Than in Chicago, Ion. 87° 37' 45" ?
5
66
Weights and Measures.
APPLICATION OF WEIGHTS AND
MEASURES.
^AD-
MEASUREMENT OF SURFACES.
165. A Surface is that which has length and breadth only.
166. An Angle is the opening between
two lines which meet at a point, as BAC.
The Lines AB and AC are called the
sides ; and the Point A, at which they
meet, the Vertex of the angle.
167. When two straight lines meet so
as to make the two adjacent angles equal,
the lines are Perpendicular to each other,
and the two angles thus formed are called
Right Angles; as, ABC, ABD.
168. A Plane Figure is one which repre-
sents a plane or flat surface.
169. The Perimeter of a plane figure is
the line which bounds it.
170. The Area of a plane figure is the quantity of surface it
contains.
171. The Dimensions of a plane figure are its length and
breadth.
172. A Rectangle is a plane figure having four sides and
four right-angles. (Art. 168.)
173. When all the sides of a rectangle are equal, it is called
a Square.
174. When its opposite sides only are equal, it is called a
Parallelogram,
Measurement of Surfaces. 67
175. The measuring unit of surfaces is a Square, each side
of which is a linear unit.
176. To find the Area of Rectangular Surfaces.
1. How many square rods in a field 28 rods long and
12 rods wide ?
Solution. — A rectangle 28 rods long and opekation.
1 rod wide will contain 28 sq. rods. And a 28 rods,
field 28 rods long and 12 rods wide will con- -j o
tain 12 times 28, or 336 square rods, Ans.
Hence, the An ^ 336 sq. rods.
V
Kule. — Multiply the length by the bj^eadth.
( 1. Area = Length x Breadth.
Formulas. — •< 2. Length = Area -^ Breadth.
( 3. Breadth = Area -+■ Length.
Notes. — 1. Both dimensions should be reduced to the same denomina-
tion before they are multiplied.
2. One line is said to be multiplied by another, when the number of
units in the former are taken as many times as there are like units in the
latter. (Art. 10, 2°.)
2. Bought a rectangular farm 245 rods long and 88 rods
wide, at $75 per acre ; what was the cost ?
3. How many yards of carpeting, 27 in. wide, will be required
to cover a floor 22 ft. long and 15 ft. wide ?
Note. — This and similar examples admit of two answers, each of
which is correct ; the one in a mathematical sense, the other in a com-
mercial sense. 1st. There are 36| sq. yds. in the floor; to cover this
requires 48f yards of carpeting, 27 in. wide.
2d. The exact number of sq. feet in a floor does not always correspond
with the quantity of carpeting which must be bought to cover it.
Since 6| breadths, 3 qrs. wide and 7^ yds. long, are required to cover
the floor, and the fractional breadth must be as long as any other, it will
be necessary to buy 7 times 7| yds. = 51^ yards.
4. A building lot is 150 ft. front and contains 2 A. ; how
far back does it extend ?
68 Weights and Measures.
5. A man bought a rectangular field containing 3750 sq.
rods, the length of which was 75 rods, at $15 per acre ; what
was its breadth and what did it cost?
6. How many rolls of paper 25 ft. long and 18 in. wide will
be required to cover a wall 26 ft. long and 13 ft. high?
7. What will it cost to concrete a court that is 268 ft. square,
at $3.86 per sq. yard ?
8. How many sq. inches in a flat roof 54 ft. long and 25 ft.
wide?
177. To find the Area of an Oblique-angled Parallelogram, the
Length and Altitude being given.
Multiply the length by the altitude.
Note. — If the area and. altitude, or one side are given, the other factor
is found by dividing the area by the given factor. (Art. 30, 3°.)
9. What is the area of an oblique-angled parallelogram
whose length is 60 ft. and its altitude 53 feet ?
Ans. 3180 sq. feet.
10. A grove in the form of an oblique-angled parallelogram
contains 80 acres, and the length of one side is 160 rods; what
is its width ?
Note. — The area of a square, a rectangle, a rhomboid and rhombus is
found in the same manner.
11. How many sq. feet in a piece of land 13 rods square?
12. One side of an acre of land in shape of a rectangle is 9
rods long ; what is the length of the other side ?
13. What cost a field 77 rd. long and 41 rd. wide, at $18.60
an acre ?
178. To find the Area of a Trapezoid, when its Parallel Sides
and Altitude are given.
14. The parallel sides of a trapezoid are 26 ft. and 38 ft., and
its altitude 14 ft. ; find its area ?
Solution.— The sum of the parallel sides 26 + 38 = 64 ft. ; \ of 64 =
32 ft., and 32 x 14 = 448 sq. ft., Ans. Hence, the
Measurement of Rectangular Bodies. 69
Rule. — Multiply half the sum of the parallel sides by
the altitude.
15. What is the area of a board 13 in. wide, one side of
which is 24 in., the other 28 inches ?
16. The two parallel sides of a field are 85 and 90 rods, and
the distance between them 54 rods ; how many acres were
there ?
MEASUREMENT OF RECTANG-ULAR
BODIES.
179. A Rectangular Body is one bounded by six rectangular
sides, each opposite pair being equal and parallel ; as, boxes of
goods, blocks of hewn stone, etc.
180. When all the sides are equal, it is a Cube ; when the
opposite sides only are equal, it is a Parallelopiped.
181. The Contents or Volume of a body is the quantity of
matter or space it contains.
182. The Dimensions of a rectangular body are its length,
breadth, and thickness.
183. To find the contents op volume of Rectangular Bodies.
l. How many cu. ft. in a box of goods 4 ft. long, 3 ft. wide,
and 2 ft. thick ?
Solution. — Since the box is 4 ft. long and
3 ft. wide, there are 12 sq. ft. in the upper face.
If the box were 1 ft. thick it must have as
many cu. ft. as there are sq. ft. in the upper
face. But it is 2 ft. thick and therefore con-
tains (4 x 3) x 2 = 24 cu. feet, Ans. Hence, the
Rule. — Multiply the length, breadth, and thickness
together. (Art. 30, 3°.)
Notes. — 1. When the contents and two dimensions are given, the
other dimension may be found by dividing the contents by the product of
the two given dimensions. (Art. 30, 3°.)
y y y y a
> /^j
I ji.n.1 1, |-||:
n^i7Fpr
70 Weights and Measures.
2. Excavations and embankments are estimated by the cubic yard. In
removing earth, a cu. yard is called a load.
2. What will it cost to dig a cellar 40 ft. long, 32 ft. wide,
and 8 ft. deep, at 25 cts. a cubic yard ?
3. How many cu. meters in a mound whose length, breadth,
and height are each 6.4 meters ?
4. How many loads of earth must be removed in digging a
cellar 40 ft. long, 20 ft. wide, and 8 ft. deep ?
5. How many cu. ft. in 10 boxes, each 7| ft. long, If ft.
wide, and 1J- ft. high ?
CISTERNS, BINS, ETC.
184. The Capacity of rectangular cisterns, bins, etc., is
measured by cubic measure, but the results are commonly
expressed in units of Liquid and Dry Measure.
185. To find the Number of Gallons in Rectangular Cisterns, etc.
6. How many gallons will a rectangular vat 6 ft. long, 5 ft.
wide, and 4 ft. deep contain ?
Solution.— The product of 6 ft. x 5 x 4 = 120 cu. feet ; and 120 x
1728 = 207360 cu. inches. Again, in 1 gallon there are 231 cu. inches,
and 207360-^-231 = 897f* gal., Ans. (Art. 69.)
7. How many bushels will a box 8 ft. long, 4 ft. wide and
3 ft. high contain?
Solution.— 8 x 4 x 3 = 96 cu. ft. and 96 x 1728 = 165888 cu. in. Since
2150.4 cu. in.=: 1 bu., 165888 cu. in. = 165888^-2150.4 = 77$ bushels., Ans.
Hence, the
Eule. — Find the number of cubic inches in the object
measured, and reduce them to liquid or dry measure, as
may be required. (Arts. 69, 71.)
8. How many gallons would a cistern 7 ft. long by 6 ft.
wide and 11 ft. deep contain ?
9. At 30 cts. a square yd., what would be the cost of plaster-
ing the bottom and sides of such a cistern ?
Measurement of Lumber. 71
10. If a reservoir 45 ft. long, 28 ft wide, contains 45360 hhd.,
how high must it be ?
n. At $1.12! a bushel, what is the value of a bin of wheat
9 ft. long, 7 ft. wide, and 4 ft. deep ?
12. A farmer had a bin 8 ft. long, 4£ ft. wide, and 2£ ft.
deep, which held 67| bu.; how deep should another bin be
made which is 16 ft. long, 4£ ft. wide, that its capacity may be
460 bushels ?
13. How many hogsheads of water will a cistern hold, which
is 5 ft. 6 in. square and 8 ft. deep ?
MEASUREMENT OF LUMBER.
186. A standard Board Foot is 1 ft. long, 1 ft. wide, and 1
in. thick ; that is, a square foot 1 inch thick. Hence,
A Cubic Foot is equal to 12 board feet.
187. A Board Inch is T V of a board foot ; that is, 1 inch
long by 12 inches wide and 1 inch thick. Hence, Twelve
board inches are equal to 1 board foot.
188. Sawed timber, as plank, joists, etc., is estimated by
cu. feet ; hewn timber, as beams, etc., either by board feet or
cu. feet; round timber, as masts, etc., by cu. feet.
189. To find the Contents of Boards, Planks, etc.
1. How many board feet in a board 13 ft. long, 18 in. wide,
and 1 inch thick ?
Explanation. — Multiplying the length operation.
in feet by the width and thickness expressed 13 X 18 X 1 =■ 234 in.
in inches, we have 234 board inches. Divid- 234-^12 = 19i ft.
ing this product by 12, the result is 19.1 board . i qi -Pf
feet, Ans. MS ' L ^ U '
2. How many board feet in a scantling 14 ft. long, 6 in.
wide, and &| in. thick ?
Solution.— Multiplying the length in feet by the width and thickness
expressed in inches, we have 14x6x2§ = 210 in., and 210 + 12 = 17£
board ft., Ans. Hence, the
72 Weights and Measures.
Rule. — Multiply the length in feet by the width and
thickness expressed in inches, and divide the product by
12 ; the quotient will be in board feet.
Notes. — 1. The standard thickness of a board is 1 inch. If less than
1 inch, it is disregarded ; if more than 1 inch, it becomes a factor in find-
ing the contents of plank, scantling, etc.
If one of the dimensions is inches, and the other two are feet, the
'product will be in Board feet.
2. If a board is tapering, multiply the length by half the sum of the
two ends
3. The approximate contents of round timber or logs may be found by
multiplying | of the mean circumference by itself, and this product by the
length.
3. How many feet in a board 14 ft. long and 18 in. wide,
and of standard thickness ?
4. Find the contents of a tapering board 15 ft. long, 16 in.
wide at one end and 11 in. at the other ?
5. What cost 125 boards 11 ft. long, and 15 in. wide, at 4£
cents a board foot ?
6. What cost 28 joists whose dimensions are 4 in. by 3J in.
and 11 ft. long, at 25 cts. a cu. foot?
7. How many cu. feet in a log 65 ft. long, whose mean
circumference is 12 ft. ?
8. How many cu. ft. in a beam 24 ft. 6 in. long, 1 ft. 9 in.
wide, and 1 ft. 2J in. thick ?
9. How many feet of boards would be required to build a
fence 4 ft. high and 126 ft. long, and what would be the
expense at $2£ for 100 feet?
10. What cost a ship's mast 56 ft. long and 9 ft. in circum-
ference, at $1. 12 J per cu. foot ?
11. How many boards 12 ft. long and 4 in. wide are required
for a floor 36 ft. by 27 ft. ?
12. How many feet of boards would be needed to make 9
piano boxes, the interior dimensions of which are 6 ft. 8 in.,
5 ft. 7 in., and 3 ft. 6 in. respectively, the boards being 1 J in.
thick ?
Masonry. 73
MASONRY.
190. Stone Masonry is usually estimated by the perch ;
Brickwork by the thousand bricks.
Notes. — 1. A perch of stone masonry is 16| ft. long, \\ ft. wide, and
1 ft. high, which is equal to 2 4 J cu. ft. It is customary, however, to call
25 cu. ft. a perch.
2. The average size of bricks is 8 in. long, 4 in. wide, and 2 in. thick.
In estimating the labor of brickwork by cu. feet, it is customary to
measure the length of each wall on the outside ; no allowance being made
for windows, doors, or corners. But a deduction of ^ the solid contents
is made for the mortar.
1. In the walls of a cellar, the thickness of which is 1 ft. 6 in.,
the height 8 ft., each side wall 52 ft., and each end wall 25
ft. ; how. many perch (25 cu. ft.) ?
2. At I4.87J a perch, what will it cost to build the walls of
the above cellar ?
3. How many bricks are required for a building the walls
of which are 58 ft. long, 25 ft. wide, 44 ft. high, and 1 ft. thick,
making no allowance for windows, doors, corners, or mortar ?
4. At $3.75 per M. for bricks, and $4.25 per M. for laying
them, deducting ^ for mortar, what will the walls of such a
building cost?
APPLICATIONS OF UNITED STATES
MONEY.
191. United States Money is added, subtracted, multiplied,
and divided like Decimal Fractions, and requires no special
rules.
1. A man has farms valued at $56850, city lots at $86960, a
house worth $12800, and other property $8750 ; what is the
whole worth? Ans. $165360.
2. If a student's expenses are $198 for board, $37.50 for
clothes, $150 for tuition, $35.87 for books, $27.37£ for inci-
74 United States Money.
dentals, annually, what would it cost a year to educate 4 boys
at the same rate ?
3. The cost of laying the Atlantic Cable was as follows :
2500 mi., at $485 per mile ; 10 mi. deep sea cable, at $1450 ;
25 mi. shore ends, at $1250 ; what was the whole cost ?
4. Bought wheat at 94 cts. a bushel to the amount of
$59.22, and sold for $70.56; what was the selling price per
bushel ?
5. In selling 86.55 tons of coal, at $5. 64 per ton, a merchant
made $100.63 ; how much did it cost him a ton ?
6. Paid $2225 for 180 sheep, and sold them for $2675 ; what
should I gain on 1500 sheep at the same rate ?
7. A man bought an acre of land for $1250 ; he afterwards
sold 100 ft. square for $1000, and divided the remainder into
lots of 25 x 100 ft., which were sold at $500 each ; how many
lots did he sell, and how much did he make in the transaction ?
METHODS BY ALIQUOT PARTS.
50 cts. = $4. 12J cts. s= $4. 40 cts. ss $|
334 cts. = $f 10 cts. ss $ 1 l 37J cts. = $|
25 cts. sa $J. Si cts. = $ T V 62J cts. = !
20 cts. ss $-§. 6£ cts. = $^g-. 75 cts. = I
16 1 cts. = $f 5 cts. s= $^. 87 J- cts. = I
192. To find the Cost of a number of like things, when the
Price of one is an Aliquot Part of $1.
8. At 33 J cts. each, what cost 576 Grammars?
Analysis.— At $1 each they would cost $576; but the 3 ) 576
price is 33J cts. = $^, and 576-J-3, or x| = 192. Hence, the jins. $192
Eule. — Multiply the given number of things by the
fractional part of $1 which expresses the price of One;
the result is the cost. (Complete Grad. Arith., Art. 208.)
9. What cost 17 chests of tea of 59 lbs. each, at 33| cts. a
pound ?
Aliquot Parts. 75
10. Sold 18 bbl. pork of 200 lb. each, at 12£ cts. a pound ;
what did it come to ?
11. Find the cost of 158 tons coal, at $5.33£ a ton.
12. 170 lb. soap, at 8 J cts. a pound.
13. 264 lb. raisins, at 25 cts. a pound.
14. 295 lb. 8 oz. butter, at 33| cts. a pound.
15. 756 yd. calico, at 20 cts. a yard.
16. 275 doz. eggs, at 12£ cts. a dozen.
17. 1260 pine apples, at 16f cts. a piece.
18. What cost 4 lb. 5 oz. 6 pwt. of gold dust, at 75 cts. a
pennyweight ?
19. A man gave 87-J cts. a sq. rd. for 503 A. of land; what
did it cost him ?
20. What would be the cost of enclosing a square lot of 160
acres with a fence costing 75 cts. a yard ? (Art. 621.)
193. To find the Number of Like Tilings when their Cost
is given, and the Price of One is an Aliquot Part of $1.
21. How many pounds of coffee at 33J cts. a pound can be
bought for $84.50?
Analysis. — Since the price is %\ a operation.
pound, $1 will buy 3 pounds, and $0.33^ = $J
$84.50 will buy 84.50 x 3 = 253.5 lb. 84 50 x 3 = 253 5
Or, at §1 a pound $84.50 will buy as Qr m / 5Q ^ $i _ gg^g lb .
many pounds as $| is contained times 6
in $84.50, or 253.5 pounds, Ans. Hence, the
Rule. — Divide the cost of the whole by the aliquot part
of $1 ivhich is the price of One.
22. How many lb. butter at 33-J- cts. can be bought for 56 lb.
tea, at 62£ cts.
23. What cost 3 bu. 2 pk. 3 qt. of peas, at 87J- cts. a peck ?
24. If a man can pay 62-J cts. on a dollar, how much can he
pay with $1352.50 ?
76 United States Money.
25. Bought 14 bbl. salt of 4 bu. each, at $1.40 a barrel, and
sold it at 10 cts. a peck ; what was the gain ?
26. At 6J cts. a foot, how many planks each measuring 26 ft.
9 in., can be bought for $36.78£?
27. How many bales of cotton of 450 lb. each, at 37J cts. a
pound, are equal in value to 15 hhd. sugar of 1800 lb. each, at
8-J cts. a pound ?
194. To find the Cost of a number of articles, the Price of
one being $1 plus an Aliquot part of $1.
28. At $1.25 a bu., what cost 568 bushels of wheat ?
Analysis.— At $1 a bu., the cost would be $568. 4 ) ^68
But the price is $1£, therefore 568 bu. will cost 568+ 142
143 (i of 568) = $710. Hence, the |^ 10 j_ ngt
Rule. — To the number of articles, add its proper frac-
tional part ; the sum will be their cost.
29. At I1.37J- per sq. rd., what cost 263 A. of land ?
30. Bought in Michigan 300 bu. of oats, at 1\ cents a
pound ; what did they cost ? (Art. 72.)
31. Bought in New York 286440 lb. wheat, what is its value
at$1.87iabushel?
195. To find the Cost, when the price per 100 or 1000 is given.
32. What cost 2925 lb. sugar, at $12.50 a hundred ?
Solution.— 2925 lb.=Yinr of 100 lb., and ??=Lj£— = $365. 62|, Arts.
33. At $4.33£ per M., what cost 2367 bricks ?
Solution.— The price per M. = $4^; then 3)2367
(2367 x 4 ) + (2367-^3) _ 4
looo- -- cost ^
Or, multiply the number of bricks by 4, add \ of ~oq
the same number to the product, and divide by 1000
by pointing off 3 figures in the result. Hence, the $10,257
Aliquot Farts. 77
Kule. — Multiply the price per hundred or thousand by
the given number of things, and divide the product by
100 or 1000, as the case may require. (Art. 10, 4°-)
Note. — In business transactions, the letter C is put for hundred; and
M for thousand.
34. What cost 536720 bricks, at $8.75 per M.?
35. What cost 125268 feet of boards, at $31.25 per thou-
sand ?
36. At $5f per hundred, how much will 25345 pounds of
flour come to ?
196. When the cost of 100 or 1000 articles, pounds, etc. , is
given, the price of one is found by simply removing the decimal
point in the given cost or dividend, as many places to the left as
there are ciphers in the divisor. (Art. 264, Com. Grad. Arith.)
37. If pine boards are $21.63 per 1000 ft., what is that per
foot? Ans. $.02163.
38. Bought wheat in N. Y. at $3.1 2 \ a cental ; what would
6410§ bu. cost at the same rate ?
39. If 12£ cw.t. of sugar cost $140, what is that a pound ?
197. To find the Cost, when the price of a ton of 2000 pounds
is given.
40. What cost 5460 pounds of hay at $8.50 per ton ?
Explanation.— At $8.50 a pound, 5460 lb. will 5460
cost $46410. But the price is per ton of 2000 lb. ; § 5q
therefore dividing by 2, and removing the decimal
point 3 places to the left, will give the answer. 2000 ) 46410 .00
Hence, the £ nSm $23,205
Eule. — Multiply the price of 1 ton by the given num
ber of pounds and divide the product by 2000.
41. What is the freight, at $5.40 per ton, on an exportation
of 9654 pounds of cotton ?
42. Bought 26 sacks of wool, weighing 560 lb. each, at $26.50
per ton ; what did it cost ?
78
United States Money.
BILLS OF MERCHANDISE.
198. A Bill is a written statement of goods sold, or services
rendered, with their prices, etc.
Note. — Bills should always state the names of both parties, the place
and time of each transaction, the name and price of each item, and the
amount.
199. A Bill is Receipted when the words " Received Pay-
ment" are written at the bottom, and it is signed by the
creditor, or by some person duly authorized.
Exam ples.
Copy and extend the following bills :
(l. Bill of Dry Goods.)
Boston, Jan. 28th, 1883.
Mr. James Mitchell,
BoH of W. Starbuck & Co.
(Cash after 30 days.)
23 yds. silk
15 yds. broadcloth,
23 yds. cambric,
13 doz. buttons,
26 skeins sewing silk,
14 yds. wadding,
47 yds. bl. muslin,
35 yds. Can. flannel,
42 yds. calico,
12 doz. Brooks' cotton,
} doz. fancy hose,
8 pr. kid gloves,
@ $2.12}
@ 3.75
@ .12}
@ .25
@ .06J
@ .08
@ .12
@ .14
@ .12}
@ 1.08
@ 10.00
@ 2.00
Amount, - -
Bec'd PayH,
W. Starbtjck & Co.
Bills of Merchandise.
79
(2. Books.)
Messrs. J
New York, May 15th t 1883.
C. Griggs & Co.,
To Clark & Maymrd, Dr.
1883.
May
1
For 150 U. S. Histories, © I0.62J
« 72 Rom. " @ 1.15
" 96 Grammars, @ .65
" 200 Com. Graded Arith., @ .75
" 125 Prac. Algebras, @ .83
" 65 Col. " @ 1.05
" 84 Physiologies, @ 1.10
Amount, - -
Redd PayH,
By Draft on Boston,
Clark & Maynard.
(3. Statement of Account.)
San Francisco, Oct. 3, 1882.
Messrs. Robert Standart & Brother,
In Acct. with Scott & Merwin, Dr.
1882.
June
4
a
15
July
Aug.
Sept.
8
10
20
July
1
20
Aug.
Sept.
10
25
165 tons R.R. iron,
25 cwt. Steel Wire,
48 doz. Axes,
125 Saws,
342 cwt. Lead,
$45.25
21.50
10.40
3.75
7.40
Or.
500bbls. Flour, @ 5.40
456 bu. Wheat, @ 1.17
Dft. on JSTew York,
112 shares Mining Stock, @ 75.00
Bal. due, - -
Rec'd PayH,
Scott & Merwin,
400
Per Charles Kingsford.
80
United States Money.
Entry Cler k s Drill.
200. Enter the following memorandum, made at Detroit,
Mich., and find the amount of the bill :
Mem.— A. B. bought of 0. D., Apr. 15th, 1883, 624 lbs. Java
coffee, at 25 cts. ; 420 lbs. green tea, at 75 cts. ; 648 lbs. gran-
ulated sugar, at 12£ cts.; 528 lbs. brown do., at 6J cts.;
350 lbs. bar-soap, at .05; 428 gal. linseed oil, at 87| cts.
Common Form
Messrs. A. B.,
Detkoit, Mich., Apr. 15th, 1883.
Bought of C. D.
624 lbs. Java Coffee, @ 25 cts.
420 lbs. Green Tea, @ 75 cts.
648 lbs. Granulated Sugar, @ 12 j- c.
528 lbs. Brown " @ 6£ c.
350 lbs. Bar Soap, @ 5 cts.
428 gal. Linseed Oil, @ 87£ c.
Amount, - -
Redd Pay%
5. W. A. Sanford, Esq., of Philadelphia, bought, June 3d,
1883, of James Conrad, 28 yds. of silk, at $1.75 a yard; 42
yds. of muslin, at 56 cts. ; 16 pairs of cotton hose, at 87J cts.;
35 pair of silk hose, at $2.10; and 25 pair of shoes, at $3.25.
What was the cost of the several articles, and how much is
due on his account ?
6. Holmes & Homer of Cincinnati, bought, July 1st, 1882,
of H. W. Morgan & Co., 100 bbls. flour, at $5.50 a barrel;
50 bbls. pork, at $8.25 ; 25 bbls. beef, at $9.75 ; 112 kegs of
lard, at $3.25 ; and 25 bu. corn, at 74 cts. What was the cost
of the several articles, and how much is due on his account ?
^^ r° » ...
EROENTAGE.
201. Percentage is the method of calculating by hundredths,
202. The term Per Cent (from the Latin per and centum),
means by the hundred, or simply hundredths.
203. The Rate Per Cent is the number of hundredths to be
found or taken. It may be expressed by the sign %, by a deci-
mal, or by a common fraction.
Table.
Sign.
Decimal.
Fraction.
Sign.
Decimal.
Fraction
1%
.01
=3
TOO"
i%
.005
— T0~0
5%
.05
=
*
H%
.025
= A
Wo
.10
=
tV
Wo
.0025
— loo
25%
.25
=
i
H%
.0625
= A
50%
.50
=s
i
m%
.1875
= A
75%
.75
=
f
3H%
•33i
= i
100?/
1.00
=
i
im%
1.125
= H
204. Since hundredths occupy two decimal places, every
per cent requires, at least, two decimal figures. Hence, if the
given per cent is less that 10, a cipher must be prefixed to the
figure denoting it. Thus, %% is written .02; 6%, .06, etc.
Notes. — 1. A hundred per cent of a number is equal to the number
itself; for }£§ is equal to 1.
2. In expressing per cent, when the decimal point is used, the words
per cent and the xigit (</ c .) mast be omitted, and vice versa. Thus, .05 de-
notes 5 per cent, and is equal to y|}, r or .;„ ; but ,03 per cent or ,00 %
denotes -fa of jfo and is equai to jjfa or ¥ ^,
6
82 Percentage.
205. To read Per Cent, expressed Decimally.
Call the first two decimal figures per cent; and those on the
right, decimal parts of 1 per cent.
Note. — Parts of 1 per cent, when easily reduced to a common fraction,
are often read as such. Thus, .105 is read 10 and a half per cent; .0125 is
read one and a quarter per cent.
Read the following as rates per cent :
1. .06; .052; .085; .094. 4. .121; .08£; .16|; .5775.
2. .012; .174; .0836; .154. 5. 1.07; 2.53; 4.65; 2.338.
3. 5.33J; 4.125; 8.0623. 6. .1857; .2352; .7225.
206. To change a Per Cent to a Common Fraction.
7. Change 35%' to a common fraction.
Solution.— 35% = .35 and T ^% = fa Ans. Hence, the
Rule. — Write the per cent for the numerator and 100
for the denominator, and reduce it to lowest terms.
207. Express the following by Com. Frac. in lowest terms :
8. 5%. 10. 30^. 12. 50%. 14. 100$.
9. 6%. 11. 25$. 13. 15%. 15. 125$.
16. To what common fraction is 6|$ equal ?
Analysis.-6|% = j& ; ^ x T ^ = flfc, or T \, Ans. (Art. 203.)
17. What fraction = 5 ±%? 26J$ ? 36#g? 28^? 12^?
10f$?
208. To change a Common Fraction to an equivalent Per Cent.
18. What per cent of a number is f ?
Analysis.— Every number is 100 % of itself, hence § 8)5.00
of 100% = 500 -h 800, or 5 h- 8 = ,62|, or 62^ f , Ans. J_ns~^
Hence, the
Percentage. 83
£ule. — Annex ciphers to the numerator, and divide it
by the denominator. (Complete Graded Arith., Art. 249.)
19. Change f ■$■ to an equivalent per cent.
Ans. .60, or 60^. (Art. 208.)
20. H = ? 22. fj = ? 24. If = ? . 26. f« = ?
21. « = ? 23. ,ft=? 25. - 2 Vo=? 27. iff = 5
209. The Parts or Elements employed in calculating per-
centage are the Base, the Bate per cent, the Bercentage, and
the Amount or Difference.
210. The Base is the number on which the percentage is
calculated.
211. The Kate or Rate per cent is the number of hun-
dredths of the base to be taken.
212. The Percentage is the part of the base indicated by the
rate per cent.
Thus, when it is said that 4% of $50 is $2, the base is $50, the rate .04,
and the percentage $2.
213. The Amount is the sum of the base and percentage.
214. The Difference is the base less the percentage.
Thus, if the base is $75 and the percentage $4, the amount is $75 + 4
= $79 ; the difference is $75— $4 = $71.
The relation between these parts is such, that if any two of
them are given, the other three may be found.
215. To find the Percentage, the Base and Rate being given.
28. What is 8% of 2346 ?
Solution. -The Base 2346 x .08 (rate) = 187.68, Percentage. Hence,
the
Rule. — Multiply the base by the rate, expressed, in
decimals.
84 Percentage.
Formula.— Percentage = Base x Rate.
Notes. — 1. Finding a per cent of a number is the same as finding a
fractional part of it. (Complete Graded Arith., Art. 208.)
2. When the rate is an aliquot part of 100, it is advisable in most cases
to take the parts of the base denoted by the corresponding fraction. Thus,
for 88£% take |, etc.
3. When the base is a compound number, the lower denominations
should be reduced to a decimal of the highest ; or the whole number to
the lowest denomination ; then apply the rule.
29. What is 5% of £28 10s. lid.
Solution.— £28 10s. lid. = £28.55, 'and £28.55 x. 05 = £1.4275, or £1
8s. 6|d., Ana. (Arts. 151, 153.)
30. 6% of 7850 = ? 34. 12% of 6785 = ?
31. 7% of 8375 = ? 35. 75^ of 9863 = ?
32. 8% of 5873 = ? 36. 100% of 6842 = ?
33. 9% of 3482 = ? 37. \%±% of 48 lb. 3 oz. = ?
38. 8$% of 3$ A. 16 sq. r. = ?
39. What is the difference between h\% of $800 and §\% of
$1050 ?
40. What is 9f % of 275J miles ?
216. To find the Hate, the Base and Percentage being given.
41. What per cent of 80 is 36 ?
Analysis.— Since percentage is the product of base x 80 ) 36.00 P.
rate, the percentage 36-^80 (the base) = .45, the rate. ^^ ~ -^
Hence, the
BULB. — DUM& the percentage by the base. (Complete
Graded Arith., Art. 119, a.)
Formula.— Rate = Percentage -4- Base.
42. What % of £28 is 16s. ? Ans. 2%%. (Art. 152, N.)
43. Of $250 is- $12? 46. Of 523 is 32?
44. Of 365 yd. is 28 in. ? 47. Of 875 is 33| ?
45. Of 500 A. is 25 A.? 48. Of 68 is m?
Percentage. 85
49. Of 26 lb. 9 oz. is 12 pwt. ? 52. Of 83 is 8| ?
50. Of 475 is 175 ? 53. Of 75 is 2| ?
51. Of 654 is 62 ? 54. Of 99 is 9J ?
55. A man bought 350 A. of land, at $40 an acre, and sold
part of it for $2240 at the same rate ; what per cent of the land
did he sell ?
56. An agent received $67.50 for collecting $4500 ; what
per cent was his commission ?
57. Bought sugar for $150 and sold it for $167.50; what
per cent was the gain ?
58. A merchant owes $8250, his assets are $3240 ; what per
cent of his debts can he pay ?
59. Sold i A. of land for what the whole cost ; what was the
per cent gain ?
60. What per cent of 365 days are 30 days ?
61. Bought a number of eggs, and sold 11 for the money
paid for 18 ; what per cent was the gain ?
217. To find the Base, the Rate and Percentage being given.
62. $500 equal 20% of what number ? .20 ) $500. 00 P.
Analysis.— Since the percentage $500 is a pro- ^ns. $2500 B.
duct of which the rate .20 is a factor, $500-h.20 Or 20% = }, and
= |2500, the base required. Hence, the $500 -h-V — $2500.
Eule. — Divide the percentage by the rate.
Formula. — Base = Percentage -f- Rate.
63. 184 is 12£% of what number?
Ans. 1472. (Complete Grad. Arith., Art. 217.)
64.
245 = 6% of ?
70.
$68.25 = \%\% of ?
65.
1248 = 10$ of ?
71.
£248 6s. = \% of ?
66.
967 = 1% of ?
72.
$250.60 = \% of ?
67.
863 == 33^ of ?
73.
1250 = \% of ?
68.
8721 = 6i% of ?
74.
450f as 125% of ?
69.
7500 = \% of ?
75.
96| = 150^ of ?
86 Percentage.
76. Paid $50 a month for house-rent, which was 9$ on the
value of the house ; what was it worth ?
77. An owner of a ship sold 25$ of it for $5250 ; what was
the ship worth ?
78. A man paid $150 for insurance on his house, which was
2J$ on the sum insured ; for how much was it insured ?
79. A grocer sold §\ cwt. sugar, at $8J per cwt., and lost
thereby 12$ ; what was the cost ?
218. To find the Base, the Amount or Difference and the Rate
being given.
80. What number increased by 15$ of itself is 4600 ?
1 + .15 =1.15
Analysis.— Since 4600 - 100% +15%, it must be -i i k \ Apac) 00
115% of the number, and 4600-^-1.15 = 4000. > +PUU. UU
Ans. 4000
81. What number diminished by 25$ of itself is 4560?
Analysis.— Since 4560 = 100% -25%, it must be 1 — ,35 = ' 75
75% of the number, and 4560-=-.75 = 6080, the num- .75 ) 4560.00
ber required. Hence, the j^T qqqq
Eule. — Divide the amount by 1 increased by the rate.
Or, Divide the difference by 1 diminished by the rate.
„ d _ i Amount -j- (1 -f Rate).
~ \ Difference -^ (1 — Rate).
What number plus What number minus
82. 12f$ of itself = 24129 ? 86. 36% of itself = 3360 ?
83. 10$ of itself = 1540 ? 87. 5$ of itself = 3078 ?
84. 33J% of itself = $3680 ? 88. 25$ of itself = 450 ?
85. 25$ of itself = 5000 ? 89. 7-|$ of itself = 6475 ?
90. Sold 1900 bbl. flour for $11520, which was 20$ above
cost ; what was the whole cost and the cost per barrel?
Percentage. 87
91. A dealer sold 1600 bbl. beef for $24000, which was a
loss of 25$ ; what did the whole cost, and what did he get a
barrel ?
92. A builder sold a house for 18250, which was 12$ more
than it cost him ; what was the cost?
Exam ples.
1. What is the cost of a house which sells at a loss of 7£$,
the selling price being $11500 ?
2. A merchant owes $12575, and his assets are $7500 ; what
per cent can he pay ?
3. Sold 2 city lots at $1500 each ; on one I made 15$, on
the other I lost 15$ ; what did I gain or lose ?
4. If 15$ of what is received for goods is gain, what is the
gain per cent ?
5. Sold goods for $29900 and made 15$ after deducting 5$
for cash ; what was the cost?
6. 240 is 33^$ more than what number ?
7. A collector who has 8$ commission, pays $534.75 for a
bill of $775 ; what amount of the bill does he collect ?
8. What is \% of $1728?
9. What is 9|$ of 275 miles?
10. What is the difference between 5£$ of $800 and 6£$
of $1050 ?
11. Bought 300 long tons coal at $3.75 a ton and sold it at
$4.60 a short ton ; what is the per cent profit ?
12. Bought a barrel of syrup for $20 ; what must I charge a
gallon in order to gain 20$ on the whole ?
13. Sold 25 tons coal at $5.64 per ton, and made $62; what
did the coal cost, and what per cent was the profit ?
14. A quarter section of land was sold for $4563, which was
8$ less than cost,; what was the cost per acre ?
15. What $ of a number is 25$ of 3 fourths of it?
16. \% of 1258 is \% of what number?
17. What % of a number is 20$ of f of it ?
88 Percentage.
APPLICATIONS OF PERCENTAGE.*
PROFIT AND LOSS.
219. Profit and Loss are gain or loss in business transac-
tions. They are calculated by percentage.
The cost is the base ; the per cent of gain or loss, the rate ;
the gain or loss, the percentage ; the selling price, the cost,
plus or minus the gain or loss.
1. A man paid $650 for a carriage, and sold it for 8% more
than it cost him ; what was his profit ?
Analysis.— 8% = .08, and $650 x .08 = $52.00, Arts.
2. A musician bought a piano for $570, and sold it for
$624.15 ; what per cent was his profit ?
Analysis. — $624.15 - $570 = $5415 (gain), and $54.15 -f- 570 = .095,
or9|%, Ans.
3. A provision dealer made $500 on a cargo of flour, which
was 20$ of the cost ; what was the cost ?
Analysis.— Since $500 are 20% of a number, 1% of that number is
*V of $500 = $25, and 100% is $25 x 100 = $2500, Ans.
Or, since $500 = £ (20%), f = $500 x 5 = $2500, Ans.
4. A merchant tailor sold a quantity of goods for $750, on
which he made 25$ ; what did the goods cost him ?
Analysis.— $750 is the cost +25% of itself; and $750 -f- 1.25 = $600
the cost, Ans.
5. A grocer sold a quantity of damaged goods for $400, which
was 20$ less than cost ; what was the cost ?
Analysis.— $400 is the cost -20% of itself, and 100% -20% = .80,
$400^-. 80 = $500, the cost, Ans.
* The Applications of Percentage in business transactions are numerous and impor-
tant. Special pains should therefore be taken to have the subject thoroughly under-
stood.
Trade Discount. 89
Or, | - \ (20 f ) = % ; since § = $400, \ = $100, and | = $500.
(Art. 215, N. 2.) Hence, the
" Profit or Loss = Cost x Bate.
Bate = Profit or Loss -^ Cost.
Formulas.— { Cost = Gain or Loss -j- Bate.
j Selling Price -f- (1 -f Bate), or
" [ Selling Price -r- (1 — Bate).
Note.— It often shortens the process to take the fractional part of the
base, indicated by the given per cent.
TRADE DISCOUNT.
220. It is customary for merchants and manufacturers to
have fixed price lists of their goods, and when the market
varies instead of changing the fixed price they change the rate
of discount. The fixed price is named the list price, and the
deduction made from it, is called the Trade Discount.
Note. — Profit and Loss are calculated on the actual cost of goods, or
sum invested ; trade discount on the list price.
221. Dealers usually announce their "terms" upon their
"bill heads" thus, Terms 3 months, or 30 days, less 5%;
terms 60 days, or %% discount in 10 days, etc.
Note. — When bills are paid before maturity, merchants usually
deduct the legal interest for the time, on amount of bill.
222. To find the Net Amount of Bills when discounts are
made.
l. A Bill of goods at list prices amounts to $105 ; what is
the net amount, the trade discount being 10^, and 5% off for
cash ?
Solution.— $105 x .10 = $10.50, and $105- $10. 50 s $94.50. Again,
$94.50 x .05 = $4,725, and $94.50 -$4,725 = $89,775, Ans. Hence, the
Eule. — Deduct the trade discount from the list price,
and from the remainder take the discount for cash.
90 Percentage.
Note. Observe that the first rate of discount only is deducted from
the list price, and the subsequent rates are deducted from the remainders.
The result is not affected by the order in which the discounts are taken.
2. What is the net amount of a bill of goods, the list price
of which is $435, sold 5$ off for cash, trade discount 8$?
3. Sold books on 3 mo. amounting to $854.75 at a discount
of 12$ from retail price, and 10$ off for cash ; what is the net
value of the bill ?
4. The gross amount of a bill is $236.37; the rates of
discount are 15$ and 8$ ; what is the net amount?
5. Find a direct discount equal to a discount of 12-§-$ and 8%.
Ans. 19£$.
Note. — To find a direct discount equal to two or more taken in
succession ; from the sum of two discounts subtract their product.
6. What direct discount is equal to a discount of 25$ and
17$?
7. On a bill of $625, what is the difference between a discount
of 30$ and a discount of 25$ and 5$ ?
8. Bought books at a discount of 20$ on the retail price,
and sold them at the retail price ; what per cent did I gain?
9. What per cent would I gain at a discount of 33£$ ?
10. With a trade discount of 8$ and 5$ for cash, goods
were sold for $825 at a profit of 15$ ; what was the cost ?
223. To Mark goods so that a given per cent may be deducted
and leave a given per cent profit.
11. Bought cloaks at $75.10; what price must they be
marked, that 15$ may be deducted and leaye 25$ profit ?
Analysis.— The selling price is 125% of $75.10, and $75.10x1.25 =
$93,875. But the marked price is to be diminished by 15% of itself, and
100%— 15% = 85% ; hence, $93,875 = 85% of the marked price. Now
$93.875^-. 85 = $110.44, the marked price. (Art. 217.) Hence, the,
Rule. — Find the selling price and divide it by 1 minus
the given per cent to be deducted ; the quotient will be
the marked price.
Commission and Brokerage. 91
12. A bookseller wishes to mark up the price of a book
which he now sells for £2, so that he can deduct \§% and yet
receive the present price ; what must be the marked price?
13. A merchant sells cloths for $268 by which he gains 23%;
how must he mark them so that he may deduct 4$ and make
the same profit?
14. Bought diamonds at $920 ; how must I mark the price
that after abating b% the profit may be 25% ?
15. What must be the price of an article from which you
deduct 20% and leave 20 cents ?
COMMISSION AND BROKERAGE.
224. Commission is an alloivance made to agents, collectors,
brokers, etc., for the transaction of business.
Brokerage is Commission paid a broker.
Guarantee is the % charged for assuming the risk of loss.
Notes. — 1. An Agent is one who transacts business for another, and is
often called a Commission Merchant, Factor, or Correspondent.
2. A Collector is one who collects debts, taxes, duties, etc.
3. A Broker is one who buys and sells gold, stocks, bills of exchange,
etc. Brokers are commonly designated by the department of business in
which they are engaged ; as, Stock-brokers, Exchange-brokers, Note-
brokers, Merchandise-brokers, Real -estate-brokers, etc.
225. Goods sent to an agent to sell, are called a Consignment ;
the person to whom they are sent, the Consignee; and the
person sending them the Consignor or Shipper.
226. The Gross Proceeds of a business transaction are the
whole sum received.
227. The Net Proceeds are the gross amount received, minus
the commission and other charges.
228. Commission and Brokerage ■ are computed by Per-
centage ; the money employed is the base ; the per cent for
services, the rate ; the commission, the percentage.
92 Percentage.
Note. — Brokerage is computed on the par value of stocks, bonds, etc.,
as the base.
1. Find Z\% commission on sales for $8168. (Art. 215.)
Am. $285.88.
2. What is the commission at %\% for selling 875 bushels of
wheat, at $1.25 ?
3. An agent collects $2850 ; how much does he pay to the
owner after deducting b% commission ?
4. A commission merchant sold goods amounting to
$2875.50 ; the charges were %\% com., %\% guarantee, cartage,
storage, etc., $18.50 ; how much was due the owner ?
5. Paid $375 to an auctioneer for selling a house ; his com.
being %\%, for how much did he sell it and what did the owner
receive? (Art. 217.)
6. An agent received $864 with which to buy goods ; he
was to have 2\% commission on the amount of purchase ; how
much was his commission and what the amount of purchase ?
7. A commission merchant received $654; he charged %\%
commission and *Z\%~ for guarantee ; what were the net
proceeds ?
8. An agent charged %% commission and $58.60 expenses
for selling a house, and sent the owner $16350 ; for what did
he sell the house ?
9. What is the brokerage, at \%> on the sale of stock, the
market value of which is $5250 ?
10. Paid a broker $25 for buying bank stock at par, com-
mission \% ; how much did he invest ?
11. The sum of $25365 sent to my agent, includes invest-
ment and commission at 3f % ; what is the investment ? What
is the commission ?
12. My agent bought tea at \% brokerage, and was paid
$450. He afterwards sold the tea at a profit to me of $6150,
deducting 1 \% commission on the sale ; how much was his
commission ?
13. A man wishes to draw on New York for an amount
sufficient to cover expenses of %% exchange and 2\% commis-
sion, and leave him the sum of $5242.50; for how much must
he draw ?
Brokerage. 93
14. What number diminished by ty% of itself is equal
to 895 ?
15. A bill of $875 was placed in the hands of a collector,
who obtained 75% of it and charged 8% commission ; how
much did the owner receive ?
16. A man invested $6350 in U. S. bonds at 105$, broker-
age 1 1%, and sold them at 115%, brokerage If % \ how much did
he gain ?
17. On what valuation is $18.25 the commission, at \% ?
18. On what sales is $825.50 the commission, at 7%%?
19. A merchant sold on a commission of 8^%, 200 bbl. pork,
each weighing 200 lb., at 12J cts. a pound ; what was the
amount of his commission, and how much did he remit to the
owner ?
20. A lawyer received $6.80, being 8% commission for col-
lecting a note ; what was the face of the note ?
21. A real-estate agent bought land for which he received
2|% commission for buying and $48.50 for charges. The whole
cost of land, commission, and charges was $8450 ; what was
paid for the land ?
22. A commission merchant sells 60 bbl. potatoes at $3.25 a
bbl., and 42 bu. beans at $2.50 a bu. ; how much is due the
consignor, the commission being 2f% ?
23. An agent who charged 2J$ for selling a house, paid the
owmer $12360 ; what did he get for the property?
24. On what amount of sales is $241.75 the commission, at
15%, after deducting $18.20 for expenses?
25. An agent received $67.50 for collecting $4500 ; what was
the rate ?
26. A man sends $3246.20 to an agent in Boston to buy
shoes, deducting his commission at 2% ; what was his com-
mission ? How much did he spend for shoes ?
27. A New York firm sell for me goods at 6% commission ;
how mucli must be sold that my broker can buy stock with
the proceeds to the value of $6250, after deducting his com-
mission of %\%t
28. A dealer in pork cleared $1565, charging 10%' commis-
sion ami paying $850 expenses of packing ; if the pork cost
him 7 cts. a pound, how many pounds did he pack ?
94 Percentage.
INSURANCE.
229. Insurance is security against loss. It is distinguished
by different names, according to the cause of the loss or the
object insured. Thus, Fire Insurance, Marine Insurance,
Accident, Health, Life Insurance, etc. (See Life Ins., Art, 566.)
Note. — Risks of transportation partly by land and partly by water, are
called Transit Insurance.
230. The parties who agree to make good the loss, are
called Insurance Companies or Underwriters.
Note. — When only a part of the property insured is destroyed, the
underwriters are required to make good only the estimated loss.
231. Insurance Companies are of two kinds: Stock Com-
panies and Mutual Companies.
232. A Stock Company is one which has a paid-up capital,
and divides the profit and loss among its stockholders.
233. A Mutual Company is one in which the losses are
shared by the parties insured.
Note. — Some companies combine the principles of Stock and Mutual
Companies, and are called Mixed Companies.
234. The Premium is the sum paid for insurance.
235. The Policy is the written contract between the insurers
and the insured. They usually run from one to five years.
236. A Valued or Closed Policy contains a certain fixed
value on the thing insured ; as of houses, goods, etc.
237. An Open Policy is one in which the value of the article
insured is to be determined in case of loss.
238. The rate of premium charged depends on the nature
of the risk and the time for which the policy is issued, the rate
for long policies being less than for short ones.
Insurance. 95
239. Rates for less than a year are called Short Rates.
Notes. — 1. Policies are renewed annually, or at stated periods, and the
premium is paid in advance. In this respect insurance differs from com-
mission, etc., which have no reference to time.
2. When a policy taken for a year is cancelled prior to the end of the
year, a Return Premium is paid to the party insured.
240. Premiums are computed by the rules of Percentage.
Rates of premium are a per cent of the sum insured, or a num-
ber of cents paid on $100.
Thus, 25 cts. on $100, is \ of 1 % ; 75 cts. on $100 is f % .
241. An Insurance Agent is a person who acts for Insur-
ance Companies iu obtaining business, collecting premiums,
adjusting losses, etc.
242. An Insurance Broker is a person who negotiates insur-
ance and receives a percentage from the company taking the
risk.
Note. — Insurance Brokers are regarded as agents of the insured.
243. The Surplus of an Insurance Company is the excess of
its assets above its liabilities.
244. To find the Premium, from the sum insured and the rate.
1. What is the premium for insuring a store and goods
valued at $12000, at \\% for 1 year ?
Solution.— $12000 x .015 = $180.00, Am. Hence, the
Formula.— Pr em i um = Sum In. x Rate. (Art. 215.)
2. What is the cost of insuring goods worth $4000, at
80 cents per $100, the policy and survey being $1.50 ?
3. If I take a risk of $12000 at a premium of 1|£, and re-\
insure it at \\%, what will be my gain ?
4. Insured a cargo from Liverpool worth £850 10s. 4d., at a
premium of \\%\ at $4.86 to the £, what is the premium in
U. S. Money?
96 Percentage.
245. To find the Rate, from the sum insured and the premiumc
5. A man paid $215 for insuring $8600 on a tenement house;
what was the rate ?
Solution.— $215. 00 h- $8600 = .025, or 2*-%, Ans. Hence, the
Formula. — Rate = Premium-?- Ami. Insured. (Art. 216.)
6. A grocer paid $40 annually for an insurance of $5000 on
his goods ; what was the rate?
7. If the owner pays $2800 for insuring a steamer worth
$42000, what rate per cent does he pay ?
8. Paid $25 for an insurance of $3000 ; what was the rate ?
246. To find the Sum Insured, when the premium and the
rate per cent are given.
9. A merchant paid $1200 premium, at 2\%, on a ship and
cargo from Liverpool to Baltimore ; it was lost on the voyage ;
what amount of insurance should he recover ?
Solution.— $1200.000-*-. 022 = $54545.455, Ans. Hence, the
Formula. — Sum Insured = Premium-?- Rate. (Art. 217.)
10. If I pay $254 premium on silks, from Havre to New
York, at 1\ per cent, what amount does my policy cover ?
11. A gentleman paid $62 annually for insuring house and
furniture, which was 2\% on half its value; what was its value ?
12. How much insurance can be obtained for $125 on a store
and contents, at 1-|% ?
13. Paid $287 to insure half the value of a cargo at 2f % 5
what was its total value ?
247. To find the sum to be insured to cover the value of the
goods and premium.
14. Goods bought in Paris for $7594, were insured at 2\% ;
what sum will cover the value of the goods and the premium ?
Anatasis. — The sum insured is 100% of itself, the premium is 21' < of
that sum, and 100% -24% = 97|%. Now $7594-:-. 97i = $7788.72, the
sum required. (Art. J518.) Hence, the
Formula. — Sum Insured == Value -f* (1 -— Rate),
Insurance, 97
15. If a warehouse is worth $266250, what sum must be
Insured, at %%, to cover the property and premium ?
16. What sum must be insured, at 3%, on a consignment of
tea worth $4200, to cover property and premium ?
17. A merchant sent a cargo of goods worth $25275 to
Canton ; what sum must he get insured at 3%, that he may
suffer no loss, if the ship is wrecked ?
18. The premiums paid for insuring two stores, are $98.25
and $146.50 ; the rate is lf% ; what sum must be insured to
cover the property and premium ?
Examples.
1. What is the annual premium on a policy insuring a house
for -jj- its value, at \% ?
2. If $125 are paid annually for insuring $24000, what is the
rate per cent ?
3. What premium must be paid for insuring $6500 on a
store for 3 years at %\% ?
4. A house is insured at f%, and the premium is $93.60;
for how much is it insured ?
5. A shipowner insures a ship and cargo for $89325, at 4-|%,
the policy covering both property and premium ; what is the
value of the property ?
6. What will it cost to insure a factory worth $26000 at \%,
and machinery worth $16800 at \%, with $1.50 for policy?
7. Paid $350 on a shipment of goods to insure \ the value,
at 2>\% ; what was the whole value ?
8. A company had $125 premium for insuring property worth
$18000 ; if similar property worth $45000 were insured at the
same rate in another company, what would be the premium ?
9. A dealer insured a stock of goods for 1 year, at \\%\ if
the short rate for 6 mo. was 83 cents on $100, and the policy
was cancelled at the end of that time, what should be the
return premium, the goods being insured for $3500 ?
Note. — Multiply the sum insured by the difference between the given
rates.
7
98 Percentage.
ADJUSTMENT OF LOSSES.
248. Losses may be partial or total.
In ordinary cases of partial loss, the insured is entitled to
indemnity only for the actual loss. If a total loss occurs, the
insurers pay the full amount of their policy.
249. If the policy contains the "Average Clause," the com-
pany pays only such a proportion of the loss as the amount
insured is to the value of the property insured.
Thus, a person who has a policy with the " Average Clause " for $1000
on property worth $2000, would receive
Note. — It is customary for Insurance Companies to reserve the right
to repair or replace the damaged property.
250. If the loss is partial, but amounts to more than half
the value of the property, the owner has the right to transfer
to the company what remains, and claim the full value of the
property.* This is called the right of abandonment, and the
company cannot refuse to take it, unless specially named in
the policy.
251. When a partial loss occurs to a vessel, the companies
pay such proportion of it as the sum insured is to the value of
the property. It is an established rule that one-third shall be
allowed the insurers for the superior value of the new material
used ; that is, " one-third off, new for old."
252. A total loss may be actual or constructive.
An Actual Total Loss is one by which the property insured
is entirely destroyed by fire or water. (Art. 230, N.)
A Constructive Total Loss is one in which some portions of
the property are saved, and are transferred by the insured to
the insurers by abandonment.
* American Cyclopedia,
Adjustment of Losses. 99
253. In such cases the insurers pay for the whole, and hold
the salvage or property saved as their own.
254. To estimate proportionate losses.
1. A merchant insured $2500 in a Mutual Co., $1500 in
the Howard, and $3500 in the Phoenix; a loss by fire of $6000
occurred ; how much should each company pay ?
Explanation. — The total sum insured was $2500 M.
$7500, the loss was $6000. Dividing $6000 by -^qq jj
$7500 gives 80 % , proportion of insurance to loss. 3500 P
Share of Mutual a $2500 x .80 = $2000.00, _oOW r.
of the Howard = $1500 x .80 = $1200.00, $7500 Sum Ins.
of the Phoenix - $3500 x .80 = $2800.00. 6000-^7500 = .80.
Hence, the
Kule. — Divide the loss by the total insurance, the quo-
tient will be the per cent which each must pay.
2. The loss by fire on a piece of property was $8000, of which
$2000 was insured in the Howard, $3000 in the Phoenix, and
$3000 in the Manhattan Company ; how much did each com-
pany contribute ?
3. The loss by fire on a store and contents was $4525 ; the
property was insured $2500 in Franklin Company, $4000 in
Mutual, $2000 in Phoenix, and $3000 in Hanover Company ;
how much should each pay ?
4. A shipment of silks valued at $25000 was insured for
$15000, with a policy containing the " average clause ;" if the
goods were damaged to the amount of $5000, how much would
be paid by the company ?
5. A cargo of oil worth $30000 was insured for 18 months at
%\% ; at the end of 12 months the policy was cancelled ; if the
short rate for 6 months was 65 cts., what should be the return
premium ?
6. A real-estate owner insured $75000 at the average rate of
\% a year for 12 years ; the entire property being at the end of
10 years destroyed by fire, the company paid the loss in full;
how much was the real loss to the company, the insurance
having been regularly paid ?
100 Percentage.
TAXES.
255. A Tax is a sum assessed upon the person, property, or
income of citizens.
256. A Property Tax is a tax upon property.
257. A Personal Tax is a tax upon the person, and is called
a poll or capitation tax.
Notes. — 1. A Poll Tax is a specific sum levied in some States upon all
male citizens not exempt by law, without regard to property.
2. In Mass. a poll tax is assessed on every male inhabitant above the
age of 20 years, whether a citizen of the U. S. or an alien. Rev. Stat.
258. A License Tax is the sum paid for permission to pur-
sue certain avocations.
259. Special Taxes are fixed sums assessed upon certain
articles of luxury ; as carriages, billiard tables, gold watches, etc.
Note — The Internal Revenue or Stamp Tax upon perfumery, watches,
proprietary medicines, etc., was repealed by Act of Congress in Oct. 1882.
260. Property is of two kinds, real and personal.
261. Real Estate is that which is fixed ; as, houses and
lands.
262. Personal Property is that which is movable; as, money,
stocks, bonds, mortgages, etc.
263. Assessors are persons appointed to make a list of
taxable property and fix its valuation for the purpose of
taxation.
264. A Collector is a person appointed to receive the taxes.
265. Property taxes are computed by Percentage.
266. An Assessment Roll is a list of all persons in the dis-
trict liable to be assessed, with their taxable property and its
valuation.
Taxes. 101
267. To Assess a Property Tax, when the sum to be raised and
the valuation of the property are given.
1. In a city whose property was valued at $2500000, a tax of
$15000 was levied ; there being 250 polls, each taxed $2, what
was the rate of the tax, and what A's tax whose real estate was
valued at $8000, and personal at $5000 ?
Explanation. — The sum to be raised is $15000 solution.
less $500 on the polls, equal to $14500 on the Town tax $15000
property; and $14500 -*- $2500000 = $.0058. or 5.8 p H « 500
mills on a dollar. OKnnnnn \ <i»i akcci
A's property is $8000 + $5000 = $13000. As he ^500000 ) $14o00
pays .0058 on $1, on $13000 he pays $13000 x .0058. Kate .0058
= $75.40 + $2 (poll tax) = $77.40.
Ans. The rate is .0058 and his tax $77.40. Hence, the
Rule. — I. From the sum to be raised subtract the poll
tax and divide the remainder by the amount of taxable
-property ; the quotient will be the rate.
III. Multiply the valuation of each man's property by
the rate, and the product plus his poll tax will be his
entire tax.
Note. — The commission for collecting taxes is commonly included in
the net sum to be raised.
2. A tax of $25250 was levied upon a township. The valua-
tion of its real estate was $1000000, the personal $400000, and
it had 500 taxable polls assessed at $1.50 each. What was the
rate of taxation, and what was A's tax whose real estate was
valued at $6000, personal property at $4000, and who paid for
two polls ?
Analysis. — Sum assessed on the polls = $1.50 x 500 = $750, and
$25250— $750 = $24500, sum assessed on property. Amount of taxable
property = $1400000, and $24500 -*-$ 1400000 = $.0175, or If %.
A's taxable property is $6000 + $4000 = $10000.
By the table the tax on $10000 = $175.
Tax on polls = $3, and $175 + $3 = $178, Ans.
3. For the purpose of grading a street, the property in a
certain locality was assessed at the rate of 6 mills on the dollar ;
what was a man's tax whose property was valued at $8500 ?
102
Percentage.
Tax Table.
Showing the tax on sums from $1 to $10000, at \\%.
Pbop.
Tax.
Pbop.
Tax.
Pbop.
Tax.
_ — ..,
Prop. Tax.
$1
10175
$10
$.175
$100
$1.75
$1000 $17.50
2
.035
20
.35
200
3.50
2000 35.00
3
.0525
30
.525
300
5.25
3000 52.50
4
.07
40
.70
400
7.00
4000 70.00
5
.0875
50
.875
500
8.75
5000 87.50
6
.105
60
1.05
600
10.50
6000 105.00
7
.1225
70
1.225
700
12.25
7000 122.50
8
.14
80
1.40
800
14.00
8000 140.00
9
.1575
90
1.575
900
15.75
9000 157.50
10
.175
100
1.75
1000
17.50
10000 175.00
4. What was B's tax whose real estate was valued at $8000,
personal $5000, and who paid for 3 polls ?
5. What is B's tax, the valuation of whose property is $4240,
and is assessed for 2 polls, at $1.50 ?
6. What is C's tax, who is assessed for 1 poll and whose
property is estimated at $31250 ?
7. D is assessed for $17225 and 1 poll ; what is his tax?
8. B is assessed for $28265 and 1 poll ; what is his tax ?
268. To find the Amount to be assessed, when the Net Sum
and the Rate for Collecting are given.
9. A union school district required $48355 to build a school-
house; what amount must be assessed in order to pay the
expense and the commission of 5% for collecting ?
Solution.— $48355-*- .95(1-. 05) = $50900, Ans. (Art. 218.)
Eule. — Divide the net sum by 1 minus the rate ; the
quotient will be the amount to be assessed. (Art. 218.)
Note. — The valuation = Amt. to be raised -=- rate.
10. What sum must be assessed to raise $12600 net, and
pay the commission at 4|$ for collecting ?
HTEEEST
(9-*-
269. Interest is the money paid for the use of money.
270. The Principal is the money for the use of which
interest is paid.
271. The Rate is the per cent of the principal, paid for its
use 1 year, or a specified time.
272. The Amount is the sum of the principal and interest.
273. Simple Interest is the interest on the principal only.
274. Legal Interest is the rate established by law.
275. Usury is a higher than the legal rate.
Table.
276. Legal rates of interest in the several States and Territories, com-
piled from the latest official sources. The first column shows the legal
rate of interest when no rate is specified ; the second the maximum rate
allowed by law.
States.
Rate%.
States.
Rate %.
States.
Rate %.
States.
Rate%.
Ala
Ark....
Arizona
Cal
Conn. . .
Colo....
Dakota.
Del
Flor. . . .
Ga
Idaho...
Ul
8
6
10
10
6
10
7
6
8
7
10
6
8
10
Any*
Any.
6
Any.
12
6
Any.
8
18
8
Ind. Ter
Ind. ..
Iowa . . .
Kan. . . .
Ky
La
Maine . .
Md.. ..
Mass.. .
Mich...
Minn . . .
Miss —
6
6
6
7
6
5
6
G
6
7
7
6
Any.
8
10
12
6
8
Any.
6
Any.
10
10
10
Mo
Montana
N. H. . . .
N. J
N. Mex..
N. Y....
N. a...
Neb
Nevada-
Ohio....
Oregon .
Penn. . . .
6
10
6
6
6
6
6
7
10
6
10
6
10
Any.
6
6
Any.
6
8
10
Any.
8
12
6
R.I
S.C
Tenn . . .
Texas . .
Utah. . . .
Vt
Va
W. Va..
W.T....
Wis
Wy
D.C....
6
7
6
8
10
6
6
6
10
7
12
6
Any.
7
6
12
Any.
6
6
8
Any.
10
Any.
10
* By special agreement.
104 Percentage.
211. Interest is an application of Percentage; the only dif-
ference is that the element of time is connected with the rate
per cent.
Note. — In computing interest, a legal year is 12 calendar months.
278. The Principal is the Base; the per cent per annum, or
a specified time, is the Rate; the Interest is the Percentage;
the Sum of the principal and interest, the Amount.
General Method.
279. To compute interest for any given time and rate.
l. What is the interest of $450 for 3 yr. 2 mo. 12 d. at 1% ?
Explanation. — First find the time by fractions.
in years and fractions of a year. Re- 12 d. = •£■§-, or | mo.
ducing the days to the fraction of a 2-1 mo.-^-12 = 4-| 01* -^j- yr.
month, if = f mo., then 2| mo. reduced 3 y r# 2 mo. 12 d. = 3.2 yr.
to the fraction of a year = £§ , or -^ yr.
Therefore, the time is 3.2 years. BT decimals.
30 12 d.
Or, finding the decimal of a year as in the margin, -j^ 24 mo.
the time is 3.2 yr., as before. (Art. 154.)
3.2 yr.
Multiplying the principal $450 by .07 = $31.50 int. 1 yr.
The interest for 1 yr. multiplied by 3.2 Time in years,
the number of years and decimals of $100.80, Ans.
a year gives the interest required. Hence, the
General Rule.
Multiply the principal by the rate ; the result will be
the interest for 1 year.
Multiply the interest for one year by the time in years
and fractions of a year ; the product will be the interest
required.
To find the amount, add the interest to the principal.
Notes. — 1. When a fraction occurs after finding two decimal figures,
it may be annexed to these figures as a part of the multiplier.
2. When the rate per month- is given, multiply the principal by the
rate per month, and that product by the number of months.
Interest. 105
280. The work may sometimes be shortened by multiplying
the principal by the product of the rate and time, instead of by
these factors separately. (Ex. 2.)
2. What is the interest of $530 for 2 yr. 3 mo. at 4% ?
Solution.— $530 x 4 = $21.20, and $21.20 x 8} (time) = $47.70.
Or, multiplying the principal by .09 (.04 x 2|) = $47.70, Ans.
3. What is the interest of $684.85 for 2 yr. 6 mo. 18 d.,
at 5%?
4. Find the interest of $3265.50 for 3 yr. 1 mo., at 8%.
5. Find the interest of $2866 for 5 yr. 3 mo., at Q%.
6. Find the interest of $3568 for 4 yr. 2 mo., at ty%.
7. Find the interest of $5465.60 for 3 yr. 4 mo., at §\%.
8. What is the interest on a note of $165, dated Jan. 4, 1880,
to Apr. 22d, 1882, at 6 per cent ?
Note.— From Jan. 4, 1880, to Jan. 4, 1882 = 2 yr.
From Jan. 4th to Apr. 4th = 3 mo.
From Apr. 4th to Apr. 22d = 18 d.
Time — 2 yr. 3 mo. 18 d.,or2.3yr.
9. W r hat is the interest of $270 from June 19, 1880, to July
1, 1881, at 1% ?
10. What is the interest of $205.63 from Jan. 22, 1879, to
Aug. 25, 1880, at 5%?
11. Find the interest and amount of $2500 for 1 yr. 3 mo.
12 d., at. 4±%.
281. Method by Aliquot Parts. (Arts. 192, 206.)
12. What is the interest of $870 for 3 yr. 4 mo. 15 d., at 1% ?
Explanation. — The given principal is
This multiplied by the rate .07 = $60.90 int. 1 yr.
For 3 years the int. is 3 times the int. for 1 yr. 3
4 mo. = \ yr., and 15 d. — } mo., and $182.70 Int. 3 yr.
$60.90 (int 1 yr.)-=-3 = int. for 4 mo. {\ oft yr.) = 20.30 int. 4 mo.
i of *20.30 = $5,075 (int. 1 mo.), $5,075-^2 = 2.5375 int. 15 d.
Total interest for 3 yr. 4 mo. 15 d. = $205.5375, Ans.
106 Percentage.
Rule. — For 1 Year. — Multiply the principal by the
rate.
For 2 or more Years. — Multiply the interest for 1 year
by the number of years.
For Months. — Take the aliquot part of 1 year's interest.
For Days. — Take the aliquot part of 1 month's interest.
Notes. — 1. For 1 month take ^ of the interest for 1 year ; for
2 months, £ ; for 3 months, |, etc.
2. For 1 day take fo of the interest for 1 month ; for 2 days, ^ ; for
3 days, fo ; for 6 days, ^ ; for 10 days, ^, etc.
3. In computing interest 30 days are commonly considered a month.
13. What is the interest of $1684 for 1 yr. 9 mo. 10 d., at 6% ?
14. Find the interest at 6% of $2340 for 1 mo. 15 days.
15. Find the interest at Q% of $8700 for 1 yr. 2 mo. 12 d.
16. Find the amount of $4470 for 10 d. at 4$.
17. What is the interest of $1234 from Apr. 10, 1874, to
Oct. 1, 1875, at 6% ?
18. What was the amount of $1895.23 from June 25, 1878,
to March 31, 1880, at 6%?
Find the interest at 6% on Find the amount at 7% on
19. $850, 1 yr. 3 mo. 15 d. 25. $1864, 2 yr. 8 mo. 5 d.
20. $689, 2 yr. 6 mo. 10 d. 26. $6500, 3 yr. 2 mo. 3 d.
21. $738, 2 yr. 4 mo. 12 d. 27. $1156, 11 mo. 20 d.
22. $358, 2 yr. 9 mo. 18 d. 28. $894, 1 yr. 6 mo. 3 d.
23. $755, 3 yr. 7 mo. 9 d. 29. $765, 2 yr. 4 mo. 20 d.
24. $468, 4 yr. 3 mo. 3 d. 30. $865, 3 yr. 2 mo. 15 d.
31. A note for $560.60, dated May 5, 1881, was paid Dec. 31,
1882, with interest at 1% ', what was the amount ?
32. If I have the use of $275 for 4 yr. 10 mo. 12 d. from
Jan. 12th, 1883, what amount must I return to the owner,
allowing 6% interest, and what will be the date of maturity ?
Interest. 107
Six Per Cent
Method.
282. At 6% the interest of $1
For 1 yr., or 12 mo., is 6 cts., ==
.06 of the principal.
For £ yr., or 2 mo., is 1 ct., =
.01 of the principal.
For T * ¥ yr., or 1 mo., is 5 m., =
.005 of the principal.
For ^ mo., or 6 d., is 1 m., =
.001 of the principal.
For -jV mo., or Id., is -J- m., =
.000£ of the principal.
Hence, the following
283. Principles.— 1°. The interest of Si at 6%, is half as
many cents as there are months in the given time.
2°. The interest of SI at 6%, is one-sixth as many mills as
there are days in the given time.
1. What is the interest of $1250.26 for 1 yr. 3 mo. 21 d., at
6% ? What is the amount ?
Explanation.— The int. of $1 for 15 m. = .075 $1250.26 Prin.
By 2°, int. of $1 for 21 d. = .0035 ^735 Int $1
Int. of $1 for 1 yr. 3 mo. 21 d. = .0785 625130
As the interest of $1 for the given time and 10.00208
rate is $.0785, the interest of $1250.26 must be Q7 *1 89
$1250.26 x .0785 = $98.14541 interest. — — -
The prin. $1250.26 + $98.14541 =$1348.40541, $98.145410, Ans.
Amount. Hence, the
Rule. — Multiply the principal by the interest of $1
for the given time and rate.
Notes. — 1. When the rate is greater or less than 6$, find the interest
of the principal at 6% for the given time ; then add to or subtract from it
such a part of itself, as the given rate exceeds or falls short of 6 per cent.
2. If the mills are 5 or more, it is customary to add 1 to the cents ; if
less than 5, they are disregarded.
3. Only three decimals are retained in the following Answers, and each
answer is found by the rule under which the Example is placed.
4. In finding the interest of $1 for days, it is sufficient for ordinary
purposes to carry the decimals to four places.
108 Percentage.
2. What is the int. of $6395 for 18 mo. 29 d., at 7% ?
3. What is the int. of $2745.13 for 3 mo. 17 d., at 5%?
4. What is the int. of $1237.63 for 18 mo. 3 d., at 8% ?
5. Find the amount of $2835.20 for 2 mo. 3 d., at 7%.
6. Find the amount of $4356.81 for 13 mo. 10 d., at §\%.
7. What is the interest of $520 from March 21, 1880, to
Dec. 30, 1882, at 7%?
8. At 6 per cent, what is the interest of $569.65 from
August 10th, 1882, to Feb. 6th, 1884 ?
9. At 7 per cent, what was the amount due on a note of
$385, dated March 15th, 1880, and payable Sept. 18th, 1881 ?
Find the int. at 6% Find the amount at 6%
10. On $842 for 2 yr. 8 mo. 13. On $850 for 3 yr. 5 mo.
11. On $648 for 1 yr. 9 mo. 14. On $519 for 4 yr. 8 mo.
12. On $952 for 3 yr. 5 mo. 15. On $1250 for 7 mo. 15 d.
Method by Days.
284. l. What is the interest of $248.60 for 90 days, at 6% ?
Analysts.— Since the int. of $1 at 6% for 30 d. is $248.60 Prin.
5 mills, for 6 d. it is 1 mill, or ^ as many mills as days. 15 ^ d.
Therefore, multiplying the principal by $ of the 124300
number of days will give the interest in mills, which olefin
are changed to dollars and cents by moving the
decimal point 3 places to the left. Hence, the 3729.00 Mills.
$3,729, Am.
Rule. — Multiply the principal by £ of the number of
days and divide the product by 1000. (Art. 264, C. G. A.)
Note.— If there is a fraction in finding £ of the days, it may be avoided
by multiplying by the whole number of days, and dividing the product
by 6000.
What is the interest of What is the amount of
2. $850 for 63 days at 6$ ? 6. $670 for 78 days at 5% ?
3. $945.50 for 33 days at 6% ? 7. $785 for 45 days at 7% ?
4. $378.68 for 75 days at 6%? 8. $1200 for 68 d. at 5% ?
5. $354.75 for 130 days at 6% ? 9. $2500 for 93 d. at 8% ?
Interest 109
10. At 6 per cent, what is the amount due on a note of
$391, dated Oct. 9th, 1881, and payable March 1st, 1882 ? •
n. At 5 per cent, what is the amount of $623 from Feb.
19th, 1883, to Aug. 10th, 1883 ?
Bankers' Method.
285. A contraction often used by hankers and others in
finding the interest on any number of dollars at 6% for 60 days,
is illustrated in the following example :
12. Find the interest of $2835.20 for 2 mo. 3 d., at 6%.
Explanation. — From the right of the operation.
dollars, cut off 2 figures ; this gives the int. for 20 ) 28 35.20
60 d. (2 mo.) ; 3d. = 4 or ^ of 60 d.; there- j 4^75
fore, $28.352-*- 20 = $1.4176, the int. for 3 d.
These results added together give the int. for $29.^696, A)IS.
2 mo. 3 d. Hence, the
Kule. — Cut off the two right-hand figures of the dollars
for 60 days interest at 6%; then add or subtract the
fractional -part of 60 days interest indicated by the time.
Notes. — 1. The same rule is applicable where the time is a multiple
of 60.
2. The interest at other rates is found as in other 6% methods.
13. What is the interest of $360 for 95 d., at 6% ?
Explanation. — Since 95 days equals 95 d. — 60 -J- 30 + 5
60 + 30 + 5 days, and 30 is $ of 60, the int. for 2 ) $3 60 = Int. 60 d.
60 d.-s- 2 gives the int. for 30 d.; and as 5d. p \ 1 SO " 30 d
are 1- of 30 d. the int. for 30 d. -r- 6 erives the '
int. for 5 days. The sum of these results is ou — ° a<
the answer. $5^ Ans%
Find the interest at 6% Find the interest at 6%
14. On $2500 for 75 days. 18. On $8360 for 78 days.
15. On $750 for 48 days. 19. On $4780 for 51 days.
16. On $6253 for 96 days. 20. On $3654 for 43 days.
17. On $4525 for 47 days. 21. On $9875 for 153 days.
110 Percentage.
286. Another short method of finding the interest on cer-
tain sums, at different per cents is explained in the use of the
following table giving the various sums on which the interest
at the per cents named, is one cent per day. Thus,
$90 at ±%.
$40 at 1\%.
$24 at 15#.
$80 " *$%.
$45 " 8%.
$20 « 18%.
$72 " 5%.
$40 " 9%.
$50 " &%.
$60 " 6%.
$36 " 10^.
$70 « ^.
$52 " 7%.
$30 " 12%.
$35 « H%.
Note. — This table if committed to memory will be found very useful,
particularly when the days are not aliquot parts of a year.
22. Find the interest on $72, at 5%, for 3 mo. 18 days.
Explanation. — Since the int. on $72, at 3 mo. 18 d. = 108 da.
5%, by the table, is 1 cent per day, for 108 d. fo] OP, An*
it is 108 cts., or $1.08. Hence, the f '
Hulk.— Point off the two right-hand -figures of the days,
for cents ; the result is the interest for the given time of
the several sums found in the table, at the % attached.
Notes.— 1. This method may be applied to any multiple or fraction of
the several sums given in the table. If the days are less than 10 a cipher
should be prefixed before pointing off.
2. The first contraction is based on the fact that the interest on
$1, at 6 °/o for 60 d. is 1 cent. The second on the fact that on given sums
at given rates the int. is as many cents as days.
23. What is the int. of $240, at 6%, for 1 yr. 2 mo. 15 d.?
Explanation.— Since $240 = 4 1 yr. == 360 d.
times $60, the int. of $60 for the
time must be multiplied by 4. The
given time = 360 +60 + 15 d., or
435 days. Cutting off two figures
gives the int. of $60 = $4.35, and
$4.35 x 4 = $17.40.
24. Int. $270 at 4=%, 280 d. ?
25. $3280 at fy%, 358 d. ?
26. $3672 at lb%, 869 d. ?
2 mo.
15 d. =
75 d.
$4
35 = Int. $60
4
$17.40, Ans.
27.
$104,845 d.,at 1%?
28.
$684, 395 d., at 8^?
29.
$320, 76
3 d., at 9% ?
Interest m
Accurate Interest.
287. The methods based upon the supposition that 360 days
make a year and 30 days a month, though common, are not
strictly accurate. As a year contains 365 days, the interest
found by these methods is ^f-, or ^ part of itself too large.
288. To compute Accurate Interest.
1. What is the exact interest, at 6%, of $2486.50 for
93 days?
Explanation. — The interest at 6% is $38.54, -^ part of which is $.53,
and $38.54- $.53 = $38.01, Am. Hence, the
Eule. — Find the interest by the 6% method and sub-
tract from it Y L 3 part of itself.
2. What is the exact interest of $8568 for 93 d., at 6% ?
3. What is the exact interest of $5200 for 123 d., at 1f ?
4. Find the accurate interest of $4560 for 120 d., at 7%?
5. Find the accurate interest of $16485 for 133 d., at 6% ?
6. Find the accurate interest of $36720 for 63 d., at 5% ?
7. What is the exact interest on a note for $5800 from Jan.
15, 1882, to July 4, 1882, at 6% ?
289. Interest on U. S. Bonds is computed on the basis of
365 days to a year ; hence, for any number of days less than a
year, take a corresponding fractional part of 1 year's interest.
Thus, for 27 d. take -gfa, etc.
Note. — According to this rule the interest of $100 at 3^ per cent for
1 day is 1 cent. At twice 3{^ % = 7f^%, or 7 T 3 o%, it is 2 cents a day
on $100. This is the rate of interest which the U. S. Seven-thirty
Treasury Notes bore, and from which they took their name.
Find the exact interest, at 4=%, 5%, and 7% of
8. $842, 105 d. 11. $1600, 192 d.
9. $1250, 126 d. 12. $2500, 230 d.
10. $1728, 160 d. 13. $8500, 183 d.
112 Percentage.
ANNUAL INTEREST.
290. Annual Interest is interest that is payable every year.
Note. — When notes are made payable " with interest annually," sim-
ple interest can be collected, in most of the States, on the annual interest
after it becomes due. This is according to the contract, and is an act of
justice to the creditor, to compensate him for the damage he suffers by
not receiving his money when due.
291. To Compute Annual Interest, when the Principal, Rate,
and Time are given.
1. What is the amount due on a note of $5000, at 6%, in
3 yr. with interest payable annually ?
SOLUTION.
Principal $5000.00
Interest for 1 year is $300 ; for 3 years it is $300 x 3, or 900.00
Interest on 1st annual interest for 2 yr. is 36.00
2d " M " 1" is 18 .00
The amount is $5954.00
Eule. — Find the interest on the principal for the given
time and rate; also find the simple legal int. on each
annual int. for the time it has remained unpaid.
The sum of the principal and its int., with the int. on
the unpaid annual interests, will be the amount.
Note. — When notes are made for long periods on collateral security,
moneyed institutions sometimes take a bond and mortgage for the
principal without interest, and take notes maturing at the time each
annual interest is payable. These notes are entitled to interest after
maturity, like any other note, and may be collected without disturbing
the original loan.
2. What is the amount of a note of $2500 payable in 4 yr.
3 mo. 12 d. with interest annually at 5% ?
3. What will be the amount due on a note of $2375, at 6%
annual interest, payable in 4 yr. 6 mo. 15 d. if no payments are
made?
4. At h% annual interest, how much will be due on a note
of $12648 in 5 years, no payments having been made ?
Problems in Interest. 113
5. At 6% annual interest, what will be the amount of a loan
of $15000 in 3 years, if notes from date with semi-annual
interest are given ?
6. At 7$, what would be the amt. of the same loan ?
Problems in Interest.
292. To find the Mate, when the Principal, Interest, and Time
are given.
1. At what rate of interest must $828 be loaned, to gain
$47.61 in 1 year 3 months and 10 days ?
Analysis.— At 1% the interest of • $828 X .01 = $8.28
$828, is $8.28 for 1 yr. The int. for 3 mo _ i yr _ 2 07
3mo., }yr.,isitheint for 1 yr., and ^ ^ '
the int. for 10 d. is ^ the int. for one 6
mo. Since the int. at 1% is $10.58 for $10.58
the time, $47.61 is as many times 1% la58 ) $47.61 ( 4J^, Am.
int. as $10.58 are contained times in
$47.61, or 4 1 times. Hence, the
Rule. — Divide the given interest by the interest of the
principal, at 1 per cent for the time.
Formula. — Rate = Interest -f- (Prin. x 1% X Time).
Note. — When the amount is given the principal and interest may be
said to be given. For, the amt. = the prin. + int. ; hence, amt.— int. = the
prin. ; and amt.— prin. = the interest.
2. At what rate will $300 yield $18 int. in 9 months ?
3. At what rate will $500 yield $34 in 1 yr. 1 mo. 18 d. ?
4. At what rate will $8450 yield $148 int. in 3 months?
5. At what per cent will $1704 amount to $1870.42 in 1 yr.
7 mo. 16 days?
6. At what per cent will $311.50 amt. to $336.42 in 1 yr. 4 mo.?
7. Required the rate of int. at w 7 hich $1728 yields $84 in
8 mo. 10 d.
8. At what % will $7300 yield $147.46 in 4 yr. 5 mo. 26 d.?
9. At what % will $556 yield $95.91 iu 3 yr. 5 mo. 12 d.?
8
114 Percentage.
10. An investment of $7226.28 yields $744.7937 per year;
what is the rate ?
293. To find the Principal, when the Interest, Rate, and Time
are given.
11. What principal at 6% will yield $450.66 int. in 3 yr.
6 mo.?
Analysis. — The int. of $1 for 3 yr. 6 mo. at 6% is operation.
$0.21, therefore $450.66 must be the int. of as many .21 ) 450.66
dollars as $.21 are contained times in $450.66, or $2146. A &oT7«
Hence, the jlnS ' ^ i4b
Eule. — Divide the -given interest by the interest of $1
for the given time and rate.
Formula.— Principal = Interest -~ (Rate x Time).
12. What principal will yield $1250 a year, at 6% interest ?
13. A professorship was founded with a salary of $3500 a
year ; what sum was invested at 6% to produce it ?
14. What sum must be invested at 6% that a young lady
now 18 may have $10000 when she is 21 ?
15. What principal at 6% per annum yields 6 cts. a day ?
294. To find the Principal, when the Amount, Rate, and Time
are given.
16. What principal at 6% will amount to $287.50 in 2 yr.
6 months ?
Explanation.— The amount of $1 for 2 yr. 1.15 ) 287.50
6 mo. at 6% is $1.15, and $287.50-h $1.15 = $250. ZZTZ
Hence, the ^ &U > AnS '
Rule. — Divide the given amount by the amount of $1
for the given time and rate.
17. What sum loaned at 1% a month will amount to $600
in 1 year ?
18. What principal at 7%, loaned from. Apr. 9th, 1881, to
Sept. 5, 1883, will amount to $1477.59 ?
Problems in Interest. 115
19. What sum at 1% will amt. to $221.07 in 3 yr. 4 mo. ?
20. What principal at 9% will amt. to $286 in 3 yr. 4 mo. ?
21. What principal at 6% will amount to $3695.04 in 1 yr.
4 mo. 18 days ?
22. What principal at 8% will amount to $442.71 in 2 yr.
2 mo. 24 days ?
295. To find the Time, when the Principal, Interest, and Rate
are given.
23. In what time will $1500 gain $198 at 6%?
Analysis.— The int. of $1500 for 1 yr. at 6% is operation,
$90 ; hence, to gain $198 will require the same prin- 90 ) $198.00
cipal as many years as $90 are contained times in 77T jT'o'vj.
$198 ; and $198-=-$90 = 2.2, or ty years. Hence, the '. * * "
Eule. — Divide the given interest by the interest of the
principal for 1 year at the given rate.
Formula. — Time = Int. -^ (Prin. x Rate).
Notes. — 1. If the quotient contains decimals, reduce them to months
and days. (Art. 153.)
2. If the amount is given instead of the principal or the interest, find
the part omitted, and proceed as above.
3. At 100%, any sum will double itself in 1 year ; therefore, any per
cent will require as many years to double the principal, as the given per
cent is contained times in 100%.
24. In what time will $850 gain $29.75 at 7$ ?
25. In what time will $273.51 amount to $312,864 at 7%?
26. In what time will $240 amount to $720, at \%% ?
27. A man received $236.75 for the use of $2820, which was
Q>% interest for the time ; what was the time ?
28. How long must $204 be on interest at 6% to amount
to $217.09?
29. How long will it take $500 at 5% to % gain $500 interest ;
that is, to double itself ?
OPERATION.
Explanation.— The interest of $500 for 1 year at 5 % , 25 ) 500
is $25 ; and $500-*-$35 = 20. Ans. 2$ years. '
Ans. 20 yr.
116
Percentage.
Tab le.
Showing in what time any given principal will double itself
at any rate, from 1 to 20 per cent Simple Interest.
Per cent.
Years.
Per cent.
Years.
Per cent.
Years.
Per cent.
Years.
1
100
6
161
11
«¥r
16
H
2
50
7
14f
12
81
17
5tf
3
33i
8
12J
13
7*
18
H
4
25
9
11*
14
7*
19
5A
5
20
10
10
15
6*
20
5
30. How long will it take $10000 to gain $5000, at 6 per cent
interest ?
31. A man hired $15000 at 1%, and retained it till it
amounted to $25000 ; how long did he have it ?
32. A man loaned his clerk $25000, and agreed to let him
have it at 5% till it amounted to $60000 ; how long did he
have it ?
PARTIAL PAYMENTS.
296. Partial Payments are payments at different times of
parts of a note or bond.
297. Indorsements are receipts of payments written on the
back of notes and bonds, stating the amount and date of the
payment.
298. To compute Interest on notes and bonds, when partial
payments have been made.
$ 965 - New York, March 8th, 1880.
l. On demand, I promise to pay George B. Curtis, or
order, Nine Hundred Sixty-jive Dollars, until interest at 7 per
cent, value received.
Heniiy Bbowx,
Partial Payments. 117
The following payments were indorsed on this note :
Sept. 8th, 1880, received $75.30.
June 18th, 1881, received $20.38.
March 24th, 1882, received $80.
What was due on taking up the note, Feb. 9th, 1883 ?
OPEBATION.
Principal, dated March 8th, 1880 $965.00
Int. to first pay't, Sept. 8th, 1880 (6 mo.) 33.7 75
Amount due on note Sept. 8th. 998.775
1st pay't (to be deducted from amt.) 75.30
Remainder, or new principal 923.475
Int. to 2d pay't, June 18th (9 mo. 10 d.) 50.278
2d pay't (less than int. due) $20.38
Int. on same principal from June 18th to March 24th,
1882 (9 mo. 6 d.) $49,559 - $20.38 = 29.1 79
Amount due March 24th, 1882 1002,932
3d pay't (being greater than the int. now due) is to be deducted
from the amount 80.00
Balance due March 24th, 1882 922.932
Int. on Bal. to Feb. 9th (10 mo. 15 d.) 56.529
Bal. due on taking up the note, Feb. 9th, 1883 $979,461
United States Rule.
Find the amount of the principal to the time of the
first payment, and subtracting the payment from it, find
the amount of the remainder as a new principal, to the
time of the next payment.
If the payment is less than the interest, find the
amount of the principal to the time ivhen the sum of
the payments equals or exceeds the interest due; and
subtract the sum of the payments from this amount.
Proceed in this manner to the time of settlement.
Notes. — 1. The principles upon which this rule is founded are,
1st. That payments must be applied first to discharge accrued
interest, and then the remainder, if any, toward the discharge of the
principal.
2d. That only unpaid principal can draw interest.
118 Percentage.
$ 650 - Boston, Jan. 1st,. 1882.
2. For value received, I promise to pay John Lincoln, or
order, Six Hundred Fifty Dollars on demand, with interest at
6 per cent. George Law.
Indorsed, Aug. 13th, 1882, $100.
Indorsed, April 13th, 1883, $120.
What was due on the note, Jan. 20th, 1884 ? ^ ^9S.9 ^
Trenton, April 10th, 1874.
3. Four months after date, I promise to pay James Gar-
field, or order, Two Thousand Four Hundred Sixty Dollars,
with interest at 6 per cent, value received.
George G. Williams.
Indorsed, Aug. 20th, 1875, $840.
Dec. 26th, 1875, $400.
May 2d, 1876, $1000.
How much was due Aug. 20th, 1876 ?
$ 5000- Indianapolis, May 1st, 1875.
4. Six months after date, I promise to pay John Folger, or
order, Five Thousand Dollars, with interest at 5 per cent, value
received. John Adams.
Indorsed, Oct. 1st, 1875, $700.
Feb. 7th, 1876, $45.
Sept. 13th, 1876, $480.
What was the balance due Jan. 1st, 1877 ?
Mercantile Method.
299. When Partial Payments are made on short notes or
interest accounts, business men commonly employ the follow-
ing method :
Find the amount of the whole debt to the time of set-
tlement ; also find the amount of each -payment from
the time it was made to the time of settlement.
Partial Payments, 119
Subtract the amount of the payments from the amount
of the debt ; the remainder will be the balance due.
$■^16- Rochester, March 21st, 1880.
5. On demand, I promise to pay to the order of Henry
Patton, Four Hundred Sixteen Dollars, with interest at 7 per
cent, value received. Johk Martin.
Keceived on the above note the following sums :
June 15th, 1880, $35.00.
Oct. 9th, 1880, $23.00.
Jan. 12th, 1881, $68.00.
What was due on the note, Sept. 21st, 1881 ?
SOLUTION.
Principal, dated March 21st, 1880 $416,000
Int. to settlement (1 yr. 6 mo.), at 7% 43.6 80
Amount, Sept. 21st, 1881 459.680
1st pay't, $35.00, Time (1 yr. 3 mo. 6 d.), Amount $38,103
2d pay't, $23.00, Time (11 mo. 12 d.), Amount 24.530
3d pay't, $68.00, Time (8 mo. 9 d.), Amount 71.292
Amount of the payments 133.925
Balance due Sept. 21st, 1881 $325,755
6. A bill of goods amounting to $850, was to be paid Jan.
1st, 1880. Received June 10th, $145 ; Sept. 23d, $465 ; Oct.
3d, $23 ; what was due on the bill Dec. 31st, 1880, int. 6% ?
7. An account of $3200 due March 3d, received the follow-
ing payments: June 1st, $310; Aug. 7th, $219 ; Oct. 17th,
$200 ; what was due on the 27th of the following December,
allowing 7% interest ?
300. Connecticut Rule for Partial Payments.
I. When the first payment is a year or more from the time
the interest commenced :
Find the amount of the principal to that time. If the
payment equals or exceeds the interest due, subtract it
from the amount thus found, and considering the re-
mainder a new principal, proceed as before.
120 Percentage.
II. When a pay't is made before a year's int. has accrued :
Find the amount of the principal for 1 year ; also, if
the payment equals or exceeds the interest due, find its
amount from the time it was made to the end of the
year ; then subtract this amount from the amount of the
principal, and treat the remainder as a new principal.
III. If the payment be less than the interest:
Subtract the payment only from the amount of the
principal thus found, and proceed as before.
$ 650 ' New Haven, April 12th, 1879.
8. On demand, I promise to pay to the order of George
Selden, Six Hundred Fifty Dollars, with interest, value
received. Thomas Sawyer.
Indorsed, May 1, 1880, rec'd $116.20.
Feb. 10, 1881, rec'd $61.50.
Dec. 12, 1881, rec'd $12.10.
• June 20, 1882, rec'd $110.
What was due Oct. 21, 1882 ?
SOLUTION.
Principal, dated April 12, 1879. . . . , $650.00
Interest to first payment, May 1, 1880 (1 yr. 19 da.) 41.06
Amount, May 1, '80 691.06
First payment, May 1, '80 ... 116.20
Remainder, or new principal, May 1, '80 574.86
Interest to May 1, '81, or 1 yr. (2d payment being short of 1 yr.). . 34.49
Amount, May 1, *81 609.35
Amount of second payment to May 1, '81 (2 mo. 20 da.) 62.32
Remainder, or new principal, May 1, '81 547.03
Amount, May 1, '82 (1 yr.) 579.86
Third payment (being less than interest due) draws no interest. . . 12.10
Remainder, or new principal, May 1, '82 567.76
Amount, Oct. 21, '82 (5 mo. 20 da.) 583.85
Amount of last payment to settlement (4 mo. 1 da.) 112.22
Balance due Oct. 21, '82 $471.63
Partial Payments. 121
301. Vermont Rule for Partial Payments.
I. When payments are made on notes bearing interest, such
payments shall be applied,
" First, to liquidate the interest that has accrued at the
time of such payments ; and secondly, to the extinguish-
ment of the principal"
II. When notes are made " with interest annually."
The annual interests ivhich reviain unpaid shall be
subject to simple interest from the time they become due
to the time of settlement.
III. If payments have been made in any year, reckoning
from the time such annual interest began to accrue, the amount
of such payments at the end of such year, with interest thereon
from the time of payment, shall be applied :
" First, to liquidate the simple interest that has accrued
from the unpaid annual interests.
" Secondly, to liquidate the annual interests that have
become due.
" Thirdly, to the extinguishment of the principal.
H 500 - Montpelier, Feb. 1st, 1878.
9. On demand, I promise to pay to the order of Jared
Sparks, Fifteen Hundred Dollars, with interest annually at
6%, value received. Augustus Morse.
Indorsed, Aug. 1, 1878, $160. Nov. 1, 1881, $250.
Eequired the amount due Feb. 1, 1882.
SOLUTION.
Principal $1500.00
Annual interest to Feb. 1, '79 (1 yr. at 6%) 90.00
Amount 1590.00
First payment, Aug. 1, 78 $160.00
Interest on same to Feb. 1, '79 (6 mos.) 4.80 164.80
Remainder, or new principal $1425.20
122 Percentage.
Remainder, or new principal $1425.20
Annual interest on same from Feb. 1, '79, to Feb. 1, '82 (3 yr.). . 256.53
Interest on first annual interest from Feb. 1, '80 (2 yr.). . $10.26
Interest on second annual int. from Feb. 1, '81 (1 yr.). . . 5.13 15.39
Amount 1697.12
Second payment, Nov. 1, '81 $250.00
Interest on same to Feb. 1, '82 (3 mo.) 3.75 253. 75
Balance due Feb. 1, '82 $1443.37
302. New Hampshire Rule for Partial Payments.*
I. When on notes drawing annual interest,
Find the interest due upon the principal, and the
annual interest at the annual rest \ next after the first
payment, from date of note.
II. If the first pa) T t. be larger than the sum of interests due,
Find the int. on such payt. from the time it was made
to end of the year, and deduct the sum of payt. and int.
from the amount of principal and interests.
III. If less than the annual interests accruing,
Deduct the payment without interest from th e sum of
annual and simple interest, and upon the balance of
such interest cast the simple interest to the time of the
next rest.
IV. If less than the simple interest due,
Deduct it from the simple interest, and add the bal-
ance without interest to the other interests due when the
next payment is made.
Proceed thus to the end of the year after the last pay-
ment, being careful to carry forward all interest unpaid
at the end of each year.
* Abstract of N. H. Court Rule. Report of Hon. C. A. Downs, State Superintendent,
t The time when the annual interest becomes due from year to year.
Partial Payments. 123
10. A agrees to pay B $2000 in 6 yr. from Jan. 1, 1870, with
interest annually. On July 1, 1872, a payment of $500 was
made; and Oct. 1, 1873, $50. What was due Jan. 1, 1876 ?
SOLUTION.
Principal $2000.00
First year's interest $120.00
2 yr. simple int. thereon 14.40 134.40
Second year's interest 120.00
1 yr. simple int. thereon 7.20 127.20
Third year's interest 120. 00
2381.60
First payment, July 1, 1872 $500.00
Int. thereon from July 1, '72, to Jan. 1, '73 15.00 515.00
Balance of principal $1866.60
Interest on same for fourth year. $111.99 +
Second pay't (less than the int. accruing during the year) 50.00
Balance of fourth year's interest unpaid 61.99 +
Annual interest on balance of principal for fifth year 111.99 +
" " " " sixth " 111.99 +
Simple int. on unpaid bal. of fourth year's int. for 2 yr 7.43 +
Simple interest on fifth year's interest for one year. 6.71 +
Balance of principal 1866.60
Amount due January 1, 1876 $2166.71
303. To Compute Interest on Sterling Money.
11. What is the int. of £175 10s. 6d. for 1 yr., at 5 per cent ?
Explanation.— Reduce 10s. 6d. to the £175.525 Prin.
decimal of a pound (Art. 154); then -05 Rate.
multiply the principal by the rate, and £8.77625 int. 1 year.
point off the product as before. The 8 on 20
the left of the point is pounds, the figures 15.52500 s.
on the right are decimals of a pound,
which must be reduced to shillings, pence, 6.30000 d.
and farthings. (Art. 153.) Hence, the Ans. £8 15s. Q\d.
Eule. — Reduce the given shillings, etc., to the decimal
of a pound; then -proceed as in TJ. S. money. Reduce
the decimals of a pound in the result to shillings, pence,
and farthings. (Art. 153.)
12. What is the int. of £56 15s. for 1 yr. 6 mo., at 6% ?
13. What is the int. of £96 18s. for 2 yr. 6 mo., at A\% ?
14. What is the amt. of £100 for 2 yr. 4 mo., at 5% ?
124 Percentage.
COMPOUND INTEREST.
304. Compound Interest is the interest of the principal and
of the unpaid interest after it becomes due.
305. To Compute Compound Interest, when the Principal,
Rate, and Time of compounding it are given.
I. What is the compound interest of $5000 for 3 years,
at 6%?
Principal $5000
Int. for 1st year, $5000 x .06 300
Amt. for 1 yr. , or 2d prin 5300
Int. for 2d year, $5300 x .06 318
Amt. for 2 yr., or 3d prin 5618
Int. for 3d year, $5618 x. 06 337.08
Amt. for 3 years 5955.08
Original principal to be subtracted 5000 00
Compound int. for 3 years $955.08
Hence, the
Eule. — I. Find the amount of the principal for the
first period. Treat this amount as a new principal, and
find the amount due on it for the next period, and so on
through the whole time.
II. Subtract the given principal from the last amount,
and the remainder will be the compound interest.
Note. — If there are months or days after the last regular period at
which the interest is compounded, find the interest on the amount last
i obtained for them, and add it to the same, before subtracting the
principal.
2. What is the compound int. of $1450 for 3 yr. 6 mo.,
at 6%?
3. What is the compound int. of $8500 for 4 yr. 6 mo.,
at5%?
4. What is the amt. of $9500 for 6 yr. 3 mo., at b%, com-
pound int. ?
Compound Interest
125
Table.
306. Showing the amount of $1, at 3, 3|> 4, 5, 6, and
compound interest, for any number of years from 1 to 20.
n
Yrs.
3%.
3|%.
4%.
5%.
6%.
Ifc
1.
1.030 000
1.035 000
1.040 000
1.050 000
1.060 000
1.07 000
2.
1.060 900
1.071 225
1.081 600
1.102 500
1.123 600
1.14 490
3.
1.092 727
1.108 718
1.124 864
1.157 625
1.191 016
1.22 504
4.
1.125 509
1.147 523
1.169 859
1.215 506
1.262 477
1.31 079
5.
1.159 274
1.187 686
1.216 653
1.276 282
1.338 226
1.40 255
6.
1.194 052
1.229 255
1.265 319
1.340 096
1.418 519
1.50 073
7.
1.229 874
1.272 279
1.315 932
1.407 100
1.503 630
1.60 578
8.
1.266 770
1.316 809
1.368 569
1.477 455
1.593 848
1.71 818
9.
1.304 773
1.362 897 ; 1.423 312
1.551 328
1.689 479
1.83 845
10.
1.343 916
1.410 599 1.480 244
1.628 895
1.790 848
1.96 715
11.
1.384 234
1.459 970 1.539 451
1.710 339
1.898 299
2.10 485
12.
1.425 761
1.511 069
1.601 032
1.795 856
2.012 196
2.25 219
13.
1.468 534
1.563 956
1.665 074
1.885 649
2.132 928
2.40 984
14.
1.512 590
1.618 695
1.731 676
1.979 932
2.260 904
2.57 853
15.
1.557 967
1.675 349
1.800 944
2.078 928
2.396 558
2.75 903
16.
1.604 706
1.733 986
1.872 981
2.182 875
2.540 §52
2.95 216
17.
1.652 848
1.794 676
1.947 900
2.292 018
2.692 773
3.15 881
18.
1.702 433
1.857 489 2.025 817
2.406 619
2.854 339
3.37 993
19.
1.753 506
1.922 501 ! 2.106 849
2.526 950
3.025 600
3.61 652
20.
1.806 111
1.989 789 ! 2.191 123
1
2.653 298
3.207 135
3.86 968
Note. — Compound interest cannot be collected by law ; but a creditor
may receive it, without incurring the penalty of usury. Savings Banks
pay it to all depositors who do not draw their interest when due.
5. What is the compound int. and amt. of $200 for 10 yr.,
at 3^?
SOLUTION.
Tabular amount of $1 for 10 yr., at U% $1.410599
Multiply by the prin 200
Amt, of $200 for 10 yr 282.119800
Subtracting the prin 200.
Compound int. for 10 yr $82.1198
126 Percentage.
Eule. — I. Multiply the tabular amount of $1 for the
given time and rate by the principal ; the product will
be the amount.
II. From the amount subtract the principal, and the
remainder will be the compound interest.
Notes. — 1. If the given number of years exceed that in the Table, find
the amount for any convenient period, as half the given years ; then on
this amount for the remaining period.
For example, the amt. for 20 years by table .at 6% =3.207135, this
multiplied by 1.123600, amt, for 2 yr. gives $3.603537 the amt. for 22
years.
2. If interest is compounded semi-annually take £ the given rate and
twice the number of years ; if compounded quarterly, take \ the given
rate and 4 times the number of years.
Thus, the amount of $400 payable semi-annually for 3 yr. at 6%, is
the same as the amt. of $400 for 6 yr, at 3%, payable annually.
6. What is the amt. of $3500 for 5 yr., at 5% com. interest?
7. What is the amount of $1350 for 12 years, at 1% ?
6. What is the com. int. of $1469 for 15 years, at 3%?
9. What is the com. int. of $2500 for 24 years, at 6% ?
10. What is the com. int. of $1650 for 30 years, at 3£$?
11. What is the amount of $1800 for 3 yr., at 6% compound
interest, payable semi-annually ?
V12. What is the amount of $1500 for 2 years, at 12$ com-
ound interest, payable Quarterly?
3. To find the principal or present vvorth of an amount at compound
interest: Divide the given amount by the amount of $1 for the given
time and rate at compound interest.
13. What is the present worth of $6036.25 due in 8 years,
at Q% compound interest?
14. What principal at compound int. will amount to
$2375.92, at 5%, in 14 years?
15. What is the present worth of $2521.81, due in 14 years,
at 6$ compound interest ?
16. What principal at 10$, will amount to $265.33 in 10
years, int. payable semi-annually ?
True Discount. 127
.
TRUE DISCOUNT.
307. Discount is a deduction from a stated price, or from
a debt paid before it is due.
308. The Present Worth of a debt, due at some future time
without interest, is the sum which put at legal interest will
amount to the debt when it becomes due.
309. True Discount is the difference between the face of a
debt and its present worth.
310. To find the Present Worth and True Discount of a time
note.
1. What is the present worth and true discount of $478.06,
due in 1 year and 8 mouths, at 6%?
Analysis.— The amount of $1, at 6%, for 1 yr. 8 mo. = $1.10. Since
$1.10 is the amt. of $1, at 6% for the given time, $478.06 is the amt. of
as many dollars, for the same time and rate, as $1.10 is contained times in
$478.06, and $478.06 -^ $1.10 = $434.60, present worth. Then, $478.06-
434.60 = $43.46, the true discount. Hence, the
Rule.— I. Divide the debt by the amount of $1 for the
given time and rate ; the quotient will be the present
woHh.
II. Subtract the present worth from the debt, and the
remainder will be the true discount.
Find the present worth and true discount of
2. $950.25, due in 1£ years, at 6%.
3. $3272.50, due in 2 yr. 3 mo., at 7%.
4. $6895, payable in 3 years, at 5.%.
5. $8650.75, payable in 3£ years, at ±\%.
6. $10000, due in 4 yr. 5 mo., at %\%.
7. What is the difference between the interest and true dis-
count of $52250, for 1 year, at 6% ?
128 Percentage.
8. If a note for $2500 be given with interest at 7% per
annum for G mo., what will it be worth 3 mo. from date ?
9. When money is worth 6%, which is preferable, $15000
cash, or $16000 payable in 1 year ?
BANK DISCOUNT.
311. Bank Discount is simple interest, paid in advance.
312. The Proceeds of a note are the part paid to the owner;
the Discount is the part deducted.
313. The Maturity of a note or draft is the day it becomes
legally due. In most States a note does not mature until 3
days after the time named for its payment.
These three days are called Days of Grace.
Notes. — 1. As interest is charged by some banks for the day of dis-
count as well as for the day of maturity, this with the 3 days grace makes
the time for which discount is taken four days more than the time named
in the note.
2. If the last day of grace occurs on Sunday or a legal holiday, the note
matures on the preceding business day. Thus, if a note matures on
Monday, and that is a holiday, it is payable on Saturday.
314. The Term of Discount is the time from the date of
discount to the maturity of the note.
Note. — In computing interest and discount on notes and drafts the
practice is not uniform as to what constitutes a year. Some compute it
on the basis of 360, and others of 365 days to a year. On Stock loans in
Wall Street, interest is computed on the basis of 360 days to a year.
315. To find the Bank Discount and Proceeds, when the
Face of a note, Rate, and Time are given.
l. What is the bank discount of $568 for 3 mo., at 6% ?
What are the proceeds ?
Solution. — The face of the note = $568
Int. of $1 for 3 mo. and grace at 6% = .0155
Discount = $8,804
Proceeds, $568-$8.804 = ^559.196. Hence, the
Commercial Paper. 129
Rule. — Find the interest of the note at the given rate
for three days more than the specified time ; the result
is the discount.
Subtract the discount from the face of the note ; the
remainder will be the proceeds.
Note. — If a note is on interest, find its amount at maturity, and taking
this as the face of the note, cast the interest on it as above.
2. Find the proceeds of a note of $850, due in 3 mo., at 6% ?
3. Find the proceeds of a draft of $885, on 60 days, at 6%.
4. Find the maturity, the term of discount and the proceeds
of a note of $5250, on 60 days, dated July 1st, 1880, and
discounted Aug. 21st, 1880, at 5%.
5. Find the difference between the true and bank discount
on $6000 for 1 year, allowing each 3 days grace, at 7% ?
6. A merchant bought $6800 worth of goods for cash, sold
them on 4 months, at 15$ advance, and got the note dis-
counted at 6% to pay the bill. How much did he make ?
316. To find the Face' of a note, that the proceeds may
amount to a given sum, when the Rate and Time are given.
7. For what sum must a note be made on 4 months, that
the proceeds may be $6400, discounted at 6%?
Solution.— The bank discount of $1 for 4 mo. 3 d. = $.0205
The proceeds of $1 = $l-$.0205 = $.9795
Therefore, The face of the note is $6400 -=-$.9795 = $6533.945
Hence, the
Rule. — Divide the given sum by the proceeds of $1 for
,p. (St.iip.ti, f.i.m.p, n.n.rl, vn+.p
the given time and rate
8. What must be the face of a note on 6 months, discounted
at 7% that the proceeds may be $900 ?
9. The avails of a note were $8350.90, the term 3 months,
and the rate of discount 8% ; what was the face of the note ?
io. How large a note on 90 days must I have discounted at
6$, to realize $5460 ready money ?
9
130 Percentage.
317. To find the face of a draft that may be bought for a
specified sum, when the per cent premium or discount is given.
1. How large a draft can be bought for $2040, at 2%
premium ?
Solution —At 2% premium, $1.02 will buy $1 draft.
Aud $2040h- $1.02 = 2000. Ans. $2000.
2. How large a draft can be bought for $2910, at 3%
discount ?
Solution.— At 3% discount, $0.97 will buy $1 draft.
And $2910^.97 = $3000, Ant. Heuce, the
Eule. — Divide the given sum by $1 increased or
diminished by the rate of premium or discount.
3. How large a draft on San Francisco can be bought for
$5200, at a premium of 2-J$ ?
4. What is the face of a draft on Chicago for which you pay
$8250, at \\% discount ?
5. A merchant invests the proceeds of a sale, amounting to
$3250, in a draft on Chicago, which he can buy at a discount
of \\% ; how large is the draft ?
6. What is the face of a draft on New York which costs
$2850, at \\% premium ?
COMMERCIAL OR BUSINESS PAPER.
318. Commercial or Business Paper includes Promissory
Notes, Drafts, Bills of Exchange, etc.
319. A Note or Promissory Note is a written promise to
pay a certain sum on demand or at a specified time.
Notes. — 1. A note should always contain the words " value received ; "
otherwise it is not valid, and the holder may be obliged to prove it was
given for a consideration, in order to collect it.
2. A note as a gift is void from want of a consideration, unless it has
passed for value into the hands of an innocent third party.
Commercial Paper. 131
320. The Maker of a note or draft is the person who
signs it.
The Payee is the person to whom it is to be paid.
The Holder is the person who has the note or draft in his
possession.
Note. — A note becomes void when founded upon fraud, or when any
material alteration is made, as in the date, amount, or time of payment.
321. A Collateral Note is one given with stocks or other
security, empowering the holder to sell, if the note should not
be paid when it becomes due.
322. A Joint Note is one signed by two or more persons.
Notes. — 1. The Face of a Note is the sum whose payment is
promised. This sum should be written in words in the body of the note,
and in figures at the top or bottom.
2. When a note is to draw interest from its date, it should contain
the words " with interest ; " otherwise no interest can be collected. For
the same reason, when it is to draw interest from a particular time after
date, that fact should be specified in the note.
3. All notes are entitled to legal interest after they become due, whether
they draw it before, or not.
323. A Negotiable Note is a note drawn for the payment of
money to "order or bearer," without any conditions.
A Non-Negotiable Note is one which is not made payable to
"order or bearer," or is not payable in money.
Notes. — 1. A note payable to A. B., or "order," is transferable by
indorsement; if to A. B., or "bearer," it is transferable by delivery.
Treasury notes and bank bills belong to this class.
2. If the words " order" and " bearer" are both omitted, the note can
be collected only by the party named in it, and is not negotiable.
3. When a note is given for any number of months, calendar months
are always to be understood.
4. If a note is payable on demand, it is legally due as soon as
presented. If no time is specified for the payment, it is understood to be
on demand.
132 Percentage.
5. If a note has been lost or destroyed by fire or other accident, its
amount may be collected upon sufficient proof.
324. An Indorser is a person who writes his name on the
back of a note and becomes security for its payment.
Notes.— 1. If an indorser of a note, draft, etc., does not wish to guar-
antee its payment, he writes " without recourse " over his name at the time
of the indorsement. This does not affect the negotiability of the note.
2. Sometimes notes and drafts are drawn to the order of the maker, to
facilitate their transfer without the indorsement of the holder. Such
notes are negotiable by delivery.
325. An Indorsement is the signature of a person written
upon the back of notes and other commercial instruments.
(Art. 297.)
Notes. — 1. A note made payable to A. B., or order, may be collected by
any one to whom A. B. may order it to be paid. This order is written on
the back of the note and is called an indorsement.
2. If A. B. writes his name only on the back of the note, it is an
indorsement in blank, and is equivalent to " Pay the bearer."
3. All the parties who write their names on a note are liable for the
amount due, but only one satisfaction can be recovered.
4. No days of grace are allowed in Alabama, Georgia, Kentucky,
or California, except the note is held by a private banker or by a bank.
326. A Draft is a written order addressed by one person to
another, directing him to pay a specified sum of money to a
third person, or to his order.
Notes. — 1. A person accepts or promises to pay a draft, by writing the
word accepted across the face, with the date and his name under it.
2. To honor a draft is to accept or pay it on presentation.
327. A Protest is a written statement made by a notary
public, that a note or draft has been duly presented by the
holder- in person for payment or acceptance, and was refused.
It protests against the Maker, Drawer, Drawee, Acceptor,
Payor, Indorser, etc., for all interest costs or damages incurred
through refusal of payment thereof.
Note. — A protest must be made out the day the note or draft matures,
and sent to the indorser immediately, to Jiold him responsible.
Commercial Paper. 133
Forms of Notes and Drafts.
328. No. I. — Time Notes without Interest. (Negotiable.)
$850.
New York, Jan. 10th, 1883.
Tliree months after date, I promise to pay George Ban-
croft, or order, Three Hundred Fifty Dollars, value received.
Henry Lincoln.
What are the bank discount and proceeds of this note ?
Note. — When no rate of interest is mentioned, the legal rate (
ate is always understood.
329. No. 2.— Time Notes bearing Interest. (Negotiable.)
$ 500 ' Philadelphia, Feb. 15th, 1883.
Sixty days after date, we promise to pay H. Foot, or order,
Five Hundred Dollars, with interest, without defalcation, value
received. John Richards & Co.
Required the bank discount and proceeds.
Notes. — 1. When banks discount time-notes bearing interest, it is cus-
tomary for them to compute the interest till maturity, and take the
amount as the face of the note.
2. In Penn. negotiable notes must contain the words " without defalca-
tion." In New Jersey they contain the words " without defalcation or
discount."
330. No. 3. — Demand Notes. (Negotiable.)
$ 120 - Chicago, April 15th, 1883.
On demand, I promise to pay W. H. Seward, or bearer,
Tivelve Hundred Dollars, value received.
Daniel Webster.
What was due on the above note June 21st, at 8% ?
4. What would be its amount at H% ? At 5% ?
Notes. — 1. Notes on demand are entitled to the legal interest of the
State in which they are made from their date to their payment.
2. If the words "or bearer" were omitted, the above note would not
be negotiable.
134 Percentage.
331. No. 5.— Notes without Grace. (Negotiable.)
$Ji.25 T %%. Baltimore, July 1, 1882.
Fifteen days after date, without grace, I promise to pay
George Brabburn, or bearer, Four Hundred Twenty-five
-ffy Dollars, value received. Silas Weight.
What was the amount due on this note at maturity ?
332. No. 6.— Notes on Demand op on Time. (Non-Negotiable.)
$ 700 ' Indianapolis, May 31st, 1882.
On demand after date, I promise to pay Robert Carter,
Seven Hundred Dollars, with interest at 8%, value received.
John Hancock.
Eequired its amount at sixty days.
7. What would be its amount, if the time were 3 mo. and
the rate 1% ?
Note. — Notes of the above form are not assignable, and can be collected
only by the drawee.
333. No. 8.— Joint Notes.
S1600. Sl , LouiSj Aug . 6> i 883 .
Two months after date, we jointly promise to pay Horace
Holben, or order, Sixteen Hundred Dollars negotiable and
'payable without defalcation or discount with 6% interest, value
received. A. H. Stebbins,
John Wakd.
Find the amount due at maturity.
Notes. — 1. The signers of a "joint note " are equally responsible for
its payment, and must be sued jointly.
2. The signers of a "joint and several " note are individually responsi-
ble for the whole amount, and either promisor may be sued alone.
Commercial Paper, 135
334. No. 9.— Notes Payable by Installments.
$ 8°°°' Richmond, Va., Oct. 16, 1883.
For value received, I promise to pay 67. C. Davenport, or
order, Two Thousand Dollars, with interest, in the following
manner, viz : Five Hundred Dollars in two months after date,
and the balance in installments of Five Hundred Dollars every
two months until the entire amount is paid.
G. L. Bennett.
What was the amount of each payment, at 6%, without
grace?
10. What would be the interest and amount of the same
note at 7^? At 5%?
335. No. N.— Sight Drafts.
$3000. New Orleans, Oct. 3d, 1883.
At sight, pay to the order of J. B. Hamilton & Co., Three
Thousand Dollars, value received, and charge the same to
J. C. Saunders.
To T. J. Sawyer, Boston, Mass.
Note. — Drafts are drawn payable to the order of a person named in
them, and are therefore not to be paid until indorsed by him.
336. No. 12.— Time Drafts.
$ 3560 - Grinnell. Iowa, Dec. 22, 1883.
Ninety days after date pay to the order of Calvin Selden,
Thirty-five Hundred Sixty Dollars, and charge the same to the
account of Sam'l Barrett & Co.
To S. Ball & Co., Trenton, N. J.
Notes. — 1. If a draft is payable at a specified time after sight, the date
of acceptance and the time of the draft determine its maturity.
2. The laws of N. Y. do not allow " grace " on sight drafts, nor on time
drafts if drawn on a bank or banker.
136 Percentage.
337. Find the date of maturity, discount, and proceeds of
the following note, offered for discount June 10th, at 6%.
$ 750 ' New York, May 8th, 1882.
13. Sixty days after date, I promise to pay George E.
Fisher, or order, Seven Hundred Fifty Dollars, value received.
Seth Low.
Solution. — Sixty days from May 8th is July 7th, and 3 days grace
make July 10th. The above note was offered for discount June 10th ;
hence, the term of discount was 30 days.
Int. at 6% for 30 d. on $750 = $3.75 Discount.
$750 -$3.75 = $746.2 5 Net proceeds.
Proof. $750.00
Date of maturity July 10th.
14. A note of $475, dated June 20, 1882, payable in 3 months
after date, was offered for discount Aug. 11th ; what were the
net proceeds at 6% ?
Find the date of maturity, the discount, and proceeds of the
following notes :
$ n6S - Newark, N. J., Dec. 1st, 1882.
15. Four months after date, I promise to pay to the order of
Claflin & Co., Eleven Hundred Sixty-three Dollars, without
defalcation or discount, value received. James Edsok.
The above note was discounted Feb. 15, 1883, at 6%; what
were the proceeds ?
$2500.
Knoxville, Tenn., Apr. 12th, 1882.
16. Ninety days after date, ice promise to pay to the order of
Wm. Day, Twenty-Jive Hundred Dollars, value received.
Monroe, Lockwood & Co.
The above was discounted May 15th, at 6% ; what were the
proceeds ?
Averaging Accounts. 137
AVERAGING ACCOUNTS.
338. An Account is a record of business transactions.
339. The Average of several unequal numbers is their sum
divided by their number. Thus the average of H, $6, and $8,
is $18-5-3 = $6.
340. A Day Book is a journal of accounts in which are
recorded the debts and credits of the day.
341. A Debtor is a party who owes another.
342. A Creditor is a party to whom a debt is due.
343. A Ledger is a book to which a summary of the
accounts of the " Day Book" is transferred for reference and
preservation.
344. The Debits or Debts are placed on the left, marked Dr. ;
the Credits or Payments on the right, marked Cr.
345. An Account Current is a running account containing
a record of the mercantile transactions between two parties,
showing the cash balance due at a certain date. The items
usually draw interest from their date, or some specified term of
credit, to the time of settlement.
Notes. — 1. It is customary for merchants, bankers, and brokers, to
render their accounts at stated times, as monthly, quarterly, semi-annually,
or annually.
2. Whether the items draw interest depends on custom or agreement
between the parties. Among wholesale merchants and jobbers, it is cus-
tomary to charge interest on accounts after six months.
3. Among retail dealers, mechanics, farmers, etc., the items seldom
bear interest ; hence, in settling such accounts, it is only necessary to find
the merchandise balance.
346. The Commercial or Merchandise Balance is the differ-
ence between the debit and credit sides of an account.
138 Percentage.
347. The Cash Balance is the sum required to settle an
account at any given date.
348. The Average of an Account is the equitable time when
the payment of several debts due at different times may be
made at one time without loss of interest to debtor or
creditor.
349. The Average Time is called the mean or equated time,
and the process by which it is found is often called Equation
of Payments.
350. The Term of Credit is the time between the contrac-
tion of a debt and its maturity. (Arts. 157, 313.)
351. The Average Term of Credit is the time at which
debts due at different times may be equitably paid.
352. Averaging Accounts depends upon the following:
Principles.
1°. The rate and time remaining the same,
Double the principal produces twice the interest.
Half the principal produces half the interest, etc.
2°. The rate and principal remaining the same,
Double the time produces twice the interest.
Half the time produces half the interest, etc. Hence,
3°. Tlie interest of any given principal for 1 year, 1 month,
or 1 day, is the same as the interest of 1 dollar for as many years,
months, or days, as there are dollars in the given principal.
353. To find the Average Time, when the items are all debits
or ail credits.
l. A bought a farm July 15th and was to pay $500 down,
$300 in 2 months, $400 in 6 months, and $600 in 8 months ;
what is the average term of credit and date when all these
payments may be equitably made at once ?
Averaging Accounts, 139
By the Interest Method.
Interest of $500 cash, for mo., at 6% = $0.00
Interest of $300 for 2 mo., at 6% = 3.00
Interest of $400 for 6 mo., at 6% = 12.00
Interest o f $600 for 8 mo., at 6% = 24.00
Ami of pay'ts = $1800 Int. = $39.00
Taking the date of the transaction, viz., July 15th, as the time for pay-
ing all the items, the debtor would lose the int. of $300 for 2 mo., $400
for 6 mo. , and $600 for 8 months. Therefore, the sura of items ($1800) is
entitled to a term of credit equal to the time required for $1800, at 6%,
to gain $39. Now, the interest of $1800 for 1 mo. = $9; and $39-i-$9
= 4^ mo., term of credit ; and July 15th + 4| mo. as Nov. 25th,
date of payment.
By the Product Method.
The first payment being cash has no solution.
product. The next payment was due in Items. Time. Product.
2 mo. and its interest for 2 mo. equals the 500 X = 00 mo.
interest of $1 for 600 months. (Prin. 300 X 2 = 600 mo.
1°-) 400 x 6 = 2400 mo.
The interest of $400 for 6 mo. equals ^q^ q 4800 mo
the int. of $1 for 2400 mo. , and the int. ~~
of $600 for 8 mo. equals the int. of $1 for 1800 ) 780
4800 months. Therefore the amount of ^Y^ ^j m g 4.1 m o.
interest due on the sum of items, equals
the int. of $1 for 7800 months, and $1800 is entitled to a term of credit
equal to T J 7 _ f 7800 months, or 4} months.
July 15 + 4$ mo. as Nov. 25th, the date of payment.
Note. — This method is the same in principle as the interest method.
2. Bought a bill of goods Apr. 20th amounting to $6000, on
the following terms : £ cash, -J- in 4 mo., and the balance in
6 mo. ; at what date may the whole be justly paid ?
Am. Av. time 3£ mo., or Aug. 5th.
3. On a certain day A bought a horse for $175 on 30 d.,
3 cows for $120 on 45 d., 80 sheep for $250 on 60 d., and 5 tons
of hay for $130 on 90 days; what is the average term of
credit ?
4. Bought a ship for $30000 ; the payments were $5000 cash,
$8000 in 4 mo., $7500 in 6 mo., $4500 in 8 mo., and the bal-
ance in a year ; what is the average term of credit ?
140 Percentage.
354. To find the Average Time when the items have different
dates and different terms of credit.
5. .Required the average date at which the following items
may be paid at once without loss of interest to either party :
April 10, merchandise on 30 days, $40.
May 1, " 40 " $54.
June 15, " 30 u $70.
" 30, " 40 " $80.
I. By the Interest Method.
Due. Time. Items. Int. at 6#.
May 10 (from May 1st) 9 d., $40 = $0.06
June 10 « 40 d., $54 = 0.36
July 15 " 75 d., $70 = 0.875
Aug. 9 " 100d.,_$80= 1.33 3
Int. at 6% for 1 day of $244 =.04 ) 2.628
65.7,or 66 d.
Ans. Date of pay't is 66 d. from May 1st, or July 6th.
Explanation. — The earliest date at which any item matures is May
10th ; therefore, taking May 1st as the standard date, and finding the
interest at 6 % on each item for the number of days from this date to its
maturity ; the sum of int. = $2,628, the sum of items = $244, which is
entitled to a term of credit equal to the time required for it to gain $2,628
interest. The int. of $244 for 1 day, at 6% = $0.04, and $2,628 -f- .04
= 65.7, or 66 d., the av. time. May 1st + 66 d. = July 6th. Hence, the
Eule. — Take as the standard the first of the month in
which the earliest item matures; find the interest on
each item- from the standard date to the date of its ma-
turity, and divide the sum of interests by the interest of
the sum of items for 1 month or 1 day, as the case may be.
The quotient will be the number of months or days
from the standard date to the average date of payment.
Add this number to the standard date and the result
will be the equitable date of payment.
Notes. — 1. If the earliest due date is the standard, its item has no
product, but it must be included in the sum of debts.
Averaging Accounts. 141
2. If the fraction in the quotient is £ day or more, 1 day is added ; if
less than \ day it is rejected.
3. In computing by the interest method, the rate forms no element of
the calculation ; hence, any rate may be used. The most convenient is
6% or 12%. At 12% the int. for 30 days, or 1 mo., is .01 ; and for 3 d.,
.001 of the principal, or \ as many thousandths as days.
4. Any date may be assumed as the standard, but it is generally more
convenient to take the first day of the month in which the earliest item
falls due, or the last day of the preceding month. Some prefer the earliest
or latest date of any item, or the earliest or latest maturity.
II. By the Product Method.
Assuming May 1st as the standard date, the term of credit for the first
item is 9 days.
The 2d item due June 10th, the time from May 1st, is 40 days, etc.
Arranging the items as below and multiplying each by the number of
days from the standard date to its maturity.
Due. Time. Items. Products.
May 10, 9 d. x $40 = 360
June 10, 40 d. x 54 = 2160
July 15, 75 d. x 70 = 5250
Aug. 9, 100 d. x _80 = _8000
Sum of items, $244 ) 15770 d ays.
Av. time, 64 T ^ d.
May 1st + 65 days = July 5th, date of pay't. Hence, the
355. Rule. — Find the date when each item matures.
Take the first day of the month in which the earliest
item becomes due as a standard, and find the number of
days from this to the maturity of each of the other
items.
Multiply each item by its number of days, and divide
the sum of the products by the sum of the items. Tlie
quotient will be the average term of credit.
Add the average time to the standard date, and the
result will be the equitable date of payment.
Notes. — 1. When an item contains cents, if less than 50, they are
rejected ; if 50 or more, $1 is added.
2. In averaging accounts, it is customary to consider 30 days a month.
But when the terms of credit are given in months, calendar months are
always meant.
142 Percentage,
6. A grocer sold the following amount of goods : June 3d,
$380 on 90 days' credit; June 10th, $485 on 30 d.; July 21st,
$834 on 70 d. ; July 28th, $573 on 40 d. ; Aug. 2d, $485 on
40 d. ; what is the average term of credit and date of payment ?
EXPLANATION. — D ue ' Time. Items. Products.
The second item is due Sept. 1, G2 d. X $380 = 235G0
July 10th. This being July 10, 9 d. x 485= 4365
the earliest date on g t ^ gQ ^ x ^ = mQQ
S^SWS S ^ * 67 d. x 573 = 38391
for the standard date. Sept. 11, 72 d. X_485 = 34920
Finding the number 2757 ) 176296
of days from this date
to the maturity of 63.9 d.
each item and proceed- July 1st + 64 d. = Sept. 3d, Date of Pay't.
ing as in Ex. 2d, the
average time is 64 days. ' Date of pay't, Sept. 3d.
Note. — When several bills are bought on common terms of credit,
find the average date of purchase, and add to the result the common term
of credit.
7. Sold goods as follows on 4 months credit : Aug. 20th,
$975; Sept. 4th, $1150; Sept. 16th, $650; Oct. 3d, $846;
Oct. 19th, $578; Nov. 19th, $1240; what is the equitable time
of payment ?
8. Bought the following bills of goods on 4 months credit :
March 10th, 1879, $250; April 15th, $260; June 1st, $540; at
what time is the amount payable ?
9. If you owe a man $84 payable in 4 mo., $120 in 6 mo.,
$280 in 3 months, what is the average term of credit?
10. If you owe one bill of $175, due in 30 days ; another of
$812, due in 60 days; another of $120, due in 65 days; and
another of $250, due in 90 days; what is the average term of
credit ?
n. Sold goods as follows: May 17th, $560 on 30 d.; June
1st, $435 on 45 d.; July 7th, $863 on 60 d.; Aug. 13th, $1000
on 15 d. ; what is the equitable time of payment ?
12. Bought March 5th, a carriage on 6 mo. for $750 ; March
10th, a span of horses for $560 on 4 mo.; April 1st, a set of
double harness $275 on 3 mo. ; May 10th, a wagon $160 on
% mo.; what is the average term of credit ?
Averaging Accounts. 143
356. To find the Extension of Credit, to which the balance
of a debt is entitled when partial payments have been made before
they are due.
13. A sold B a bill of goods March 12th, on 6 months,
amounting to $1740 ; July 10th, B paid him $500 ; Aug. 6th,
he paid $700 more ; to what additional credit is B entitled on
the balance ?
Explanation.— March 12th + 6 operation.
months equals Sept. 12th, the due $500 X 64 = 32000
date. From July 10th to Sept. 700 X 37 = 25900
12th, is 64 days. From Aug 6th _~ } —
to Sept. 12th, is 37 days ; there- L
fore the int. of $500 = int. of $1, 1740 107f d.
32000 days, and the int. of $700 = g . £^h 1Q7 d = p^ m ^
int. of $1, 25900 days ; both pay- r
ments equal the int. of $1, for 57900 days.
Therefore, B is entitled to the use of the balance ($1740—1200) = $540
for ^fa of 57900 days, or 107| days additional time, or extension of credit
on the balance. The equitable date of payment is Dec. 28th. Hence, the
Eule. — Multiply each -payment by the time from its
date to the maturity of the debt, and divide the sum of
the products by the balance remaining unpaid. TJie
quotient will be the equitable extension of credit.
Note. — If a partial payment is made before a debt is due, equity
requires that the debtor should have an extension of credit on the balance,
equivalent to the interest of the pre-payment. But the creditor is not
always willing to allow this and is not required to do it, by law.
14. A man bought a bill of goods on 90 d., amounting to
$2340.75 ; if he pays $1000 down, what extension ought he to
have on the balance ?
15. A man owes $1569.75, payable in 90 days ; 60 days
before it is due he pays $350.86, and 30 days later $211.89
more ; what extension ought he to have on the balance ?
Note. — In finding the average date of payment some accountants omit
the cents and units of dollars, using only the nearest number of tens in
the multiplication. Thus, the numbers in the last example would be
$157, $351, and $212. This shortens the process materially.
144
Percentage.
357. To find the Average Time when an account has both
debits and credits.
16. What is the average time and date of paying the follow-
ing account :
Dr. Geo. Bancroft in acct. with Miller & Co. Or.
1883.
1883.
May 21
For Mdse. 3 mo.
$500
May 24
By Cash.
$300
" 28
a a a
250
June 8
" Sundries 60 d.
400
June 9
" " 30 d.
160
July 21
" Cash.
100
Dr.
Product Method.
Or.
Due.
Items.
Days.
Prod.
Due.
Items.
Days.
Prod.
Aug. 21
$500
112
56000
May 24
$300
23
6900
" 28
250
119
29750
Aug. 7
400
98
39200
July 9
160
69
11040
July 21
100
81
8100
$910
800
110
96790
54200
$800
54200
) 42590 ( 387 T *r days, or 390 d.
Ans. Bal. $110, due in 390 d. from May 1st, or May 25th, 1884.
Explanation. — Having found when each item of debt and credit
becomes due, by adding its term of credit to its date, we assume as the
standard date the first day of the month in which the earliest item on either
side of the account matures, viz.: May 1st.
Multiply each item on both sides by the number of days between its
maturity and the standard date, and divide the difference between the
sums of the products (42590), by the difference between the sums of the
items (110). The quotient is the average time of payment.
Since the time from May 1, 1883, to May 1, 1884 = 1 year, the date of
payment is 390 d.— 365 d. = 25 d. Hence the bal. $110 is equitably due
May 25th, 1884.
Dr.
Interest Method.
Cr.
Due.
Items.
Time.
Interest.
Due.
Items.
Time.
Aug. 21
$500
112 d.
$9,331
May 24
$300
23 d.
" 28
250
119 d.
4.95|
Aug. 8
400
99 d. '
July 9
160
69 d.
1.84
July 21
100
81 d.
$910
800
$16.13
9.10
$800
Int.
$1.15
6.60
1.35
$97lO
Int.at6%on $110 fori d, = ,018)7.03 ( 390 days from May 1, '83, or May 25,
Averaging Accounts. 145
Explanation. — Taking the interest at 6^, there is a bal. due at the
assumed date, May 1st, '83, of $110, and a loss of $7.08 interest. To bal-
ance this loss of int., the payment must be deferred till the int. of $110 shall
be equal to $7.03. The int. of $110, at 6% for 1 d., is .018, and $7.03-r-
.018 = 390. Hence, the time of payment should be 390 d. = 1 yr. 25 d.
from May 1st, '83 = May 25th, 1884.
358. From the preceding illustrations we derive the fol-
lowing
Rules.
1. Product Method. — Write the date at which each
item on both sides matures, and assume the first day of
the month in which the earliest item on either side
becomes due, as the standard date. Find the number of
days from this standard to the maturity of the respec-
tive items.
Multiply each item by its number of days, and
divide the difference between the sums of products by
the difference between the sums of items ; the quotient
will be the average time.
If the greater sum of items and the greater sum
of products are both on the same side, add the average
time to the assumed date ; if on opposite sides, subtract
it ; and the result will be the date when the balance of
the account is equitably due.
Notes. — 1. In finding the maturity of notes and drafts, 3 days grace
should be added to the specified time of payment.
2. When no time of credit is mentioned, the transaction is understood
to be for cash, and the payment due at once.
II. Interest Method.— Find the interest of each item
for the time from the. standard date to the maturity of
the respective items, and divide the balance of the
interests by the interest of the balance of items for 1 day
or 1 month ; the quotient will be the number of days or
months, as the case may be, between the standard date
and the time of settlement.
When the balance of account and interest are both, on
the same side, add this to the standard date ; if on oppo-
10
146
Percentage,
site sides, subtract it ; the result will be the date of set-
tlement.
Note. — The average time will be the same whatever the rate of
interest.
359. It is advisable for the learner to solve the following
examples by both the preceding methods :
17. Balance the following account by both methods.
Dr. J. H. Strong & Co. in acct. with Smith & Crane. Cr.
1883.
Mar. 25
To Mdse., 60 d.
$560
Apr. 30
By Sundries, 30 d.
$450
Apr. 7
a (( a
830
July 13
" Cash.
500
May 2
a a {(
730
Aug. 31
" Dft., 30 d.
260
Note. — In this example the bal. of items and excess of products being
on opposite sides, the average time is subtracted from the standard date.
18. What is the balance of the following account and
when due ?
Dr. H. Morgan in acct. with Lockwood & Co. Cr.
1880.
1880.
July 20
To Sundries.
$760
Aug. 26
By Flour.
$520
Aug. 10
a ((
540
Sept. 12
" Stocks, 30 d<
300
Sept. 15
a a
850
Oct. 1
" Cash.
385
19. Find the average time of paying the following account :
Dr. George Jenkins. Vr s
1881.
1881.
Mar. 1
To Mdse,, 30 d.
$500
Apr. 12
By Draft, 20 d.
$400
Apr. 5
" << 3 mo.
700
May 10
" Cash.
540.
May 20
" " 4 mo.
850
June 4
a, a
60O
Averaging Accounts. 147
20. What is the balance of the following acct. and when due ?
Dr. Wm. H. Jackson. Or.
June 1
To bal. of acct.
$745.37
June 10
By grain, 30 d.
$545.60
" 20
" silks, 30 d.
1050.83
July 12
a (( tt
675.31
July 14
" wh. g'ds,"
971.55
" 31
" cash.
900.40
Aug. 3
" sundries,"
1260.10
Aug. 15
" note, 30 d.
1000.00
21. At what date can the balance of the following account be
equitably paid ?
D
W. H. Hendeickson.
Or.
1882.
1882.
Apr. 7
To Mdse., 2 mo.
$300
May 1
To Mdse., 60 d.
$350
July 5
" " 3 mo.
500
June 10
" M 30 d.
500
Aug. 10
" "I mo.
400
Aug. 30
" Cash.
250
360. In the following examples different dates may.be
assumed -as the standard.
22. What is the balance of the following account and when
equitably due ?
Dr.
A. P. Holmes in acct. with Lord & Taylor.
Or.
1878.
1878.
Aug. 14
To Sundries.
$1100
July 5
By Mdse.
$585
" 21
a ((
950
" 18
a a
640
Sept. 1
a a
760
Aug. 11
a <(
965
* 10
<( (4
1000
Sept. 20
a a
800
Am. Bal, $820, Due Oct, 28, 1878,
148 Percentage.
23. Find the balance of the following acct. and when due :
Dr. A. B. in acct. with 0. D. Cr.
1880.
1880.
Aug. 11
For Mdse.
$160
Sept. 2
By Sundries.
$75
Sept. 5
a u
240
Oct. 10
" Note, 30 d.
100
Oct. 20
(( 1 horse.
175
Nov. 1
" Cash.
110
24. Find the bal. of the following acct. and when due :
Dr. Wm. Gorham in acct. with John - Hendrix. Cr.
1880.
1880.
Feb. 10
For Mdse., 4 mo.
$450
Mar. 20
By Sundries, 3 m.
$325
May 11
<.( a o (t
500
July 9
" Draft, 60 d.
150
July 26
a a o li
360
Sept. 15
" Cash.
400
25. Average the following account :
Dr. James Green & Co.
Or.
1882.
1882.
Jan. 10
To Mdse., 3 mo.
$450
!jan. 1
By Bal. of Acct.
$485
" 25
" " 30 d.
265
Feb. 10
" Note, 3 mo.
2500
Apr. 20
« " 3 mo.
850
Mar. 1
1
u Draft, 30 d.
360
\I 26. Balance the following account :
* Dr. C. J. Hamilton.
Cr.
1880.
1880.
Jan. 20
To Sundries, 30 d.
$500
Jan. 20
Byrealestate,60d.
$400
Feb. 12
60 d.
340
Mar. 1
" Draft, 60 d.
200
Mar. 1
30 d.
300
:
" 20
"Cash.
400
Cash Balance.
149
27. Average the following account ;
Dr. Henry J. Raymond & Co.
Or.
1882.
1882.
Aug. 10
To Mdse., 60 d.
$150
Aug. 25
By Mdse., 30 d.
1500
Oct 1
" Cash.
350
Sept. 20
" " 30 d.
350
" 18
" Dft., 30 d.
250
28. Find when the balance of the following account becomes
due:
A. B. bought of C. D., July 16th, 1883, merchandise $350 ;
Aug. 11th, $465; Sept. 9th, $570; Sept. 14th, $850; Oct. 18th,
$780. The former paid August 1st, $360; Sept. 30th, in grain
$340; Oct. 5th, cash $500; Oct. 21st, $625.
Cash Balance.
361. To find the Cash Balance of an account, at a given date.
29. Find the cash balance of the following acct., due July
15th, 1880, at 6% int. :
Dr. Thomas Packard in acct. with Henry Selden. Cr.
1880.
Mar. 10
To Mdse., 30 d.
$650
1880.
Apr. 20
By Bal. acct.
$500
Apr. 1
" Cash.
1000
May 13
" Dft. on 90 d.
940
May 26
" Note, 60 d.
1260
June 1
" Bank Stock.
1000
OPERATION.
Date.
1880.
Apr. 9
" 1
July 28
Days.
Items.
Products.
Date.
1880.
Days.
Items.
97
$650
63050
Apr. 20
86
$500
105
1000
105000
Aug. 14
-30
940f
-13
1260*
June 1
44
1000
2910 28200f 2440
2440 196250
Bal. of items, $470 103380
6 1 000 ) 92J870 Balance of products.
Bal. of int., $15,478
And $470 + $15.48 = $485.48, Cash balance.
Products.
43000
44000
16380*
103380
150 Percentage.
Analysts. — Taking the given date of settlement, July 15th, as the
standard, we find the maturity of each item, as before, in days. The
third item of debits is a note on 60 d., with 3 days grace ; hence, it is not
due till 13 days after the settlement, or July 28th. This is indicated by
the sign — , and the item being entitled to interest for 13 days, its
product is placed on the credit side of the account.
The second item of credits is a draft on 90 days, with 3 days grace, and
it is not due till Aug. 14th, 30 days after settlement, which is also
indicated by the sign — , and its product is placed on the Dr. side.
Since each item is multiplied by its number of days, dividing the
balance of products by 6000 gives $15.48 = interest of bal. at 6%. And
the bal. of items, $470 + $15. 48 = $485.48, the cash balance required.
Hence, the
Rule for Product Method.
Find the number of days from the given date to the
maturity of eaeh item.
Multiply each item on both sides by its number of
days ; if the maturity of any debit item extends beyond
the date of settlement, place its product on the credit
side ; if the extension is a credit, place its product on the
debit side.
Divide the balance of products by 6000, and the quo-
tient will be the balance of interest at 6%.
J¥7ien the balance of items is on the same side with
the balance of interest, add the interest to the items ;
if on opposite sides, subtract it; the result will be the
cash balance required.
Notes. — 1. In settling mercantile accounts interest is not always
reckoned. This matter is regulated by. previous agreement. When
interest is charged it is calculated from the time the account is due. It
may first be found at 12% as in averaging accounts, and the result
changed to the legal rate.
2. The reason for placing the product of an item on its own side
when it becomes due before the time of settlement, is because it is
entitled to interest for the intervening time.
In like manner, if a credit extends beyond the settlement, equity
requires that interest should be allowed on that item. Hence, its
interest for that time must either be subtracted from its own side, or be
added to the opposite. The latter is the more convenient, and therefore
adopted.
Cash Balance.
151
362. The amount due on an account current at a given date
may be found by the interest method, or by the product
method. When interest is not charged it is only necessary to
find the merchandise balance. (Art. 346.)
30. What is the cash balance on the following account, July
1st, 1881, interest at 6% ?
Dr.
A. B. in account with C. D.
Or.
1881.
! 1881.
March 1
For Mdse.
$120
! April 2
By Sundries.
$300
May 10
a a
340
" 20
" Cash.
450
May 22
" " on30d.
560
June 8
" dft. on 30 d.
120
Interest Method.
Items.
Days.
Int.
Due.
1881.
Items.
Days.
Int.
$120
122
$2.44
April 2
$300
90
$4.50
340
52
2.95
" 20
450
72
5.40
560
10
0.93
July 11
120*
-10
1020
0.20*
870
$9.90
870
6.52
6.52
$150-
$3.38 =
$146.62 ca
ish balance.
Ba
1. of Int.
, $3.38
Due.
1881.
March 1
May 10
June 21
Kule for Interest Method. — Take the given date of
settlement as the standard and multiply the respective
items by the number of days between this date and the
due date of each item.
Find the interest on each item at the given rate, and
the difference between the sums of debit and credit
interest will be the balance of interest.
WTien the balance of items and the balance of interest
are both on the same side, add them, when on opposite
sides, subtract them, the result will be the cash balance.
Note. — Interest tables are much used in making out accounts current.
After an account is balanced it is considered the same as cash and draws
interest on the amount.
152 Percentage.
363. Second Form of an account current including interest.
Br. A. B. in % current with 0. D. Cr.
1881.
Days. Int.
Items. !
1881.
Days.
Int.
Items.
March 1
Mdse.
122 2.44
$120.00
April 2 Sundries.
90
4.50
$300
May 10
(i
52 2.95
340.00 1
■ 20 Cash.
72
5.40
450
May 22
" as June 21
10 I0.93
560.00
July 11 Dft. on 30 d.
-10
120*
July 1
Int. on dft.
10 0.20*
July 1 Bal. of Int.
3.38
U u
Bal. of Int.
3.38
11
" M Acct.
146.62
Balance.
9.90
1020.00
1
9.90
1020.00
ii ii
$146.62
Note. — Since the date when the draft is due, is 10 days beyond the time
of settlement, interest is charged for that time to the Dr. side. As the
balance of interest is on the Cr. side, the draft is credited to items on that
side and charged to interest on the other.
31. Find the cash balance of the following %, Aug. 5th,
1882, at
Dr.
\o/?
Geo. Bancroft in % with H. Greely.
Cr.
1882.
June 10
To Mdse.
$200
1882.
June 15
By Cash.
$100
* 30
a a
300
" 30
a a
150
July 11
a a
120
July 6
a a
200
" 24
a a
250
" 30
a a
300
32. Find the cash balance of the following
i, Oct. 30, 1882,
at
Dr.
James Morris in
% with John Jay.
Cr.
1882.
Jan. 5
To Mdse., 60 d.
$182
1882.
Feb. 1
By bal. of %.
$300
Feb. 12
u " 30 d.
270
Mar. 30
" Cash.
250
Mar. 7
" " 30 d.
480
Apr. 20
a a
200
Apr. 15
" " 60 d.
640
June 15
" Note, 30 d.
300
May 9
" " 60 d.
530
Aug. 1
" Cash.
400
33. Find the cash balance of the same account at
Averaging Accounts Current
153
34. What is trie cash balance of the following acct., Dec. 31st,
1809, at Y/o ?
Dr. S. Parkhurst in acct. with G. P. Putnam. Or.
1869. !
Sept. 10 To Mds., 30 d.
$1250.15
1869.
Sept. 25
By Mds., 60 d.
$1560.50
Oct. 1
" " 60 d.
1015.60
Oct. 10
" " 90 d.
948.30
" 23
" " 45 d.
1500.85
" 30
" M 40 d.
1430.65
Nov. 15
" " 60 d.
1743.44
Dec. 15
" " 30 d.
1365.42
35. What is the cash balance on the following acct., Jan.
10th, 1882 ?
Dr. S. B. Chittenden in acct. with A. T. Stewart. Or.
1881.
Aug. 4
To Sundries,3 m.
$1400
July 5
By Mdse., 3 mo.
$685
* 20
a a a
1050
" 18
a <( tt
840
Sept. 10
a a a
780
Aug. 11
a (( a
960
" 24
a a tt
1300
" 18
" Draft, 30 d.
800
36. Reduce the following transactions to the form of an
acct. bearing interest at 6%, and find the cash balance :
Feb. lith, 1870, C bought goods of D amounting to $1250;
March 14th, a bill of $2160 ; Apr. 10th, a bill of $1700; Apr.
30th, a bill of $1070 ; May 6th, a bill of $2000. March 1st,
1870, sold a bill to D of $1640 ; March 20th, a bill of $1160;
Apr. 15th, a bill of $1600 ; May 1st, a bill of $1340 ; May 21st,
a bill of $1000 ; what was the cash balance June 10th, 1870 ?
37. What was the cash balance due July 20th, 1869, on the
following account, at 1% int. ?
s(Dr. George Clark & Co. in acct. with Chas. Anderson. Cr.
1869.
Mar. 1
For Mdse., 3 mo.
$500
1869.
Apr. 5
By Mdse., 3 mo.
$350
" 20
" 2 mo.
750
" 20
" " 2 mo.
900
Apr. 10
" 5 mo.
410
May 1
" " 4 mo.
620
May 21
" 1 mo.
600
" 22
" Cash.
200
1 54 Percentage.
38. Find the balance due Sept. 1st, at 6% on the preceding
amount.
39. Find the balance of the same account due Nov. 1st,
at 6%.
40. Reduce the following memoranda to the form of an
account, and find the cash balance due Jan. 1st, 1879 :
Aug. 1st, 1878, A bought goods of B amounting to $560 ;
Aug. 26th, $840 ; Sept. 21st, $1000 ; Oct. 12th, $1370 ; and
Nov. 1st, $600. A sold B, Sept. 11th, 1878, wheat amounting
to $350 ; Oct. 1st, wool amounting to $760 ; Oct. 31st, $400
worth of butter ; and Nov. 16th, paid him $1000 cash.
Account Sales.
364. An Account Sales is a record of the goods sold by an
agent for his principal, with his expenses and charges.
Notes. — 1. The charges include freight, cartage, storage, advertising,
insurance, commission, guaranty, etc.
2. The invoice or sales form the credit side of the account, and the
expenses the debit side.
l. H. Standart, of Detroit, sold March 12, 1883, the
following consignment of goods for J. L. Starbuck & Co., of
Boston :
150 pieces Merrimac prints, at $4 ; 135 pieces shirting, at
$7.50; 1 case of 85 Bay State shawls, at $8.75 ; 65 pieces flan-
nel, at $12.50; 300 pair shoes, at $2.25; 150 pair boots,
at $4.20.
Charges for freight, $35.00 ; cartage, $3.50; storage, $5.00 ;
insurance, $6.50; commission and guaranty, b%. What were
the net proceeds ?
Averaging Accounts Sales.
155
Account Sales of Merchandise for acct. and risk of
J. L. Starbcjgk & Co., Boston.
Mar. 12
To J. Smith, 150 pes. Mer. pr. @ $4
" 135 pes. Shirt.® $7.50
Hoyt & Co., 1 c. 85 B.S.sh.@$8.75
" 65 pes. flan. @ $12.50
L. Wood, 300 pr. shoes @ $2.25.
" 150 pr. boots @ $4.20,
Charges.
Freight, --------
Cartage, - -
Storage, --.-----
Insurance, -- -
Commission and Guaranty, 5$, -
Net Proceeds, - -
$600
1012
50
743
75
812
50
675
630
$4473
$35
3
50
5
6
50
223
69
273
$4200
75
69
06
2. Put the following into the form of an Account Sales :
James Scott, of New Orleans, sold on account of J. Hamil-
ton, of Cincinnati, Nov. 16th, 1882, 300 bbls. of pork to
W. Gerard & Co., at $27 ; 1150 hams, at $1.75, to J. Ramsey ;
875 kegs of lard, each containing 56 lb., at 12 cts., to Henry
Parker, and 750 lb. of cheese, at 18 cts., to Thomas Young.
Nov. 30th, 1882, paid freight, $65.30; cartage, $15.25;
insurance, $6.45; commission and guaranty, at 5%. What
were the net proceeds ?
3. Samuel Basset, of New York, sold on account of James
Field, of St. Louis, Dec. 3d, 1882, 85 bales cotton, at $96.50;
63 barrels of sugar, at $48.25 ; 37 bbls. molasses, at $35.
Paid freight, $45.50 ; insurance, $15; storage, $35.50; com-
mission and guaranty, 3 \%. What were the net proceeds ?
365. The Commission and other charges are considered due
by some at the average date of sales ; by others at the average
maturity of sales. This is usually settled by agreement.
156
Percentage.
Note. — The method of averaging an account sales is the same as that
for averaging an account having both debits and credits, except in the
matter of adjusting the date for the commission and other charges.
366. To Average an Account Sales, and find when the net pro-
ceeds are due.
4. Average the following, and find the due date of net
proceeds:
Eeceived on consignment, 1000 bbl. flour from B. & Co.,
Chicago.
Sales.
July
11
Aug.
5
u
20
Sept.
2
July
1
u
1
a
3
200 bbls. flour, sold on 30 d.
350 " " " 10 d.
250 " " * 30 d.
200 " " " 60 d.
Charges.
Freight, - -
Cartage,
Storage, -
Commission, 2\% on $5920, •
Commercial Balance, -
55.50
6.20
6.00
5.75
|$1100
00
2170
00
1500
00
1150
00
$5920
$450
25
30
75
150
00
148
00
779
$5141
00
00
00
SOLUTION.
I. Find the average date of sales
Date.
Due Aug. 10
" Sept. 19
" Nov. 1
Items.
$1100
2170
1500
1150
$5920
Days.
40
45
80
123
Products.
$44000
97650
120000
141450
) 403100
Av. time of sales, 68 days.
Sales due July 1st + 68 d. = Sept. 7th.
Averaging Accounts Sales. 157
II. Find the average date of Charges :
Date.
Items.
Days.
Products.
ue July 1
$450.25
$00.00
u u 1
30.75
00.00
« 3
150.00
2
300.00
" Sept. 7
148.00
68
10064.00
779.00
) 10364.00
A v. time, 13 days.
Charges due July 1st + 13 d. = July 14th.
Averaging the sales and expenses, they now stand as follows :
Date. Items. Days. Prod. Date. Items. Days. Prod.
Due July 14 $779 13 10127 | Due Sept. 7 $5920 68 402560
_779 ^0127
15141 ) 392433
Av. time, 76 d.
Net proceeds $5141 due July 1st + 76 d. = Sept. 15. Hence, the
Rule. — I. Find the amount and the average date of
sales. The date of sales will be the date of the commis-
sion and guaranty. (Art. 357.)
II. Find the average date of the charges, make the
charges the debits and the sales the credits, and find the
average date for paying the balance.
5. Put the following items into the form of an account sales,
find the net proceeds and date of payment :
A. B. Harrison, of Buffalo, sold a consignment of goods
from Chase & Co., Chicago, as follows: Nov. loth, 1882,
135 chests tea, at $45, on 30 d. ; 'Nov. 20, 75 sacks coffee, at
$28, on 2 mo.; Dec. 1, 256 kegs lard, at $4.50, 30 d.; same
date 285 tubs butter, at $18.37, on 2 mo. Paid freight
Dec. 1, $23.75; cartage, $5.40; storage, Dec. 10, $7.80;
commission, 2J$.
6. Same parties sold Sept. 1, on 3 mo., 3520 lb. sugar, at
!12J; Sept. 15th, 25 chests tea, each 85 lb., at .98, on 2 mo.;
Oct. 2, 28 half-chests Oolong tea, 42 lb. each, at $1.05, on
2 mo. The charges were paid Oct. 15, freight and cartage $85,
commission and guarantee 5%.
1
AET^ERSHIP.
fe- 11 -^-
367. Partnership is the association of two or more persons
for the transaction of business.
368. The persons thus associated are called Partners.
369. The association is called a Firm, Company, or House.
370. The Capital is the money or property furnished by the
Partners.
371. The Assets or Resources of a firm are various kinds of
property belonging to it.
372. The Liabilities are its debts.
373. The Net Capital or Worth of a firm is the excess of its
property above its liabilities.
374. The Insolvency of a firm is the excess of its liabilities
above its property or resources.
Note. — The Net Insolvency is the difference, made by the gains of a
firm, between its present and former insolvency.
375. The Net Gain or Loss is the difference between the
total gains and total losses.
376. Partnerships are General, Special, or Limited.
377. A General Partnership is one in which not only the
property of the firm, but the private property of each of the
partners is liable for its debts.
378. A Special Partnership is one in which a person puts
in a certain amount of money, and loses only that amount in
case oifailure*
Partnership. 159
379. A Limited Partnership is one in which, if certain
things are done, a person's private property shall not be respon-
sible for the firm debts.
Notes. — The things required in most States for the formation of
limited partnerships are : - v
1st. The arrangements must be in writing, signed and recorded in a cer-
tain public office.
2d. There must be at least one general partner.
3d. The special partners can take no actim part in the business, and
their names must not appear in the firm name.
4th. The amount which the special partners contribute must be actually
paid in and duly advertised. If any one of these requirements is omitted*
the partnership becomes general.
380. The gains and losses of a firm are divided according
to the previous agreement between the partners. Thus,
In some cases the gains or losses are divided in proportion to>
the capital, or the average investments of the partners.
In others the inequalities of 'their investments are adjusted
by allowing each partner a specified salary, which is taken
from the gains of the firm before they are divided, no interest
account being kept.
But the more common practice is to credit each partner with
interest on his capital and charge him interest for sums he
draws out ; then divide the gain or loss according to certain
percentages or fractional parts.
Notes.— 1. Upon dissolution the partners are individually liable for
the existing debts of the firm.
2. If a partner assigns his interest in the business, the word " release"
must be used in order to pass the whole interest.
381. To find the Net Gain or Loss of a Partnership.
l. A and B commenced business with a capital of $8000
cash and $3000 merchandise, and bills payable $1450. At the
end of the year they had $5500 in banfc^$4500- ij% goods, and
$2950 in bills receivable, and debts ow<£t by firm $9$). What
was the net gain or los§ of the firm ?
160 Percentage.
Assets at Commencement.
Cash $8000
Mdse 3000
Assets 11000
Liabilities 1450
Net capital $9550
$12000- $9550 = $2450, Net gain, Ans. Hence, the
Assets at Close.
Cash in bank $5500
Mdse 4500
Bills receivable 2950
Assets 12950
Liabilities 950
Net capital $12000
Rule. — To find the Net Gain. — Subtract the net capital
at commencement from the net capital at closing.
To find the Net Loss.— Subtract the net capital at clos-
ing from the net capital at commencement.
382. To divide the Gain or Loss in proportion to each partner's
capital, when employed for the same period.
l. A and B formed a partnership ; A furnished $3000,
B $5000 ; they gained $2000, and agreed to share the profit or
loss in proportion to the capital of each ; what was each
partner's share ?
1st Method.— $3000 + $5000 = $8000 Capital of firm.
f $$=§» hence A ' s share=$2000 x f = $750 A's gain.
5ooo_5^ m B's share = $2000 x § = $1250 B's gain.
Proof.— Whole gain = $2000
2d Method.— The gain $2000-=-$8000 (cap.)=.25, or 25%. (Art. 216.)
$3000 x .25 = $750 A's gain.
$5000 x .25 = $1250 B's gain.
Proof. — Whole gain-'
3d Method.— $8000 : $2000 : : $3000 : A's gain, or $750.
$8000 : $2000 : : $5000 : B's gain, or $1250. Hence,
Rules. — I. By Fractions. — Make each man's capital the
numerator, and the irliole capital the denominator of
a common fraction ; multiply the whole gain or loss by
these fractions, and the products will be the respective
shares of the gain or loss.
Partnership. 161
II. By Per Cent. — Find what per cent the gain or loss
is of the whole eapital, and multiply each man's capital
by it.
III. By Proportion. — The whole capital is to each part-
ner's capital, as the whole gain or loss to each paHner's
share of the gain or loss.
2. A and B buy a store which rents for $950 a year ; A
advanced $3500, B $4800; how much rent should each
receive ?
3. A and B form a partnership, A furnishing $2200 and B
$2500 ; they lose $800 ; what is each one's share of the
loss?
^4. The net gains of A, B, and C for a year are $12800 ; A
furnishes $25000, B $18000, and $15000 ; how should the
profit be divided?
5. A invested $12000 and B $8000 in a business. A's share
of the gain or loss is to be § and B's -J. At the close of the
year their resources are $25000 in goods and cash, and liabilities
$15000 ; what is the net capital, and what each partner's share
of the gain or loss ?
6. X, Y, and Z bought a ship on speculation ; X put in
$30000, Y $20000, and Z $15000 ; they sold it at a loss of
$7500 ; what was each man's share of the loss ?
7. A, B, C, and D form a partnership with a capital of
$57000 ; A furnishing $10000, B $12000, C $5000, and D the
remainder ; they make 15% of the joint stock ; what is each
partner's share of the profit ? v
8. The shares of the joint stock of a firm consisting of three
partners, are as £, -J, and J ; they divide a profit of $3900 ;
what is each partner's share ?
9. A put $7500 and B $6000 into a land speculation ; and
A's share of the loss was $225 ; what was B's share ?
10. Two men formed a partnership, the former furnishing
3 times as much capital as the latter ; they gained $12500 ;
what was each one's share of the gain ?
168
Percentage.
-4- 11. A, B, and entered into partnership; A furnishing £,
B \ and C the rest of the capital. On winding up the busi-
ness, O's share of the profit was $4518 ; what were the respec-
tive dividends of A and B ?
383. When each partner is allowed to withdraw a stated sum,
and no interest account is kept. (Art. 380.)
12. A and B form a partnership, investing $6000 each, and
agree to share the gains or losses equally. A drew out $1200
and B $1000. Kequired the gain or loss of each at the end of
the year, their books showing the following results :
Resources.
Cash $7000
Mdse. per inventory 7200
Bills receivable 2400
Debts due per Ledger 5000
Total resources $21600
Liabilities.
Firm owes per Ledger $3000
Bills payable 1600
Total liabilities $4600
Net capital at closing is $21600- $4600 =
A invested $6000
Less withdrawal 1200
$17000
A's Cr. balance.
B invested $6000
Less withdrawal 1000
A's i net gain = $3600.
$5000 B's Cr. balance. $9800
Net gain of firm $7200
B's ^ net gain =
A invested $6000
Withdrew _1200
4800
A's £ net gain 360
A's net cap. at closing $8400
Proof.
B invested $6000
Withdrew 1000
5000
B's I- net gain. 3600
B's net cap. at closing $8600
$8400 + $8600 = $17000, firm's net capital.
Notes. — 1. Amounts withdrawn are sometimes considered resources.
But money withdrawn by a partner cannot properly be said to belong to
the resources of the firm.
2. When a partner has a fixed salary it is generally considered a part
of his investment.
Partnership Settlements.
163
13. A and B formed a partnership ; A furnished $15000, B
11250, and agreed that A should share J of the gain or loss,
and B f. During the partnership A withdrew $600 and B
$400. What were their gains or losses at the close, their
resources being $21000 and liabilities $30000, no interest acct.
being kept.
OPERATION.
Liabilities £30000
Less resources 24000
Firm's net insolvency. ...... 6000
A's floss 18750
B's § loss 12500
Total loss $31250
A's investment $15000
Lessarnt. withdrawn 600 $14400
B's investment $11250
Less amt. withdrawn 400 10850
Firms net investment 25250
Add firm's insolvency 6000
Firm's net loss $31250
A's | loss $18750 less net invest. $14400 = $4350, A's net insolvency.
B's f loss $12500 less net invest. $10850 = 1650, B's net insolvency.
Proof.— $6000, Firm's net insol.
14. A, B, and C formed a partnership; A put in $5000,
B $4000, and C $2500. A withdrew $1000, B $800, and C
$500. They agreed to share the gain or loss in proportion to
their original investments, no interest account being kept.
At the close, what was each partner's share of gain or loss,
and the net capital of each, as shown by the following
statement :
Resources.
Cash in bank $3475
Mdse. per inventory 5150
Bills receivable 4225
Debts due firm . . . . . 3150
Total resources $16000
Liabilities.
Bills payable $3000
Rent, etc 700
Debts firm owe 2300
Total liabilities $6000
15. A put $10000 into a partnership and B $5000. They
agreed to divide the gain or loss in proportion to their original
investments, and to keep no interest account. During the year
A withdrew $800 and B $500 ; what was the net capital of
each at the close of the year, their resources being $25800 and
their liabilities $18500 ? What per cent of their investment
was the gain or loss ?
164 Percentage,
384. When one or two partners are allowed a fixed salary and
no interest account is kept.
16. A and B formed a partnership, agreeing to share the gains
or losses according to their investments; A furnished $20000,
and was to receive a salary of $1000, B furnished $15000, and
was to have $750 salary ; what was the gain or loss of each and
what his net capital at the close, by the following statement :
Resources. Liabilities.
Cash on hand $6000 Bills payable $14000
Mdse. per inventory 5000 Rent, etc 1500
Bills receivable _3500 Total liabilities $15500
Total resources $14500
Liabilities $15500
Resources 14500
Firm's net in sol 1000
A's 2 loss 215711
Total loss $37750
A's invest
Add salary 1000 $21000
B's invest 15000
Add salary 750 15750
Firm's net invest 36750
Add firm's net insol 1000
Firm's net loss $37750
A's | loss, $21571.43 less net invest. $21000 = $571.43 A's net insolvency.
B's f loss, $16178.57 less net invest. $15750 = 428.57 B's "
Proof $1000.00 Firm's net insol.
17. A and B each invested $6000. A received a salary of
$1000 a year, and B $1500 for services. A drew out $650, B
$500. What was each partner's interest in the firm at the end
of the year, by the following statement :
Resources $48500
Liabilities 1250 Firm's net cap $36000
A's investment $6000
A's salary 1000
7000
Less amt. withdrawn 650
A's credit balance 6350
B's investment $6000
B's salary 1500
7500
Less amt. withdrawn 500
B's credit balance 7000 13350
Net gains of firm $22650
Partnership Settlements.
165
A's credit balance $6350
B's credit balance $7000
" i gain 11825
" net capital
" Again 11325
" net capital $17675
385. To find each partner's interest at the end of the year or
close of the partnership.
18. A and B formed a partnership Jan. 1st, 1882, and agreed
to share the gains or losses equally. A's capital was $6000 and
B's $7250 ; each partner was allowed 6% on his capital and
charged 6% for the sums withdrawn. March 1st, A withdrew
$300; July 9th, $250 ; Sept. 10th, $200 ; Dec. 18th, $150. B
withdrew Apr. 17th, $100; Aug. 4th, $400; Nov. 23d, $250.
"What was each partner's interest in the business Jan. 1st, 1883,
their resources being $26500 and liabilities $6000 ?
Resources $26500
Liabilities 6000
$20500 Firm's net capital-
A's amt. withdrawn $900 ; Av. date July 7th, 178 d. to Jan, 1st.
B's " " $750; " " Aug. 27th, 127 d. " "
A's capital - $6000
Less withdrawn 900 $5100.00
Int. on cap. 1 yr $360
Less int. on $900, 178 d 26.70 333.30
A's credit balance $5433.30
B's capital $7250
Less withdrawn 750 $6500.00
Int. on cap. 1 yr $485
Less int. on $750, 127 d 15.87 419.13
B's credit balance $6919. 13
Firm's net capital $20500.00
A's credit balance $5433.30
B's " " 6919.13 12352. 43
Firm's net gains $8147.57
B's credit bal $6919.13
" igain 4073.781
" net capital $10992.9H
A's credit bal $5433.30
" i gain 4073.78^
" net capital $9507.08^
Firm's net capital, $20500.
166
Percentage.
19. C and D formed a partnership with a capital of $12000
apiece. They agree to share the gains or losses equally, each
receiving interest on his capital and paying interest on all
sums he withdraws. At the close of the year they had cash in
bank $8000, merchandise $32500, bills receivable $2000. They
owed bills payable $4000, other debts $5040. During the year
C drew out $2015, the int. on which to the end of the year was
$40.50. D drew out $4100, the int. on which to the end of
the year was $32. How much did they gain or lose, and what
was each partner's net capital at the end of the year ?
20. A firm of 3 partners commenced business with a capital
of $6000 each. The gains and losses were to be shared equally,
each was to have interest on his capital and pay interest o*n
sums withdrawn, which sums were considered as taken from
the gains and not from the capital. What was the net gain or
loss, and what each partner's net capital at the end of the year,
when their accounts were as follows :
Assets.
Cash $4250.00
Mdse 16500.00
Bills receivable 1000.00
Debts due firm 4120.67
Partners' withdrawals with interest.
Adrewamt 1027.72
B " " 2070.11
C " " 3242.04
$32210.54
Liabilities.
Bills payable $500.00
Personal debts 630.35
Cap. with interest 19080.00
Net gain 12000.19
A's± gain... $4000.06
Drew out.... 1007.57
A's bal 2992.49
B'sigain.... 4000.06
Drew out.... 2049.6 1
B's bal 1950.45
C'sigain
4000.06
Drew out.... 3213.92
C's bal $786.14
$32210.54
21. The firm of A & B formed a partnership Jan. 1st for
1 year, investing $8000 each. They were to have 6% interest
on their capital and be charged 6% on sums withdrawn. The
gains or losses were to be shared equally. Apr. 4th A drew out
$500, July 10th $400, and Sept. 5th $200. B drew out May 6th
$700, Aug. 12th $300, and Oct. 4th $400. What was each
partner's net capital on closing, the net gains being $3850 ?
Partnership Settlements. 167
386. To divide the gain or loss in proportion to each partner's
capital, when employed for different periods, or by Averaging
their investments.
Note. — An Average Investment is a sum invested for a certain period,
equivalent to several investments for different periods. (Art. 348.)
22. A and. B enter into partnership ; A furnishes $4000 for
8 months, and B $6000 for 4 months ; they gain $2300 ; what
is each one's share of the profit ?
Explanation. — In this case the profit of each partner depends on two
elements, viz. : the amount of his capital and the time it is employed.
The Int. of $4000 for 8 mo. - Int. $4000 x 8 = $32000 for 1 mo.
And " $6000 " 4 mo. = " $6000 x 4 = $24000 " 1 mo.
Whole capital = $56000
They gained $2800; and $2800 -=-$56000 = .05, or 5%.
$32000 x .05 = $1600.00, A's share.
$24000 x .05 = $1200.00, B's share. Hence, the
Rule. — Multiply each partner's capital by the time it
is employed. Consider these products as their respective
capitals, and proceed as in the last article.
Note. — The object of multiplying each partner's capital by the time it
is employed is, to reduce their respective capitals to equivalents for the
same time, or to average their investments. (Art. 353.)
23. A, B, and C form a partnership ; A furnishing $1500
for 9 mo., B $1700 for 10 mo., and C $1400 for 15 months ;
they lose $1600; what is each man's share of the loss ?
24. Jan. 1st, A, B, and C form a partnership ; A puts in
$4000, but after 6 mo. withdraws $1000 ; B puts in $3000, and
adds $500 after 4 mo. ; puts in $2000 for the year ; they gain
$1800 ; what is the share of each ?
25. A, B, and began business Jan. 1st, when A put in
$7500, and July 1st he put in $2500 more ; B put in Jan. 1st
$12000, and May 1st withdrew $4000 ; C put in Jan. 1st
$10000, Aug. 1st he added $3000, and Oct. 1st he withdrew $7000.
At the close of the year the profit was $8500 ; how much ought
each to have, the gains being divided according to their average
investment ?
168 Percentage.
OPERATION.
Jan. 1st, A invested $7500 x 12 = $90000 for 1 mo.
July 1st, A « 2500 x 6 = 15000 $105000
Jan. 1st, B " 12000 x 12 = 144000
May 1st, B withdrew 4000 x 8= 32000 112000 $217000
Jan. 1st, C invested 10000 x 12 = 120000
Aug. 1st, C " 3000 x 5 = 15000 135000
Oct. 1st, C withdrew 7000 x 3 = 21000 114000
Total average investment for 1 month = $331000
A's share of profits, $8500 x iff = $2696if f
B's " " $8500 x iff = $28763 4 3 4 T
C's " " $8500 x H 4 - = $2937j|f
Proof.— $8500, entire profits.
Explanation. — Each investment and withdrawal is multiplied by the
number of months between its date and the time of settlement. The
products of each partner's withdrawals are subtracted from the products of
his investments, and the remainder is his average investment. The sum
of the average investments is the denominator and each separate invest-
ment the numerator of the fractions which indicate each partner's share
of the gain.
Note. — The same result may be obtained by either of the preceding
methods (Art. 382). When the first method is used, the fractions should
be reduced to their lowest terms.
26. A and B formed a partnership and divided the gain or
loss in proportion to their average investments. A put in
$6000 for 12 months, and afterwards $4000 for 6 months. He
withdrew $3000 for 4 mo., then $6000 for 2 mo., before the
close of the partnership. B put in $7000 for 12 mo., then
$6000 for 8 mo. He withdrew $4000 for 5 mo., then $8000 for
2 months. They gained $4560; what was each partner's share ?
27. X, Y, and Z formed a partnership ; X putting in $3000
for 1 year, Y $4500 for 8 months, and Z $5000 for 6 months ;
they lost $4000 ; what was each man's share of the loss?
28. Three men hire a pasture for $87.50. A put in 10 cows
for 7 months, B 60 sheep for 5 months, and 12 horses for
3 months ; 5 sheep being considered equal to 1 cow, and
4 horses equal to 5 cows ; how much should each pay ?
29. A and B are partners, A putting in $4500 and B $2500 ;
after 6 mo. they take in C who furnished $10000 ; their gain
for the year was $5000 ; what was Mie share of each ?
Bankruptcy. 1G9
30. Two men entered into speculation and their profits dur-
ing the year were $6240. At first A ? s capital was to B's as 3
to 2 ; after 4 months A withdrew £ of his and B £ of his ; how
ought the gain to be divided ?
31. A firm commenced business with a capital of $15600,
and doubled it in 1 year. A put in ^ for f of the yr., B -f for
£ of the yr., and the balance for f| of the yr. What was
each partner's interest in the concern at the end of the year ?
32. A and B are partners, each furnishing $10000 ; after
4 mo. A took out $1000 and B $1500 ; 4 mo. later each took out
the same sum as before, and at the end of the year the assets
of the firm were $15136 ; to what share was each entitled ?
33. Three men form a partnership and contribute $20000,
$30000, and $40000 respectively. A drew out $3000, B $4000,
and $5000 a year and in 3 years the assets of the firm were
$120000 ; how much belonged to each ?
BANKRUPTCY.
387. A Bankrupt is a person who is insolvent, or unable to
pay his debts.
388. Bankruptcy is the state of being insolvent or a
bankrupt.
Note. — After the assets of a bankrupt have been applied to meet his
liabilities, he still remains liable for them unless discharged by a Court
of Bankruptcy, or by a compromise with creditors.
389. The Assets of a bankrupt are the property in his
possession.
The Liabilities are his debts.
390. The Net Proceeds are the assets less the expense of
settlement. They are divided among the creditors according
to their claims.
Note. — The claims of a certain class of creditors, as employees and
others, are paid in full up to a certain amount. These are called "Pre-
ferred Creditors."
170
Percentage,
391. To find each Creditor's Dividend, the Liabilities and Net
Proceeds being given.
l. A merchant failing in business made the following state-
ment:
Liabilities.
Notes outstanding $1200
A. Booth & Co 2500
Bliss &Co 8750
Total $12450
Assets.
Cash $2737
Real Estate 1500
Merchandise 2950
Total 7187
Expenses of settling 215
Net assets $6972
The net assets $6972.00-*- $12450 liabilities = .56, or 56%, rate.
Dividend to creditors is $1200 x .56 = $672 on notes,
$2500 x .56 = $1400 to Booth & Co., and
$8750 x .56 = $4900 to Bliss & Co. Hence, the
Rule. — Find what per cent the net proceeds are of the
liabilities, and multiply each creditor's claim by it.
2. A bankrupt owes A $6500, B $4600, and D $3800; his
assets are $5950, and the expenses of settling $1700 ; what per
cent and how much will each creditor receive ?
3. A R. R. Co. went into bankruptcy, owing $48500, and
having $13300 assets ; the expense of settling was h% of the
amount distributed to creditors. What per cent and how
much did a creditor receive on $8350 ? (Art. 216.)
4. A manufacturer failed, owing A $12260, B $13850, and
C $14560 ; his assets were $28350, and the expenses of settling
were $1250. He owed $850 to employees who were to be paid
in full ; what per cent and how much did the other creditors
receive ?
GENERAL AVERAGE.
392. General Average is the equitable apportionment of
losses at sea among the owners of a cargo, when the safety of
the vessel required a portion of it to be thrown overboard.
Notes.— 1. The voluntary sacrifice of property for safety is called
Jettison.
General Average. 17i
2. The parties whose goods are sacrificed are not paid in full, but bear
their proportion also for the loss sustained.
3. Insurance companies bear their proportion of the loss, as found by
general average.
393. To establish a valid claim for a general average, three
things must be made apparent :
1st. An imminent common peril, and necessity for sacrifice.
2d. A voluntary sacrifice oi apart to save the remainder.
3d. The success of the effort to save a part, as a result of the
sacrifice.
Note. — The jettison is included in the contributory interests, and bears
its proportion of the loss.
1. A, B, and C freighted a vessel with flour from New York
to New Orleans; A had on board 1800 barrels, B 1200, and C
600 ; on her passage 600 barrels were thrown overboard.
Beckoning the value of the flour at $5.50 a barrel, what was
the average loss ?
Note. — Find the per cent of loss as in the last Article, the sum of the
values of the contributory interests being as the base. (Arts. 219, 254.)
2. In a heavy storm, the master of a London packet threw
goods overboard to the amount of $15000. The whole cargo
was valued at $74000, and the ship at $38000 ; what per cent
loss was the general average ; and how much was A's loss, who
had goods aboard to the amount of $16000 V
3. If an Insurance Co. had assumed a risk amounting to
$12000, at 2|% on the vessel and cargo mentioned in the above
example, and paid a general average loss, what would have
been its real loss by the disaster ? (Art. 215. )
4. The sloop Huron, from Chicago, carried 3000 bushels
wheat for T. Hamilton & Co., insured in Co. B. for $3000, at
2% ; 2500 barrels flour, valued at $5 a barrel, for G. Standart,
insured in Co. C. at 2\% ; and 500 bu. corn, valued at 50 cts. a
bu., for Gardner & Co , insured in Co. D. at \\%. The vessel
was insured for $25000, \ its value, in Co. A., at 3%. During a
storm the flour was thrown overboard ; what per cent was the
general average, and what the loss of each.
(s^^
394. The arrangement of problems under different heads,
as Profit and. Loss, Commission, Interest, Proportion, etc., is
convenient for reference and review, but experts perform most
of their business calculations by Analysis.
395. No specific rules can be given for the solution of
problems by analysis. Common sense and judgment are the
best guide.
396. The reasoning in general proceeds from that which is
known or self-evident, to that which is required ; from a part
to the whole, or from the whole to a part ; from a given cause
to its effect, or from a given effect to its cause.
397. Like Numbers only can be compared. When fractions
have a common denominator, their numerators are compared
like integers.
398. In finding what part one number is of another, the
number denoting the part is the numerator and that with
which it is compared the denominator.
Note. — If either or both the given numbers are fractional, they
should be reduced to a c. d. ; their numerators are then compared like
integers.
l. A merchant made $8368 in two years, and the differ-
ence in his annual gain was $986 ; what was his yearly
profit ?
Solution. — The sum minus the difference equals twice the less number.
Therefore, $8368-$986 = $7383, and $7382-5-3 = $3691, the less.
And $3691 + $986 = $4677, the greater.
General Analysis. 173
2. Bought a span of horses and a carriage for $1856 ; the
• horses were worth $268 more than the carriage ; what was the
price of each ?
3. To what number must 962 be added 3 times to make
8472?
4. Bought a horse for $465, and sold it for $240; what part
of the cost did I get ?
Solution.— $240 = ffg, or H oi $465 ; hence I got |f of $465.
5. What part of 112 yards are 96 feet? What part of
112 rods ?
6. Wliat part of ^ is -J^ ?
Note. — Reduced to a c. d. the given fractions become £ £ and §§, which
are like fractions. Now 22 is f § of 35, Ans.
7. If y\ of a ship cost £273 2s. 6d., what will g% cost ?
8. What part of £f is ^ ? 9. What part of 46f is 18| ?
10. A merchant lost $5367, which was ^ of his capital ;
what was his capital ?
Analysis. — Since $5367 = T 3 ff of his capital, ^ of it was \ of $5367, or
$1789, and \%, or the whole, was $17890, Ans.
11. A drover being asked how many sheep he had, replied,
2149 are equal to T 7 g- of them ; how many sheep had he ?
12. A man being asked his age replied, If you add to it its
half, its third, and three times three, the sum is 130; what
was his age ?
13. | of a number exceeds \ of it by 20; what is the
number ?
14. A real-estate agent sold a house for $7265 ; what was his
commission at 3% ?
Solution. — Since his commission on $1 was $ T f TT , on $7265 it was
$7265 x jf, = $217.95, Ans.
15. A house valued at $8241 is insured for f its value at \%\
what is the premium ?
174 General Analysis,
16. A country trader buys a stock of goods amounting to
$3450 ; the commission charged for buying was %\% \ bow
much must he remit to pay for the goods and commission ?
17. An auctioneer sold a lot of goods amounting to $15600
at %\% commission, and 2\% for guaranty ; the charges were,
for advertising $25.50, for storage, labor, and cartage $34.50 ;
how much was due the owner ?
18. A miller bought a cargo of wheat for $12600, and sold it
at a profit of 15£% ; how much did he gain ?
Solution.— 15^% is .155 of $1. Therefore, on $12600 lie gained
$12600 x .155 = $1953, Ans.
19. Bought a quantity of lumber for $5200 ; paid for freight
and cartage $85, commission $135. I gained 28% on the
entire cost ; for how much was it sold, and what was my
profit ?
20. If 12% of $97.50 be lost, what amount will remain ?
21. A man owning f of a bank, sold 35% of his share ; what
per cent of the whole was left ?
22. 24 is f per cent of what number ?
23. A man owned -f of a mine, and sold f of his interest for
$1710; what was the whole cost?
24. What is the interest of $840 for 2 yr. 8 mo. 24 d.
at 6%?
Analysis.— The prin. $840 x .06 = $50.40, int. 1 yr.
Int. for 2 yr. at 6% = $50.40 x 2 = $100.80
Int. for 8 mo. (f yr.) = $50.40 x f = 33.60
Int. for 24 d. (f mo.) = $4 20 x § = 3.3 6
Int. for 2 yr. 8 mo. 24 d. = $137.76
Or, the int. of $1 for 1 yr. is $.06 ; for 2 yr. 8 mo. 24 d. = 2\l yr., it
is SH x .06, or 41 ?g 06 , and the int. of $840 will be *H**£X ^M-
= $137.76, Ans.
25. What is the interest of $1165.50 for 5 yr. 3 mo. 9 d.
at n ?
26. What principal on interest from Apr. 9, 1881, to Sept. 5,
1883, will amount to $1477.59, at 7 per cent f
General Analysis. 175
27. If #600 at simple interest amounts to 8684 in 2 yr. and
4 mo., what is the rate per cent ?
Analysis.— $684, arat.— $600, prin. = $84, int.
The interest of $600 for 1 yr. at \% = $6.00.
The interest of $600 for %\ yr. at 1 % = $14.00.
Since $14 int. require the prin. at 1% fy yr., $84 int. for the same time
will require as many per cent as $14 are contained times in $84, or
<j?c, Ans.
28. If $800 yield $56 interest in a certain time, what will
$390 yield at the same rate ?
29. If you invest $12250 in R. R. stock and receive an
annual dividend of $1102.50, what is the rate of interest ?
30. In 1 yr. 4 mo. $311.50 amounted to $348.88 at simple
interest ; what was the rate per cent ?
31. An investment of $8226.28 yields $844.7937 annually;
what is the rate of interest ?
32. How long must $1200 be on interest at 6% to amount to
$1344 ?
33. How long must $3000 be on interest at 5% to amount to
$3500 ?
34. At 6% interest, what is the present worth of $1500 due
in 1 year and 4 months ?
Note.— The amt. of $1 for the time is $1.08.
35. What is the present worth of $4500 due in 6 mo., when
the rate of interest is 5% ?
36. What must be the face of a note for 60 d. to be dis-
counted at 6% at a bank, that the proceeds may be $1000?
37. What must be the face of a note for 90 d. to be dis-
counted at a bank at 7$, that the proceeds may be $3250 ?
38. If a trader gained 20% on the cost of goods by selling
them for $2150, what was the cost ?
39. A broker sold a house for $7284 and made thereby 12J% ;
what did it cost him ?
40. How much shall I gain by borrowing $3560 for 1 yr.
6 mo. 10 d. at 6$, and lending it at 7% for the same time ?
176 General Analysis.
41. A man hired a house for 1 yr. at $600 ; after 3 mo. he
takes in his friend B., and in 3 months more he takes his
friend 0. ; how much rent should each pay at the end of the
year?
42. A reservoir has 3 hydrants ; the first will empty it in
8 hours, the second in 10, the third in 12 hours ; if all run
together, how long will it take to empty it ?
43. If 55 tons of hemp cost $880, what will 220 tons cost at
the same rate ?
Analysis.— If 55 tons cost $880, 1 ton cost & of $880 = $16, and
220 tons cost $16 x 220 = $3520, Ana.
Or thus, 55 tons are -^ of 220 tons = \ of the whole number of tons.
If the cost of \ is $880, the whole will cost $880 x 4 = $3520, Ana.
44. If $500 yields $35 interest in 1 year, how much will
$2900 yield in the same time ?
45. Bought stock at par and sold it at 3% premium, thereby
gaining $750 ; how many shares of $100 each did I buy ?
46. A lawyer received $6.80 for collecting a note at 8$ com-
mission ; what was the face of the note ?
47. How many times will a wheel 16 ft. 6 in. in circumfer-
ence, turn round in running 42 miles ?
48. If I buy stocks at 10$ below par and sell at 10$ pre-
mium, what per cent do I gain on my investment ?
49. In what time will $240 amount to $720, at 12$ simple
interest ?
50. A house sold for $13000, which was 5$ advance on the
cost ; what was the cost ?
51. How much should be discounted on a bill of $3725.87,
due in 8 mo. 10 d., if paid immediately, money being worth 5$ ?
52. If A puts in $4000 for 8 mo., B $6000 for 7 mo., and
$3500 for 1 yr., and they gain $2320, what is each partner's
share ?
53. A clerk who engaged to work for $900 a year, com-
menced at 12 o'clock Jan. 1st, 1882, and left at noon, the
21st of May following ; how much ought he to receive ?
General Analysis. 177
54. A church clock is set at 12 o'clock Saturday night;
Tuesday noon it had gained 3 min. ; what will be the true
time when it strikes 8 the following Sunday morning ?
55. Divide 7500 into 3 parts in the proportions of £, -J,
and \.
56. A man failing in business owed $75000 ; his assets were
$14500 ; he owes A $10000, B $3750, and C $12362.50. How
much will each creditor receive ?
57. A cistern has 3 pipes ; the first can fill it in £ hour, the
second can fill it in -J- hour, and the third can empty it in
1 hour. In what time will the cistern be filled if they all run
together ?
58. A, B, and C when in partnership gained $4560; A's
stock $4800 was f of B's and B's was f of C's ; what was the
gain of each ?
59. A tradesman owes $2400, \ of which is now due, \ is due
in 3 months, \ in 4 months, and the remainder in 6 months ;
what is the equated time of payment ?
60. What is the difference between the simple and compound
interest of $800 for 1 yr. 6 mo. 6 d., at %% payable semi-
annually ?
61. A note of $400 was given Jan. 1, 1881, at 6% int., on
which a payment of $25 was made the first of each subsequent
month during the year; what was due Jan. 1, 1882 ?
62. A merchant's profits average 15%, and his losses by bad
debts amount to $1500; what is the amount of his sales, if his
net income is $3100 ?
63. What is the accurate interest on $1500, at 6%, for the
months of July and August ?
64. If goods are marked at 25% advance on the cost, but are
sold at a discount of 16% on the asking price, what is the gain
per cent ?
65. How many cords of wood can be piled on } of an acre of
land if the pile is made 11 ft. high ?
66. A and B are partners; A's capital is twice B's, B gains
50% and A loses $4000, when A has § as much as B ; what was
the original capital ?
J^ATIO
Definitions,
399. Ratio is the relation of one number to another.
Thus, the ratio of 6 to 3 is 6-^-3, and is equal to 2.
400. The Terms of a Ratio are the numbers compared.
401. The Antecedent of a ratio is the first term.
402. The Consequent is the second term. The two terms
together are called a Couplet.
403. Ratio is commonly denoted by a colon ( J ), which is a
contraction of the sign of division.
Thus, the ratio "6 : 3," is equivalent to 6 -*- 3.
404. Ratio is also denoted by writing the consequent under
the antecedent in the form of a fraction.
Thus, the ratio of 8 to 4 is written f , and is equivalent to 8 : 4.
405. Only like numbers can be compared with each other.
406. A Simple Ratio is the ratio of two numbers, as 8 : 4.
407. A Compound Ratio is the product of two or more sim-
ple ratios. They are commonly denoted by placing the simple
ratios under each other.
Thus, 4:2) . ft _ . , 4 .
q „ V or, 4 x 9 : 2 x 3, is a compound ratio.
408. A Compound Ratio is reduced to a simple one by mak-
ing the product of the antecedents a new antecedent, and the
product of the consequents a new consequent,
Ratio. 179
A Direct Ratio is the antecedent divided by the consequent.
409. A Reciprocal or Inverse Ratio is a direct ratio
inverted, and is the same as the ratio of the reciprocals of the
two numbers compared.
Tims, the reciprocal of 8 to 4 is \ to \ — 4 : 8, or £ .
Note. — The reciprocal of a ratio, when a fraction is used, is expressed
by inverting the terms of the fraction which denotes the simple ratio.
When the colon is used, the order of the terms is inverted.
410. The ratio between tivo fractions which have a com-
mon denominator, is the same as the ratio of their nu-
merators.
Thus, the ratio f : f is the same as 6 : 3.
Note. — When the fractions have different denominators, reduce them
to a common denominator; then compare their numerators. Compound
numbers must be reduced to the same denomination.
411. Since the antecedent corresponds to the numerator of a
fraction, and the consequent to the denominator, changes on the
terms of a ratio have the same effect upon its value as like
changes have upon the terms of a fraction. (Art. 179, Com-
plete Graded Arith.)
»
412. The ratio, antecedent, and consequent are so related to
each other, that if any two of them are given the other may
be found. Hence, the
( 1. The Ratio = Antecedent -±- Consequent.
Formulas. < 2. The Consequent = Antecedent -r- Ratio.
1 3. The Antecedent = Conseqiient x Ratio.
1. The consequent is 16, ratio 8, what is the antecedent ?
2. The antecedent is 6§, consequent 9, what is the ratio ?
3. The antecedent is 15£, ratio 9f, what is the consequent?
4. The consequent is 46, ratio 12, what is the antecedent ?
5. What is the reciprocal ratio of f to j? Of £ to £ ?
t^EOPOETIOK
413. Proportion is an equality of ratios.
Thus, the ratio 8 : 4 = 6 : 3, is a proportion. That is,
Four quantities are in proportion, when the first is the same multiple or
part of the second, that the third is of the fourth.
414. The Sign of Proportion is a double colon ( J J ), or the
sign (=)-
Thus, the proportion above is expressed 8 : 4 : : 6 : 3. Or, 8 : 4 = 6 : 3,
and is read " 8 is to 4 as 6 to 3," or " the ratio of 8 to 4 equals the ratio of
6 to 3."
415. The Terms of a proportion are the numbers com-
pared.
416. The Antecedents of a proportion are the first and third
terms.
417. The Consequents are the second and fourth terms.
Thus, in the proportion 4 : 8 : : 3 : 6, the 4 and 3 are the antecedents,
and 8 and 6 the consequents.
418. The antecedents or the consequents, or both, may
have more than one element ; but whatever elements are
contained in one antecedent must be contained in its con-
sequent.
419. In every proportion there must be at least four terms
expressed or understood ; for, the equality is between two or
more ratios, and each ratio has tivo terms.
420. The relation of the four terms of a proportion to each
other is such, that if any three of them are given, the other or
unknown term may be found. .
Proportion. 181
421. A proportion may, however, be formed from three
numbers, for one of the numbers may be repeated, so as to
form ttvo terms ; as, 2 : 4 : : 4 : 8.
Note. — When a proportion is formed of three numbers, the middle
number is called a Mean Proportional.
422. The Extremes of a proportion are the first and last
terms.
423. The Means are the two middle terms.
424. Principles. — 1°. In every proportion the product of
the extremes is equal to the product of the means.
2°. Hie product of the extremes divided by either of the
means, gives the other mean.
3°. The product of the means divided by either extreme, gives
the other extreme.
425. Find the unknown term x in the following :
1. 9 : 154 = 153 : x. 5. 130 lb. : x = $150 : $850.
2. 75 : 900 = x : 85. 6. x : 80 = 240 : 200.
3. 28 : 14 = 36 : x. 7. 10 A. : i A. = fee : $14.50.
4. |: 3 = 8: 16, 8. 24 : x = 648 : 243.
SIMPLE PROPORTION.
426. Simple Proportion is an equality of two simple
ratios.
427. The required or unknown term of a proportion may be
found either by considering the relative magnitude of the
given terms, or by comparing them as causes and effects.
428. To find the unknown term of a proportion, when the other
three terms are given.
I. By Relative Magnitude.
l. If 18 chairs cost $54, what will be the cost of 144 chairs ?
182 Proportion.
Analysis. — 18 chairs are the statement.
same part of 144 chairs, as $54 are 18 ch. : 144 ch. : : $54 : %x
of the required cost. As the answer ±4^4 _ x> t h e un k. nown te rm.
is money, make $54 the third 3
term, 18 chairs the first term, and ^-iir^ = $432, Am.
144 the second. The product of PkOOF. ^t =■ Ai or 1 \ .
the means divided by the given
extreme gives the other extreme, or unknown term. Hence, the
Rule. — I. Arrange the numbers so that the third term
may be of the same hind as the answer.
II. When the answer is to be larger than the third
term, make the larger of the other two numbers the
second term; but when less, -place the smaller for the
second term, and the other for the first.
III. Multiply the second and third terms together, and
divide the product by the first ; the quotient will be the
fourth term or answer.
Notes. — 1. The factors common to t\\e first and second, or to the first
and third terms, should be cancelled.
2. The first and second terms must be reduced to the same denomina-
tion. The third term, if a compound number, must be reduced to the
lowest denomination it contains.
II. By Cause and Effect.
429. A Cause is that which does something.
An Effect is something which is done.
Notes. — 1. Men or animals and machinery, goods bought or sold,
money at interest, time, etc., are causes; for the increase of either,
increases the effect produced. Work done, provisions consumed, cost of
goods, etc., are effects.
2. In examples of freight, distance and magnitude may be regarded as
causes, producing money for their effect.
3. A little practice will give great facility in distinguishing between
causes and effects.
Simple Proportion, 183
430. 2. If 8 men mow 24 acres in 1 day, how many acres
will 25 men mow in the same time ?
Analysis. — In this example the statement.
2d effect is required, which is an ex- tstC. 2d C. IstE. 2dE.
trenie. Put X in its place. 8 m.: 25 m. : : 24 A. : X A.
8 m. (1st cause) is to 25 m. (2d cause) as (25 X 24) -v-8 =c 75 A., Ans,
24 A. (1st effect) is to x A. (2d effect).
Since the product of the means equals that of the extremes, the prod-
uct of two numbers and one of the numbers is given, to find the other
number or unknown term. (25 x 24)-s-8 = 75 A., Ans.
3. If 25 bushels of wheat make 8 barrels of flour, how many
bushels will be required to make 54 barrels ?
Analysis.— In this example statement.
the 2d cause is required, which *•*<*• 2d c - lstE - 2 <1E.
we represent by x bu. The 25 bu. : X bu. : : 8 bbl. : 54 bbl.
product of the extremes, or x = (54x25)-^8 = 175 bu., Ans.
perfect terms, divided by the
mean, gives the required term, which is 175 bushels. Hence, the
Kule. — Make the first cause the first term, the second
cause the second term, the first effect the third term, and
the second effect the fourth term ; -putting x in the place t
of the unknown tej*m.
If the unknown term is an extreme, divide the prod-
uct of the means by the given extreme ; if a mean,
divide the product of the extremes by the given mean,
(Art. 424, 2°, 3°.)
Notes. — 1. All the elements contained in one antecedent or cause must
be in its consequent, and all the elements in one consequent or effect must
be in the other as factors.
2. In inverse proportion, 1st C. : 2d C. : : 2d E. : 1st E.
3. In continued action, causes embrace both an agent and time.
4. An effect may be a simple result, or both a result and time, or it may
embrace length, breadth, and thickness.
4. If a ship has sufficient water to last a crew of 28 men for
18 months, how long will it last 25 men ?
18.4 Proportion.
5. If 18 ounces of silver will make 8 teaspoons, how many
spoons will 24 pounds of silver make ?
6. If a railroad ear runs 225 kilometers in 8 hours, how far
will it run in 12f hours ?
7. If 20 yards of cloth, £ yd. wide, are required for a dress,
what must be the width of a piece 12 yds. long to answer the
same purpose ?
8. If the interest of $675.25 is $55,625 for 1 year, how
much will be the interest of $4368.85 ?
9. What cost 11 lb. 4 oz. of tea, if 3 lb. 12 oz. cost $3.50?
10. Find the value of the unknown term in $4 : x : : 9:16.
11. If I own f of a farm and sell f of my share for $2300,
what is the value of the whole farm at the same rate ?
12. If 14 acres of meadow yield 32| tons of hay, what will
5J acres produce at the same rate ?
13. If 36 horses eat 92 hektoliters of oats in a week, how many
hektoliters will 55 horses eat in the same time ?
COMPOUND PROPORTION.
431. Compound Proportion is an equality between a com-
pound ratio and a simple one, or between two compound
ratios. Thus,
. " > : : 24 : 63, and \ ' > : : j ' > are compound proportions.
For, 7x3x24 = 2x4x63, and 2x3x9x4 = 4x2x3x9. It is read,
' ' The ratio of 2 x 4 is to 7 x 3 as 24 to 63."
Note. — The value of a compound ratio equals the product of the simple
ratios of which it is composed. Thus, £ x § = § x |>
432. The terms of a compound ratio may be considered
in their relations to each other as causes and effects, as in
Simple Proportion.
Notes. — 1. All the terms of a compound proportion are given in pairs
of the same kind, except one which is of the same nature as the term
required.
2. The order of the terms and of each ratio is the same as in Simple
Proportion.
Compound Proportion. 185
l. If 4 men mow 60 acres in 10 d., how many acres can 6
men mow in 8 days ?
Analysis.— In this problem the statement,
1st cause is 4 men and 10 days, the l8t c - 2d C. 1st E. 2d E.
2d cause is 6 men and 8 days, the 1st 4 m. : 6 m. ) _ . .
effect is 60 A., the 2d effect z A. is 10 d. : 8 d. ) '' '' ''
required. Dividing the product of
the means by the product of the extremes gives 72 A., the term required.
The factors may be arranged in 2 6
the form of a fraction, and the 6 X $ X $0
work much abridged by cancella- x — ^ x 10 = Ans.
tion.
2. If 8 men can dig a ditch 60 ft. long, 8 ft. wide, and 6 ft.
deep in 15 d., how many days will 24 men require to dig a ditch
80 ft. long, 3 ft. wide, and 8 ft. deep ?
Analysis. — In thi s statement.
problem the causes and lstc - 2dc - lstE - 2dE
effects are both compound
8 m. : 24 m.
ratios. The required term w *"* ' ^ i : : J 8 f t. : 3 ft.
x is the 2d cause and is one lo d. I X d. J f P -ft • Q ff
of the means. Dividing
the product of the extremes + r - AlA A ^ &
by that of the means gives x = * * ** * W * * * » = 20 = 31 d .
x = 3* days, Am. Hence, U X 00 X $ X 6
the 4
Rule. — Arrange the causes and effects as in Simple
Proportion, putting x in the place of the required term.
When all the means are given, their continued product
is the dividend and the product of the extremes the
divisor.
When the extremes are given, their product is the
dividend, that of the means the divisor, and the quotient
is the answer.
Equal factors in the divisor and dividend should be
cancelled.
> Notes. — 1. The terms of each couplet in the compound ratio must be
reduced to the same denomination, and each term to the lowest denom-
ination contained in it, as in Simple Proportion.
186 Proportion.
2. When the same quantity is an element of both causes or of both
effects, or when both antecedents or both consequents are the same quan-
tity, it may be represented by the figure 1.
3. If the wages of 75 boys for 84 days were $68.75, how
many days could 90 boys be employed at the same rate for
$41.25 ?.
4. If 25 persons consume 300 bu. of wheat in 2 years, how
much will 139 persons consume in 6 years ?
5. If a stack of hay 1 6 ft. high contains 12 cwt., what will
be the height of a similar stack containing 6 tons ?
6. If a man pays $30 for freight on 90 bbl. flour to go 160
miles, what must he pay for 360 barrels to go 90 miles ?
7. A quarter-master wished to remove 160000 lb. of provi-
sions from a fortress in 18 days; it was found that in 12 days
35 men had carried away but 25 tons, how many men would be
required to carry the remainder in 6 days ?
8. If 6 journeymen make 132 pair of boots in 4J weeks,
working 5-J days a week, and 12f hours per day, how many pair
will 18 men make in 13| weeks, working 4 J days per week,
and 10 hours per day ?
9. If 4 lbs. of yarn will make 12 yards of cloth 1 \ yard wide,
how many pounds will be required to make a piece 200 yards
long, and If wide ?
10. If $800 will earn $11.50 in 168 days at 6%, how much
will $640 earn in 192 days at 9% ?
11. From a sheet of paper 25 in. long and 18 in. wide, a
printer cut 30 pages for a book. How many of the same size
pages could he cut from a sheet 24 in. long and 20 inches
wide ?
12. If 3 men can do a piece of work in 6 days, working 10
hours a day, how long will it take 16 men to do twice the
amount of work, when they work at it 9 hours a day ?
13. If 2 compositors can set 50 pages in 6 d. of 10 hr., when
each page contains 36 lines of 48 letters, how many compositors
will be required to set 192 pages, each having 40 lines of 54
letters, in 4 days of $ hours ?
Partitive Proportion, 187
14. If $1200 will earn 819.20 interest in 6 mo. 12 d. at 6%,
at what rate will $240 earn $14.40 in 4 months ?
15. If 100 horses consume a stack of hay 20 ft. long, 11 ft.
3 in. broad, and 31 ft. 6 in. high in 9 days, how long will a
stack 18 ft. long, 5 ft. broad, and 14 ft. high supply 80 horses ?
16. Bought a pile of stone 24 ft, long, 12 ft. high, and 9 ft.
wide for $120, and gave a note for $300 for a similar pile 12 ft.
wide and 36 ft. long ; how high was the second pile ?
17. If 5 pumps, each having a length of stroke of 3 ft.,
working 15 hr. a day for 5 d. empty the water from a mine,
what must be the stroke of each of 15 pumps which would
empty the same mine in 12 d., working 10 hr. a day, the
strokes of the former set of pumps being four times as fast as
those of the latter ?
PARTITIVE PROPORTION.
433. Partitive Proportion is dividing a number into two or
more parts which shall have a given ratio to each other.
434. To divide a number into two or more parts, when the
ratio of the parts to each other is given.
l. A and B divided $396 in the ratio of 5 to 7 ; how much
had each ?
Analysis. — Since A had 5 opebation.
parts and B 7, both had 54-7, (396 -r- 12) X 5 = $165, A's part,
or 12 parts. Hence, A will ( 396 _^_ 12 ) x 7 = $231, B's "
have -/a and B ^ of the money.
Now fl of $396 = $165, and T 7 ¥ of $396 :
IstC. 2dC. IstE. 2dE.
Or, Sum of parts : whole No. : : each part : share of each. Hence, the
Rule. — Divide the given number by the sum of the pro-
portional numbers, and multiply the quotient by each
one's proportional part.
2. Divide 624 into three parts which shall be to each other
as 6, 8, and 12.
188 Proportion.
3. Divide 450 shares of stock among 3 persons, in propor-
tion to the number of shares owned by each ; A holds 400, B
200, and C 300 ; how many shares will each receive ?
4. Three men engaged in trade agreeing to share the gains
or losses in proportion to their investments ; A's capital was
$6000, B's $8000, C's $10000; they gained $8800; what was
each man's share ?
5. A, B, 0, and D commenced business with a capital of
$18500; A invested $800 less than B, and invested $1000
more than A, and D $900 less than C ; how much did each
invest ?
6. Divide 560 into parts, so that the second may be 4 times
the first.
Analysis. — The 1st part + 4 times the 1st part equals 5 parts. Since 5
parts equal 560, 1 part = 560 -f- 5 or 112, and 112 x 4 = 448 the 2d part.
7. Divide the number 582 into 4 such parts that the second
may be twice the first, the third 21 more than the second, and
the fourth 54 more than the first.
8. If C has twice as much money as B, and if $12 be taken
from A's money, it will be equal to \ of B's ; how much has
each, the sum of their money being $645 ?
9. If 6 lbs. of coffee cost $2,40, and 20 lbs. of coffee are
worth 12 lbs. of tea, what will 120 lbs. of tea cost ?
10. If 8 grammars cost $6.40, and 9 grammars are worth
6 geographies, 48 spellers 10 geographies, 3 arithmetics 18
spellers, 15 readers 9 arithmetics, how much will 8 readers
cost ?
n. A, B, and C are in partnership; A puts in \ of the cap-
ital, B T 5 ¥ , and C the remainder ; they gain $2150 ; what is
the share of each ?
12. If | of A's money and £ of B's equal $900, and f of B's
is twice § of A's, what sum has each ?
13. A father divided $18500 among 3 children, so that the
portion of the second was greater by one-half than that of the
first, and \ the first was equal to \ of the third; what was the
share of each ?
jXCHAN GE,
435. Exchange in Commerce is of two kinds, Domestic or
Inland and Foreign.
436. Domestic Exchange is making payments between
different places in the same country by Drafts, or Bills of
Exchange.
437. Foreign Exchange is making payments between places
in different countries, in the same manner.
Note. — In commercial law, the different States of the United States are
considered foreign to each other. But for the purposes of the present
work transactions between them will be treated under Domestic Exchange.
438. The Par of Exchange is the standard by which the
value of the currency of different countries is compared, and is
either intrinsic or commercial.
439. Intrinsic Par is a standard having a real and fixed
value represented by gold or silver coin.
440. Commercial Par is a conventional standard, having any
assumed value which convenience may suggest.
Note. — The fluctuation in the price of bills from their par value, is
called the Course of Exchange.
441. A Bill of Exchange or Draft is a written order direct-
ing one person to pay another a certain sum, at a specified
time.
442. A Sight Draft is one payable on its presentation.
443. A Time Draft is one payable at a specified time after
date or presentation.
Note — Drafts or Bills of Exchange are negotiable like promissory
notes, and the laws respecting them are essentially the same.
190 Exchange.
444. An Acceptance of a draft is an engagement to pay it.
As evidence, the drawee writes the word accepted across the
face of the draft, with the date and his name.
Note. — Days of Grace are allowed on time drafts unless otherwise
specified, but the number varies in different countries, from 3 to 12 days.
DOMESTIC EXCHANGE.
445. To find the Cost of a Draft, when the Face and Rate of
Exchange are given.
l. What cost the following sight draft, at 2\% premium ?
$ 2 7°°- New Orleans, Jan. 30th, 1882.
At sight, pay to the order of James Calkins, twenty-seven
hundred dollars, value received, and charge the same to the
account of Selden" Bros., & Co.
To S. Bliss & Co., New York.
Explanation. — The remittor of the above sight draft is James
Calkins, who bought it at the bank and had it made payable to his order.
He owes J. Smith of New York $2700. He writes on the back of the
draft, " Pay to the order of J. Smith," and signs his name. When
Smith receives it he signs his name also on the back and takes it to
S. Bliss & Co., for payment.
Solution.— At Sj% premium, the cost of $1 draft is $1,025, and $2700
will cost $1,025 x 2700 = $2767.50, Ans.
2. What cost a sight draft on San Francisco for $2500, at
2\% discount.
Solution. — A draft of $1 at %2\% discount will cost $0,975, and
$2500 x .975 = $2437.50, Ans. Hence, the
Rule. — Multiply the face of the draft by the cost of $1.
What cost a sight draft for What cost a sight draft for
3. $8515, at \\% premium ? 9. $4265, at \\% discount?
4. $6845, at \% premium ? 10. $8500, at \% discount ?
5. $9875, at \% premium ? 11. $8763, at 50^ discount?
6. $7365, at 2% premium ? 12. $4562, at 75^ discount?
7. $3876, at 25</> premium? 13. $8423, at \% discount?
8. $8245, at 50^ premium ? 14. $9654, at \% discount?
Domestic Exchange. 191
Notes. — 1. On time drafts, both the rate of exchange and the interest
are commonly included in the quotation prices. Brokerage is usually
included in the rate of exchange.
2. When the rate of exchange exceeds the cost of shipping gold or cur-
rency by express, one of them is sent instead of drafts.
15. What is the cost of the following time draft, at 1 \% pre-
mium, and interest at Q% ?
$5000.
Philadelphia, June 4th, 1883.
Sixty days after sight, pay to the order of George Wil-
liams, five thousand dollars, value received, and charge the
same to the account of H. Avery & Co.
To S. Pakkhurst, Baltimore, Md.
Explanation. — The above time draft, purchased by G. Williams from
H. Avery & Co., is sent by W. to a creditor, A. B„ in Baltimore, with the
indorsement " Pay to the order of A. B.," with signature. When A. B.
receives it he takes it immediately to S. Parkhurst, who writes or stamps
the word "accepted" across its face, with date and signature. The
maturity of the draft is 63 days from the date of acceptance.
Solution. — The cost of a sight draft of $1, at 1\ % premium=$1.0125
Subtracting the interest on $1 for 63 days (3 d. grace), at 6 % = 0.0105
The cost of $1 draft = 1.0020
Multiplying by 5000
Cost of draft for $5000 =$5010. 0000, Ans.
Note — 3. Since the bankers in Philadelphia have the use of the money
for 63 days before the house in Baltimore will pay the draft, the interest
for that time, at the given rate, is deducted from the cost.
16. Find the cost in Denver of a draft on New York at 90
days sight, for $6265, at 2% premium, interest being 6% ?
17. Bequired the worth in Lexington, Ky., of a draft on Bos-
ton for $4500, at 30 days sight, at 1% discount and interest 6%,
18. What is the worth of a draft of $5600 on St. Louis, at
30 days sight, premium 1-J$, including interest ?
19. A commission merchant in Chicago sold for a firm in
Detroit a consignment of French china. The sales amounted
to $10500, the commission was b% on sales. He sent a 30 days
draft at \% discount in payment of the net proceeds; what did,
it cost him, interest being 6% ?
192
Exchange.
FOREIGN MONEYS OF ACCOUNT.
446. The value of the money unit of Foreign Countries in
United States money is published annually by the Secretary of
the Treasury. The following is the Report Jan. 1st, 1883.
Country.
Austria
Belgium
Bolivia
Brazil
British America..
Chili
Cuba
Denmark
Ecuador
Egypt
France
Great Britain. . . .
Greece
German Empire..
Hay ti
India
Italy
Japan
Liberia
Mexico
Netherlands
Norway
Peru
Portugal
Russia
Sandwich Islands
Spain
Sweden
Switzerland ....
Tripoli » . .
Turkey . . ... .
U. S. of Colombia
Venezuela
Monetary Unit.
Florin
Franc.
Boliviano
Milreisof 1000 reis...
Dollar
Peso
Peso
Crown
Peso
Piaster
Franc
Pound sterling
Drachma
Mark
Gourde
Rupee of 16 annas
Lira
Yen
Dollar
Dollar.
Florin
Crown
Sol
Milreis of 1000 reis. . .
Rouble of 100 copecks.
Dollar
Peseta of 100 centimes.
Crown
Franc of 100 centimes.
Mahbub of 20 piasters.
Piaster •. .
Peso.
Bolivar
Standard
Silver. . .
G. and S
Silver...
Gold....
Gold....
G. and S
G. and S
Gold....
Silver
Gold
G. and S,
Gold
G. and S.
Gold
G. and S.
Silver....
G. andS.
Silver....
Gold....
Silver. . . .
G. and S,
Gold
Silver
Gold
Silver
Gold
G. and S.
Gold
G. and S.
Silver....
Gold
Silver
G. and S.
Value in
U. S. Money.
.40,7
.19,3
.82,3
.54,6
$1.00
.91,2
.93,2
.26,8
.82,3
.04,9
.19,3
4.86,6|
.19,3
.23,8
.96,5
.39
.19,3
.88,8
1.00
.89,4
.40,2
.26,8
.82,3
1.08
.65,8
1.00
.19,3
.26,8
.19,3
.74,3
.04,4
.82,3
.19,3
Foreign Moneys. 193
Notes. — 1. The Franc of France, Belgium, and Switzerland, the
Peseta of Spain, the Drachma of Greece, the Lira of Italy, and the
Bolivar of Venezuela are the same in value.
2. The Peso of Ecuador and of U. S. of Colombia, the Boliviano of
Bolivia, and the Sol of Peru are the same in value.
3. The Crowns of Norway, Sweden, and Denmark are also the same
in value.
Quotations of Foreign Bills of Exchange.
Sterling, 60 d., $482$. Reichsmarks (4).
sight, $485. For long sight, .94f @ .94^
Cable transfers, $4.85 @ $4.85 J. For short sight, .95 @ .95$.
Commercial, $4.80 @ $4.80$. Amsterdam, 60 d., .39$.
Francs, 60 d., 5.23f @ 5.23$. " 3d. sight, .40$.
Notes. — 1. Bills at 60 days are generally less than sight bills, because
of the interest on them for the time.
(For intrinsic par, see Table, Art. 446.)
2. Cable Transfers signify the method of sending funds to persons
abroad by means of the Atlantic Cable.
Payments are often effected by telegraph between distant places in the
United States.
3. Commercial Bills are drafts drawn upon merchants.
4. Exchange on Paris is quoted by giving the number of francs and
centimes to $1. The same applies to all countries where the franc and its
equivalents are used.
5. Amsterdam quotations give the number of United States cents to
the guilder or florin. Intrinsic par of 1 guilder = 40 r 8 T cents.
6. Quotations in Reichsmarks are based on the cost of 4 reichsmarks ;
hence, .94| @ .94$ signify the number of cents to be paid for 4 marks.
447. The value of the unit of foreign moneys of account
being given as in the table (Art. 446), the cost and face of
bills are easily found by Analysis.
448. To find the value of Sterling money In U. S. money.
l. Change £410 12s. 8-|d. to U. S. money.
8.5d.
12.708
Explanation. — Reducing the 12
shillings and pence to the decimal 20
of a pound, as in the margin, and
multiplying by the value of £1 as
410.635 +
given in the table, the result is ^10.635 X 4.8665 = 11998.355.
$1998.355, Ans.
194 Exchange.
FOREIGN EXCHANGE.
449. Bills of Foreign Exchange are commonly drawn in the
money of the country in which they are payable.
450. A Set of Exchange consists of three bills of the same
date and tenor, called First, Second, and Third of exchange.
They are sent by different mails in order to save time in case of
miscarriage. When one is paid, the others are void.
Note. — Exchange with Europe is chiefly done through the large
commercial centers, as London, Paris, Geneva, Amsterdam, Antwerp,
Bremen, Vienna, Hamburg, Frankfort, and Berlin.
451. A Letter of Credit is a draft made by a banker m one
country, addressed to foreign bankers, by which the holder
may draw fnnds at different places in any amount not exceed-
ing the limits of the letter of credit.
Note. — Travellers generally prefer letters of credit to bills of exchange,
because they can draw at any time and at different places such, sums as
their convenience may require.
452. Sterling Bills or bills on Great Britain are quoted by
giving the market value of £1 exchange in dollars and cents.
453. To find the Cost of Sterling Bills, when the Face and
Rate of Exchange are given.
l. Eequired the cost of the following bill on London, at
$4.8665 per pound.
£875 16s. Baltimore, Jan. 10, 1882.
At ten days sight of this First of Exchange {Second and
Third of same tenor and date unpaid), pay to the order
of Peter Cooper, Eight Hundred Seventy-five Pounds
Sixteen Shillings Sterling, value received, and charge the same
to account of Henry Hayward, Jr.
To James Kent & Co., Bankers, London.
Analysis. — Reducing 16s. to decimals of a pound, the face of the bill
£875 16s. = £875.8. Since £1 is worth $4.8665, £875.8 are worth $4.8665
x 875.8 = $4262.0807, the cost. Hence, the
Foreign Exchange. 195
Kule. — Reduce the shillings and pence to the decimal
of a pound, and multiply the face of the bill by the given
rate of exchange. (Art. 446.)
2. An importer owed a manufacturer in Sheffield, Eng.,
£1740 10s.; what cost a bill on London for the amount,
exchange being $4.87-$-?
3. When exchange on Manchester is $4.88, what cost a bill
of £3520 ?
4. A merchant in New York gave an order to a broker to
remit to Liverpool £15000. With exchange at $4.89^ and
brokerage \%, what did it cost him in U. S. money ?
5. What cost a bill of exchange for £2800 15s. 9d. at $4.85 ?
At$4.82J?
6. What cost £3560 18s. 3d. at $4.80? At $4.89£? At
$4.83-|?
454. To find the face of Sterling Bills, the cost and rate of
exchange being given.
7. A merchant paid $4256.40 for a sight bill on London ;
exchange being $4. 86, what was the face of the bill ?
a a *Aoa it*. oi i 4.86 ) $4256.40
Analysis. — Since $4.86 will buy £1 exchange, i
$4256.40 will buy as many pounds as $4.86 are 875.8
contained times in $4256.40, or £875.8. (Art. 20
153.) Hence, the . « OWK .. f ,
' . Ans. £875, 16s.
Ecjle. — Divide the cost of the bill by the given rate of
exchange ; the quotient will be the face of the draft.
Reduce the decimals, if any, to shillings and pence.
(Art. 153.)
Note. — When the cost and face of the bill are given, the rate of
exchange is found by dividing the latter by the former. (Art. 216.)
8. An importer paid $15265.40 for a bill of exchange on
Birmingham; exchange being $4.87, what was the face of the
bill?
9. Paid $25275 for a bill on Edinburgh; exchange being
$4. 87 J, what was the face of the bill ?
196 .Exchange.
10. Paid $8500 for a bill on Dublin, exchange at $4.88;
what was its face ?
n. The cost of a bill on Liverpool for £825 16s. 6d. was
$3964.50 ; what was the rate of exchange ?
12. The cost of £492 17s. 6d. was $1850; what was the
rate ?
13. On an invoice of £850, what is the difference between
its valuation at the Custom House and an exchange rate of
$4.80? -
14. At $2946.50 for £600, what was the rate ?
Note. — The cost of imported goods is generally estimated by adding
the charges of importation to their value in the money of the country
from which they come.
15. An English merchant consigned to an agent in New
York the following invoice : 188 pieces of broadcloth, 37J
yards each ; 165 pieces of silk, 52 yds. each ; 68 pieces velvet,
21 yds. each ; the agent sells the cloths at $4.93 per yard; the
silks at $1.27 ; and the velvets at $2.62-§- ; pays 35% duties, and
charges 2\% commission; $83.25 for storage, and sends his
principal a draft on the Bank of England for the amount ; the
rate of exchange being $4.85-|, what was the amount of the
draft in sterling money ?
16. A merchant imports 160 pieces of broadcloth, 24 yd.
each, costing $2.75 per yd. The duties and other charges
amounted to $650. What must be the face of a sterling bill
of exchange to pay for the goods, and what price per yard
must he sell them to make 15% profit ?
455. Bills of France, Belgium, and Switzerland are quoted
by giving the value of $1 U. S. money in francs and centimes.
Note. — Centimes are commonly written as decimals of a Franc.
17. Required the cost of a bill on Paris of 3000 francs,
exchange 5.25 fr. to a dollar.
Solution.— Since 5.25 fr. will buy $1 exchange, 3000 francs w: 1 buy
as many dollars as 5.25 are contained times in 3000, or $571 42, Ans.
Foreign Exchange. 197
18. An invoice of goods costing 8324.50 fr. was passed
through the Custom House ; what is the difference in U. S.
money between its custom-house value and the exchange
rate 5.22 ?
19. Paid $600 for a bill on Geneva ; what was the face of
the bill, exchange being 5.16 fr. to $1 ?
Analysis.— If $1 will buy 5.16 fr., $600 will buy 600 times as many,
and 5.16 x 600 = 3096 francs, Am.
20. Bought a bill on Havre for $4500; exchange being 5.23,
what was the face of the bill ?
21. What cost a bill on Antwerp for 1200 francs, at 5.20 fr.
exchange ?
22. What is the difference between exchange at 5.24 fr. and
the custom-house value on a bill for 68000 francs ?
456. Bills ou Germany are drawn in marks (reichsmarks).
They are quoted by giving the value of four marks in U. S.
cents. The intrinsic par value of 4 marks is 95.2 cents.
457. Bills on Austria and Netherlands are drawn in florins
or guilders, and are quoted by giving the value of 1 florin in
U. S. cents.
23. An agent in Amsterdam remitted a draft on New York
for which, including brokerage \%, he paid 975 guilders;
what was the face of the draft, exchange at 40.2 cents to a
guilder ?.
24. What cost a bill on Frankfort for 840 marks, exchange
being $.94$ ?
Analysis. — Since 4 marks are worth $.945, the worth of 840 marks is
840 times \ of $.945, or $198.45, Arts.
Note. — Multiply the exchange value of 4 marks by the given amount
and divide the product by 4, or divide before multiplying.
25. What cost a bill on Berlin for 3800 marks at $.96 J ?
198 Exchange.
NOTE. — When the value of an invoice at the Custom House is required,
multiply the given amount in marks by the intrinsic par of 1 mark 23.8;
the product will be in cents.
26. What is the face of a bill on Hamburg when exchange is
.94J and th e cost of a draft $1856 ?
458. The method of finding the face of a foreign bill of
exchange is essentially the same as that of domestic bills.
27. Eequired the face of a bill on Hamburg for which $2500
was paid, exchange being 95 cents.
Analysis. — Since 95 cents will buy 4 marks, $2500 will buy as many
times 4 marks as .95 is contained times in $2500 or 2631 j^, and 2631^ x 4
= 10526 T 6 ¥ marks, Ans.
28. What would be the Custom House valuation of the
same bill ?
Solution.-$2500.00-j-23.8 cts. = 10504 T 2 T \ marks. Ans.
29. Find the face of a bill on Frankfort costing $1762 in
gold, exchange at .95 \.
30. Paid $2800 for a bill on Berlin, exchange .93|; what was
the amount of the bill ?
31. What is the cost of a bill of 3800 florins on Amsterdam,
exchange being 39§- cents to a florin ?
Analysis. — Since 1 florin costs 39| cents, 3800 florins will cost 3800
times as much, and $.395 x 3800 = $1501. Hence, the cost of the bill
is $1501.
32. What is the cost of a bill of 2500 roubles on Russia,
exchange being 65.8 cents to a rouble ?
33. What is the value of an invoice entered at the Custom
House for 8750.50 florins ?
34. A bill for 8500 guilders cost $5355.00 ; what was the rate?
35. Bought at par 375 rupees of India, 385 Austrian
guilders, 850 crowns of Denmark, brokerage \% ', what was the
cost in U. S. money ?
36. Sold 954 Russian roubles at par, and paid \% brokerage ;
what was the net sum received ?
Duties or Customs. 199
DUTIES OR CUSTOMS.
459. Duties or Customs are taxes imposed by Government
on imported and exported merchandise.
460. A Tariff is a list of goods alphabetically arranged, with
the rates of duties, drawbacks, etc., on them, charged and
allowed on the importation and exportation of articles of for-
eign and domestic produce.
461. The Free List is the list of imported articles which are
exempt from duty.
462. Duties are of two kinds, Specific and Ad Valorem.
A Specific Duty is a fixed sum imposed on each article, ton,
yard, gallon, etc., without regard to its value.
An Ad Valorem Duty is a certain per cent on the cost of
goods in the country from which they are imported.
Note. — On some goods both a specific and ad valorem duty is charged ;
as on statuary marble $1 per cu. ft. and 25% ; on woolen goods 50 cts. a
pound and 85 % .
463. In estimating specific duties, certain allowances are
made, called tare, draft, leakage, and breakage.
Tare is an allowance for the weight of the box, bag, cask,
etc., containing the goods.
Draft is an allowance made for waste and impurities.
Leakage is an allowance for waste on liquors imported in
Breakage is an allowance of a certain per cent on liquors
imported in bottles.
Notes. — 1. Tare is calculated either at the rate specified in the
invoice, or at rates established by Act of Congress.
2. Leakage is commonly determined by gauging the casks, and
Breakage by counting.
200 Custom House Business.
3. In making these allowances and in estimating weights and curren-
cies, if the fraction is less than $ it is rejected ; if $ or more, 1 is added.
4. The Long Ton of 2240 pounds is used in computing Duties.
464. Gross Weight is the entire weight of goods and packages.
Net Weight is the weight after all allowances have been
deducted.
CUSTOM HOUSE BUSINESS.
465. The United States are divided into various districts,
each of which has a Port of Entry and a Custom House.
466. A Custom House is a building or office established by
Government where duties are collected, vessels are entered,
cleared, etc. The larger Ports have a Collector, a Naval
Officer, a Deputy-Collector, Surveyors, Appraisers, Inspectors,
Weighers, etc.
467. On the arrival of a vessel in Port, the Master is
required to present his manifest and invoice to the Collector or
Consul, and pay his entrance and clearance fees.
468. A Manifest is a memorandum signed by the Master of
a vessel, giving its name, its tonnage, its cargo, with the place
where he received it, and the names of the shippers and con-
signees.
469. An Invoice contains a description of the goods with
their cost, in the weights, measures and currency of the
country from which they are imported. The invoice with its
marketable value, must be authenticated by a Consul of the
U. S., or by one of a country in amity with the United States,
or by two respectable resident merchants.
470. Ad Valorem duties are assessed only on the actual cost
or general market value of the goods in the country from which
they come. Specific duties, on the quantity landed. (Art.
462, N.)
Note. — The law has recently been changed which made the dutiable
value of merchandise include the cost of transportation, commissions, etc.
Duties or Customs. 201
471. The Entrance Fee is the annual tax paid for permission
of a vessel to enter Port. It is based on the measurement, or
tonnage of the vessel.
472. The Registry of a ship is its enrolment at a custom house.
473. A Bill of Lading is & formal receipt for goods taken on
board a vessel, signed by the master, binding himself to deliver
them in good condition, for a certain remuneration or
freightage.
Note. — Bills of lading are made out in triplicates ; one is sent by mail
to the consignee, a second is sent by the master of the ship, and the third is
retained by the consignor or shipper. In all cases the bill of lading is the
evidence of shipment, and title to the goods shipped.
474. A Bonded Warehouse is a building for the storage of
bonded goods on which the duties have not been paid, but
have been secured by bond of the owner in double their
amount.
Note. — All goods remaining in bond, are charged 10% additional duty
after one year, and if left beyond 3 years, are regarded as abandoned to
the government, and sold under regulations prescribed by the Secretary
of the Treasury.
475. A Drawback is money refunded for import duties
previously paid, or for internal revenue tax paid on such
articles as fermented liquors, medicines, etc., when these are
exported.
Excise Duties are taxes or licenses for the manufacture or
sale of certain articles produced and consumed at home ; as
tobacco, whiskey, etc.
1. A merchant imported 610 gallons of olive oil ; allowing
2% for leakage, what was the specific duty at 25 cts. per
gallon ?
Solution. -2% of 610 gal. = 12.2 gal., and 610-12.2 = 597.8 gal.
Finally, 597.8 x .25 = $149.45, Ans.
2. What is the specific duty on 825 lb. soap, at 15 cts. a pound ?
202 Duties or Customs.
3. What is the duty at 30% ad valorem, on an invoice of
English goods amounting to 4)1500 10s. 6d.?
4. Find the duty on a bill of English carpeting amounting
to £6250 5s. 6d., at 35% ad valorem.
5. Taylor & Co. imported 2 cases of goods, each weighing
175 lbs., costing £1215 10s. and paid a specific duty of 30 cts.
per pound and 35% ad valorem. What was the amount of
duty ? What did the goods cost him ?
6. A. T. Stewart imported goods from Paris amounting to
28425 francs. What was the ad valorem duty at 35%, in United
States money ?
7. What is the duty at 40% on an invoice of French jewelry,
amounting to 8560 francs ?
8. The value of an invoice of French china is 19285 fr. ;
what is its cost in New York, at 50% duty ?
9. What is the duty on an invoice of books from Vienna the
value of which was 6429 florins, at 38% ?
10. Find the duty on an invoice of woolen cloths from
Germany valued at 8437 Reichsmarks, at 45%.
/ n. What is the duty on an invoice of linens amounting to
£3256 sterling at 27%, allowing $4.866£ to a pound ?
12. What is the duty on an invoice of 650 yd. of broadcloths
which cost in London 16s. 6d. per yard, at 40% ad valorem,
the value of a pound sterling being as above ?
13. Find the duty at 33% ad valorem, on 1 case of shawls
valued at £42 5s., 1 case of linens at £37 10s., duty 40%; 1
case prints at £8 5s., duty 20% ; incidental expenses £1 5s.,
commission 2|% ; consul's fee 15s. What is the total cost in
TJ. S. money?
14. Required the duty and total cost of 1 case of French
silks, value 3500 francs, duty 50% ad valorem ; 1 case velvets,
value 28000 francs, duty 50%, expenses, cartage, shipping, etc.,
625 francs, and commission 2J%.
15. What is the duty and total cost of 2500 pieces bleached
calico, 33 yd. each in length, and 1J yd. wide ; price 6d. per
yd., duty 4 cts. per sq. yd., and expenses at Liverpool £65 10s.?
What is the amount of a bill of exchange at $4.87 to cover
the cost ?
Duties or Customs.
203
476. What is the total cost and amount of duty on the
following invoice, at the rate of 50%' for silks and 35% for
broadcloths ?
l. Invoice of two packages merchandise purchased by A. J.
Smith, London, for account and risk of H. B. Clafltn & Co.,
New York, forwarded per Steamer " Alaska" from Liverpool.
Marks.
o>
Nos.
$875
$876
Packages and Contents.
1 Case silks, 10 p'c's, Av. 45
yd. each
Discount 6 %
1 Case Broadcloths, 12 p'c's,
Av. 48 yards each
Discount 2| %
Consul's fees . . .
Com. 2£%
Cost Silks
Charges
Ins. and Freight
Packing and Cartage .
Charges for shipping.
£440, 13, 8
10, 8
Yds.
Price.
£ s. d. \
450
6,6
576
10,8
2, 15, 6
4,3
14,0
Cost.
£ s.d.
146, 5,0
8, 15, 6
137, 9,6
307, 4,0
7, 13 , 7
299, 10, 5
137, 9,6
3, 13, 9
£440,13,8
Broadcloths . . .
Charges
on £441, 4, 4
.. £137, 9, 6
.. 7, 7 , 2
£144,16, 8
. . £299,10, 5
.. 7, 7 , 2
£306,17, 7
11, 0,7
£451, 14, 3
£ 68, 14, 9
104, 16, 8
10,8
£625, 16, 4
Or, $3045.53 )
Duties £173, 11, 5 at $4.8665 = $842.92 \
Duty on Silks 50%
" Broadcloths 35%..
Consul's fees
Total cost
Note. — Each invoice is accompanied by a proper Bill of Lading, signed
by the master of the vessel, stating the number of boxes or packages
received, their marks, weight, and size, the names of the shipper and
consignee, the prices charged for freight, primage, etc.
204 Custom House Business.
IMPORT ENTRIES.
477. Goods are entered at the Custom House by marks and
numbers which should correspond to those on the Invoice and
Bill of Lading.
478. The principal entries are
1. Merchandise for immediate consumption.
2. Merchandise for storage in a Bonded Warehouse.
3. Merchandise for immediate transportation in bond to
another part of the country.
4. Merchandise for transportation in bond to a foreign
country.
5. Merchandise for export of imported goods, or of goods
made in this Country, for the benefit of a Drawback.
Course of an Import Entry in the New York Custom House.
1. The Entry is made in duplicate, one copy for the Collec-
tor's Office, the other for the Naval Office. It is a fair
statement of the cost of the goods mentioned in a foreign
invoice, the name of the Importer, name of the vessel, date
of arrival, etc.
2. The Collector's Entry Clerk endorses the Invoice with
the value of the goods in the currency of the country from
which they were imported, notes the rates of duty, the deduc-
tions to be made, etc., and places the Collector's Stamp on it,
which notes the name of the vessel and date of arrival. He
then marks the duty on the face of the Collector's copy of
entry, and makes out a Permit for the goods mentioned in the
Entry to be landed.
3. The entry is then taken to a Record Clerk in the
Collector's Office, who charges it to the Naval Officer. The
Naval Office Entry Clerk examines the work of the Collector's
Entry Clerk, and if correct, endorses it and checks the permit.
The entry is returned to the Record Clerk, who charges it to
the Deputy Collector.
Import Entries. 205
4. The Deputy Collector sees that the oath on the entry is
taken, designates the packages to be sent to the public store
for examination, signs each invoice under the steamer stamp
and the numbers of packages, and returns the entry to the
Record Clerk, who charges it to the Bond Clerk for the draw-
ing of a Bond if necessary. The entry is then sent to the
Delivery Clerk for the Importer.
5. The Importer takes the entry to the Cashier's Office for
the payment of duty. The Cashier checks the duty statement
of the Collector's Entry Clerk, etc., and gives the Importer the
permit and the Naval Office copy of entry.
6. The Importer presents copy of entry, etc., to Naval
Officer, who checks the papers, records payment of duty, and
gives the Importer a permit signed by himself and the Deputy
Collector. The Importer then presents the permit at the store
where the goods are, pays storage, and receives packages not
marked for appraiser.
7. The Appraiser, with the designated package before him,
compares the goods in it with the invoice, verifies and
determines the quantity and value thereof, and makes his
return to the Collector.
8. The entry and invoice are charged to an amendment or
liquidating clerk, who in accordance with the Appraiser's
report, makes up a statement of the duty as it should be,
in the invoice. If the ascertained duty is found to be less than
that originally paid by the Importer, the excess is refunded;
if greater, the deficit must be supplied. .
9. At the closing of a vessel's account, all the entries, with
the manifest of the cargo and the Inspector's return, are
placed on file.
Note.— Much of the labor of making entries, obtaining permits, etc.,
is done through Custom House Brokers, who are familiar with the
necessary steps.
206 Banks and Banking.
BANKS AND BANKING.
479. Banks are Incorporated Institutions which deal in
money. There are two classes, National and State-banks.
480. Banking has three departments of business :
1st. Receiving money for safe keeping, subject to the order
of the depositor.
2d. Loaning money, discounting notes, drafts, etc.
3d. Issuing notes or bills for circulation.
481. The Income of Banks is chiefly derived from loans and
circulating notes.
482. Banks make no charge for keeping deposits, and pay
no interest on them, except in rare cases, at a low rate. The
privilege of loaning a portion of them is a large source of
income, and ample equivalent for the care and responsibility.
Notes. — 1. According to the laws of the U. S., Banking Associations
may be formed of any number of persons not less than five.
2. No association may be organized with a capital less than $100000,
with the exception that in places whose population does not exceed 6000,
they may be formed with the approval of the Secretary of the Treasury,
with a capital of $50000.
3. In cities the population of which exceeds 50000, the capital must
not be less than $200000, the stock being divided into shares of $100.
483. A National Bank is required to transfer and deliver to
the U. S. Treasurer an amount of Kegistered Bonds not less
than one-third of the capital stock paid in. These are held as
security for the circulating notes delivered to the banks depos-
iting them.
Notes. — 1. Banks having a capital of $500000 are limited in their
circulation to 90% of the par value of the registered bonds deposited at
Washington ; those having a capital between $500000 and $1000000 to
80%; between $1000000 and $3000000 to 75%, and above $3000000
to eo%,
Banks and Banking. 207
2. By act of July 12th, 1870, no National Bank organized after that
date can have a circulation above $500000.
3. A Bank reducing its circulation may deposit with the Treasurer,
legal tenders or specie in sums of not less than #9000, and withdraw a
proportionate amount of the bonds previously deposited.
484. National Bank notes are redeemable in lawful money
by the banks which issue them, and by the Treasurer of the
United States.
Note.— By act of June, 1874, every National Bank is required to keep
on deposit in the treasury of the U. S., a sum equal to 5% of its circula-
tion for redeeming its bills.
485. A Reserve Fund equal to 25% of their deposits, is
required to be kept by National Banks in the cities of New
York, Boston, Philadelphia, Albany, Baltimore, Pittsburgh,
Washington, New Orleans, Louisville, St. Louis, Cleveland,
Detroit, Chicago, Milwaukee, and San Francisco, and 15% by
all other National Banks.
Note. — These are called '" Reser ve Cities," and the excess above the
requirements is called the Surplus Reserve.
486. A Surplus Fund, of the net earnings of the Bank, is
also required by law to be set aside, before the usual semi-
annual dividends are declared, until this fund amounts to 20$
of the capital.
487. An Annual Tax of 1% is paid to the United States by
National Banks on the average amount of their circulation.
Notes. — 1. The circulation of State Bank Notes ceased after Aug. 1,
1866, when a tax of 10 Jo was imposed by Congress upon each issue.
2. A Stockholder of a National Bank is liable for an amount equal to
the par value of the Stock he holds.
3. The Revised Statutes require National Banks which go into voluntary
liquidation, to deposit in the Treasury within six months, an amount of
lawful money equal to their outstanding circulation.
The law also requires that a sufficient amount, thus deposited for the
payment of circulating notes, must remain in the Treasury until the last
outstanding note shall have been presented. Hence, it will be seen the
Government derives the benefit of notes which are lost or destroyed by
fire and water.
208
Bank Account Current
4. Savings Banks and private bankers do not issue notes for cir-
culation.
[For the organization and regulation of National Banks, see Revised
Statutes of U. 8., and for State Banks, the laws of the different States.]
Exam ples.
488. l. What amount of Bank Notes is a National Bank
allowed to issue, which deposits $500000 in U. S. Bonds to
secure its circulation ? What is its redemption fund? (Arts.
484, 483.)
2. If a National Bank reducing its circulation, deposits with
the U. S. Treasurer $27000 in legal tenders, and sells the Bonds
withdrawn at 115-J, what are the proceeds ? (Art. 483, N. 3.)
3. What is the semi-annual tax upon a National Bank
whose average circulation is $925460 ?
4. A capitalist has on deposit $450000, of which lh% is coin,
45% greenbacks, and the balance is National Bank notes ; what
is the value of the bank notes ?
5. A bank having failed was placed in the hands of a
Eeceiver, who declared a dividend of 45% in favor of the
depositors. A's balance was $6526.50, B's $8417.95, and C's
$4562.87 ; how much did each receive ?
Bank Account Current.
489. l. Daily balances at 6% interest, to Apr. 26, 1883.
Bank Account Current.
1883.
Dr.
Cr.
Jan. 1
800
5
300
" 31
200
Feb. 6
300
March 4
500
Apr. 8
100
" 16
300
" 26
Bal. 1113.28
Int. 13.28
$1813.28
$1813.28
Daily Balances.
Items.
800
500
700
400
900
800
1100
Days,
x 4 =
x26 =
x 6 =
x26 =
x35 =
x 8 =
xl0 =
Int. at Q%
Products.
3200
13000
4200
10400
31500
6400
11000
6 ) 79700
$13,283
Bank Checks.
209
Explanation. — On J.an. 1, $800 were credited, and remained till the
5th, when $300 were debited." $800 being on int. 4 d., the product is
3200, that is, the int. of $800 for 4 d. = the int. of $3200 for 1 day. A
debt of $300 being made Jan. 5, there remained a balance of $500 on int.
till the 31st, or 26 d., when a credit of $200 is added, making $700 till
Feb. 6, etc. The int. by Art. 284, is $13.28, which is added to the credit
side of the account. The bal. due is $1113.28. Hence, the
Rule. — Multiply the debit and credit balance for each
day, by the number of days between it and the next debit
or credit ; add the products and find interest by Art. 284.
Notes. — 1. The balance of interest must be entered on the debit or
credit side of the account as the case may be, after which it draws interest
like the other items.
2. If the balance of items is sometimes credit and sometimes debit,
take the balance of products before dividing.
2. What is the balance due on March 1st, for the following
account current at 5% ?
The National Exchange Bank, in acct. with S. S. Carlisle.
Bank Account Current.
Daily Balances.
Products.
1833.
Dr.
Cr.
Dr.
Cr.
Days.
Dr.
Cr.
Jan. 1
200
" 18
150
" 28
250
" 31
125
Feb. 4
150
225
" 12
250
BANK CHECKS.
490. A Check is an order for money drawn on a Bank or
Banker, payable at sight.*
491. When a check is drawn payable to bearer, it is trans-
ferable without endorsement; when drawn payable to a
person named, or his order, it must be endorsed by the person
to whom it is made payable.
* The law requiring that every check have a two-cent revenue stamp placed upon it,
was repealed July 1st, 1883.
210 Bank Checks.
Notes. — 1. The payment of a check may be countermanded by the
drawer, at any time before it is paid or accepted by the Bank.
2. The holder of a check should present it without unnecessary delay,
otherwise, if the Bank should fail, the drawer will not be responsible.
3. A check should be dated on the day it is drawn, and state the day
when it is to be paid, if payable in the future.
4. The amount of a check should always be written in words, and the
same amount in figures placed in the left-hand corner at the bottom, the
cents being written in the form of a common fraction, as §8 T %%.
492. A Certified Check is one upon which the Paying Tel-
ler or Cashier writes or stamps the word "Certified" or
"Good/' and under it his signature. The bank thus guarantees
payment.
JTo. 873. JJew York, Oct. 29, 1883.
®lje €l)emical National Bank.^
(Pay to Alfred J. Pouch J$ w „ or Order
Three Thousand ^L-Q^ollars
^ -V. W. Hunter.
4*
493. A Certificate of Deposit is a written or printed state-
ment issued by a Bank, certifying that a certain person has
deposited in it a specified amount of money.
Brooklyn, Qec. 12, 1883.
(Commercial Bank.
George Brown has deposited in this l^ank. Four
Hundred Dollars to the credit of Himself, pay-
able on the return of this Certificate, properly endorsed.
John J. Vail, Cashier.
Note. — Certified checks and certificates of deposit are often used in
making remittances, instead of drafts.
Clearing Houses. 211
CLEARING- HOUSES.
494. A Clearing House is an Association of Banks, whose
representatives meet for the purpose of daily exchanges of
checks and drafts, and the settlement of balances.
495. The New York Clearing House is composed of 45 Na-
tional Banks, 12 State Banks, and the U. S. Sub-Treasury at
New York. The other city banks, both National and State,
make their exchanges through the agency of some member of
this Association.
496. The New York Clearing House, established in 1853,
is the oldest institution of the kind in this country. Since
that time 22 others have been established in different cities.
497. Each bank is represented every morning by a messen-
ger and a settling clerk. The former brings the checks, drafts,
etc., upon the other banks, which his bank received the day
previous. These are called the " exchanges" and are assorted
for each bank and placed in envelopes. On the outside of
each envelope is a slip on which is listed the amounts of the
various items which it contains. These envelopes are arranged
in the same order as the desks for the several banks.
498. At a signal from a bell struck at ten o'clock precisely,
each messenger moves forward to the desk next his own, and
delivers the envelopes containing the checks, etc., for the
Bank represented by that desk, to the clerk on the inside.
The clerk receiving it, signs and returns it to the messenger,
who immediately passes to the next desk, delivering the
exchanges as before, and passes on until he has reached his
own desk again, having delivered his entire exchanges for all
the Banks. This occupies about ten minutes.
499. The messengers then receive from their several clerks
the envelopes containing the exchanges, and return to their
Banks reporting their condition. The clerks then report to
the Assistant .Manager the amount they have received. They
are allowed forty-five minutes after the delivery of the
exchanges to enter and prove their work.
212 . Savings Banks.
500. The debit Banks are required to pay their balances to
the Manager before half-past one o'clock the same da}', and
immediately after that hour the credit Banks respectively
receive the amounts due them.
Notes. — 1. A record is kept of the daily transactions of each Bank,
and a statement of the loans, specie, legal tenders, deposits and circulation
made weekly to the Manager of the Clearing House, so that the move-
ment of each Bank can be determined, and its condition pretty accurately
estimated.
2. The rapidity with which exchanges are made by this method is a
marvel. The business of a single day has amounted to $295,821,422,
and the exchanges during the year preceding Oct. 1, 1881, exceeded
$48,000,000,000.
SAVINGS BANKS.
501. Savings Banks are institutions which receive small
sums of money on deposit, and place them at interest for the
benefit of the depositors.
502. They usually declare a dividend of the interest due the
depositors, semi-annually, on the first days of January and
July, which, if not withdrawn, is passed to the credit of the
depositor on the books of the Bank, and bears interest the
same as a new deposit. Hence, Savings Banks pay Compound
Interest.
503. Some Savings Banks allow interest to commence on
deposits on the 1st day of Jan., April, July, and October.
Others, when deposits are made on or before the 1st day of
any month, allow interest to commence on the 1st day of that
month. This method is preferable for persons having a small
income.
Notes. — 1. No interest is allowed on any sum withdrawn before the
1st day of Jan. or July for the time between the last dividend and the
withdrawal, and no interest is allowed on fractions of a dollar. The
smallest balance remaining on deposit the entire term is entitled to
interest.
2. Deposits are usually paid on demand, though the Bank is entitled
by law to 60 or 90 days notice.
Savings Banks. 213
504. The laws of the State of N. Y. do not allow Savings
Banks to have on deposit for one individual a sum exceeding
$3000, exclusive of accrued interest, unless such deposit was
made before May 17th, 1875, or by order of a court of record,
or of a Surrogate.
Notes. — 1. Savings Banks are restricted to 5% per annum regular
interest; but if their surplus earnings amount to 15% of their deposits,
they are required to declare an extra dividend once in 3 years.
2. Savings Banks in this State are allowed to pay interest on sums
deposited during the first ten days of Jan. and July, and the first three
days of April and October from the first of these months.
505. In the following examples deposits draw interest from
the 1st of Jan., April, July, and October, at 5%, unless other-
wise mentioned.
l. A man deposited in a Savings Bank, July 1, 1882, $175 ;
how much interest should be credited him Jan. 1, 1883 ?
and $175 x .02^ = $4.37* , Am.
2. A man deposited $320 in a Savings Bank Jan. 1, 1881,
and July 1, $240 ; how much was due him Jan. 1, 1882, allow-
ing 4% interest ?
Analysis.— July 1, Int. on $320 (6 mo.) = 320 x .02 = $6.40.
New Principal July 1 = $320 + $240 + $6.40 = $566.40
Int. 6 mo., Jan. 1 * = ($566 x .02) = 11.3 2
Amt. due Jan. 1, 1882 = $577.72
Note. — Though interest is not reckoned on the fractional parts of a
dollar, in finding the amount at the close of a year these are included.
3. Jan. 1, 1880, a clerk deposited in a Savings Bank $150 ;
March 12th, $48; June 17th, $125; and Sept. 30th, $150.
Withdrew Apr. 10th, $25; July 12th, $34; Oct. 10th, $50;
what was the balance due Jan. 1st, 1881, int. 4% quarterly ?
Note. — In order to determine more easily the quarterly balances
entitled to interest, the account may. be arranged in the following form,
showing the amount due at each regular interval, the time, and the int.
on the successive amounts.
214
Savings Banks.
ir *
Date.
Deposits.
Drafts.
I
Bal.
Time.
\ Int. 4%.
1880.
Jan. 1
March 12
Apr. 10
150
48
125
3
150
6
$482.
23
34
57-
%5
34
50
-$109
= $c
150
173
267
3G7
173.57
3 mo.
3 mo.
3 mo.
3 mo.
Ans.
1.50
1.73
June 17
July int.
12
Sept. 30
Oct. 10
3.23
2.67
3.67
July
1881.
Jan. 1 int.
6.34
J a n.
Explanation.— $150 draws int. 3 mo. The 2d dep. ($48- $25) + $150
(Apr. bal.) = $173 draws int. 3 mo. 3d deposit ($125 + $3 July int. —$34,
dft.) + $173 (July bal.) = $267 draws int. 3 mo. 4th deposit ($150-$50,
dft.) -f $267 (Oct. bal.) = $367 on int. 3 mo. The sum of deposits with
interest, less the sum of drafts gives the balance due.
4. A deposited Jan. 1, 1881, $125 ; March 15, $140 ; July 5,
$65. He withdrew Feb. 15, 1881, $30; Apr. 10, $12; Oct. 15,
$20. What was due Jan. 1, 1882, interest being ±%, payable
quarterly ?
Date.
Deposits.
Drafts.
Balances,
1881.
*
Jan. 1
$125
1
Feb. 15
$30 |
| $95
•
Mar. 15
140
Jj- • .
-
Apr. 10
12
128
*H£
*
*. 1.90 (6 mo.)
•' 1.28 (3 mo.)
July 5
65
$226.18 due, July 1,
1881.
Oct. 15
20-
45 . .
1882.
'
Jan. 1 Int.
5.42 (6 mo.)
$276.60 Amt. due.
Savings Banks.
215
Note.— The drafts are usually deducted from the last deposits made.
Thus, the draft of $30 taken from $125, leaves a bal. of $95 on int.
from Jan. 1. The draft of $12, Apr. 10th, leaves $128 on int. from
Apr. 1, etc. (Art. 504, N. 2.)
5. Jan. 1," 1883, B deposited $120 in a Savings Bank;
Feb. 20, $60 ; Apr. 1, $150 ; May 30, $80 ; what interest pay-
able semi-annually at 4$ was due July 1, 1883 ?
6. On the 4th of Jan., 1881, a mechanic deposited $84 in a
Savings Bank ; March 25, $50 ; Oct. 9, $96. He withdrew
May 1, $12, and on the 20th of Oct., $21 ; allowing deposits to
draw interest at 4$ from the first day of every quarter, how
much will be due him Jan. 1, 1882 ?
7. Balance the following, Jan. 1, 1884: deposits Jan. 1,
1883, $250 ; Feb. 6, $58 ; Apr. 10, $64. Checked out March
15, $50 ; May 13, $75, interest beginning from the first of each
quarter.
8. What would be due a depositor at the end of the year,
who had a balance of $563 in bank Jan. 1 ; Jan. 8, he added
$75 ; March 28, $65 ; May 15, $84 ; Apr. 12, withdrew $15 ;
Oct. 11, $60, int. allowed from the 1st of the month following
a deposit ?
9. The balance due n clerk Jan. 1, 1882, at a Savings Bank
was $150 ; April 1, he deposited $75 ; July 2, $87 ; and Oct. 3,
he drew out $25; how touch did the bank owe him Jan. 1,
1883, interest payable semi-annually "A
« . V *
• k io. Balance" the following pass-book Jan. 1, 1883 :
* r, .
Dr. Dime Savings Bank in acct. with J. Hamilton. Cr.
Jan. 1
Mar. 31
Oct. 1
Three hundred fifty dollars
One hundred twenty dollars
InJ. to July, at 5%.
Three hun. seventy-five dol.
Int. to January.
Aug. 1 One hundred twenty dollars
Oct. 15 Sixty-five dollars.
Stocks
506. Stocks represent the capital or property of incor-
porated companies.
507. An Incorporated Company is an association authorized
by law to transact business, having the same rights and obliga-
tions as a single individual.
508. The capital stock of a company is divided into equal
parts called Shares.
Note. — The par value of a share varies in different companies. It is
usually $100, and will be so regarded in this work, uuless otherwise
stated.
509. A Stock Certificate is a paper issued by a corporation,
stating the number of shares to which the holder is entitled,
and the par value of each share.
510. The Par Value of stock is the sum named in the
certificate.
511. The Market Value is the sum for which it sells.
Notes. — 1. When shares sell for their nominal value, they are at par;
when they sell for more, they are above par, or at & premium; when they
sell for less, they are below par, or at a discount.
2. When stocks sell at par they are often quoted at 100 ; when at 1%
above par, they are quoted at 107, or at 1% premium ; when at 15% below
par, they are quoted at 85, or at 15 fc discount.
512. A Preferred Stock is one which is entitled annually to
a stated per cent dividend out of the net earnings, before the
common stock dividend is declared, and may be cumulative or
not.
Note. — When cumulative, if the earnings are not sufficient to pay the
dividend for any year, the holder of preferred stock is entitled to the back
dividends before any other payments are made.
Stocks and Bonds. 217
513. An Installment is a payment of part of the capital.
514. An Assessment is a sum required of stockholders to
replace losses, etc.
515. The Gross Earnings of a company are its entire
receipts from its ordinary business.
516. The Net Earnings are the remainder after all expenses
are deducted.
517. A Dividend is a sum divided among the stockholders
from the net earnings of the company.
Note. — Companies sometimes declare a Scrip Dividend, entitling the
holder to the sum named, payable in stock at par value.
518. A Bond is a written agreement to pay a sum of money,
with a fixed rate of interest, at or before a specified time. The
term is applied to National, State, city, and railroad bonds, etc.
Notes. — 1. Bonds are named from the parties who issue them, the
rate of interest they bear, and the date at which they are payable, or
from all united. Thus, "IT. S. 4's of 1907," means that these bonds bear
4% interest, and are redeemable after 1907, at the pleasure of the
Government.
2. Bonds of States, cities, corporations, etc., are named by combining
the rate of interest they bear with the name of the State, corporation, etc.,
by which they are issued ; as, Ohio G's, N. Y. Central 5's, etc.
3. Convertible Bonds are those which may be exchanged for stock,
lands, or other property.
519. Bonds are also known as first, second, etc., Mortgage
bonds, Income bonds, and Consols.
520. A Coupon is a certificate of interest due on a bond, to
be cut off when paid, as a receipt.
Notes. — 1. Income bonds are those on which interest is paid, if earned,
and are not usually secured by a mortgage.
2. The term "Consols" is applied to Bonds issued in place of two or
more classes of outstanding bonds, which are thus consolidated into one
class. The term originated in England.
218 Stocks and Bonds.
521. A Mortgage is a conveyance of real estate or other
property, as a pledge for the payment of a certain amount of
money.
Note. — If either the principal or interest is not paid when due, the
mortgagee has a right to take or sell the property.
United States Bonds.
522. United States Bonds are known as Coupon Bonds and
Registered Bonds.
523. Coupon Bonds have Interest Certificates or Coupons
attached to them, and are negotiable by delivery. For this
reason they sell higher in foreign markets than registered
bonds.
Registered Bonds are those payable to the order of the
owner, whose name is recorded in the office of the Register of
the Treasury, at Washington, D. C. They can be transferred
only by assignment duly acknowledged.
Notes. — 1. Letters relating to the transfer of registered bonds or the
payment of interest on the same, should be addressed to the Register of
the Treasury.
2. The transfer books are closed for 30 days previous to the day for
the payment of dividends ; and stockholders desiring the place of pay-
ment changed, must give notice to the Register one month at least before
the dividends are due.
3. When bonds are sent for transfer, state where the interest is to be
paid, inclose the stock of different loans in separate envelopes, and name
on each the amount of stock and the date of the Act of Congress authoriz-
ing its issue.
4. Powers of Attorney for the assignment of U. S. Bonds, and the
assignments, must be properly filled, before transmission to the Register.
5. Powers of Attorney to draw interest should be addressed to the
First Auditor of the Treasury.
6. In quotations of bonds, the accrued interest from the day of closing
the transfer books, is included in the price.
Stocks and Bonds. 219
NATIONAL DEBT OF THE UNITED STATES.
524. The National Debt of the United States is divided
into Bonds, Funded Loads, Refunding Certificates, Navy Pen-
sion Fund, debt bearing no interest, etc. No nation has a
common name for all its debt.
Funded Debt Bearing Interest.
Bonds at 6% continued at 3 J $149,682,900.00
" at b% " " 401,503,900.00
" at 4\% 250,000,000.00
" at 4^ 738,772,550.00
Refunding Certificates, 4% 575,250.00
Navy Pension Fund, 3% 14,000,000.00
$1,554,534,600.00
Debt bearing no Interest since maturity 11,528,265.26
Non-Interest-bearing Debt.
Legal-tender Notes $346,681,016.00
Certificates of Deposit 9,590,000.00
Gold Certificates 5,188,120.00
Silver « 68,675,230.00
Old Demand Notes 59,920.00
Fractional Currency 7,075,926.92 437, 270 ,212.92
Total principal $2,003,333,078.18
525. Bonds to the amount of $64,623,512, known as
"Currency Sixes," were issued to the Pacific Railroads,
and the interest on them is payable by the United States ;
but they are not included in the above estimate, as the
Government holds mortgages on the roads to cover the
amount.
Note. — These took their name from the fact that the interest on them
is payable in currency or any legal tender. All United States Bonds are
exempt from taxation.
526. Of the funded loans there are registered bonds of the
various issues, in denominations of $50, $100, $500, $1000,
$20000, and $50000 ; and coupon bonds of $50, $100, $500,
and $1000.
220 Stocks and Bonds.
The Funded Debt of Foreign Countries.
527. Consols are the leading funded securities of the Eng-
lish Government ; bearing 3% interest, payable semi-annually.
This debt amounted in 1882 to $3,814,500,000, of which
$3,545,000,000 were Consols, or Consolidated Annuities, re-
deemable only at the pleasure of the Government.
528. The funded debt of France bears the title of Rentes.
The rate of interest is usually 5%. This debt in 1882 was
$4,750,337,109. Besides this the "Bons du tresor" amount
to $65,000,000.
529. The German Empire has only about $70,000,000
funded debt bearing 4% interest, known as 4% Imperial bonds.
530. In 1882 Austria had a funded debt of $1,450,000,000,
the larger part bearing b% interest, known as "Austrian Consols."
531. Russia had a debt of $2,421,417,932, a portion of
which bears a nominal interest of 5 and 5|$. They are
known as Oriental loans, and are below par.
Prussia has a debt of $498,500,000, of which $220,000,000
is consolidated (zuheilung) at an average of 4% interest.
Italy has an immense debt, of which $380,000,000 are in
" Rentes " of 3 and 5 per cent.
STOCK EXCHANGES.
532. Stock Exchanges are Associations organized for buying
and selling stocks and bonds and other similar securities.
533. Members are elected by ballot. The qualifications for
membership are good character and solvency.
534. The Officers are a President, Vice-President, Treasurer,
Clerk, Secretary, Standing Committee, Finance Committee,
Committee on Listing Stocks, and a Nominating Committee.
Notes. — 1. Every Association makes its own By-Laws, which are
stringent and rigidly enforced.
The Stock Exchange. 221
2. A system of Arbitration supersedes all appeals to the law for the
settlement of disputes.
535. The New York Stock Exchange is composed of 1200
members, the maximum allowed by their By-Laws. It is said
that seats at this Board have recently been sold at prices rang-
ing from $20,000 to $30,000.
536. The Exchange is open for business from 10 a.m. to
3 p. m. Before any new securities are allowed to be quoted or
sold on the Exchange, they are subjected to a rigid examina-
tion by the Committee on "Listing" Stocks.
537. There are two lists of Stocks, one is known as the
Regular list, the other as the Free list.
538. Ordinarily Stocks and Bonds are quoted at a certain
per cent on the par value of $100 per share. Stocks of the
par value of $50 are called half stocks, and those whose par
value is $25 are called quarter stocks, and the price quoted
is the percentage of the par value.
The commission for buying or selling Stocks or U. S.
Bonds is | of 1% (i%).
Mining Stocks are quoted at so much per share, and the
commission varies according to the price of the stock.
539. Pipe-line certificates are quoted at so much per bbl. for
1000 bbl. of crude Petroleum oil.
540. Stocks sold " regular way " are paid for and delivered
on the next business day. On sales made " buyer three " or
" seller three " no interest is charged ; on contracts longer than 3
days, the buyer pays interest, unless otherwise specified. ~No
contracts for more than 60 days are recognized.
Notes. — 1. "Seller 3," means deliverable on either of 3 d., at the
option of the seller. "Buyer 3," means the buyer can demand delivery
within 3 d., but must take and pay for it the third day.
2. Quotations are termed "flat" when the accrued interest is included
in the price named.
222 Stocks and Bonds.
541. Margin is cash or, other security deposited with a
broker on account of either the purchase or sale of securities,
and to protect him against loss in case the market price of the
securities bought or sold varies so as to be against the interests
of the customer. It is usually 10$ of the par value of the
stock.
Note. — Brokers charge interest on the sums expended and allow
interest on the margins deposited.
542. A Bear is an operator who believes the market price of
stocks will fall
543. A Bull is an operator who believes the market price
of stocks will advance.
Note. — Hence a bull will buy stocks in order to profit by the I i /her
price at which he expects to sell, and a bear will sell in order to profit by
the lower price at which he expects to buy.
544. Hypothecating stocks and bonds is depositing them
as collateral security for money borrowed.
Note. — The securities must be greater than the loan by at least 10%
of their par value, and in every case by an amount equal to 20% of the
amount of the loan. This excess is called the margin of the loan..
545. Watering Stock is increasing the number of shares of
an incorporated company without a corresponding increase in
their value.
546. A Corner is produced when one or more operators
owning or controlling, all the stock of a company are able to
purchase still more for either immediate or future delivery.
When they demand the stock, the sellers are unable to find
it in the market.
547. A Syndicate is a combination of Brokers, Bankers, or
Capitalists who undertake to place large loans, and transact
other business.
Note.— Stock Privileges known as " Puts." " Calls," " Spreads," and
" Straddles," are not recognized by the Stock Exchange,
Stock Investments. 223
Quotations in Stocks.
548. The following are taken from a report of sales at the
New York Stock Exchange in Dec, 1883. The abbreviations
which appear will be explained hereafter in the Appendix.
10000 4's, coup 123£ I Cen. Pac. 1. g 104i @ 104£
50000 4's, reg 122| Erie, 5th 105
800003's, " 101
25000 4£V 114J
2000 N. C. 4's, en 81}
1000 Tenn. f. new S 38
10 sh. Am. Ex. Bank 130
100 Chi. & N. W. pf 142}
100 Mut. Un. s. f. 6's 84£
Cur. 6's,'95 127i
Chi. Bur. & Q. 5's Deb 91|
N. Y. Central 116 @ 116|
N. Y. Elevated 105
Chi. & W. Ind. s. f 106.|
N.J. Central 83 £
Va. Mid. inc 63|
Seller's Option.
500 Sh. N. Y. EL © 1 5, S. 60. New YorK) Dec . 15> 1883>
I have Purchased of Lockwood Bros. Five Hundred
(500) Shares of the Capital Stock of the Netv York Elevated
Railroad Company, at one hundred five dollars ($105) per share;
payable and deliverable at seller's option within sixty (60)
days ivith interest at the rate of 6% per annum.
H. B. Stevenson.
Buyers Option.
500 Shares N. Y. 0. @ 116, B. 30. New York> Dec . 28> 1883 .
/ have Sold to E. J. Marshall Five Hundred (500)
Shares of the Capital Stock of the Neio York Central Railroad
Company, at one hundred sixteen per cent; payable and
deliverable at buyer's option within thirty (30) days with
interest, at the rate of six (6) per cent per annum.
C. B. Hatch.
STOCK INVESTMENTS.
549. Premiums, Discounts, Dividends, and Assessments,
are computed by Percentage.
The par value of the stock is the Base ; the per cent of
premium, dividend, or discount is the Rate; the premium,
discount, or dividend is the Percentage.
224 Stocks and Bonds.
550. To find the Cost of stock, the par value and the rate of
premium, discount or dividend being given.
1. What cost 50 shares R. R. Stock, at 6% premium, par
value 1100, brokerage \% ?
Analysis. — The cost of 1 share, at 6 % premium + \ % brokerage =
$106,125. Cost of 50 shares = $106,125 x 50 = $5306.250, Ana.
2. What cost 60 shares of R. R. Stock, at 8% discount,
brokerage \% ?
Analysis. — The cost of 1 share, at 8% discount, and \% brokerage =
$92,125. Cost of 60 shares = $92,125 x 60 = $5527.50, Ans. Hence, the
Rule. — Multiply the cost of 1 share by the number of
shares.
Note. — In finding the entire cost of stocks the rate % of brokerage is
added to the rate above or below par, as both are calculated on the same
amount. (Art. 538.)
3. What must be paid for 800 shares Telegraph stock, at
25$ premium, brokerage \% ?
4. What are 60 shares Erie R. R. stock worth, at 15J<£
discount?
5. What must be paid for U. S. bonds, par value $5000, at
106, brokerage \% on the par value ?
Solution.— 50 shares, at 106 = $5300, and {\% brokerage) $6.25 =
$5306.25.
6. What cost 75 shares Union bank stock, at 8f% premium,
brokerage \% ?
7. The premium on stocks sold was $858, the par value
$7550 ; what was the cost ?
8. The discount on a Mining stock is 15j% par value $50;
what is the value of 23 shares ?
551. To find the premium, discount, dividend, or assessment,
the number of shares and rate being given.
9. What would a stockholder of New York and New Haven
R. R Co. receive, who owns 500 shares, from a 4=% dividend?
Stock Investments. 225
Solution.— 500 shares at $100 = $50000 tlie par value,
$50000 x .04 = $2000.00, Ans. Hence, the
Rule. — Multiply the par value of stoelc by the rate %.
10. A western R. R. Co. called for an assessment of 12\% ;
how much must a man pay who owns 350 shares ?
11. The stock of a mining Co. was sold at a discount of 4$$;
how much was received for 800 shares, par value $50 a share ?
552. To find the Rate %, the par value of stock, the premium,
discount, dividend or assessment being given.
12. The capital stock of a Co. was $100000, the dividend
$22000; what was the rate per cent?
Solution.— $22000.00 -*- $100000 = .22, or 22%, Ans. Hence, the
Rule. — Divide the premium, discount, assessment, or
dividend, by the par value of the stoelc.
13. The discount on 75 shares Panama R. R. stock was
#725 ; what % was it ?
14. A man owning 25 shares Western Union, was assessed
$85 ; what was the rate per cent ?
553. To find the number of shares, when the sum invested and
the cost of I share are given.
15. How many shares of factory stock at 6% discount and
brokerage \%, can be bought for $76200 ?
Analysis. — Since the discount is 5% and brokerage }%, the cost of 1
share is 95%+£%,.or 95J% of $100 = $95.25. As $95.25 will buy 1
share, $76200 will buy as many shares as $95.25 are contained times in
$76200, and $76200 -j- $95.25 = 800 shares, Ans. Hence, the
Rule. — Divide the sum invested by the cost of one
share.
16. How many shares of Mutual Union telegraph stock, at
15$% discount and brokerage \%, can you buy for $13500 ?
226 Stocks and Bonds.
17. Find the number of pipe line certificates at 115J, that
can be bought for $15150, brokerage \%.
18. What number of elevated railroad shares at 105,
brokerage \%, will $75150 pay for?
19. Find the number of shares of Union Pacific, at 20%
discount, that can be bought for $32000 ?
554. To find how stock must be bought which pays a given per
cent dividend, to realize a specified per cent on the investment.
20. At what price must I buy stock which pays 6% dividend,
so as to realize 8% on the investment?
Analysis. — Since the annual income of $1 is .06, this must be T f^ of
the price to be paid; then -^ = .06 -*- .08 = $. 75, and £{$ = $75.
Hence, the
Kule. — Divide the rate which the stock pays by the
required rate, the quotient will be the price of $1 stock.
21. What must be paid for U. S. 4's that 8% may be received
on the investment ?
22. What must be paid for stock that yields 20% dividends,
so as to realize 1\% on the investment ?
555. To find what sum must be invested to yield a given
income, when the market value, and the rate of interest are given.
23. What sum must be invested in N. Y. 5's, at 108£, to
produce an annual income of $2500 ?
Analysis. — The income $2500 -j- $5 (int. on 1 share) = 500 shares, and
108^ (price of 1 share) x 500 = $54250. Hence, the
Kule. — Multiply the market value of 1 share by the
number of shares.
24. How much must be invested in U. S. 4's, at 123§, to
yield $3500 annually?
25. What must be invested in Nebraska 8's, at 75, to yield
an income of $3540 annually ?
Stock Investments. 227
26. What sum must be invested in stock at 112, which pays
10% annually, to obtain an income of $3200 ?
27. How much must be invested in Alabama 6's, at 85, to
realize $2500 a year ?
28. How much must be invested in stock at 106, to yield an
income of $6000, the stock paying 10% dividend annually ?
556. To find the % of income from a given investment, without
regard to its maturity.
29. What is the % income on bonds bought at 125, paying
1%% interest ?
Analysis. — Since the int. on 1 share ($100) is $12, the int. on $125 is
fa of $12, and $12-s-$125 = .09?, or 9f#, Ana.
30. Bought 5% bonds at 75 ; what will be the % income ?
Solution.— $5^-75 = .06|, or 6|%, Ana. Hence, the
Rule. — Divide the income per share by the cost per
share.
31. Find the per cent of income on U. S. 4}'s, bought at
tut
32. What is the per cent of income on Iowa 6's, bought at
108}, brokerage \% ?
33. Which is the more profitable, $10000 invested in 3 per
cents at 101, or in 4 per cents at 122}?
34. If a person were to transfer $29000 stock from 3} per
cents at 99 to 3 per cents at 90-| what would be the difference
in his income ?
35. A man agreed to take 300 shares of mining stock, par
value $50 ; after the third installment was paid amounting to
75^ of the par value, a dividend of 3% was declared ; how
much and what % on the actual cost did he receive ?
228 Stocks and Bonds.
557. To find the % income from a given investment payable in
a given time.
36. What per cent income will be received if I buy U. S. 4's
at 112, payable at par in 16 years?
Analysis — Since the bond matures in 16 years, the premium on 1 share
($12) decreases j-f, or $| each year. The int. $4— $f = $3£ income. And
$3.25-r-$112 (cost of 1 share) = ^\\\°/c the rate required.
37. Bought Tennessee bonds at 38, bearing ±% int., having 25
years to run ; what per cent will be realized if they are paid at
par at maturity ?
38. What per cent income will be gained from S% bonds,
bought at 90, and payable at par in 20 years ?
Analysis. — Since the maturity is 20 years, the discount ($10) decreases
£&, or $| each year. The int. $8 + -| = $8£ income ; and $8.50h-$90 =
$.09,*, or 9|% the required rate. Hence, the
Rule. — First find the average annual decrease of the
premium or discount.
If the bonds are at a premium, subtract it from the
given rate of interest; if at a discount, add it to the
interest ; the result will be the average income of one
share.
Divide the average income of one share by the cost of
one share, and the quotient will be the rate per cent of
income.
Notes. — 1. When bonds are at a premium, the longer the time before
maturity, the greater will be the rate per cent of income.
2. "When bonds are at a discount, the longer the time before maturity,
the less will be the rate per cent of income.
39. What rate per cent of income will be received on IT. S.
4J's at 114, payable at par in 16 years?
40. Bought Kentucky bonds at 90, due at par in 30 years,
drawing 8% interest ; what is the per cent of income ?
41. In 1882 Milwaukee and St. Paul 6'§, due at par in 1930,
were bought for 108 ; what interest will this pay ?
/Stock Investments. 229
Note. — Other methods of analysis than those given are often used by
dealers in stocks and bonds. Take Ex. 41. The amt. of $100 (1 share) at
6% for 48 years equals $388. Subtracting cost, $388— $108 = $280, total
income. The question now becomes, " What per cent of $108 will yield
$280 in 48 years?" In 1 year, 1% of $108 = $1.08, and in 48 years
$1.08 x 48 = $51.84. If $51.84 = 1 % , $280 = as many % as $51.84 are
contained times in $280, or §^ % .
42. If I pay 108 for U. S. 4's, having 15 years to run, what
% will I receive if I keep them till they mature and they are
paid at par ?
558. To find how stock must be bought which has several
years to run, and pays a given % dividend, to realize a specified
per cent on the investment.
43. At what price must 6% bonds, payable in 8 years, be
bought to realize 4=% on the investment.
Analysis.— The Amt. of $100, at 6% in 8 yrs. = $148.
The Amount of $1, at 4% in 8 yrs. = $1.32.
$148-s-$1.32 = $112j& per share. Hence, the
Rule. — Find the amount of $100 for the given time
and rate, and divide it by the amount of $1 for the
same time, at the rate required.
44. Bought railroad 6% bonds payable in 5 years, and expect
to realize 11% on the investment ; what did I pay ?
45. What must I pay for 5 per cent bonds, which mature in
15 years, that my investment may yield 4 per cent ?
46. What shall I pay for a bond of $500, having 12 years to
run, with interest at 6%, in order to make it an 8% invest-
ment?
Practical Examples.
559. l. At what price must a stock paying semi-annual
dividends of 2% be bought, to yield 6% per annum on the
capital invested ?
2. If the semi-annual dividends are 2\%, how must the
stock be bought to yield 5% ?
230 Stocks and Bonds.
3. Which is the more profitable investment, a stock at 120,
paying 8% annually, or a 20-year bond at 90, paying 6% annually ?
4. Three companies, A, B, and C, are to be consolidated on
the basis of the relative market values of their stock.
Thus, A's capital $1,000,000, Market value 100%;
B's " $1,500,000, " " 50%;
C's " $625,000, " " 40%.
The capital of the consolidated company is to be $2,000,000,
in 20000 shares of $100 each. What proportion and what
amount of the capital should be allotted to each of the old
companies ; and how much stock in the new company should
the holder of 1 share of the stock of each of the old companies
be entitled to ?
5. When 3% government bonds are quoted at 101, what sum
must be invested to yield an income of $800 a year ?
6. What is the accurate interest on an investment of $5000
in U. S. 4£'s at 114J, from Jan. 1 to March 1, inclusive ?
7. If a man buys stock at 17% above par, what per cent does
he receive on his investment, if the stock pays a dividend of
8\% on its par value ($100) ?
8. A man bought 8 shares of stock at 108|, and after keep-
ing it 11 months received a dividend of $7 a share, and sold
the stock then at 109£ ; what per cent did he receive on his
investment ?
9. How many shares of Mutual Union Telegraph stock at
84J, can be bought for $12000, brokerage \% ?
10. Bought Oct. 12th, 400 Pacific Mail at 42J, and 200 Mich.
Cen. at 92 £; Nov. 10 sold the former at 42 J, and the latter at
92| ; what was my gain ?
n. Which would be the better investment, $12120 in N. J.
Central at 84, paving 3% annual dividends, or the same invested
in Chemical Bank stock at 2020, paying 15% every 2 months?
12. A customer deposited $500 margin with a broker
Nov. 23, who purchased for him 50 shares Mich. Central at 80.
He sold the same stock Nov. 30th at 98 ; what was the gain,
brokerage \% ?
Stock Investments.
231
OPERATION.
Dr.
Nov. 23.
To 50 sh. Mich. Cen. at 80. . $4000
Brokerage \% 6.25
Nov. 30. Int. on $4006.25, 7 days
fa
By margin deposited
Nov. 23.
•* 30.
Nov. 30.
Note
By 50 sh. Mich. Cen. at 98. . $4900
Less Brokerage | % . . . . 6.25
Int. on $500, 7 days
—The brokerage, £ of 1% is equal to
$12.50 on 100 shares of stock at the par value of
$100 each.
4006
25
4
67
4010
500
4893
75
58
5394
$1383
Balance
Less margin
500
Gain. .
$883
92
13. A man bought 100 shares Union Pacific at 79}, and sold
the same at 82f ; what was the gain, less \% brokerage ?
14. Governments yielding $240 a year at 4$ interest, were
sold at 108, and the proceeds invested in land at $75 an acre ;
how many acres were bought ?
15. What cost 25 shares of 111. Cent, at a premium of 33$ ?
16. What rate of dividend on the above would be equal to
6$ interest on the investment ?•
17. If the N. Y. Cen. declares a dividend of 15$, how much
will a man receive who owns 250 shares ?
18. What per cent on his investment if he bought the above
stock at 95 ? What per cent if bought at 116 ?
19. Which is the better investment, R. R. stock at 25$
discount, and paying a semi-annual dividend of 4$, or money
loaned at 10$, interest payable annually ? What % better ?
20. If the annual dividend on a stock is 15$ and money is
loaned at 10$ per annum, what should be the price of the stock?
21. On 84 shares of stock 2 semi-annual dividends were
declared, one at 5$, the other at 4$, the investment paid 10$;
what did the stock cost ?
22. A man's income from $2000 worth of stock is $75 semi-
annually ; what is the per cent per annum ?
232 Produce Exchanges.
23. At what per cent discount must 6% stock be bought,
that the investment may pay 9% ?
24. If a stock yields 15$ per annum, what is its value when
money is worth 8% ?
25. March 4th, deposited with my broker $500 margin,
for purchasing 50 shares Mo. Pacific K. R. stock at 92J. The
stock was sold March 28th at 96f . Allowing 6% interest on
the deposit, and charging 6% interest on the purchase, and \%
brokerage, what was the net profit on the transaction ?
26. Sold "short" through my broker 200 shares Mich.
Cent, at 90, and "covered" my "short" at 86|. Allowing \%
commission for buying and selling, what was my net profit ?
27. What rate per cent income will be received on U. S. 4's
at 108, payable at par in 15 years ?
28. A man's income from U. S. 4's of 1907, bought at 123,
and 3's at 101, is $350. If bought at par an equal sum would
have been invested in each ; how much was his investment ?
How many shares of each stock did he buy ?
29. Paid 86} for stock bearing 8% annual dividends ; and
received each year $480 ; what was the investment ?
30. Borrowed $100000 upon 1000 shares N. Y. Cent, at 120.
If the market price falls to par, how much more of the same
stock must I deposit with the lender to keep up the original
margin ? (Art. 544, N.)
PRODUCE EXCHANGES.
560. Produce Exchanges, or Boards of Trade, are Associa-
tions of dealers in Produce. They make their own By-Laws
and are conducted by a Board of Directors, usually including
a President, Vice-President, Secretary, and Treasurer, who are
elected by ballot.
The fee for membership is $1000 and upwards. They have
committees on Complaints, Arbitration, Appeals, Trades, Prices,
Transportation, Information and Statistics, etc.
Produce Exchanges. 233
561. The department which most concerns the public, is the
Inspection by their committees of the great staples of food, as
grain, flour, the various kinds of provisions, peas, beans, beef,
pork, lard, butter, cheese, eggs, and all the important products
of the country.
To protect the public against fraud and adulterations, they
classify these various articles according to quality, after careful
inspection, and adopt marks or brands for each, by which they
become known in the markets of the world.
What the Stock Exchange is to financial securities, the
Produce Exchange is designed to be to the staples of food.
Note. — Exchanges have already become important accessories of
commerce. They facilitate speculation as well as regulate it ; they are
courts of arbitration for settling disputes, and are considered almost a
necessity to the interests they represent. Many associations have
mutual life insurance attachments connected with them. In addition to
the stock and produce exchanges there are Real Estate, Petroleum, Cotton,
Tea, Coffee Exchanges, etc., each with a separate organization, the
avowed objects of which are to advance the interests of trade and
commerce.
1. What % do I make by purchasing flour at $7.50 per barrel
cash and selling it for $8.25 on 3 mo. credit, when money is
worth 6% ?
2. A man has a bin 28 ft. long, 5 ft. 4 in. wide, and 4 ft.
deep, filled with wheat ; what is it worth at $1.15 per bushel?
Note. — The quantity of grain in bins, etc:, is found by reducing it to
cubic inches and dividing the result by the number of cubic inches in a
bushel. (Art. 71.)
3. A dealer has 3 bins of wheat containing 700, 950, and
1000 bu. respectively ; he has sold 3 lots of 400 bu., 1 lot of
75 bu. 1 pk. 5 qt., and 6 lots each of 10 bu. 3 pk. 2 qt. ; what is
the value of what he has left at $1.15 per bushel?
4. Bought wheat at $1.10 a bushel, allowing \\% for waste
and 2 cts. a bu. for storage; how must it be sold to gain 8%?
5. The net proceeds of a shipment of hay, sold at $28 per
ton, were $12580 after deducting 3% commission and $500 for
other charges; how many tons of hay were shipped ?
234 Storage.
6. A dealer received 10000 barrels of flour to sell on com-
mission, and was to invest the proceeds in TJ. S. notes at Y^%
interest; he paid $759 charges, sold the flour at $9 a barrel and
charged 3% commission on the sales ; what amount of notes
could he buy at 36% premium, brokerage \% ?
7. A produce merchant bought 30000 bu. corn at $0.55,
paying $450 charges, and $225 storage ; he sold it at 25$
advance on the entire cost on 90 days time ; at what price per
bu. did he sell it, and what per cent did he gain at the time of
sale, money being 7% interest ?
8. The net proceeds of a sale of 1000 tons of hay at $20 per
ton were $18325, after deducting $875 for charges; what was
the rate % of commission ?
9. A dealer expended equal sums in wheat, rye, and oats ;
on selling he made H% on the wheat, b% on rye, and lost 15$
on the oats ; the whole sum received was $1782 ; what sum did
he invest in each kind of grain ?
10. A grain merchant bought 9000 bu. wheat, paying at his
option $1 cash per bu., or $1.10 on 3 mo.; which would be the
more advantageous, to buy on credit, or to borrow the money at
7% and pay cash ?
STORAGE.
562. The business of Storage is done by commission and
forwarding merchants. The prices charged are regulated by
the Board of Trade of the city in which the Storage is made,
unless by a special agreement.
563. The rates are usually fixed at a certain price per barrel,
bushel, box, bale, etc., for one month of 30 days.
Notes. — 1. In some cities a full month's storage is charged for any part
of a month they may remain in store, in others 15 days or less are called
| mo. and over 15 days a whole month.
2. On Grain the charge per bushel for storage varies in different
cities.
Storage.
235
564. Accounts of Storage ordinarily contain an entry of
articles received and delivered with the date of each. They are
somewhat similar to bank accounts.
565. To Average a Storage Acct. according to actual time.
l. Received on storage and delivered the following : May 1,
1883, 1000 bbl. flour; May 26, 2000 bbl. Delivered, May 16,
500 bbl.; June 1, 1000 bbl.; June 12, 1100 bbl.; July 2, 400
bbl. ; what was the cost of storage at 6 cts. a mo. per barrel ?
Acct. of Storage of flour received and delivered for acct. of
A. Hamilton of Chicago.
Date.
Received.
Delivered.
Balances.
Days.
Products.
1883.
May 1
1000 bbl.
1000 bbl.
15
15000
" 16
500 bbl.
500 "
10
5000
" 26
2000 "
2500 "
5
12500
June 1
1000 "
1500 "
11
16500
" 12
1100 "
400 "
20
8000
July 2
400 «
000 "
00
0000
3000 bbl.
3000 bbl.
30 ) 57000
Storage for 1 month for 1900 bbl.
1900 x. 06 =$114.00, Ans.
Rule. — Multiply the number of barrels, etc., by the
number of days they are in store between the time of
entrance and delivery. Multiply each balance by the
number of days it remains unchanged. Divide the sum
of products by SO, the quotient is the number of articles
in store for one month.
2. Received and delivered on account of Samuel Barrett of
New Orleans sundry bales of cotton as follows: Received
Jan. 1, 1884, 2310 bales ; Jan. 16, 120 bales ; Feb. 1, 500 bales;
Feb. 12, 200 bales. Delivered Feb. 12, 1200 bales ; March 6,
800 bales ; April 3, 400 bales ; April 10, 300 bales. Balance
the account to May 1, and find the storage due at 15 cents a
bale per month.
236 Life Insurance,
3. Eeceived on storage, and delivered the following merchan-
dise : Received Jan. 1, 1884, 100 bbl. rye meal ; Jan. 15, 200 bbl.
rye meal ; Feb. 10, 300 bbl. corn meal ; Feb. 20, 10 bbl. oat
meal. Delivered Jan. 15, 100 bbl. rye meal; Jan 30, 150 bbl.
rye meal ; Feb. 28, 200 bbl. corn meal. What is the amount of
storage due March 1st, at 5 cents a barrel per month ?
Note. — When different rates are charged for different kinds of goods
in store at the same time, a separate calculation must be made for each
kind.
LIFE INSURANCE.
566. Life Insurance is a contract by which a company or
party agrees to pay a certain sum of money on the death of
the person insured, or when he reaches a certain age.
567. Life Insurance Companies are divided into Stock,
Mutual, and Mixed (Stock and Mutual), and Co- Operative
Companies. (Arts. 232, 233.)
Note. — The first three are defined under ° Insurance." (Art. 229.)
568. In a Co-Operative Insurance Company each member is
assessed a fixed sum to meet losses by deaths as they occur. This
sum is graduated according to age at the time of becoming
a member, and the sum for which he is insured.
569. The Policy is the Contract which specifies the rate
of premium, the parties to whom the money is to be paid, etc.
Notes. — 1. The money may be paid to any one named by the insured.
If payable to himself, it becomes a part of his estate at his death, and is
liable for his debts.
2. If payable to another, it cannot be touched by his creditors ; nor can
he in his will deprive the party of its benefits.
3. The agreement is not to indemnify the insured for a loss, as in Fire
and Marine Insurance, but to pay a specified sum. Hence, a person may
insure his life for any amount, or in as many Companies as he pleases.
570. Policies vary according to the nature of the insurance.
The more prominent are the Ordinary, Limited, Term, Endow-
ment, and Annuity Policies.
Life Insurance. 237
Note. — Two persons may insure by a Joint Policy and the sum
insured is payable to the other on the death of either.
571. An Ordinary Life Policy stipulates to pay to the
parties named in it, a certain sum of money on the death of
the insured, the annual premium being paid during his life.
Note. — The holder of an Annuity Policy receives a certain sum
every year during his life. It is secured by a single cash payment.
572. A Limited Policy is one on which the premium is paid
annually for a limited number of years, specified at the time
the policy is issued, or until the death of the insured, if that
should occur before the end of the period named.
Note. — The premiums on this class of policies are payable annually, or
all at one time. If they are all paid at once, the insured receives an
annual dividend in cash.
573. Term Policies are payable at the death of the insured,
if he dies during a given term of years, the annual premium
continuing till the policy expires.
574. An Endowment Policy guarantees the payment of a
certain sum of money at a specified period, and is payable at
the death of the insured, if he dies within that period. It
becomes an endowment payable at the end of the period to the
insured, if he is still living.
Note. — An endowment policy is a combination of a term, policy and a
pure endowment. These policies are issued for periods from 10 to 35
years, and may be paid by single payments or by annual premiums.
575. The Premium is a fixed sum paid annually, or at
stated periods. It varies according to the expectation of life.
(App. p. 297.)
576. The Reserve Fund is a sum which, put at a given rate
of interest, with the premiums on existing policies, is intended
to be sufficient to meet all obligations when they become due.
Note.— The legal rate of interest on reserve funds in the State of New
York is 4| % , in Massachusetts 4$ ,
238
Life Insurance,
ANNUAI
PREMIUM RATES FOR AN INSURANCE OP $1000.
PAYABLE
AS INDICATED, OR AT DEATH,
IF PRIOR.
Age.
At
In 10
In 15
In 20
In 25
In 30
In 35
Age.
Death.
years.
years.
years.
years.
years.
years.
25
16.91
100.23
62.65
44.46
34.04
27.54
23.30
25
26
17.34
100.27
62.71
44.54
34.14
27.66
23.46
26
27
17.79
100.32.
62.77
44.62
34.24
27.80
23.64
27
28
18.26
100.38
62.84
44.71
34.36
27.95
23.84
28
29
18.76
100.43
62.92
44.80
34.49
28.12
24.06
29
30
19.30
100.50
63.00
44.91
34.62
28.30
24.31
30
31
19.85
100.56
63.09
45.02
34.78
28.51
24.58
31
32
20.44
100.64
63.19
45.15
34.96
28.74
24.89
32
33
21.06
100.72
63.29
45.30
35.15
29.00
25.23
33
34
21.73
100.81
63.41
45.46
35.36
29.29
25.60
34
35
22.42
100.91
63.54
45.64
35.61
29.61
26.01
35
36
23.16
101.02
63.69
45.84
35.88
29,97
26.47
36
37
23.94
101.14
63.85
46.06
36.18
30.37
26.98
37
38
24.78
101.27
64.04
46.31
36.52
30.81
27.54
38
39
25.66
101.42
64.24
46.60
36.90
31.30
28.16
39
40
26.61
101.58
64.48
46.91
37.32
31.85
28.84
40
41
27.60
101.76
64.73
47.27
37.80
32.46
29.59
41
42
28.66
101.97
65.03
47.67
38.33
33.14
30.42
42
43
29.79
102.21
65.36
48.12
38.92
33.89
31.32
43
44
30.99
102.48
65.74
48.63
39.58
34.73
32 31
44
45
32.27
102.78
66.17
49.20
40.32
35.65
83.40
45
46
33.64
103.13
66.65
49.85
41.15
36.67
46
47
35.11
103.53
67.19
50.56
43.07
37.79
47
48
36.66
103.98
67.81
51.37
43.09
39.03
48
49
38.33
104.49
68.50
52.27
44.23
40.39
49
50
40.10
105.06
69.26
53.27
45.48
41.87
50
51
41.99
105.70
70.12
54.38
46.86
51
52
44.01
106.41
71.08
55.61
48.38
52
53
46.16
107.20
72.14
56.98
50.06
53
54
48.47
108.08
73.32
58.50
51.89
54
55
50.92
109.07
74.63
60.17
53.90
55
56
53.55
110.16
76.09
62.02
56
57
56.35
111.38
77.71
64.06
57
58
59.35
112.73
79.51
66.31
58
59
62.56
114.23
81.50
68.78
59
60
65.99
115.90
83.71
71.49
60
61
69.67
117.75
86.15
61
62
73.59
119.81
88.84
62
63
77.81
122.09
91.81
63
64
82.33
124.63
95.08
64
65
87.17
127.43
98.68
65
Life Insurance.
239
577. The true value of a policy surrendered is the legal
reserve less a certain per cent for expenses.
The market value is the sum the company will pay the holder
on its surrender.
Notes. — 1. Reserve Endowment, Tontine Investment, and some other
special policies, guarantee to pay the holder a definite amount at the
termination of fixed periods.
2. Some companies apply all credited dividends to the continuance of
the insurance. Others apply the legal reserve to the purchase of term
insurance at the regular rates.
578. Finding the annual premium for an ordinary life or endow-
ment policy when the rate and sum insured are given ; by the Tables.
1. What is the annual premium for an ordinary life policy of
$3000, issued to a person 35 years of age ?
Solution. — By the Table the annual premium for $1000 at 35 years
of age is $22.42 ; hence, for $3000 it is 3 times $22.42 = $67.26, Am.
2. Find the annual premium for an ordinary life policy of
$10000, issued to a person 40 years old.
3. A young man at the age of 25 years took out an ordinary
life policy of $20000 ; he died at the age of 45 years ; how
much more than he had paid in premiums did his heirs receive ;
no allowance heing made for interest ?
TABLE OF ANNUAL
KATES
FOR
ENDOWMENT
POLICIES OF $1000.
PAYABLE AS
INDICATED.
Age.
In 10
years.
$103.91
In 15
years.
In 20
years.
Age.
Age.
In 10
years.
In 15
years.
In 20
years.
Age.
36
25
$66.02
$47.68
25
36
$105.75
$68.12
$50.11
26
104.03
66.15
47.82
26
37
106.00
68.41
50.47
37
27
104.16
66.29
47.98
27
38
106.28
68.73
50.86
38
28
104.29
66.44
4815
28
39
106.58
69.09
51.30
39
29
10443
66.60
48.33
29
40
106.90
69.49
51.78
40
30
104.58
66.77
48.53
30
41
107.26
69.92
52 31
41
31
104.75
66 96
48.74
31
42
107.65
70.40
5289
42
32
104.92
6716
48.97
32
43
108.08
70.92
53.54
43
33
105.11
67.36
49.22
33
44
108.55
7150
54.25
44
34
105.31
67.60
49.49
34
45
109.07
72.14
55.04
45
35
105.53
67 85
49 79
35
46
109.65
72.86
55.91
46
240 Life Insurance.
4. A man at the age of 32 years has an investment of $15000
at 6% interest, which he intends to leave his family ; what will
be its amount in 25 years at compound interest ? How much
will his family receive if he takes out a life policy and pays the
premium with the interest on his investment ?
5. What annual premium must I pay for a twenty-year
endowment policy of $12000 ; my age being 40 years?
6. What is the annual premium on a 20-year endowment
policy for $16000; the age being 45 years?
7. How much more is received at the expiration of the 20
years, than has been paid out in annual premiums ?
8. If a person 36 years of age secures an endowment policy
for $1000 for 20 years, payable to himself or his heirs, what
will be his loss if he survives and pays his premium annually?
9. A man insured his life at the age of 46 years for $15000
on the ordinary life plan. He died at the age of 75 ; having
paid the premiums annually, how much had the insurance
company received ? How much would a 10-year endowment
cost for the same sum ?
10. What is the annual premium for a 15-year endowment
policy of $12000, issued to a person 32 years of age ?
11. When 46 years of age a man took out a 10-year endow-
ment policy of $10000. He survived the period of endow-
ment ; having paid the annual rates, how much less did he
receive than he had paid the company, reckoning interest at
12. A gentleman at the age of 45 insures his life on the
ordinary life plan for $18000. How much must be put at 5%
interest to meet the annual premiums ?
13. If he lived to be 65 years old, would his family receive
more, or less, if the premiums were put at h% interest in a
savings bank ? How much ?
14. A lady 35 years of age took out a life policy for $5000
for the benefit of her husband, paying the entire premium at
the rate of $369.91 on $1000, in one payment. She died in 5
years after securing the policy ; how much less would the
company have received if she had paid the premium at the
annual rates ?
Annuities, 241
ANNUITIES.
579. An Annuity is a specified sum of money paid annually,
or at equal periods ; as, semi-annually, quarterly, monthly; to
continue a given number of years, for life, or forever.
580. A Perpetual Annuity is one of unlimited duration.
581. A Certain Annuity begins and ends at a fixed time.
582. A Contingent Annuity depends upon some unforeseen
event, as the death of an individual, or his arrival at a certain
age. Life Insurance, Pensions, Dowers, Leases, etc., belong
to this class of incomes.
583. An Annuity in Possession or an Immediate Annuity is
one that begins immediately. When the Annuity begins at
some future time it is called a Deferred Annuity, or Annuity
in Reversion.
Note. — The term of reversion may be definite or contingent.
584. If Annuities are not paid when due, they are said to
he forborne, or in arrears,
585. The Present Value of an Annuity is the sum which, at
the given rate of interest, will amount to' its final value.
586. The Amount or Final Value of an Annuity is the sum
which all its payments with interest on each will amount to
at its termination.
Note. — Annuities, like debts, are entitled to interest after they are due.
587. Annuities at Simple Interest are computed by the
principles of Arithmetical Progression, the Annuity being the
first term ; the interest of the annuity for 1 year, the common
difference ; the time in years, the number of terms ; and the
annuity plus the interest due on it for the number of years less
1, the last term.
16
242 At 8i7nple Interest
588. To find the Amount or Final Value of an Annuity at
Simple Interest, when the Time and Rate are given.
1. What is the amount of $100 annuity for 5 years, at 6% ?
Analysis. — The first annuity is not due until the end of the first year,
and draws interest only from the time it falls due. The second is not due
until the end of the second year, and draws interest 1 year less than the
first ; the third one year less than the second; and so on till all the pay-
ments are made. Hence, the arithmetical series
100 + (6x4), + 100 + (6x3), + 100 + (6x2), +100 + 6, +100.
589. The last payment equals the given annuity plus the
product of the annual interest by the number of payments
less 1.
590. The terms are now the annuity or first payment, the last
payment, and the number of payments, to find the sum of all
the payments.
The sum of the two extremes, 100 + 124 = 224, and 224-T-2 = 112, the
average value of all the payments. Now, 112 x 5 = 560, the sum or final
value of the annuity. Hence, the
Eule. — I. To the annuity add the product of the
annual interest of the annuity by the number of pay-
ments less 1, for the last payment.
II. Multiply half the sum of the first and last pay-
ments by the number of payments, and the product will
be the final value of the annuity.
2. What is the amount of an annuity of $150 for 8 years,
when money is worth 6% simple interest ?
591. To find the Present Worth of Annuities at Simple Interest.
3. What is the present worth of $1 20 annuity for 4 yr., at 7%?
Solution. — By the preceding rule the final value of the annuity is
$530.40. The present worth of $530.40 due in 4 years, at 7% simple
interest — $414,375 (Art. 310). Hence, the
Rule. — First find the amount or final value of the
given annuity for the given time and rate ; then find
the present worth of this amount as in true discount.
4. What is the present worth of $600 annuity for 8 yr., at 6%?
Annuities. 243
ANNUITIES AT COMPOUND INTEREST.
592. Annuities at compound interest are computed by the
principles of Geometrical Progression, the annuity being the
first term; the amount of $1 for 1 year, the ratio; the
number of payments, the number of terms, and the annuity
multiplied by the amount of $1 for 1 year or period, raised to
the power whose index is 1 less than the number of payments,
is the last term.
l. What is the amount or final value of an annuity of $100
for 4 years, at Q% compound interest.
Analysis. — The first annuity is not due until the end of the first year
or period ; the second is not due until the end of the second year or period,
and draws interest 1 year less than the first ; the third draws interest 1
year less than the second, and so on until all the payments are made.
Hence, assuming $1 for the annuity, we have the following series :
$1, 1 x 1.06, 1 x (1.06 x 1.06), 1 x (1.06 x 1.06 x 1.06) ;
or, $1, 1 x 1.06, 1 x (1.06) 2 , 1 x (1.06) 3 , etc.
That is, each successive term = the 1st term xby the ratio raised to a
power whose index is 1 less than the number of the term. Therefore, the
last term = 100 x 1.191016 = 119.1016. Hence,
593. To find the last term or payment
Multiply the first term by that -power of the ratio
denoted by 1 less than the number of terms.
594. The terms are now the annuity or first payment, the last
payment, and the ratio, to find the sum of all the payments.
Since, $100 (annuity) x (1.06) 3 = $119.1016, the last payment,
$119.1016x1.06, the ratio, = $126.247696. Then, $126.247696 - $100
(annuity) = $26.247696 ; and $26.247696 -h .06 = $437.4616, the sum of
the terms, or final value of annuity. Hence, the
Rule. — Multiply the last term by the ratio, and sub-
tracting the first term from the product, divide the
remainder by the ratio less 1.
Note.— The labor of computing annuities at Compound Interest is
greatly diminished by the use of the following tables :
244
At Compound Interest.
Table I.
595. Amount of $1 annuity at Compound Interest, from
1 year to 40, inclusive.
Yrs.
1
8*.
8tf.
4*
ft.
w.
7%.
Yrs.
1.000 000
1.000 000
1 000 000
1.000 000
1.000 000
1.000 000
1
2
2.030 000 1 2.035 000
2.040 000
2.050 000
2.060 000
2.070 000
2
3
3.090 900 3.106 225
3.121 600
3.152 500
3.183 600
3.214 900
3
4:
4.183 627
4.214 943
j 4.246 464
4.310 125
4.374 616
4.439 943
4
5
5.309 136
5.362 466
5.416 323
5.525 631
5.637 093
5.750 739
5
6
6.468 410
6.550 152
6.632 975
6.801 913
6.975 319
7.153 291
6
7
7.662 462
7.779 408
7.898 294
8.142 008
8.393 838
8.654 021
7
S
8.892 336
9.051 687
9.214 226
9.549 109
9.897 468
10.259 803
8
9
10.159 106 10.368 496
10.582 795
11.026 564
11.491 316
11.977 989
9
10
11.463 879
11.731 393
12.006 107
12.577 893
13.180 795
13.816 448
10
11
12.807 796 13.141 992
13.486 351
14.206 787
14.971 643
15.783 599
11
12
14.192 030 14.601 962
15.025 805
15.917 127
16.869 941
17.888 451
12
13
15.617 790
16.113 030
16.626 838
17.712 983
18.882 138
20.140 643
13
14
17.086 324
17.676 986
18.291 911
19.598 632
21.015 066
22.550 488
14
15
18.598 914
19.295 681
20.023 588
21.578 564
23.275 970
25.129 022
15
16
20.156 881
20.971 030
21.824 531
23.657 492
25.670 528
27.888 054
16
17
21.761 588
22.705 016
23.697 512
25.840 366
28.212 880
30.840 217
17
18
23.414 4,35
24.499 691
25.645 413
28.132 385
30.905 653
33.999 033
18
19
25.116 868
26.357 180
27.671 229
30.539 004
33.759 992
37.378 965
19
20
26.870 374
28.279 682
29.778 079
33.065 954
36.785 591
40.995 492
20
21
28.676 486
30.269 471
31.969 202
35.719 252
39.992 727
44.865 177
21
22
30.536 780
32.328 902
34.247 970
38.505 214
43.392 290
49.005 739
22
23
32.452 884
34.460 414
36.617 889
41.430 475
46.995 828
53.436 141
23
24
34.426 470
36.666 528
39.082 604
44.501 999
50.815 577
58.176 671
24
25
36.459 264
38.949 857
41.645 908
47.727 099
54.864 512
63.249 030
25
26
38.553 042
41.313 102
44.311 745
51.113 454
59.156 383
68.676 470
26
27
40.709 634
42.759 060
47.084 214
54.669 126
63.705 766
74.483 823
27
28
42.930 923
46.290 627
49.967 583
58.402 583
68.528 112
80.697 691
28
29
45.218 850
48.910 799
52.966 286
62.322 712
73.639 798
87.346 529
29
30
47.575 416
51.622 677
56.084 938
66.438 848
79.058 186
94.460 786
30
31
50.002 678
54.429 471
59.328 335
70.760 790
84.801 677
102.073 041
31
32
52.502 759
57.334 502
62.701 469
75.298 829
90.899 778
110.218 154
32
33
55.077 841
60.341 210
66.209 527
80.063 771
97.343 165
118.933 425
33
34
57.730 177
63.453 152
69.857 909
85.066 959
104. 183 755
128.258 765
34
35
60.462 082
66.674 013
73.652 225
90.320 307
111.434 780
138.236 878
35
36
63.271 944
70.C07 603
77.598 314
95.836 323
119.120 867
148.913 460
36
37
66.174 223
73.457 869
81.702 246
101.628 139
127.268 119
160.337 400
37
38
69.159 449
77.028 895
85.970 336
107.709 546 |
135.904 206
172.561 020
38
39
72.234 238 80.721 906
90.409 150
114.0D5 028
145.058 458
185.640 292
39
40
75.401 260 ! 84.550 278
1
95.025 516
120.7!)!) 774
154.761 C66
199.635 112
40
Annuities.
245
Tab le II.
596. Present Worth of $1 annuity at Compound Interest,
from 1 year to 40, inclusive.
Yrs.
1
3*.
SK*.
<¥.
5*.
6£.
7%.
Yrs.
0.970 874
0.966 184
0.961 538
0.952 381
0.943 396
0.934 579
1
2
1.913 470
1.899 694
1.886 095
1.859 410
1.833 393
1.808 017
2
3
2.828 611
2.801 637
2.775 091
2.723 248
2.673 012
2.624 314
3
4
3.717 098
3.673 079
3.629 895
3.545 951
3.465 106
3.387 209
4
5
4.579 707
4.515 052
4.451 822
4.329 477
4.212 364
4.100 195
5
6
5.417 191
5.328 553
5.242 137
5.075 692
4.917 324
4.766 537
6
7
6.230 283
6.114 544
6.002 055
5.786 373
5.582 381
5.389 286
7
8
7.019 692
6.873 956
6.732 745
6.463 213
6.209 744
5.971 295
8
9
7.786 109
7.607 687
7.435 332
7.107 822
6.801 692
6.515 228
9
10
8.530 203
8.316 605
8.110 896
7.721 735
7.360 087
7.023 577
10
11
9.252 624
9.001 551
8.760 477
8.306 414
7.886 875
7.498 669
11
12
9.954 004
9.663 334
9.385 074
8.863 252
8.383 844
7.942 671
12
13
10.034 955
10.302 738
9.985 618
9.393 573
8.852 683
8.357 635
13
14
11.296 073
10.920 520
10.568 123
9.898 641
9.294 984
8.745 452
14
15
11.937 935
11.517 411
11.118 387
10.379 658
9.712 249
9.107 898
15
16
12.561 102
12.094 117
11.652 296
10.837 770
10.105 895
9.446 632
16
17
13.166 118
12.651 321
12.165 669
11.274 066
10.477 SCO
9.763 206
17
18
13.753 513
13.189 682
12.659 297
11.689 587
10 827 603
10.059 070
18
19
14.323 799
13.709 837
13.133 939
12.085 321
11.158 116
10.335 578
19
20
14.877 475
14.212 403
13.590 326
12.462 210
11.469 421
10.593 997
20
21
15.415 024
14.697 974
14.029 160
12.821 153
11.764 077
10.835 527
21
22
15.936 917
15.167 125
14.451 115
13.163 003
12.041 582
11.061 241
22
23
16.443 608
15.620 410
14.&56 842
13.488 574
12.303 379
11.272 187
23
24
16.935 542
16.058 368
15.246 963
13.798 642
12.550 358
11.469 334
24
25
17.413 148
16.481 515
15.622 080
14.093 945
12.783 356
11.653 583
25
26
17.876 842
16.890 352
15.982 769
14.275 185
13.003 166
11.825 779
26
27
18 327 031
17.285 365
16.329 586
14.643 034
13.210 534
11.986 709
27
28
18.764 108
17.667 019
16.663 063
14.898 127
13.406 164
12.137 111
28
29
19.188 455
18.035 767
16.983 715
15.141 074
13.590 721
12.277 674
29
30
19.600 441
18.392 045
17.292 033
15.372 451
13.764 831
12.409 041
30
31
20.000 428
18.736 276
17.588 494
15.592 811
13.929 086
12.531 814
31
32
20.. 338 766
19.068 865
17.873 552
15.802 677
14.084 043
12.646 555
32
33
20.765 792
19.390 208
18.147 646
16.002 549
14.230 230
12.753 790
33
34
21.131 837
19.700 684
18.411 198
16.192 204
14.368 141
12.854 009
34
35
21 .487 220
20.000 661
18.664 613
16.374 194
14.498 246
12.947 672
35
36
21.a32 252
20.290 494
18.908 282
16.546 852
14.620 987
13.035 208
36
37
22.167 235
20.570 525
19.142 579
16.711 287
14.736 780
13.117 017
37
38
22.492 462
20.841 087
19.367 864
16.867 893
14.846 019
13.193 473
38
39
22.808 215
21.102 500
19.584 485
17.017 041
14.949 075
13.264 928
39
40
23.114 772
21.355 072
19.792 774
17.159 086
15.046 297
13.331 709
40
246 Annuities.
597. To find the amount or Final Value of an Annuity.
Kule. — Multiply the tabular amount of $1 by the
annuity, the product will be the final value. (Table I.)
Note. —When payments are made semi-annually, take from the table
twice the given number of years, and £ the given rate of interest.
2. What is the final value of $600 for 8 years, at 6% ?
Solution.— Tab. Amt. of $1, at 6% for 8 years = $9.897468 ; and
$9.897468 x 600 = $5938.4808, Ans.
3. What is the final value of an annual pension of $150 for
15 years, at 4$ ?
4. A widow is entitled to $140 a year for 18 years, at 10%
semi-annual compound interest ; what is its final value ?
598. To find the Present Value of an Annuity.
Kule. — Multiply the present worth of $1 by the Given
Annuity. (Table II.)
5. What is the present worth of $300 due in 7 years, at 6% ?
Solution.— Present worth of $1, at 6% for 7 yr. = $5.582381 ; and
$5.582381 x 300 = $1674.7143, Ans.
6. What is the present worth of an annual ground rent of
$500, at 4%, for 12 years ?
7. What is the present worth of an annuity of $500 for 8
years, at 4% ?
8. What is the present worth of an annuity of $3000, at %%,
for 20 years ?
599. To find the Present Worth of an Annuity in Reversion.
Kule. — Find the present worth of $1 to the time the
annuity begins, also to the time it ends ; and multiply
the difference between these values by the given annuity.
Annuities. 247
9. What is the present worth of an annuity in reversion of
$1000, at 6%, which begins in 3 years, and then terminates
after 5 years ?
Solution.— The present worth of $1, at 6% for 3 yr. = $2.673012
"8 yr. = $6.209744
Their difference $3.536732 x 1000 (annuity) = $3536.732, Ans.
10. The reversion of a lease of $450 per year, at h%, begins in
3 years and continues 9 years; what is its present worth ?
li. A father bequeathed his son, 11 yrs. of age, a 5% annuity
of $1000, to begin in 3 years and continue 10 years ; what
would be the amount when the son was 21 years old ? What
is its present worth ?
600. To find the Present Worth of a Perpetual Annuity.
Eule. — Divide the given annuity by the interest of $1
for 1 year, at the given per cent.
12. A man wished to establish a perpetual professorship in a
college, at $2000 a year ; what sum must he invest in Gov't 5's
to yield this income ?
Solution.— $2000. 00 -^-. 05 = $40000, Ans.
13. An estate in New York pays $3000 annually, at 6%
interest, on a perpetual ground rent ; what is the value of the
estate ?
Note. — When the annuity is payable for any period less than a year,
before dividing by the interest of $1 for 1 year, the annuity must be
increased by the interest which may accrue on the parts of the annuity
payable before the end of the year.
14. What is the present worth of a perpetual annuity of
$250 in arrears for 10 years, allowing ?>% compound interest.
Note. — There is now due the amount of $250 annuity for 10 yr. at 3%,
which must be added to the present worth of the perpetuity.
15. What is the present worth of a perpetuity of $500, in
arrears for 30 years, allowing compound interest at 5 per
cent?
248 Sinking Funds.
SINKING FUNDS.
601. Sinking Funds are sums of money set apart at regular
periods for the payment of indebtedness. They are properly
derived from an excess of income above expenses.*
602. To find what sum must be set apart annually, as a sinking
fund, to pay a given debt in a given time.
1. A certain town borrowed $20000 to build a Union School-
house, and agreed to pay 6% compound interest; what sum
must be set apart, as a sinking fund annually, to pay the debt
in 10 years ?
Analysis.— The amt. of $1 at 6% comp. int. for 10 yrs. is $1.790848,
and that of $20000 is 20000 times as much, or $35816.96. (Art. 306.)
Again, the amt. of an annual payment or annuity of $1 at 6% for 10
yrs. is $13.180795 ; since to pay $13.180795 requires an annuity of $1 at
6% for 10 yrs., a debt of $35816.96 will require 35816.96-T-13. 180795 =
$2717.36, Ans. Hence, the
Rule. — Divide the amount of the debt at its maturity,
at compound interest, by the amount of an annuity of $1
for the given time and rate, and the quotient will be the
sinking fund required.
2. What sum must be set apart annually to rebuild a bridge
costing $30000, estimated to last 17 years, allowing 5% com-
pound interest ?
3. A railroad company bought $100000 worth of rolling
stock, payable in 5 yr. with %% compound int. ; what sum must
be set apart annually as a sinking fund to discharge the debt ?
4. The National debt of the United States is about
$2,003,000,000 ; what must be the excess annually of revenue
over expenditure, allowing 5% comp. interest to pay the debt
in 21 years.
* Sinking Funds were first introduced into England in 1716, and renewed in H86 by-
Messrs. Price and Pitt, who contended that by applying a certain amount of revenue to
the purchase of stocks the dividends of which should be reinvested in the same manner
a sinking fund would be established, which at compound interest would increase so that
the largest debt might be paid. But the fallacy of this idea was proven by Dr. Hamilton,
who showed that the sinking fund had really added to the debt, and demonstrated that
the only true sinking fund consists in an excess of revenue above expenditure.
Sinking Funds. 249
603. To find the number of years required to pay a given debt,
by a given annua! sinking fund.
5. A village built a school-house costing $12000, and raised
$1700 a year to pay for it ; allowing 6% compound interest,
how many years will it require to cancel the debt?
Analysis.— Since a sinking fund of $1700 at 6% for a certain time has
a present worth of $12000, a sinking fund of $1, for the same time and
rate, has a present worth of TT Vir P a *t as much ; and $12000 ---$1700 =
$7.05882. Looking in Table (Art. 596) in col. 6%, the time correspond-
ing with this present worth of $1 is 9 years, which is the number of whole
years required, with a balance due of $738 .51.
The amt. of the debt $12000 at 6% comp. int. in 9 yr. = $20273.748
The amt. of s. fund $1700 " " " " = 19535.238
Balance due at the end of 9 yr $738.51
Hence, the
Eule. — Divide the debt by the given sinking fund, and
the quotient will be the present worth of $1 for the time.
Loolc for this number in Table (Art. 596) in the col.
denoting the given rate, and opposite in the column of
time will be found the number of years.
Notes. — 1. If the exact number is not found in the column take the
years standing opposite the next smaller number.
2. To ascertain the balance due* at the end of the number of whole
years, find the difference between the amount of the debt at the given rate
for the time taken out, and the amount of the sinking fund for the same
time and rate. (Tables, Arts. 595, «306.)
6. The national debt of Great Britain is about £800,000,000;
allowing 5% compound interest, how many years would it
require to cancel it by an annual sinking fund of £48,000,000 ?
7. The national debt of France is about $4,750,000,000 ;
allowing 3% int., how long would it take to discharge it by a
sinking fund of $200,000,000 a year ?
8. The Dom. of Canada had a debt in 1881 of $199861537,
and a sinking fund of $44465757; allowing 4$ int., how
many years will be required to cancel the debt?
250 Sinking Funds.
604. To find the amount of a sinking fund, the rate of interest
and the time being given.
9. If a Railroad Co. sets apart an annual sinking fund of
$20000, and puts it at 7% compound interest, what will be its
amount in 10 years ?
Analysis. — The amount of a sinking fund of $1 in 10 jr., at 7%, is
$13.816448 (Table, Art. 595) ; therefore, the amount for the same time
and rate of a sinking fund of $20000 = 13.816448x20000 = $276328.96.
Hence, the
Eule. — Multiply the amount of $1 for the given time
and rate as found in Art. 595 by the annual sinking
fund.
10. What will be the amount in 12 years of a sinking fund
of $12000, yielding 5% compound interest ?
605. Sinking Fund Bonds are securities issued by Corpora-
tions, based on the pledge of a special income which is fancied
for their redemption.
Note. — This income is derived in the case of Railroads from the sale
of lands, from rents, etc., or from a per cent of the earnings. These
bonds are bought and sold in the stock market like Mortgage Bonds.
11. A Kailroad Co. issued sinking fund bonds at 6% for
$200000, payable in 10 years; if at compound interest, what
sum must be set apart annually to meet interest and principal
when due ? (Art. 602.)
12. What would be the amount in 10 years, at 6% simple
interest ?
13. If the funded securities were drawing an annual income
of 4:% compound interest, by how much would the amount
necessary to meet principal and interest at 6% be reduced ?
14. With the above reduction what sum would be needed
annually as a sinking fund to pay the amount when due at 4$ ?
f
OWER8 and
606. A Power is a product of equal factors.
Thus, 2x2x2 = 8, and 3x3 = 9; 8 and 9 are powers.
Note. — Powers are named according to the number of times the equal
factor is taken to produce the given power.
607. The First Power is the number itself.
608. The Second Power is the product of a number taken
twice as a factor, and is called a Square.
609. The Third Power is the product of a number taken
three times as a factor, and is called a Cube.
610. An Exponent is a small figure placed above a number
on the right to denote the power.
It shows that the number above which it is placed is to be
raised to the power indicated by this figure. Thus,
611. The expression 2 4 is read, "2 raised to the fourth
power, or the fourth power of 2."
1. Express the 4th power of 84. 3. The 7th power of 350.
2. Express the 5th power of 248. 4. The 8th power of 461.
612. To find any required Power of a Number.
5. What is the 5th power of 8 ?
Solution.— 8 5 -8x8x8x8x8 = 32768, Ans.
Rule. — Take the number as many times as a factor as
there are units in the exponent of tli e required power.
252 Powers and Roots.
Notes. — 1. A common fraction is raised to a power by involving each
term. Thus, (f) 8 = T V
2. A mixed number should be reduced to an improper fraction, or the
fractional part to a decimal ; then proceed as above.
Thus, (2£) 2 = (|) 2 = - 2 ¥ 5 - ; or 2£ = 2.5 and (2.5) 2 = 6.25.
3. All powers of 1 are 1 ; for 1 x 1 x 1, etc. = 1.
613. A Root is one of the equal factors of a number.
Note. — Boots are named from the number of equal factors they contain.
614. The Square Root is one of the two equal factors of a
number.
Thus, 5 x 5 = 25 ; therefore, 5 is the square root of 25.
615. The Cube Root is one of the three equal factors of a
number.
Thus, 3 x 3 x 3 — 27 ; therefore, 3 is the cube root of 27, etc.
616. The character (y') is called the Radical Sign.
Note. — It is a corruption of the letter R, the initial of the Latin radix,
a root.
617. Roots are denoted in two ways :
1st. By prefixing to the number the Radical Sign, with a
figure placed over it called the Index of the root ; as ^/4, ^/8.
2d. By a fractional exponent placed above the number on
the right. Thus, 9*, 27*, denote the square root of 9, and the
cube root of 27.
Notes. — 1. The figure over the radical sign and the denominator of
the exponent, each denote the name of the root.
2. In expressing the square root, it is customary to use simply the
radical sign (\/)> the 2 being understood. Thus, the expression <y/25 = 5,
is read, " the square root of 25 = 5."
618. A Perfect Power is a number whose exact root can be
found; as, 9, 16, 25, etc.
Square Boot. 253
619. An Imperfect Power is a number whose exact root can
not be found. This root is called a Surd.
Thus, 5 is an imperfect power, and its square root 2.23+ is a surd.
Note. — All roots as well as powers of 1, are 1.
SQUARE ROOT.
620. Extracting the Square Root is finding one of two equal
factors of a number. (For demonstration, see Complete Grad.
Arith., Art. 733.)
621. To extract the square root of a number.
l. Find the square root of 5625.
49
725
725
Explanation. — Since the number consists of two operation.
periods of two figures each, its root will have two of 25 ( 78
figures. The greatest square in the first period is 49,
its root is 7, which is placed in tlie quotient. Sub-
tracting this square from the left hand period and 145
placing the next period on its right, the dividend is
725. Doubling the root found for a trial divisor, and
taking the first two figures for a trial dividend, the
next quotient figure is 5 ; writing this also in the divisor, multiplying the
divisor thus completed by this last figure of the root, and subtracting
there is no remainder. Therefore, 75 is the required root. Hence, the .
General Rule.
I. Separate- the number into periods of two figures
each, beginning at units, and count both ways.
II. Find the greatest square in the first period on the
left, and place its root on the right. Subtract this
square from the period, and on the right of the remain-
der place the next period for a dividend.
III. Double the part of the root thus found for a trial
divisor ; and finding how many times it is contained in
the dividend, omitting the right hand figure, annex the
quotient both to the root and to the divisor.
254 Powers and Hoots.
IV. Multiply the divisor thus increased by the last
figure placed in the root, subtract the product from the
dividend, and place the next period on the right of the
remainder.
V. Proceed as before, till the root of all the periods
is found.
Notes. — 1. If there is a remainder after the root of the last period is
found, annex periods of ciphers, and proceed as before. The figures of the
root thus obtained will be decimals.
2. If the trial divisor is not contained in the dividend, annex a cipher
both to the root and to the divisor, and bring down the next period.
3. It sometimes happens that the remainder is larger than the divisor;
but it does not necessarily follow that the figure in the root is too small.
4. The left hand period in whole numbers may have but one figure ;
but in decimals, each period must have two figures. Hence, if the number
of decimals is odd, a cipher must be annexed to complete the period.
Find the square root of the following numbers :
2. 2916. 5. .0784. 8. .00953361.
3. 531441. 6. .766961. 9. 617230.2096.
4. 287.65. 7. 1073.741. 10. 3685.000289.
622. To find the Square Root of Fractions.
11. What is the square root of -^?
Solution.— ^/^ = f, Am. Hence, the
KulE. — Reduce the fraction to its simplest form and
find the square root of each term separately.
Notes.— 1. If either term of the given fraction, when reduced, is an
imperfect square, reduce the fraction to a decimal, and proceed as above.
2. Mixed numbers should be reduced to improper fractions, or the
fractional part to a decimal.
12. What is the square root of ^ ? A?is. .375, or f.
i3. ViR = ?
Square Root
15. vm = ?
255
14. VA¥W = ? is. V
17. What is the square root of 28$ ?
Solution. -28| = H 1 and V 1 ! 1 = V =
623. 27*e square described on the
hypothenuse of a right-angled triangle is
equal to the sum of the squares of the
base and altitude.
{Altitude = V Hypothenuse 2 — Base 2 .
Hypothenuse = V Base 2 + Altitude 2 .
Base = V 'Hypothenuse P — Altitude 2 .
18. What is the length of a side of a square field containing
21 a V acres.
19. The distance between the diagonal corners of a square
field is 60 rods ; what is its area in acres, and what the length
of a side ?
20. Find the square root of the product of squares of 11 and 16.
21. The cube of 3.5 is the square root of what number ?
' 22. A ladder 20 ft. long is standing 12 ft. from the bottom.
of a house, and leaning against its side 4 ft. below the eaves ;
how high is the house ?
23. The entire area of a cubic block is 384 inches ; what is
the area and length of a diagonal of one of its faces ?
24. A telegraph wire 69 ft. long fell from the roof of a house
36 ft. high and struck the opposite curb stone; how wide was
the street ?
25. What is the length of a diagonal path across a park
containing an acre in the form of a square ?
26. A rope 11 6 ft. long will reach from a point in the street
to a window on one side the street 35 ft. high, and to a window
on the opposite side 45 ft. high i how wiete is the street..
256
Powers and Moots,
CUBE ROOT.
624. Extracting the Cube Root of a number is finding one
of its three equal factors.
Boots: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Cubes: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000.
Peikciples. — 1°. The cute of a number cannot have more
than three times as many figures as its root, nor but two less.
2°. If a number is separated into periods of three figures each
beginning at units place, the number of figures in the cube root
vrill be the same as the number of periods.
625. To extract the cube root of a number.
l. Find the cube root of 1860867.
1860867(123, Ans.
1
102 x 3 =
10 x 3 x 2 =
2 2 =
1st Complete Div.,
120 2 x 3 =
120 x 3 x 3 =
3 2 =
2d Complete Div.,
Explanation. — The cube of the first period is 1, which is placed in the
root. Bringing down the next period for a dividend, find a trial divisor
by squaring the root already found with a cipher annexed, and multiply
this square by 3, the product, 300, is contained in 800, two times. Write
2 in the root, and complete the divisor by adding to it 3 times the product
of the root already found with cipher annexed, multiplied by the next
figure of the root, making 60, also add the square of this next figure.
The divisor completed is 364. Multiply it by the root figure and subtract
the product, the remainder is 132. Bring down the next period, and for a
second trial divisor, multiply the square of the root (12) with cipher
annexed, by 3, making 43200. This is contained in the dividend 3 times.
Completing the divisor as before, the root is 123, Arts. Hence, the
300
860
60
4
728
364
132867
43200
1080
9
44289
132867
Cube Moot 257
General Rule.
1. Separate the given number into periods of three
figures each ; begin with units and count both ways.
II. Find the greatest cube in the first period on the
left, and place its root on the right. Subtract this cube
from the period, and to the right of the remainder
bring down the next period for a dividend,
III. For a trial divisor, multiply the square of the root
thus found, considered as tens, by three ; find how many
times it is contained in the dividend, and write the
quotient for the second figure of the root.
IV. To complete the trial divisor, add to it three times
the product of the root previously found with a cipher
annexed, by the next root figure, also add the square of
this next figure.
V. Multiply the divisor thus completed by the last
figure placed in the root. Subtract the product from
the dividend ; ami to the right of the remainder bring
down the next period for a new dividend. Find a new
trial divisor as before, and thus proceed till the root of
the last period is found.
Notes. — 1. If there is a remainder after the root of the last period is
found, annex periods of ciphers, and proceed as before. The root figures
thus obtained will be decimals.
2. If a trial divisor is not contained in the dividend, put a cipher in
the root, two ciphers on the right of the divisor, and bring down the next
period.
3. If the product of the divisor completed into the figure last placed in
the root exceeds the dividend, the root figure is too large. Sometimes the
remainder is larger than the divisor completed ; but it does not necessarily
follow that the root figure is too small.
Find the cube root of the following numbers :
2. 39304. 5. 109095.488 8. 1.658503.
3. 104329. 6. 216.68921. 9. 125.000512.
4. 1.74088. 7. 46268279. 10. 41063625.
258 Powers and Roots.
626. To find the cube root of a common fraction, reduce the
fraction to its lowest terms, then extract the root of its numera-
tor and denominator.
Notes. — 1. When either the numerator or denominator is not a perfect
cube, the fraction should be reduced to a decimal, and the root of the deci-
mal be found as above.
2. A mixed number should be reduced to an improper fraction.
11. What is the cube root of ^^ ?
Solution. — */$%% = |, Am.
Find the cube root of the following:
12. «f 13. fffr. 14. ^f£. 15. -rHh*
16. Extract the cube root of the square of 999.
17. Find the fifth power of 8 and extract its cube root.
18. What is the inside measurement of a cubic box that
will hold 2^ bushels of wheat ?
19. What is the side of a cubic bin which may be exactly
filled by 600 bu. wheat, allowing 2150.4 cu. in. to a bushel ?
20. What is the length of one side of a cubic cistern that
will hold 160 hogsheads of water ?
21. Extract the cube root of 205692449327.
22. If a cubical box contains 54872 cu. inches, what is the
length of one side ?
23. What is the cube root of 67917312 ?
24. Find the cube root of 444194947 ?
SIMILAR SURFACES AND SOLIDS.
627. Similar Surfaces and Similar Solids are those which
have the same form, and their like dimensions proportional
Notes. — 1. All circles and all rectilinear figures are similar, when their
several angles are equal each to each, and their like dimensions propor-
tional.
Similar Surfaces and Solids. 259
2. The like dimensions of circles are their diameters, radii, and circum-
ferences.
3. The like dimensions of spheres are their diameters, radii, and
circumferences ; those of cubes are their sides.
4. The like dimensions of cylinders and cones are their altitudes, and
the diameters or the circumferences of their bases.
5. Pyramids are similar, when their bases are similar polygons, and
their altitudes proportional.
G. Polyhedrons (£. e., solids included by any number of plane faces) are
similar, when they are contained by the same number of similar polygons,
and all their solid angles are equal each to each.
628. Principles. — 1°. The Areas of similar surfaces are to
each other as the squares of their like dimensions. Conversely,
2°. The Like Dimensions of similar surfaces are to each
other as the square roots of their areas.
3°. The Contents of similar solids are to each other as the
cubes of their like dimensions. Conversely,
Jf°. The Like Dimensions of similar solids are as the cube
roots of their contents.
1. If one side of a triangle is 9 inches, and its area is 36
inches, what is the area of a similar triangle the correspond-
ing side of which is 18 inches ?
Solution.— 9 2 : 18 3 : : 36 in. : x in., or 144 inches, Ans.
2. The area of a triangle is 36 inches, and one side of it is
9 inches ; what is the corresponding side of a similar triangle
whose area is 144 inches ?
Solution.— ^36 : <\/T44 : : 9 in. : x in., or 18 in., Ans.
3. If the area of a triangular pyramid is 16 sq. feet, and one
side of the base is 20 inches, what is the area of a similar
pyramid the corresponding side of which is 30 inches?
4. A quarter section of land is 160 rods square ; what is the
length of one side of a square tract containing 36000 acres ?
5. The area of a triangle is 206 sq. inches, its altitude 24
inches ; what is the area of a similar triangle whose altitude is
56 inches?
260 Powers and Boots.
6. If the diameter of a circle is 20 feet, what will be the
diameter of another circle 3 times the area of the first ?
7. If a ball weighs 40 pounds whose diameter, is 6 inches,
what will a ball whose diameter is 12 inches weigh?
Solution.— 6 3 : 12 3 : : 40 lb. : x lb., or 320 lb., Ana.
8. If a ball which weighs 64 pounds is 8 inches in diameter,
what is the diameter of a similar ball weighing 343 pounds ?
Solution.— ^64 lb. : /^/343 lb. : : 8 in. : x in., or 14 inches, Ana.
9. If a pyramid 20 ft. high contains 4600 cu. ft., what are the
cubic contents of a similar pyramid 100 ft. high ?
10. If a stack of hay containing 8 cwt. is 8 ft. high, what
will be the height of a similar stack containing 3 tons?
11. If a cylindrical cistern 5 feet in diameter contains 65.44
cubic feet, what will a similar cistern contain whose diameter
is 20 feet?
12. If an ox that girts 6 feet weighs 900 pounds, what will
be the weight of an ox that girts 7 feet ?
13. A half peck measure is 9J in. diameter and 4 in. deep ;
what are the dimensions of a similar measure that will hold a
bushel ?
14. If a cable 2 centims in diameter will sustain 217
kilograms, how many kilograms will a cable 9 centims in
diameter sustain ?
15. If a ball 5 inches in diameter weighs 75 pounds, how
much will a ball 11 inches in diameter weigh ?
16. If a globe 5 centimeters in diameter is worth $450, what
is the value of a globe 10 centimeters in diameter?
17. Two similar triangular fields contain respectively 80 and
90 acres ; a side of the former is 75 rods, what is the corres-
ponding side of the latter?
18. If a pipe 3 centims in diameter fills a cistern in 4 hr.
16 min., what must be the diameter of a pipe which can fill it
in 49 minutes ?
ENSURATION.
19-
PLANE FIGURES.
629. Mensuration is the process of measuring lines, sur-
faces,, and solids.
Note. — For the measurement of rectangular surfaces and solids, see
Arts. 165, 179.
630. A Regular Polygon has all its sides and all its angles
equal.
631. A polygon having three sides is called a triangle ; four
sides, a quadrilateral j five sides, a pentagon ; six sides, a hex-
agon ; seven sides, a heptagon ; eight sides, an octagon ; etc.
632. The Altitude of a quadrilateral
having two parallel sides is the perpendic-
ular distance between these sides ; as, AL.
633. The Diagonal of a figure is a straight line AB which
joins the vertices of two opposite angles. (Art. 166.)
634. A Vertical Line is a right line per-
pendicular to a horizontal line. (Art. 167.)
635. A Rhomboid is an oblique-angled par-
allelogram.
%>
*
j?
636. A Rhombus is an equilateral rhom-
boid.
240
262
Mensuration.
637. A Trapezoid is a quadrilateral
which has two of its sides parallel.
638. A Trapezium is a quadrilateral
haying four unequal sides, no two of
which are parallel.
Note. — The line AB is the diagonal of
the adjoining figure.
639. A Triangle is a polygon haying three sides
and three angles.
640. The Base of a triangle is the side AB on
which it is supposed to stand.
ad a
641. A Vertical Angle is the angle opposite the base; as 0.
642. An Equilateral Triangle is one haying
three equal sides.
643. The Altitude of a triangle is the per-
pendicular CD drawn from the vertical angle
to the base.
AREA OF PLANE FIGURES.
644. The Area of a plane figure is the surface bounded by
its perimeter.
645. It is proved by Geometry that
TJie area of a triangle is equal to half the area of a parallelo-
gram of equal base and altitude.
Illustration. — Let ABCD be a parallelogram
whose altitude is the perpendicular EB.
Connect the diagonal corners by the straight
line BD, and the parallelogram will be divided
into two equal triangles, the altitude of each
being EB.
Area of Plane Figures.
263
The area of a parallelogram or rectangle is equal to the length multi-
plied by the breadth. The sides mast be reduced to the same denomina-
tion before multiplying.
Note. — The perimeter of a parallelogram of unequal sides is greater
than that of a square of equal area.
Illustration. — Let the adjoining figure
be a garden whose area is 16 sq. rods. If a
fence is put around it in its square form, its
length will be 16 rods. Bat if a the width is
exchanged for an equal area in the rear, the
length of the garden will then be four times
its width and the length of fence required
will be 20 rods.
4 rods.
4 x 4 = 16 eq. rods.
1. A lot of ground 80 ft. long by
20 ft. wide was cut diagonally by a
railroad, leaving a triangular plot of the same base and altitude;
what was its area ?
2. What will it cost to pave a roadway 80 feet long and 15
ft. wide, at $1.50 per sq. yard ?
3. What will it cost to plaster a room 15 ft. 6 in. long, 13 ft.
8 in. wide, and 9 ft. high, at 26 cents a square yard ?
4. Two fields contain 10 acres each ; one is in the form of a
square, the other is 4 times as long as it is wide ; what would
be the difference in expense of fencing them at $2.25 per rod ?
5. If the fence were built 4£ ft. high, of boards 8 in. wide,
the lower one raised 2 in. above the ground, and a space of 3
in. between the boards, how many sq. feet of boards would be
required for both fields ?
6. How many more for one than for the other ?
7. A piece of land containing 2 acres is 5 times as long as it
is broad ; what are its length and breadth ?
8. How many bricks 8 in. long and 4 inches wide will pave
a yard that is 100 ft. by 50 ?
9. How many yards of carpeting J yd. wide will cover a
floor 27 ft. 3 in. long and 22 ft. 6 in. wide? How many
breadths will it require ?
10. If the room were 23 ft. 8 in. wide, how much would you
need to buy allowing for waste ?
264 Mensuration,
AREA OF TRIANG-LES.
646. To find the Area of a Triangle, when the Base and
Altitude are given.
Multiply the base by half the altitude. (Art. 632.)
Note. — Dividing the area of a triangle by the altitude gives the base.
Dividing the area by half the base gives the altitude.
1. What is the area of a triangle whose base is 24 feet and
altitude 16 feet ?
2. The base of a triangle is 28 centimeters and the altitude
16 centimeters ; what is the area?
3. A board 16 feet long is 22 inches wide at one end, and
tapers to a point; what is the value at 4J cents a sq. foot ?
647. To find the Area of a Triangle, when the Three Sides
are given.
From half the sum of the three sides subtract each side respec-
tively ; then multiply half the sum and the three remainders
together, and extract the square root of the product.
4. What is the area of a triangle whose sides are respectively
12 feet, 16 feet, and 18 feet ?
Solution.— (12 + 16 + 18)-*-2 = 23 ; 23-12 = 11 ; 23-16 = 7 ; 23-18 =
5. And 23 x 11 x 7 x 5 = 8855 ; ^8855 = 94.1 + sq. ft., Ana.
5. How many acres in a triangular field whose sides are
respectively 45, 55, and 60 feet ?
6. What is the area of an equilateral triangle whose side is
24 feet ?
648. To find the Altitude, when the Area and Base are given.
Eule. — Divide the area by half the base.
7. What is the altitude of a triangle whose area is 37J square
yards and base 5 yards? Ans. 15 yards.
Circles. 265
8. At $6.25 a sq. rod, a triangular lot cost $1281.25 ; the
base was 40 rods, what was the length ?
9. The base of a triangle is 128 ft., area 298f sq. yd. ; what
is the altitude ?
10. A house lot containing 12 A. 56 sq. rods was in the form
of a triangle, the base of which was 56 T | T rods ; what was the
altitude ?
649. To find the Base, when the Area and Altitude are given.
Kule. — Divide the area by half the altitude.
11. What is the base of a triangle whose area is 156 sq. ft.
and its altitude 12 feet ? . Ans. 26 feet.
12. What is the base of a triangle whose area is 144 acres
and its altitude 60 rods ?
13. Find the base of a triangle whose area is 5280 sq. yd.,
and altitude 240 yards.
14. A garden contains -J of an acre in shape of a triangle,
the altitude of which is 2 rods 4 ft. 3 inches ; what is the
base ?
15. A triangular field whose altitude is 70£ rods, contains
12 A. 56 sq. rods; what is the base ?
CIRCLES.
650. A Circle is a plane figure bounded
by a curve line, every part of which is
equally distant from a point within called
the center. a
651. The Circumference of a circle is
the curve line by which it is bounded.
652. The Diameter is a straight line drawn through the
center, terminating at each end in the circumference, as AB.
266 Mmswratim.
653. The Radius is a straight line drawn from the center to
the circumference, and is equal to half the diameter, as CE.
Note.— From the definition of a circle, it follows that all the radii are
equal; also, that all the diameters are equal.
654. From the relation of the circumference and diameter
to each other, we derive from Geometry the following
Pki^ciples.— 1°. TJie Circumference=the Diameter x 8.U16
nearly.
2°. The Diameter of a Circle = the Circumference -f- 3.1416
nearly.
3°. The Area of a Circle = half the Circumference x by the
Radius.
Notes. — The diameter of a circle may also be found by dividing the
area by .7854 and extracting the square root of the quotient.
2. The area of a circle may also be found by multiplying the square of
its diameter by the decimal .7854, or, by multiplying the circumference by
\ the diameter.
3. The decimal .7854 is found by taking \ of the area of a circle whose
circumference is 1, that is \- of 3.1416.
1. What is the circumference of a disc of 15 inches radius ?
Solution.— 15 x 2 x 3.1416 = 94.248 inches, Ans.
2. What is the diameter of a lake 721 r. in circumference ?
Solution.— 721 rods-s-3.1416 = 229.5+ rods, Ans.
3. What is the area of a race-course 320 rods in circum-
ference ?
Solution.— 320.0000-4-3.1416 = 101.859 rods = diameter,
Radius = 50.929, and ^ circumference = 160 rods.
50.929 x 160 = 8148.64 sq. rods., Ans.
4. A cistern is 29 feet 8 inches in circumference; what is the
diameter ?
5. What is the difference in the perimeters of 2 acres of land,
one a circle the other a square ?
Circles. 267
6. What is the diameter of a circular piece of land measuring
4| acres ?
7. How many sq. feet in a circular grass plot 45 feet in
diameter ?
8. A circular fish-pond is 850 ft. in circumference; what is.
its area ?
9. The diameter of a circular piece of land is 84 feet ; how
long a fence will be required to go around it ?
io. A horse is tied to a post in a meadow, by a rope 45| ft.
long ; how much ground can he graze upon ?
n. What is the area of a circle whose diameter is 120 rods?
12. What is the diameter of a circle whose circumference is
94.318 yards ?
13. What is the circumference of a circle whose diameter is
45 rods? 120 rods?
14. How many acres in a circular park whose circumference
is 2 miles ?
655. The Area of a square inscribed within a circle, is
found by taking twice the square of its radius.
15. What is the largest square stick of timber that can be
cut from a log 36 inches in diameter ? What is the length of
one side ?
Solution.— (18 x 18) x 2 = 648 sq. in. = Area.
= 25.45+ in., Ans.
16. How large a stick of square timber can be made from a
log 20 inches in diameter ?
17. The circumference of a circle is 3 ft. 4 in. ; what is the
side of a square of equal area ?
18. What is the difference between the area of a square
circumscribed about a circle 18 inches in diameter, and the
area of the largest square that can be inscribed within the
same circle ?
19. The circumference. of a circle is 3 meters 4 decimeters;
what is the area of a square inscribed within it ?
268
Mensuration.
656. To find the side of a square equal in area to a given
circle.
Rule. — Multiply the diameter by .8862, or the circum-
ference by £821.
20. The diameter of a circle is 20 feet; what is the side of a
square of equal area ?
Solution.— 20 ft x .8862 = 17.7240 feet, Ana.
21. A field is 150 rods in circumference; what is the side of
a square field of the same area ?
22. The distance around each of two gardens is 25 rods ; one
is in the form of a circle, the other a square ; which contains
the more land, and how much ?
SOLIDS.
657. A Solid is that which has length, breadth, and
thickness.
658. A Prism is a solid whose bases are
similar, equal, and parallel, and whose sides
are parallelograms.
Note. — When their bases are parallelograms they
are called parallelopipeds, or parallelopipedons.
659. All rectangular solids are prisms.
660. A Right Prism is one whose sides are
perpendicular to its bases.
661. A Rectangular Prism is one whose bases are rectangles,
and its sides perpendicular to its bases.
662. A Triangular Prism is one whose bases
are triangles.
Notes. — 1. Prisms are named from the form of their
bases, as triangular, quadrangular, pentagonal, hexa-
gonal, etc.
2. When their sides are all equal to each other they
are called cubes.
Solids. 269
663. The Lateral Surface of a prism is the sum
of all its faces.
664. A Cylinder is a circular body of uniform
diameter, whose ends are equal parallel circles.
665. The Altitude of a prism or a cylinder is
the perpendicular distance between its bases.
666. To find the Lateral Surface of a Prism or Cylinder.
Eule. — Multiply the perimeter of the base by the
altitude.
Note. — To find the entire surface, the area of the bases must be added
to the lateral surface.
1. What is the lateral surface of a prism, the altitude of
which is 18 feet and its base a pentagon, each side of which is
8 feet.
Solution.— 8 ft. x 5 = 40 ft. the perimeter.
40 ft. x 18 = 720 square feet, the surface, Ans.
2. What is the convex surface of a cylinder the circumfer-
ence of whose base is 62 inches, and the altitude 3 feet?
Solution.— 62 in. x 36 = 2232 sq. inches, Ans.
3. How many square feet of canvas will be required to
cover a cylinder 16£ feet in circumference and 25 feet
long?
4. How many square feet of surface m a stove pipe 22 inches
in circumference and 12 feet long ?
5. What is the convex surface of a log 25 ft. in circumfer-
ence and 18 ft. long ?
6. What is the convex surface of a cylinder 3 ft. long and
1\ ft. in diameter? What is its entire surface ?
270 Mensuration.
667. To find the Contents of a Prism or Cylinder, when the
Perimeter of the Base and the Altitude are given.
Rule. — Multiply the area of the base by the altitude.
Note. — This rule is applicable to all prisma, triangular, quadrangular,
etc. ; also to all parallelopipedons.
7. The standard bushel of the United States is 18J inches
in diameter and 8 inches deep ; how many cubic inches does it
contain ?
Solution.— The diam. 18^ in. x 3.1416 = 58.1196 in. = circumference.
58.1196^-2 = 29.0598 ; and 18|-*-2 = 9} ;
29.0598 x 9i = 268.8031 sq. in. = area.
And 268.8031 x 8 = 2150.4248 cu. in., Am.
8. What are the contents of a log 15 ft. long and 2 ft. in
diameter ?
9. The standard liquid gallon is 231 cubic inches; how
many gallons in a can 22 inches in diameter and 3 feet high ?
10. How many en. feet in a triangular prism, the area of
whose base is 920 square feet and height 20 feet ?
11. What are the contents of a quadrangular prism whose
length is 25 centimeters, and the base a rectangle 3 by 5
centimeters ?
12. How many liters will fill a cistern 2 meters long, 5 decims
wide, and 8 decims deep ? How many kiloliters of water ?
13. What are the contents of a triangular prism, each side
of which is 30 inches wide and 5 feet long ?
Fyramicl, Frustum. Coue. Frustum
Solids. 271
668. A Pyramid is a solid whose base is a triangle, square,
or poly y 07i, and whose sides terminate in a point, called the
vertex.
Note. — The sides which meet in the vertex are triangles.
669. A Cone is a solid which has a circle for its base, and
terminates in a point called the vertex.
670. The Altitude of a pyramid or a cone is the perpen-
dicular distance from the base to the vertex.
671. The Slant Height of a pyramid is the distance from
the middle of any side of the base to the vertex.
672. A Frustum of a pyramid or cone is the part which is
left after the top is cut off by a plane parallel to the base.
673. To find the Lateral or Convex Surface of a Regular
Pyramid or Cone.
Eule. — Multiply the perimeter of the base by £ the
slant height.
To find the entire surface, Add the area, of the base to the
convex surface.
14. What is the lateral surface of a regular pyramid whose
slant height is 15 ft, and the base is 30 ft. square?
Solution.— Perimeter of base = 30 x 4 = 120 ft.
120 x 7| (| slant height) = 900 sq. ft., Arts.
15. What is the surface of a pyramid whose base is an
equilateral triangle measuring 4 ft. on each side, and slant
height 16 feet ?
16. What is the convex surface of a cone, the diameter of
whose base is 7 ft. and its altitude 12 feet ?
17. What is the entire surface of a triangular pyramid whose
slant height is 25 feet, and each side of the base 10 feet.
18. What is the entire surface of a right cone, the diameter
pf the base and the slant height being each 40 feet ?
272
Mensuration.
674. To find the Contents of a Pyramid op a Cone, when the
Base and Altitude are given.
Kule. — Multiply the area of base by % the altitude.
Note.— The contents of a frustum of a pyramid or cone are found by
adding the areas of the two ends to the square root of the product of those
areas, and multiplying the sum by ^ of the altitude.
19. What are the contents of a pyramid whose base is 144 sq.
feet, and its altitude 33 feet ?
Solution. — 144 sq. ft. x 11 (| of altitude) = 1584 cu. ft., Ans.
20. What are the contents of a cone the area of whose base
is 1865 sq. feet, and its altitude 36 feet?
Solution.— 1865 x 12 ft of altitude) = 22380 cu. ft.
21. A monument in the form of a square pyramid, is 2 ft.
10 in. square at base, and 11 ft. high; at 175 lb. to a cu. ft.
what is its weight ?
22. What are the contents of a round log whose length is
20 ft., diameter of larger end 12 in., and smaller end 6 inches ?
23. The altitude of a frustum of a pyramid is 27 ft., the ends
are 4 ft. and 3 ft. square ; what is its solidity ?
675. A Sphere or Globe is a solid ter-
minated by a curve surface, every part of
which is equally distant from a point
within, called the center.
676. The Diameter of a sphere is a
straight line drawn through its center
and terminated afc both ends by the
surface.
677. A Hemisphere is one-half a sphere.
678. The Radius of a sphere is a straight line drawn from
its center to any point in its surface.
Gauging of Casks. 273
679. To find the Surface of a Sphere, the Circumference and
Diameter being given.
Eule. — Multiply the circumference by the diameter.
24. Require the surface of a globe 4 inches in diameter.
Solution.— 4x3.1416 = 12.5664 in circumference.
12.5654 x 4 = 50.2656 sq. in. surface, Ans.
25. What will it cost to gild a ball 12 inches in diameter, at
10 cents a square inch ?
26. Required the surface of the earth, its diameter being
8000 miles.
27. The diameter of a sphere is 100 centimeters; what is its
surface ?
680. To find the Solidity of a Sphere, the Surface and
Diameter being given.
Rule. — Multiply the surface by £ of the diameter.
28. Find the solidity of a sphere whose diameter is 12 inches
and its surface 4.91 sq. feet ?
Solution. — 4.91 x 144 ■= 707.04 sq. in. surface.
707.04 sq. in. x 2 = 1414.08 cu. in., Ans.
29. What is the solidity of the earth, its surface being
196900278 sq. miles, and its mean diameter 7916 miles ?
30. Find the solidity of a cannon ball 3 decimeters in
diameter ?
31. The basin of a fountain is a hemisphere 22-| ft. in
diameter; what are its cubical contents ?
32. How many hogsheads of water will it contain ?
GAUGING OF CASKS.
681. Gauging is finding the capacity or contents of casks
and other vessels.
682. The mean diameter of a cask is equal to half the sum
of the head diameter and bung diameter. (Art. 339.)
274 Mensw*ation.
Note.— The contents of a cask are equal to those of a cylinder having
the same length and a diameter equal to the mean diameter of the cask.
683. To find the Contents of a Cask, when its Length, its
Head, and Bung Diameters are given.
Rule. — Multiply the square of the mean diameter by
the length in inches, and this product by .0034 f or
gallons, or by .0129 for liters.
Note. — In finding the contents of cisterns, it is sufficiently accurate for
ordinary purposes to call a cubic foot = 7$ gallons.
1. How many gallons in a cask whose length is 35 inches, its
bung diameter 30 inches, and head diameter 26 inches?
Solution.— (30 + 26) -4- 2 = 28 in., the mean diameter. (Art. 682.)
28 2 x .7854 = area of base.
Area of base x length = contents in cubic inches, which are reduced to
gallons by dividing by 231.
Instead of using the factor .7854, if we divide it by 231, the number of
cubic inches in a gallon, and multiply by the quotient .0034, the operation
is shortened, and the result is in gallons. Thus,
28 2 x 35 x .0034 = 93.296 gal., Ans.
2. What is the capacity in gallons of a cask whose length is
26 inches, its head diameter 17, and bung diameter 22 inches ?
3. Find the contents in liters of a cask whose length is
54 inches, its bung diameter 42, and head diameter 36 inches ?
4. Required the contents in gallons of a rectangular cistern
4£ ft. long, 3J ft. wide, and 6 ft. deep.
6. What are the contents in gallons of a cask 36 in. long, its
head diameter 26 inches, and bung diameter 32 inches?
6. What will be the cost at 60 cents a gallon of a cask of
molasses, whose, length is 16 in., the head and bung diameters
10 and 12 inches ?
7. A cylindrical ash-receiver is 18 inches in diameter and 28
inches high ; how many bushels will it contain?
8. What must be the depth of a cylindrical measure 18|
inches in diameter to contain a bushel ?
Tonnage of Vessels. 275
TONNAGE OF VESSELS.
684. Tonnage is the weight in tons which a vessel will carry
It is estimated by the following
Carpenter's Rule.
Multiply together the length of the keel, the breadth at
the main beam, and the depth of the hold in feet, and
divide the product by 95 (the cu. ft. allowed for a, ton) ;
the result will be the tonnage.
For a double decker, instead of the depth of the hold,
take half the breadth of the beam.
Note. — A Register Ton = 100 cu. ft. is the legal standard.
* m . • m J 40 cu. ft, U. S., or ) ",. A . u
A Shipping Ton = 1 . > used in estimating cargoes.
1. What is the tonnage of a double decker with 300 ft. keel
and 42 ft. beam ? Ans. 2785^ tons.
2. What is the tonnage of a single decked vessel whose
length is 150 ft, the breadth 30 ft., and the depth 12 ft?
Rules for the Measurement of Grain.
685. To estimate the quantity of grain heaped in conical form
on the floor.
Rule. — Square the depth and the slant height in
inches, multiply the difference of the squares by the
depth, and multiply this product by .0005 ; the result is
the contents in bushels.
Note. — When heaped against a straight wall, take one-half the product
before multiplying by the decimal.
3. A conical heap of grain left by a thrashing-machine was
5-J- ft. high, and the slant height was 9 ft. ; how many bushels
did it contain ?
4. A quantity of wheat heaped against a straight wall was
4 ft. high, and its slant height was 7 ft. ; how many bushels
were there ?
276 Mensuration.
5. A quantity of grain was heaped in a conical form in a
corner, perpendicular height 4 ft. 3 in., slant height 7 ft. 1 in. ;
what is its value, at $1.66| a bushel?
686. To measure the height of an object standing in a plane.
6. What is the height of a tree standing in a plane which
casts a shadow 50 feet, measured with a pole 5 ft. long, casting
a shadow 10 ft.?
Solution. — Take a pole of any convenient length, and placing it in a
perpendicular position, measure the length of its shadow, which we will
suppose to be 10 feet, then by Proportion
10 ft. (shadow of p.) : 50 ft. (shadow of t.) : : 5 ft. (1. of p.) : height of tree.
50 x 5 = 250, and 250^-10 = 25 feet, Am.
7. What is the height of a pyramid, standing in a plane,
which casts a shadow of 100 feet, measured with a pole 7-J ft.
long which casts a shadow of 15 feet ?
8. The shadow of a tower was 36f ft., and that of a cane 2|
ft. high standing near it was at the same hour 9 inches ; what
was the height of the tower ?
LUMBER
687. Doyle's Rule for finding the number of square feet of
boards a round log will yield :
For logs 16 feet in length, Subtract Jf from the diameter
in inches ; the square of the remainder will be the num-
ber of square feet of inch boards the log will yield to each
16 feet.
l. How much square-edged inch lumber can be cut from a
log 24 inches in diameter and 12 ft. long.
Solution.— 24-4 = 20, 20 2 = 400 sq. ft.; 12 ft. = |f = f of 16 ft.
' 400 x | = 300 sq. feet., Ant.
Note. — This rule is not accurate for perfectly straight logs, but gives
a sufficiently just approximation for the average, and is much used by
lumbermen on account of its simplicity.
lAumber. 277
2. How many square feet of boards will a log yield which is
36 iuches in diameter and 18 feet long?
3. How many sq. feet of boards can be cut from a log 24
feet long and 18 in. diameter ?
4. How many from a log 18 ft. long and 12 ft. diameter ?
688. To find the number of inch boards which a given thick-
ness of log will yield.
Eule. — Divide the thickness of the log, less \ inch, by
1{ inch.
5. How many boards may be cut from a log 17{ in. thick ?
Solution.— 17£ in — \ in. = 17f in. 17f-t*l£ = 14 boards, Ans.
6. How many boards may be made from a log 16^ in. thick?
7. How many square-edged boards of equal width can be
made from a log 18 ft. long and 1G inches in diameter, allowing
J inch for saw cut, and what would be the board measure of the
whole ?
689. To find the cubic feet in round timber.
Eule. — Square { the mean girt in inches, multiply
it by the length in feet, and divide the product by
Note. — This rule only approximates the exact quantity, something
being allowed for crooks and waste.
8. The mean girt of a log is 36 in., its length 40 ft.; what are
its contents in cubic feet ?
9. How many cu. ft. of timber in a log 26 ft. long, and whose
mean girt is 48 inches ?
Note. — The size of square timber that a log will yield may be found
by multiplying the diameter of the smaller end by .707.
10. The diameter of the smaller end of a log is 18 inches ;
what is the width of the square timber that may be sawed
from it ?
TJESTIONS
FOR REVIEW.
690. l. Add seven hundred thousand two hundred sixty,
twelve million twelve, fifty-four thousand four hundred, six
million two thousand twenty-seven.
2. From the above sum subtract three million sixty-five
thousand three, minus six hundred thirty-eight thousand four
hundred nineteen.
3. Add eighty-four million fifteen, sixty-seven thousand
sixty-eight, five million ten thousand seventeen, three hun-
dred thousand twenty, three million eight thousand seventy-
five, nine hundred million twenty-seven.
4. (8143 + 24429) -^-34 x 12 = what?
5. A lady went shopping with $15.50 in her purse ; she paid
28 cents for needles, $2.25 for gloves, $5.75 for a dress, and
$2.25 for ribbon ; how much money had she left?
6. If the divisor is 19, the quotient 37, and the remainder 11,
what is the dividend ?
7. A> person owning f of a mine sold f of his interest for
$1710 ; what was the whole mine worth ?
8. A market woman having eggs for sale, counted her stock
and found that T \ of them made 147 ; how many had she ?
9. In a certain battle f of the forces were lost, and there
were 9800 men left ; how many were there at first ?
10. If | of f of a ship is worth $9370, what is the whole
worth ?
11. What is the quotient of 65 bu. 1 pk. 3 qt., divided by 12?
12. How many bushels will a box 8 ft. long, 4 ft. wide, and
3 ft. high contain ?
Test Questions for Review. 279
13. One factor of a number is 11, the other 3708311605 ;
what is the number ?
14. If the quotient is 610, the remainder 17, and the dividend
45767, what is the divisor ?
* 15. Find the g. c. d. of 192, 744, and 1044.
16. The sum of two numbers is 143J, their difference 17J ;
what are the numbers ?
17. Find the sum, difference, product, and quotient of -J
and -|.
18. What number multiplied by \ of itself will produce 12£?
19. A man paid $275 for a horse, which cost | as much as
his carriage ; what did he pay for the carriage ?
20. At $7f a barrel, how many barrels of flour must be given
for 530 barrels of potatoes worth %Z\ a barrel ?
21. Bought a sleigh for $75, which was f of 3 times the price
of the harness; what was the price of the harness?
22. A man paid $40 cash for a cow and sold her at a credit
of 8 months for $45; how much did he gain, reckoning interest
at 6%?
23. How many planks 18 ft. long and 15 inches wide, will
be needed to floor a barn 63£ ft. long and 33£ wide ?
24. A man's salary this year is $600, which is J more than
it was last year; what was it last year ?
25. If a pipe of 5 inches diameter will discharge a cistern in
12 hours, in what time will a 3-inch pipe discharge it ?
26. A broken tree rested on the stump 20 ft. from the ground,
and its top touched the ground 50 ft. from the stump ; how
high was the tree ?
•27. What is the length of a diagonal drawn on the floor of a
room 30 ft. long and 24 ft. wide ?
28. A man sold his horse for $100 and gained 25%; what
per cent would he have gained if he had sold at $120 ?
29. What cost six $500 U. S. 6% currency bonds, at 22£%
premium ?
280 Test Questions for Heview.
30. Three men hired a pasture for $150 ; A pastured 4 cows
12 weeks, B 6 cows 10 weeks, and 8 cows 15 weeks ; how
much should each pay ?
31. In a school of 280 pupils, 12 were absent ; what was the
per cent of attendance ?
32. A market woman bought 150 oranges at the rate of 5
for 2 cts., and sold % of them at the rate of 3 for 1 ct., and the
remainder at the rate of 2 for 1 ct. ; did she gain or lose, and
how much ?
33. If 1^- pounds of beef and 1-^- pounds of flour are allowed
for a ration, how much will 560 rations cost if the price of
beef is llf cts. and of flour 3J cts. per pound ?
34. How many hektars of land can a man buy for $946, if
he pays at the rate of $86 for every 7 hektars ?
35. When brooms are sold at $3 £ per doz., what will be the
cost of 16| gross sold at 5% discount on bills over $100 ?
36. If the interest of $1800 for 12 mo. is $108, what will be
the interest of the same sum for 8 mo. ?
37. If a tree 50 ft. high casts a shadow 60 ft. long, how long
will be the shadow of a tree 80 ft. high ?
38. A number diminished by J of itself is 1140 ; what is the
number ?
39. What is the sum, difference, product, and quotient of
263|, and 175f ?
40. A retail dealer's profits this year are $8350, which is ^
less than last year ; what were they last year ?
41. The wholesale price of Grammars is 98 cents apiece ; but
for cash they are J less ; what is the cash price ?
42. A merchant fails for $12575, and his assets are $7500.
What per cent of his debts can he pay ?
43. What is the value of a house which brings $11,500 when
sold at a loss of 7£ per cent. ?
44. If on the day of the battle of Lexington 1 cent had been
placed at compound interest at 6%, what would have been the
amount on the 19th of April, 1884 ?
Test Questions for Review. 281
45. How much do I gain or lose if I obtain at a bank $1000
for 1 year at 6% discount, and then put it at interest for the
same time and rate ?
46. The average quantity of wheat required to make a barrel
of flour is 4^ bushels ; the cost of conversion is* 56 cts. a barrel.
If wheat in Chicago is 98J cts. a bushel, and expense of trans-
portation 15 cts. a bu., what would be the profit to a New
York miller if 8500 bu. were sent from Chicago, and sold,
when converted into flour, for $8 \ a barrel ?
47. How many bushels of grain are in a conical pile 5 ft.
high and 26 ft. in circumference ?
48. How many bushels of wheat can be placed in a car 20 ft.
long, 8 ft. wide, and 7 ft. high ?
49. How many such cars would be required to transport
8700 bushels ?
50. Two city lots are sold at $2500 each. How much is
made or lost if one is sold at a profit of 15 per cent and the
other at a loss of 15 per cent ?
51. What is the exact interest on a note of $1175 from
September 12th to December 24 ?
52. At a recent examination a student received 83 per cent
in History, 94 in Algebra, and 87 in Philosophy ; what was
his average per cent ?
53. A man having 4 tracts of land containing respectively
175 acres, 210 acres, 318 acres, and 268 acres, divided it into
4 farms ; what was the average number of acres in each ?
54. The population of New York and Philadelphia together
in 1880 was 2053469, the difference was 359129 ; what was the
population of each city ?
55. How many centars in a piece of land 145 meters long,
and 23.2 meters wide ?
56. How many square feet of glass in 8 windows of 12 panes
each, size 10 in. by 14 ?
57. If a staff 3 ft. 8 in. long cast a shadow 2 ft. 6 in., what is
the height of a steeple that casts a shadow of 248 ft. at the same
hour?
282 Test Questions for Review.
58. What are the proceeds of a note for $750, discounted at
a bank for 30 days at 6 per cent ?
59. A R. R. Co. declared a scrip dividend of 6%; to how
many shares was a stockholder entitled, who held 50 shares of
the original stock ?
60. Sold at wholesale a bill of merchandise at 25% discount,
and h% off for cash ; what was the whole discount ?
61. What is the length of a rope extending from the top of
a stake 13 ft. high to the top of a pole 40 ft. high, standing
35 ft. from the stake ?
62. A merchant increased his capital the first year by \ of
itself, the second year by -f , the third year he lost -f of all he
had, and had $15000 remaining ; what was his capital at first?
63. What per cent of an acre is 1 sq. yard ?
64. What part of 8 square feet is 2 feet square ?
65. How many cu. meters in a wall 24 meters long, 8 -fa m.
high, and 52 cm. thick ?
66. What would be the cost of building this wall is $4.25
per cu. meter ?
67. If a cistern 19J ft. long, 10J ft. wide, and 12 ft. deep,
hold 546 barrels, how many barrels will a cistern hold that is
18 ft. long, 9 ft. wide, and 15 ft. deep?
68. If $500 is deposited for a child at birth, at 1% compound
interest payable semi-annually, what will it amount to when
the child is 21 years old ?
69. The following payments have been made on a note of
$10000 given March 1st: April 3d, $200; April 25th, $10;
May 20th, $3000; July 1st, $400; December 15th, $4000.
How much will settle the note January 1st ?
70. What must be the inside diameter of a globe that will
contain 5 gallons of water ?
71. If a measure 60 centimeters deep holds a hektoliter,
what is the depth of a similar measure holding a centiliter?
72. A man owes $2400, \ of which is now due, \ of it in 3
months, \ of it in 4 months, and the remainder in 6 months;
what is the equated time of payment ?
Test Questions for Review. 283
73. What is the g. c. d. of 529, 782, and 1127 ?
74. For what amount must a 60-day note be written to yield
$250, when discounted at a bank ?
75. If a ball 2 inches in diameter weighs 4 pounds, what is
the weight of a ball 6 inches in diameter ?
76. A piece of cloth of 14 yd. sold for $61.25, which was a
gain of 25% ; what was the cost per yard ?
77. What is the g. c. d. of 1177, 1819, 2782, and 4708?
78. A gentleman has a note due at bank on which he
received $575 for 3 mo. at 4% discount ; he goes to another
bank and obtains the money to take up the note, for which he
pays 6% for 6 mo. ; what was the face of the last named note ?
79. What are the contents of a sphere, diameter 60 inches ?
80. How many hektars in a piece of land -| mile square ?
81. How many hektoliters in a box, length 2.25 m., width
1.75 m., depth 1 meter ?
82. What annuity at 6% compound interest will amount to
$10000 in 20 years?
83. What must be the diameter of a cylindrical cup 6 in.
high, to hold a gallon ?
84. If a stock is bought at 109J and an annual dividend of
7% received, what per cent is*that on the investment ?
85. A draft on New Orleans bought at \% premium for
$12000, was sent to an agent to pay for cotton purchased at
1\% commission ; what was the value of the cotton ?
86. Find the amount of duty on the following: 8 casks
raisins, at 11 cts. a lb., gross weight 888 lb., tare 12 lb. per
cask, duty 25$ ad valorem ; 12 boxes sugar, 400 lb. each, at
7 cts. per lb., tare 10%, duty 24% ad valorem ; 60 hhd. molasses,
at 54 cts. per gal., leakage 2%, duty 20$.
87. Mr. A. deposits $20 twice each year, 1st of Jan. and
July, in a savings bank which pays 5% per annum, adding
the accrued interest at the end of each 6 months; what sum
will stand to his credit in the bank on the day after he makes
his sixth deposit ?
284 Test Questions for Review.
88. If it cost $312 to enclose a field 216 rods long and 24
rods wide, what will it cost to enclose a square field of equal
area with the same kind of fence ?
89. Three notes bearing interest are dated respectively July
3, 1883, Oct. 9, 1883, and Feb. 6, 1884 ; if a single note were
substituted for the three, what should be its date ?
90. Ralston & Baxter received a consignment of 8500 bu.
wheat from Jones & Co., Milwaukee. Their account sales is as
follows: Oct. 20, 1883, to C. & Co. 2500 bu., at $1.12 on 30 d.;
Oct. 22, to D. & Co. 2500 bu., at $1.11 J on 10 d. ; Nov. 1,
3000 bu. to J. & Co., at $1.10 on 60 d.; Nov. 12, 500 bu. to
R, & Co., at $1.15 on 30 d. Charges Oct. 15: Freight on
8500 bu., at.l2|; weighing, $42.50; towing, $14; demurrage,
$10 ; commission, 2 \%. What is the equated time for the pay-
ment of the net proceeds, the commission being due at average
due date of sales ?
91. What is the present worth of a reversionary lease of $250,
which begins in 12 years, and continues 25 years at 5%, com-
pound interest ?
92. A man wishes to inclose a garden 56J feet long and 40^
ft. wide, with an iron fence the sections of which shall be of
equal length ; what ie the length of the longest sections that
can be used ?
93. What number multiplied by \ of itself equals 32 ?
94. What number multiplied by f of itself equals 54 ?
95. What number is that which if doubled and the product
divided by 3, the quotient squared, that square increased by \
of itself, the result will be \ of the square of 12 ?
96. What is the quotient, if the cube of 75 is divided by \ of
1000?
97. What is the profit of buying peaches at 60 cents a
hundred, if 10% of them decay, and the remainder sell at 2
cents apiece ?
98. At 40 cents per centar, what would it cost to plaster a
hall 76 ft. long, 54 ft. wide, and 18 ft. high, deducting 10% for
windows and woodwork ?
Test Questions for Review. 285
99. How many bushels of wheat equal 63 hektoliters?
100. What is 75$ of the difference between the square root
of 256 and the second power of the same number ?
101. A field containing 6 A. 12 sq. r. is 3 times as long as it
is wide ; what are its length and breadth ?
102. What is the smallest sum of money for which you can
buy oxen at $85, or cows at $35 each ?
103. What is the distance from a comer of a cubical block
to the opposite diagonal corner, the sides being 9 sq. feet ?
104. A field \ as wide as it is long contains 8 J A. 32 sq. r.;
what length of fence is required to go around it ?
105. A man paid for tobacco an average of $25 a year from the
age of 18 until he was 60, when he died and left $1500 for his
heirs ; if he had deposited in the savings bank each year the
money spent for tobacco, how much might he have left at b%
semi-annual compound interest?
106. The diameter of a circle is 10 inches ; what is the side
of the square that may be inscribed in it ?
Note. — The diameter of a circle forms the hypothenuse of the two
right-angled triangles which equal the square inscribed in it.
107. What is the side of a square equal in area to a circle
150 meters in diameter?
108. In what time will $1265 at 6%, yield $85.25 ?
109. If the interest of $3865 for 8 mo. is $180.03, what would
be the principal on which $360.85 is paid for 2 yr. 4 mo. 15 days?
no. Find the difference between the square root of the least
common multiple of 6, 12, 18, 36, 48, and the square of their
greatest common divisor.
in. In 15 hektars how many square rods?
112. An agent sold flour at $7.92 a barrel, at a loss of 4%; at
what price should it be sold to gain 8% ?
113. In 126589 meters how many kilometers ?
114. How many miles, rods, etc., in the above?
115. If flour sold at $12 a barrel gains 15$, what would be
the gain % if sold at $11.25 ?
m
If
* s> j ( _
PPENDIX.
(1 g ^15r^ a «*
DRILL EXERCISES.
691. The following and similar exercises should be practised
till the combinations can be read without hesitation :
(1.)
(2-
)
(3.)
M
(5.)
6.
59 75
643
74
725 87
8462 34
7425 34,
a.
7.
27 82
350
62
842 73
2351 23
6534 23,
b.
8.
46 71
128
49
523 27
3162 34
5623 14,
c.
9.
28 15
352
73
435 54
4273 43
4731 25,
d.
10.
34 63
243
25
327 43
5384 52
5842 36,
e.
11.
29 50
455
63
276 32
6275 63
4953 27,
f.
12.
68 71
729
31
586 34
3284 32
2586 54,
&•
13.
97 53
426
76
235 20
1635 34
4234 62,
h.
14.
82 43
623
25
463 52
2586 89
1736 44,
i.
15.
64 25
321
35
958 76
7434 26
5398 29,
J-
16.
18 12
238
17
386 29
5869 73
1234 56,
k.
17.
19 50
125
51
315 46
3276 42
7891 01,
1.
18.
62 25
436
25
434 57
1635 38
1234 16,
m.
19.
64 37
536
63
372 46
5913 84
6843 75,
n.
20.
53 63
257 47
657 32
6284 35
7616 24,
0.
P.
a.
R.
s.
Note. — The numbers in the above examples should be added perpen.
dicularly for the first five examples, then horizontally through the 20th.
They may be taken in columns of two or more figures at a time.
Subteaction. — 21, 22. In col. marked "P" (at bottom)
subtract 7th from 6th ; 9th from 8th.
23-28. In " T * take b from a ; d from c ; f from e ; g from
h ; i from j ; k from 1.
Drill Exercises, 287
29-34. In "S" take b from a; c from d; e from f; h from
g ; i from j ; 1 from k.
Multiplication. — 35-50. Multiply the numbers in " T " by
those in "P," begin "a."
Division". — 51-65. Divide each of the above products by the
numbers in i ■ Q."
Note. — These exercises may be continued and extended at pleasure.
Drill in Percentage.
692. l. Selling price $95, cost $84 ; required the gain %.
2. Profit $30, cost $128.50 ; required the gain %.
3. Loss 12%, cost $125.25 ; required selling price.
4. Selling price $225.50, loss 18% ; required cost.
5. Cost $120, selling price $160 ; required gain %*
6. Profit $350, cost $800 ; required gain %.
7. Loss $25.50, cost $175 ; required loss %.
8. Selling price $1875, loss 15% ; required cost.
9. Profit 6£%, cost $1200 ; required selling price.
10. Principal $240, int. $26.40, rate 8\%\ required time.
11. Principal $450.75, rate 9%, time 4 yr. 7 mo. 15 d.; amount?
12. Principal $425.45, rate 6%, time 3 yr. 6 mo. ; required
compound interest.
13. Insured $6700, rate \%, time 1 yr.; required the
premium.
14. Principal $800, interest $32, time 8 mo.; required rate.
15. Tax $12500, property $2400000; required rate.
16. Principal $2500, time 1 yr. 4 mo., rate 7-&%; amount?
17. Difference discount and int. of $900, 3 yr. 4 mo. 20 d.- 6$.
18. Bank discount $168.13, at 6% ; 8 yr. 5 mo.
19. Bank discount $900, at 8% ; 9 months..
20. Amount £35 4s. 6d., 2 yr. 8 mo., at 6$;
21. Net proceeds 320 A., at $22.50; commission l Q%.
22. Insurance $10000, at \% ; policy $1.
288 Appendix.
23. Cost $400 for 9 cwt. 52 lb. coffee, gain 1%% ; required
selling price.
24. Interest $685.50, at 10%, time 3 yr. ; required principal.
25. Paid $6180, brokerage 3% ; required amt. of draft.
26. Discount $1600 for 60 d., 6%; required the avails.
27. Amt. $860 from Jan. 25, 1882 to Jan. 5, 1883, at 9%.
28. Amount of $124.17 for 11 mo. 29 d., at 9%.
29. Interest of $3000 for 6 mo. 15 d., at 7&%.
30. Prin. $860.56, int. $149.63, time 2 yr. 8 mo. 3 d. ; rate ?
31. Avails of note, $8000, at 6%, 6 mo.; required its face.
32. Principal $475, at 6%, amount $57095 ; rate.
33. Present worth of $2500, due in 9 mo., 6%.
34. Cost of bill $2500, discount %\% ', required the face.
35. Principal $750, amount $960.85 at 7^% ; time.
36. Gain $384, at 12-|% J required the cost.
37. Interest of $1200 for 2 yr. 3 mo. $168.75 ; required
the rate.
38. Prin. $5000, at 7 T 3 o%, from Jan. 1 to March 1, 1884 ;
required the accurate interest.
39. Income is $800 from IT. S. 5's, at 104 ; required the
investment.
40. Prin. $860, at 6%, amount $900 from Jan. 1 to what day?
41. Bought bill of goods amounting to $6845, and less charges
$65, sold same at 12-§-% advance, took note for 60 d. and with
proceeds from 6% discount, bought bill on London at 109J ;
required the face of the bill.
42. Goods marked 25% advance on cost, are sold at 15%
below the marked price ; what per cent is the gain ?
43. If you hire money at a bank, at 6% for 4 mo., to buy a
horse at $180, what does the horse really cost you ?
44. What rate of interest does a man pay, who gets his notes
discounted at a bank for 90 days at 6% ?
45. If a bank borrows $100000 at 6 per cent and discounts a
30-day paper for the same amount at 6 per cent, what are the
profits ?
Drill Exercises. 289
46. The true discount of 81215, due in 10 mo. 20 d., is 890 ;
what is the rate ?
47. Which is better, and how much, 6% bonds at 90, or 8%
bonds at 130, both due at the same time ?
Metric Drill.
693. l. A man sold J of a farm of 170 hektars, which cost
500055 francs, at 3500 fr. per Ha., T ^ of it at 2800 fr. per Ha,,
and the remainder at cost; what was the gain or loss?
2. If with 34 kilograms of wool, 25 meters of flannel 60
centims wide can be made, what length of similar flannel, 80
centims wide, can be made with 108 Kg. of w T ool ?
3. How many fields containing 2 Ha. 47 ars each can be
made on a farm of 313 Ha, and 69 ars?
4. How many hektoliters of wheat will a bin contain which
is 7 meters square and 2.7 meters deep ? What will it cost at
$2 per bushel ?
5. Express the rate per hour of a mail train in terms of that
of a mail cart, the former traveling 4J myriameters an hour,
the latter 135 kilometers in 10 hours ?
6. If 26 men working 10 hr. a day can dig a trench 50 meters
long, 4 meters 25 centims broad, and 6£ meters deep in 12 d.,
how many men will it require to dig a similar trench 125
meters long, 3 meters 6 cm. broad, and 9 m. 35 cm. deep in 18
d., if they work 12 hr. a day?
7. It requires 14375 sq. bricks to pave a path 184 meters
long and 4 m. 5 centims broad ; find the side of each brick.
8. What is the radius of a circular bed whose circumference
is 3 meters 50 centimeters ?
9. If 13 square meters 20 square decims of canvas are
required to cover a cylindrical column, the radius of whose
base is 28 centims ; what is the height of the column ?
10. If a pipe 3 centims in diameter will empty a cistern in 8
min., what is the diameter of a pipe that will empty it in 18 min.?
li. How many cubic decimeters in a globe 6 decimeters in
diameter ?
290 Appendix.
GREATEST COMMON DIVISOR OF FRAC-
TIONS.
694. The Greatest Common Divisor of two or more fractions
is the greatest number that will divide each of them and give
an integer for the quotient.
695. To find the Greatest Common Divisor of two or more
fractions.
I. Find the g. c. d. of -f, if, and 2f .
Analysis.— Reducing if to lowest terms, 2f operation.
to an improper fraction, and all to the least ^-| — -f^, 2-f- = -% -.
common denominator ; the fractions are |f, f f, led = 45.
and Y/. The <j, c. d. of the numerators is 4. 7 -P "NT - 4.
Since 36, 24, and 100 denote 45ths, it follows Q\ C ' tl * 0t SSm ~
that their g, c. d. is not 4 integral units, but 4 Hence, ^j, Ans.
forty- fifths of 1 unit. Hence, the
Eule. — I. Reduce mixed numbers to improper frac-
tions, compound and complex fractions to simple ones,
and all to lowest terms.
II. Reduce these fractions to the least common denom-
inator, and write the greatest common divisor of the
numerators over it.
Find the fj. c. d. of the following fractions :
2- A, 1 f
5. 12f, 8J, 9J..
8. *, ItV. la-
3. } of f, 1\, 4|.
6- i, f, h f
s'- ii i, n-
4. i, i, i, !•
7. 3A, M, Ht-
10. |^ff, 8f
11. A farmer has 67| bu. oats, 33| bu. rye, and 70-J btt.
wheat, which he wishes to keep separate and send to market
in the largest bags possible, each containing the same number
of bushels; required the number of bags, and the quantity
in each.
Least Common Multiple of Fractions. 291
12. A man has 4 fields containing- 6$ A., 7 T ^- - A., 10| A.,
and 8| A. respectively, which he divided into the largest
possible house lots of equal size ; how many lots did he make,
and what was the size of each ?
LEAST COMMON MULTIPLE OF FRAC-
TIONS.
696. The Least Common Multiple of two or more fractions
is the least number that can be divided by each of them and
give an integer for the quotient.
697. To find the I, c. m. of two or more fractions.
I. What is the I. C m. off, ^, and 2^-?
Analysis. — Reducing T \ to lowest terms, operation.
and 2 f V to an improper fraction, the given ^ — J y 2^ = ^-J.
fractions become f, £, and ff, and the/, r.m. j (t „, }i of N 33
of the numerators is 33. Since the numera- i £ t\
tors 3, 3, and 33 are dividends, and the 9* <'" <*• oi ■ L) - = 4 -
denominators 8, 4, and 16 are divisors, it Hence, ^ 3 - = 8J. AflS.
follows that the I. c, tn. 33, is not 33 integral
units, but so many fractional parts of the greatest common divisor of the^-
denominators, which is 4. And 4 placed under 33 forms the fraction
^ = 8£, which is the /. c. m. required. Hence, the
Eule. — I. Reduce mixed numbers to improper frac-
tions, compound and complex fractions to simple ones,
and all to their lowest terms.
II. Find the least common multiple of the numera-
tors and write it over the Greatest common divisor of the
denon vinators.
Mud the I. c. m. of the following fractions :
3. 5i,7J,3flf, 5. 16^,8^, 5 t V
292
Append*
IX.
6. A, B, and C start at the same time and place to go round
a circular race-course; A can make the circuit in | of a day,
B in f, and C in £ of a day ; in how many days will they first
meet at the place of starting, and how many times will each
have gone round the course ?
7. Three yachts start at the same time and place to sail
round a light-boat, 1 mile distant; the first sails 52 r. a min-
ute, the second 70 rods, and the third 100 rods a minute ; when
will they first be together, and how far from the starting point?
8. In a certain park, the circular walk is one mile long.
Three boys undertook to walk around this in one direction till
all should meet again at the starting point; No. 1, walks 2} m.
an hour; No. 2, 3J m.; No. 3, A\ m.; how many hours must
they walk, and how many times must each go around?
Table of Prime Numbers from I to 3407.
1
173
409
659
941
1223
1511
1811
2129
2423
2741
3079
2
179
419
661
947
1229
1523
1823
2131
2437
2749
3083
3
181
421
673
953
1231
1531
1831
2137
2441
2753
3089
5
191
431
677
967
1237
1543
1847
2141
2447
2767
3109
7
193
133
683
971
1249
1549
1861
2143
2459
2777
3119
11
197
439
691
977
1259
1553
1867
2153
2467
2789
3121
13
199
443
701
983
1277
1559
1871
2161
2473
2791
3137
17
211
449
709
991
1279
1567
1873
2179
2477
2797
3163
19
223
457
719
997
1283
1571
1877
2208
2503
2801
3167
• 23
227
461
727
1009
1289
1579
1879
2207
2521
2803
3169
^ 29
229
463
733
1013
1291
1583
1889
2213
2531
2819
3181
31
233
467
739
1019
1297
1597
1901
2221
2539
2833
3187
. 37 -
239
479
743
1021
1301
1601
1907
2237
2543
2837
3191
* 41
241
487
751
1031
1303
1607
1913
2239
2549
2843
3203
43
251
491
757
1033
1307
1609
1931
2243
2551
2851
3209
47
257
499
761
1039
1319
1613
1933
2251
2557
2857
3217
53
263
503
769
1049
1321
1619
1949
2267
2579
2861
3221
59
269
509
773
1051
1327
1621
1951
2269
2591
2879
3229
61
271
521
787
1081
1361
1627
1973
2273
2593
2887
3251
67
277
523
797
1063
1367
1637
1979
2281
2609
2897
3253
71
281
541
809
1069
1373
1(557
1987
2287
2617
2903
3257
73
2S3
547
811
1087
1381
1663
1993
2293
2621
2909
3259
79
298
557
821
1091
1399
1667
1997
2297
2633
2917
3271
83
307
563
823
1093
1409
1069
1999
2309
2647
2927
3299
89
311
569
827
1097
1438
1693
2003
2311
265?
2939
&301
97
313
571
829
1103
1427
1697
2011
2333
2659
2953
3307
101
317
577
839
1109
1429
1699
2017
2339
2663
2957
3313
103
331
587
853
1117
1433
1709
2027
2341
2671
2963
3319
107
337
593
857
1123
1439
1721
2029
2347
2677
2969
3323
109
347
599
859
1129
1447
1723
2039
2351
2683
2971
3329
113
349
601
863
1151
1451
1733
2053
2357
2687
2999
3331
127
353
607
877
1153
1453
1741
2063
2371
2689
3001
3343
131
359
613
881
1163
1459
1747
2069
2377
2693
3011
3347
137
367
617
883
1171
1471
1753
2081
2381
2699
3019
3359
139
373
019
887
1181
1481
1759
2083
23*3
2707
3023
3861
149
379
631
907
1187
1483
1777
2087
2389
2711
3037
3371
151
383
641
911
1193
1487
1783
2089
2393
2713
3041
3373
157
389
643
919
1201
1489
1787
2099
2399
2719
3049
3389
163
397
047
929
1213
1493
1789
2111
2411
2729
3061
3391
16?
491
653
937
1217
1499
1801
2113
2417
2731
3067
3407
Contractions in Multiplication. 293
698. Property of the number 9 :
Any number divided by 9 will leave the same remainder as
the sum of its digits divided by 9.
1. Let it be required to find the excess of 9's in 7548467.
Adding 7 to 5, the sum is 12. Rejecting 9 from 12, leaves 3 ; 3 and
4 are 7, and 8 are 15. Rejecting 9 from 15, leaves 6 ; 6 and 4 are 10.
Rejecting 9 from 10, leaves 1 ; 1 and 6 are 7, and 7 are 14. Finally,
rejecting 9 from 14 leaves 5, the excess required.
Note. — It will be observed that the excess of 9's in any two digits
is always equal to the sum, or the excess in the sum, of those digits.
Thus, in 15 the excess is 6, and 1 + 5=6; so in 51 it is 6, and 5 + 1 = 6.
699. To prove Multiplication by Excess of 9's.
Find the- excess of 9 's in each factor separately; then
multiply these excesses together, and reject the 9's from
the result ; if this excess agrees with the excess of 9's in
the answer, the work is right. <« •
2. What is the product of 1842 x 324 ?
1842 Excess of 9's in the multiplicand is 6.
324 Excess of 9's in the multiplier is 0.
596808, Ans. 9 6x0 = 0. The excess of 9's in prod, is also 0.
3. Multiply 54683 by 348 and prove the answer.
CONTRACTIONS IN MULTIPLICATION. '
700. To multiply by any number within 12 (or less) of 100,
1000, etc.
Eule. — Annex as many ciphers to the multiplicand as
there are figures in the multiplier, and subtract as many
times the multiplicand from the result as there are
units in the complement of the multiplier.
1. Multiply 2564 by 993.
Solution.— 1000-993 = 7 ; 2564 x7 = 17948.
2564000-17948 = 2546052, Arts.
2. Multiply 5863 by 88. 4. Multiply 54326 by 991.
3. Multiply 45832 by 989. 5. Multiply 67543 by 9996.
294 Appendix.
701. To square any number between 50 and 60.
Rule. — Add the units of the given number to 25 for
the hundreds, and for the tens and units annex the
square of the units.
6. Find the square of 53.
Solution.— 5 2 = 25, and 25 + 3 (the units) = 28 ; 3 2 = 9 ; 2809, Ans.
7. What is the square of 54? Of 55 ? Of 58 ?
8. What is the square of 52 ? Of 56 ? Of 59 ?
702. To square a number ending in 5.
Rule. — Multiply the number of tens by itself plus 1,
and to the right of the product annex 25.
9. What is the square of 25 ?
Solution.— The tens (2) plus 1 = 3, and 2x3 = 6, then 625, Arts.
10. What is the square of 45 ? Of G5 ? Of 85 ? Of 95 ?
Note. — This rule may be extended to more than two places of figures.
11. Find the square of 125.
Solution. — 12 x 13 = 156 and 25 annexed = 15625, Ans.
12. Find the square of 105. Of 115. Of 145. Of 135.
703. To multiply any number by II.
Rule. — On the right place the units of the multipli-
cand, then add the digits successively from right to left,
carrying as usual, and write results in the product.
13. Multiply 4572 by 11. ,
Solution. — Place 2 for the first product figure, then 2 + 7 = 9 (the 2d),
7 + 5 = 12 (2 the 3d), 5 + 4 + 1 = 10 (0 the 4th), and 4 + 1 (carried) = 5, the
last figure. Then 50292, Ans.
14. Multiply 5364 by 11. 16. 2693 x 11 = ?
15. Multiply 7532 by 11. 17. 2854 x 11 = ?
Finding the Time between Two Dates. 295
704. The product of the sum and difference of two numbers
is equal to the difference of their squares.
705. The square of any number consisting of tens and units
is equal to the square of the tens, plus tiuice the product of the
tens by the units, plus the square of the units.
706. The cube of any number consisting of tens and units is
equal to the cube of the tens, plus 3 times the square of the tens
by the units, plus S times the tens by the square of the units,
])lux the cube of units.
Finding the Time between Two Dates.
707. The process of finding the time between two dates by
Compound Subtraction is liable to lead to error in consequence
of the greater number of days in some months than in others.
It is the custom with Banks when the time is given in
months, to consider them calendar months in reference to the
maturity of the paper, but even then they compute the
discount by days.
Time table, showing the number of days :
To the Corresponding Day
OP
From any
Day of
1
2
3
4
.5
6
7 8
9
10
11
12
Jan.
Feb.
Mar
Apr.
May
June.
151
July.
Aug.
Sept.
Oct.
273
Nov.
304
Dec.
334
January . . .
BBS
31
59
90
120
181
212
243
February . .
334
365
23
59
89
120
150 181
212
242
273
303
March
30(5
337
365
31
61
92
122
153
184
214
245
275
April
275
306
334
365
30
61
91
122
153
183
214
244
May
245
276
304
335
365
31
61
92
123
153
184
214
June
214
245
273
304
834
365
30
61
92
122
153
183
July
184
215
243
274
304
335
365
31
62
92
123
153
August . . .
153
184
212
243
273
304
334
365
31
61
92
122
September.
122
153
181
21-2
242
273
303
334
365
?0
61
91
October
92
123
151
182
212
243
273
304
335
365
31
61
November .
Gl
93
120
151
181
21->
242
273
304
334
365
30
December. .
31
62
M
121
151
182
212
243
274
304
335
365
l. How many days from May 13 to Aug. 23 ?
Explanation.— Find "May" in the column of months at the left;
and on the same line under " Aug." find 92, which is the number of days
from any day in May to the same dr-f in Aug. But Aug. 23 is 10 days
more than Aug. 13, and 92 + 10 = 102 d., Ana.
296 Appendix.
Note.— If the required date be earlier in the month than the date from
which the time is counted, subtract the difference from the tabular number.
2. How many days from May 13 to Aug. 1 ?
Explanation.— From May to Aug. is 92 d., but to Aug. 1 is 12 d.
less than to Aug. 13 ; and 92—12 = 80 d., Ans.
Note. — If the given date is in a leap year it will be necessary to add
cr subtract one more day when Feb. intervenes
708. If it is required to find a day which is a given number
of days after a certain date, look in the table opposite the mo.
having the given date, and find the number of days next larger,
subtract the given days and count back for the required date.
3. Find the date that is 125 days after July 4th.
Explanation.— Opposite July, the next larger number than 125, is
153 in Dec; 153-125 = 28, and 31-28 = 3. Hence, Nov. G is tha date.
709. To find the time for which a note must be drawn, so that
it will not fall due on Sunday or a Legal Holiday.
Rule. — Find the number of days by the Table, and
dividing them by 7, the quotient will be the number
of weeks and days. Then count the odd days from the
day of the week on which the note is dated.
4. A note was drawn on Friday the 1st of Feb., to run 3
months ; what day of the week will it fall due ?
Solution. — Three months from Feb. 1st brings May 1st, which by
Table is 89 d. in a common year, or 90 d. leap year. 89-5-7 = 12 and 5 d.
over. Friday + 5 d. gives Wednesday, or in leap year, Thursday.
5. If a note is dated Tuesday, Apr. 1st, to run 60 days, what
day of the week will it fall due ?
6. The birthday of Shakspeare was April 23, 1564; how
many years, months, and days from that to the present time ?
7. Suppose a note is made on Wednesday, the 13th of Feb.,
1884, payable in 3 months from date; what day would it be
due?
Life Insurance Tables.
297
LIFE INSURANCE TABLES.
710. The Expectation of Life is the probable number of
years a person may live after he has reached a specified age.
It is found by dividing the number of those who survive
that age by the number of those who attain it.
American Experience Table of Mortality.
Adopted by the State of N. Y. in estimating life endowments.
Com-
Number
Deaths
Com-
Number
Deaths
Com-
Number
Deaths
pleted
surviving at
in each
pleted
surviving at
in each
pleted
surviving at
in each
Age.
each Age.
Year.
Age.
each Age.
Year.
Age.
each Age.
Year.
10
100.000
749
40
78,106
765
70
38,569
2,391
11
99,251
745
41
77,341
774
71
36,178
2,448
12
98,505
743
42
76,567
785
72
33,730
2,487
13
97,762
740
43
75,782
797
73
31,243
2,505
14
97,022
737
44
74,985
812
74
28,738
2,501
15
96,285
735
45
74,173
828
75
26,237
2,476
16
95,550
732
46
73,345
848
76
23,761
2,431
17
' 94,818
729
47
72,497
870
77
21,330
2,369
18
94,089
727
48
71,627
896
78
18.961
2,291
19
93,362
725 |
49
70,731
927
79
16,670
2,196
20
92,637
723
50
69,804
962
80
14,474
2.091
21
91,914
722
51
68,842
1001
81
12,383
1,964
22
91,192
721
52
67,841
1,044
82
10,419
1,816
23
90,471
720
53
66,797
1,091
83
8,608
1,648
24
89,751
719
54
65,706
1,143
84
6,955
1,470
25
89,032
718
55
64,563
1,199
85
5,485
1,202
26
88,314
718
56
63,364
1,260
86
4,193
1,114
27
87,596
718
57
62,104
1,325
87
3,079
933
28
86,878
718
58
60,779
1,394
88
2,146
744
29
86,160
719
59
59,385
1,468
89
1,402
555
30
85,441
720
60
57,917
1,546
90
847
385
31
84,721
721
61
56,371
1,628
91
462
246
32
84,000
723 i
62
54,743
1,713
92
216
137
33
83,277
726
63
53,030
1,800
93
79
58
34
82,551
729 ;
64
51,230
1,889
94
21
18
35
81,822
732 :
65
49,341
1,980
95
3
3
36
81090
737
66
47,361
2,070
37
80,353
742
67
45,291
2,158
38
79,611
749
68
43,1&3
2,243
39
78,862
756
69
40,890
2,321
Notes. — 1. Wigglesicorth's tables, prepared from data in this country,
have been adopted by Massachusetts in estimating life estates.
298 Appendix.
2. Among the prominent English tables of mortality are the Carlisle
tables by Milne, and the Northampton tables by Dr. Price. The former
are generally used in England.
711. According to the Carlisle tables, of 10000 persons born
together, 5528 reach 32, and 2771 reach G7 years of age. The
expectation of life to the age of 67 therefore, of a person now
32 is §||-|- = \ nearly, or 1 chance in 2.
Illustration. — What is the net premium to insure $1 during the
year succeeding the age of 60, the present age being 40 ?
By Table, the number living at 60 is, ... . 57917
61 is, ... . 56371
The number dying during the year is, . 1546
Pres. w. of $1, due in 20 y. at 4=% (Art. 306, N. 3), . $.45638
Present worth of $1546 = $705,563
By Table, the number surviving at 40 is 78106.
Then, 705.563-^-78106 = .00903, net premium.
Explanation. — The Table above shows that of 78106 persons now
living at the age of 40, 1546 will die during the year succeeding 60. The
present worth at 4 % of $1546 payable 20 years hence is $705,563, which
divided among 78106 persons now living, gives the premium which would
secure an insurance of $1 to each of them in case of death during the
given year.
LIFE ESTATES AND ANNUITIES.
712. The rule prescribed in New York State for estimating
the value of life estates is as follows :
84th Rule of the Supreme Court to ascertain the gross sum
in payment of life estates.
Whenever a party, as a tenant for life, or by the courtesy, or in dower,
is entitled to the annual interest or income of any sum paid into court,
and invested in permanent securities, such party shall be charged with
the expense of investing such sum, and of receiving and paying over the
interest or income thereof ; but if such party is willing and consents to
accept a gross sum in lieu of such annual interest or income for life, the
same shall be estimated according to the then value of an annuity at six
per cent on the principal sum, during the probable life of such person
according to the Portsmouth, or
Life Estates and Annuities.
299
Northampton Annuity Table.
713. Showing the value of an annuity of $1 at 6%.
Age.
No. of years
purchase
the Annuity
is worth.
Age.
No. of years
purchase
the Annuity
is worth.
Age.
No. of years
purchase
the Annuity
is worth.
|
! Age.
Xo. of years
purchase
the Annuity
is worth.
1
10.107
25
12.063
49
9.563
73
4.781
2
11.724
26
11.992
50
9.417
74
4.565
3
12.348
27
11.917
51
9.273
75
4.354
4
12.769
28
11.841
52
9. 129
76
4.154
5
12.962
29
11.763
53
9.980
77
3.952
6
13.156
30
11.682
54
8.827
78
3.742
7
13.275
31
11.598
55
8.670
79
3.C14
8
13.337
32
11.512
56
8.509
80
3.281
9
13.335
33
11.423
57
8.343
81
3.156
10
13.285
34
11.331
58
8.173
82
2.926
11
13.212
35
11.236
59
7.999.
83
2.713
12
13.130
36
11.137
60
7.820
84
2.551
13
13.044
37
11.035
61
7.637
85
2.402
14
12.953
38
10.929
62
7.449
86
2.266
15
12.857
39
10.819
63
7.253
87
2.138
16
12.755
40
10.705
64
7.052
88
2.031
17
12.655
41
10.589
65
6.841
89
1.882
18
12.562
42
10.473
66
6.625
90
1.689
19
12.477
43
10.356
67
6.405
91
1.422
20
12.398
44
10.235
68
6.179
92
1.136
21
12.329
45
10.110
69
5.949
93
0.806
22
12.265
46
9.090
70
5.716
94
0.518
23
12.200
47
9.846
71
5.479
24
12.132
48
9.707 j
72
5.241
Rule. — Calculate the interest at 6%, for one year, upon
the sum to the income of which the person is entitled.
Multiply this int. by the number of years purchase set
opposite the person's age in the Table, and the product is
the gross value of the life estate of such person in said sum.
l. If a widow 42 years of age is entitled to dower in real
estate worth $10500, what is the gross present value of her
right of dower ?
300 Appendix.
Solution.— J of $10500 = $3500; int. 1 yr. at 6% =$210.00. The
number of years' purchase which an annuity of $1 is worth at the age of
42 is 10.473, and $210 x 10.473 = $2199.33, Ans.
2. If a man 60 years of age is tenant by the courtesy in the
whole of an estate of $8000, what is the gross value of his life
estate at present ?
Note. — If the annuities are payable semi-annually, one-fifth of the
value of a year's purchase should be added to those values.
3. A lady whose estate was valued at $500000 died, leaving
her husband, then 45 years old, a life interest in the whole
estate ; what was the gross value of his interest at her death ?
4. A man left an estate worth $15000, of which his widow,
aged 54, was to receive during her life the interest on J, payable
semi-annually ; what was the gross value of her portion in the
premises.
5. A gentleman purchased a life annuity of $1000, belonging
to a person 20 years old; what should it have cost him?
BUSINESS INFORMATION AND FORMS.*
R ECEI PTS.
714. A Receipt is a written acknowledgment that a debt
is paid.
Note. — A man is not bound by laic to give a receipt ; but by courtesy
and custom they are always given when desired.
715. A full receipt states the amount received, the date,
place, and kind of payment, by whom and in whose behalf the
payment was made, by whom and in whose behalf received,
and to what debt or purpose it is to be applied.
When the receipt is signed by the person to whom the pay-
ment was due, his signature is enough. But when the business
is done through an agent, he writes his principal's name, and
his own name below it, with "per" or "by" as a prefix to
signify the agency.
* For forms of Bills, Notes, Drafts--, etc., see pp. 79, 118, 133-136.
Business Information and Forms. 301
Notes. — 1. Partial payments should be endorsed on the note or bond,
and the party making the payment should also take a receipt for it.
8. When a receipt is given by a person who makes his mark instead of
writing his name, it should be witnessed.
Receipt in Full.
S225 T 7 / W . Boston, Jan. 31, 1884.
Received from H J. Smith, Two Hundred Twenty-five ffy
Dollars, in full of all demands, to date.
Osgood & Co.,
per W. Simmons.
For Payment on Account.
Philadelphia, Feb. 4, 1884.
Received from Wm. Rowland, One Hundred Forty-five fyy
Dollars, on account.
For a Note.
New York, March 1, 1884.
Received from Everett Graw & Co., their note of this
date, at three months, in our favor, for Eighteen Hundred
Tiventy-seven f-fo Dollars, which, when paid, will be in full
for account rendered to 28th inst.
$1827^° . J- C. Byrnes & Co.
Receipt for Interest.
New York, Jan. 15, 1884.
Received of Ginn, Heath & Co., Two Hundred Forty -six
Dollars, in full for six months interest due this day on their
Bond to me, bearing date Oct. 18, 1882, for Eight Thousand
Two Hundred Dollars.
$246. L- E. Clark.
Due Bill for Goods.
New York, Feb. 6, 1884.
Due to Henry Jones, on demand, Twenty-five -ffo Dollars,
to be paid in goods from my store.
T®Kjr~ K. H. Macy.
302 Appendix.
Order for Goods.
Brooklyn, May 1, 1884.
Messrs. Journeay & Burnham,
Gentlemen :— Please pay to John Wood, or order, Sixty-
three Dollars in goods from your store, and charge the same to
our account.
Burtis & Co.
Installment Receipt.
CD
O
CD
$2000. 400 Share s.
Brooklyn (£. E. ft. QTompanrj.
Received, Brooklyn, Jan. £9, 1S&4, of A. J. Pouch,
Two Thousand (Xollai^s, being Tvjenty-fLve (Dollars per
Share, and the Ihird Installment on Four Hundred
Shares of the Capital Stock of the Brooklyn Elevated
Railroad Company; for which said Shares a full
Certificate will be given, upon payment of all Install-
ments due thereon, and the surrender of this Certificate.
C D , A B ,
Secretary, (president.
Shipping Receipt.
Albany, Jfay 9, '84-.
JHbany,Jtfay 9, '84- \ Received from Wm. Wfills $ Co., in
,„- . ., , , ■ good order, on board the C. Vibbard
Shipped on board '
bound for J\[ew York, the packages
Ijound for_ . marked and entered as below :
(
) Mar-hs
(Packages \ J & 4 doz. boxes Oswego Starch.
JAarks J M> °- 6 barrels Apples.
RoU. B. Smith , fig't.
Business Information, and Forms. 303
Bank D raft.
No. 2350.
Auburn <Eitn Sauk.
$254 . Auburn, Feb 24, 18 '8 4
(Pay to the order of Charles T. Burtis
_. Two Hundred Fifty-four (Dollars.
To JVassau Flank] ) James M. Seymour,
JTew York ) Cashier.
Dividend Check.
JTew York, Jdaroh 12, 188//.
XlUctjanics' National Bank.
(Pay to Charles T. JlUlg or fearer,
Four Hundred Fifty-eight 'Dollars,
and charge to (Dividend JJo 35.
_____ H. B. Smith,
$408 . General F>ook Keeper.
General Form of Agreement.
This Agreement made the day of between A— B — of
City and State , of the first part, and C — D — of City and
State of the second part,
WITNESSETH: — That the said G D , party of the second part,
in consideration of the sum hereinafter named, doth covenant and agree
to and with the said A B of the first part, that (insert agreement).
And the said party of the first part doth covenant and agree to pay unto
the said C D (insert agreement of A B .)
And for the true and faithful performance of all agreements above
mentioned, the parties to these presents bind themselves each unto the
other, in the sum of dollars as fixed damages to be paid by the
failing party.
In witness whereof we have hereunto set our hands and seals the day
and year first above written.
Signed, sealed, and delivered ) A B . (Seal.
in the presence of \ C — D . (Seal.)
304 ^Appendix.
716. Letters of Credit can be procured from Foreign
Exchange Bankers, by depositing the amount in money or m
securities. A small commission is charged besides the regular
rate of exchange. (Art. 451.)
Circular Letter of Credit.
No. B S6581. New yoRK Feb ^ mL
Gentlemen : — We request that you will have the goodness to
furnish Mr. Henry R. Rusted, the bearer, whose signature is
at foot, with any funds he may require to the extent of £500 (say
Five Hundred Pounds Sterling), against his drafts upon
Messrs. Brown, Shipley & Co., London; each draft must
bear the number (No. » 36581) of this letter, and ive engage
that the same shall meet due honor.
Whatever sums Mr. Husted may take up, you will please
endorse on the back of this Circular letter, which is to continue
in force till Feb. 22, 1885, from the present date, Feb. 22, 188 %
We are respectfully, gentlemen,
Your obedient humble servants,
Brown Brothers & Co.
The Signature of
Henry R. Husted.
To Messieurs the Bankers,
Mentioned on the third page of this Letter of Credit.
INSTRUMENTS UNDER SEAL.
717. A Contract is a formal bargain made between two or
more persons, upon sufficient consideration, to do or not to do
some act which shall be lawful.
718. A Deed is a writing or instrument signed, sealed,
and delivered. As generally used, it is for the conveyance of
property.
719. A Bond is a sealed obligation for the payment of
money, and usually has a penalty annexed in case of failure to
comply with the conditions annexed.
Book Accounts. 305
720. Ground Rents are leases of building lots, the rents of
which are considered equal to the int. on the value of the land.
Note. — Bonds and Mortgages on real estate, and Ground Rents are
regarded with a good degree of favor as investments.
721. A Fee-Simple interest is absolute ownership in an estate.
722. A Ground Rent Deed conveys land with a reservation
of a specified sum of money in the nature of rent to be paid at
stated times, and may be for life, for a term of years, or in fee.
Notes. — 1. Instruments under seal are not barred by the statute of limita-
tions like ordinary debts.
2. In ordinary cases where the consideration is expressed, there is
no difference between an agreement under seal or otherwise, except that
the former can be more easily proved and is therefore to be preferred.
BOOK ACCOUNTS.
723. In order to collect a debt on the evidence of a book
account, a full copy of the account must be made out, and it
must be accompanied with an affidavit, as follows :
Form of Affidavit for Goods Sold and Delivered.
State of
County of
Henry Smith of being duly sworn (or affirmed), deposes and
says, that James Brown of , County of , and State of ,
is justly and truly indebted unto him, the deponent, in the sum of
dollars, for goods sold and delivered by him to the said James Brown ;
and that he has given credit to the said James Brown for all payments
and set-offs to which he is entitled ; and that the balance claimed, accord-
ing to the foregoing account, is justly due; and that the said account is
correctly stated.
Sworn and subscribed this day of , a. d., 1884, before me
Charles C. Jones,
Commissioner for the State of .
724. Items and dates should be given in the account, as a
general charge cannot be sustained by evidence of this kind.
The entry must be made in form at the date of purchase for
the purpose of charging the debtor, not as a mere memo-
randum.
20
306
Appendix.
Note. — In order to be admissible as evidence, entries should be made
without alteration, erasure, or interlineation, and by a person authorized
to attend to that department.
The Statute of Limitations of the United States.
725. The time within which suit must be commenced for
the collection of a debt, varies in different classes of cases from
one to twenty years, and differs in different States.*
For accounts m general it begins from the date of the last
item or payment, and in every case the time is renewed by
every partial payment.
States and Terri-
tories.
Alabama ...
Arkansas . . .
Arizona
California...
Colorado —
Connecticut
Dakota
Delaware . . .
Dist. of Columbia
Florida
Georgia
Tdabo
Illinois
Indiana
Iowa
Kansas
Kentucky
Louisiana
Maine
Maryland
Massacbusetts . . .
Michigan
Minnesota
Mississippi
6
<
a
o
o,
O
11
if
a
Yrs.
1
bo
"2
Yrs.
Yrs.
Yrs.
3
6
10
20
3
5
5
10
2
4
4
5
2
4
4
5
6
6
6
3
6
6
17
17
6
6
20
20
3
6
20
20
3
3
12
12
4
5
20
20
4
6
20
2
4
4
5
5
10
10
20
6
10
20
10
5
10
10
20
3
5
5
15
5
15
15
15
3
5
10
10
6
6
20
20
3
3
12
12
6
6
20
20
G
6
10
10
6
6
10
10
3
6
7
7
States and Terri-
tories.
Missouri
Montana. ..
Nebraska . . .
Nevada
New Hampshire
New Jersey
New Mexico . . .
New York
North Carolina.
Ohio
Oregon
Pennsylvania . .
Rhode Island. . .
South Carolina.
Tennessee
Texas
Utah
Vermont
Virginia
Washington ....
W. Virginia
Wisconsin
Wyoming
Yrs.
5
B
4
2
O a
Yrs.
10
10
5
Yrs.
10
10
5
4
20
16
6
20
10
15
10
20
20
20
10
4
4
8
20
6
10
20
5
Yrs.
20
10
5
5
20
20"
15
20
10
15
10
Notes.— 1. In the States of Kentucky and Virginia a store account
may run two years. In W. Va. 3 years.
2. In the case of notes, etc., if the debtor at any time makes a written
acknowledgment of indebtedness, the claim is renewed.
* Clark's Commercial Law.
Stock Clearing Houses.
307
STOCK CLEARING- HOUSES.
726. A Stock Clearing House is an association of dealers,
to facilitate the balancing of transactions in Stocks or Bonds.
Note. — Stock Clearing Houses are in successful operation in some of
the large cities of Europe. An attempt was made to establish one in
New York, which was partially successful. The following is a glimpse
of the plan proposed :
727. Each member reports to the Clearing House on a blank
form, the names of parties with whom he has had dealings,
and the balances in his favor or against him, of all transactions.
At 12 : 30 the clerks in the Clearing House tabulate all the
balances as reported, and notify each member from whom he
will receive, or to whom he will deliver the stocks shown by
his report.
Note. — A settling price is fixed by the Clearing House for each stock,
and members are required to receive only as many shares of any stock as
they may have bought more than they have sold. The difference between
the "settling price" and the buying or selling prices of the original
transactions must be paid in cash.
The followir
ig is the form ol
a Report
to the Clearing House :
To Receive.
To Deliver.
Balance.
U. P.
N.Y.C.
Name.
U. P.
N.Y.C.
To Receive. To Deliver.
750
500
J. G. Hewitt
C. T. Burtis
800
Chas. S
100
.Andr
evvs.
U. P. 50
400 N. Y. 0.
800
300
Chas. S. Andrews. .
J. G. Hewitt 1
I 500 1
i 1000 1 1
C. T. Burtis.
TJ. P. 200
N. Y. C 200
1000
100
C. T. Burtis
Chas. S. Andrews..!
1 300 |
1 750 1
J. G. Hewitt.
250 U. P.
N. Y. C. 200
Explanation. — These three reports show that 2550 shares of TJ. P.
Railroad Stock and 900 shares N. Y. Central were bought and sold ; but
the transactions are settled through the Clearing House by the delivery of
400 shares of N. Y. C. stock and 250 shares of U. P. stock.
Thus, Andrews' balance shows that he is to receive 400 N. Y. C, Burth
and Hewitt each report balances of 200 N. Y. C. to deliver. They are
notified by the Clearing House to deliver to Andrews.
308 Appeiidkc.
728o Abbreviations used in Stock Quotations.
Ad Adjustments.
Allts Allotments. Applied to shares giving the
privilege of others, at specified prices.
As , Assented.
U. S. c. 3's, or 4's U. S. currency bonds at 3% or 4% int.
B. c Between calls.
B. 30 Buyer's option at 30 d.
B. 20, flat Buyer's option at 20 d. without interest.
Bds., or b Bonds.
" C " before price Cash.
Certs Certificates.
Com Common stock.
Cons., or en Consolidated.
Conv., or cv Convertible. May be exchanged.
Coup. , or c Coupon.
Cur., or c Currency.
Deb Debentures.
D. s. f. 5's Deb. secured by sinking fund, at 5% int.
Div Dividend.
Ex. d., or e. d Without dividend.
Ex. coup Without coupon.
Ext Extended.
Fd Funded.
Gen General.
Gtd Guaranteed.
L. g Land grants.
L., or 1 Lot, the aggregate of several sales.
L. s Land Scrip.
Inc. 6's Income bonds, at 6% interest.
Mort., or m Mortgage.
N. 6's New Q% bonds.
Pref., or pf Preferred.
Pur. m. fd Purchase money funded.
Reg., or r Registered.
R. e . . Registered and extended.
Sep Scrip.
S. 30 Seller's option at 30 days.
S. F., or s. f Sinking fund.
W. n Without notice.
2d M. s. f . 7's '85 Sinking fund bonds secured by 2d mort.,
payable at 7% in 1885.
Con. M, & s. f. 6's Consolidated mort. and sinking fund, at 6%.
V| S^— ' ■ * ■■■♦
1 ISOELL AKEOTJS JP|XAMPLES.
1. What number is that to which if 16 be added, then 25 subtracted
from the sum, the difference be multiplied by 21, and the product divided
by 28, the quotient will be 63 ?
2. How many gills, pints, and quarts, of each, an equal number, are
there in a hogshead ?
3. A company of 175 men have provisions enough to last 6 months ;
if 47 of them leave, how long will the same provisions last those that
remain ?
4. A farmer had 45 head of cattle, and hay enough to last them 5|
months ; if he buys 13 head more, how long will the same hay last the
whole ?
5. Six men bought a ship together worth $45268, for which A paid \
of the whole, B \, and the others paid the balance equally ; how much
-did each pay ?
6. A manufacturer hired an equal number of men, women, and
children, at 75 cts., 62| cts , and 37^ cts. each per day, and the daily
wages of the whole amount to $113.75 ; how many of each class did he
employ ?
7. A man bought a drove of horses for $17947, and after selling 62 of
them, at $83 apiece, the remainder netted him $51 each ; how many did
he buy, and for how much apiece must he sell them to make $2510 by
the operation ?
8. A merchant bought 868 yards of cloth at $6.50 a yard ; he after-
wards sold 253 yards at $5| per yard to one customer, and 368 yards at
$8] to another ; how many yards had he left, and what was the net cost
to him ?
9. A man bought 148 acres of land, at $23 per acre, and 260 acres at
$17 ; he afterwards sold 300 acres at $25 ; how many acres had he left,
and what did it stand him in per acre ?
10. A garrison of 450 men has provisions for 5 months ; how many
must be discharged, that the same provisions may last 71 months?
11. In a certain county are 105260 topers, who drink 3 glasses of liquor
apiece every day, at a cost to them of 8 cents a glass ; how many barrels
of flour would this useless expense pay for, per annum, when flour is $8
a barrel ?
310 Miscellaneous Examples.
12. A grocer having bought 1328 pounds of butter at 27* cents a pound,
afterwards sold 263 pounds at 28f cents, and 375 pounds at 29| cents ; how
much had he left, and what must he get for it in order to gain $215 by
the operation ?
13. A drover brought 1463 sheep, and 285 lambs to market, the former
costing him $5.15 per head, and the latter $2.17 per head ; having sold
320 sheep and lambs together at $5| a head, he wishes to know at what
price per head he must sell the remainder in order to gain 20% on the
money invested.
14. A man bought a lot of silver containing tea-spoons, dessert-spoons,
and table-spoons, of each an equal number, weighing respectively 5 pwt.
6 gr. ; 13 pwt. 10 gr. ; and 1 oz. 11 pwt. 8 gr. ; the weight of the whole
was 6 lb. 8 oz. ; how many spoons were there of each kind?
15. A man bought a drove consisting of cows, calves, and oxen, in
equal numbers, for $3693.375 ; for cows he gave $27i apiece, for calves
$4^, and for oxen $43f ; how many were there of each kind ?
16. A liberty pole 108 ft. high was broken in such a manner that its
top struck the ground 36 ft. from its foot, the other end resting on the
top of the part left standing ; how high from the ground was it broken.
(Art. 704.)
17. A man pays $1500 per annum interest on various mortgages, at
Ifo ; how much money does he hire?
18. What must be the face of a note to cover the discount for 90 d., at
6%, and yield $472.86?
19. A man spent | and £ of his money and $20 besides, when he had
$80 left ; how much had he at first ?
20. A barn was 38 ft. wide at the gable ends, and the ridge of the
roof was 5 ft. above the eaves ; how many ft. of boards would cover the
gable ends ?
21. Sold goods for $2543.50 at a profit of 5%, and took a note at 60 d.,
which was discounted the same day, at 6% per annum; what was the
net profit ?
22. Which is the better investment, U. S. 3's, at 103|, or Bait. & O.
1st 6's 1919, atll4i?
23. Bought Boston H. & E. 1st M. 7's due in 1900, at 114; what is the
per cent income on the investment ?
24. What is the weight of an iron cylinder 15 ft. long and 10 in. in
diameter, allowing 4 cu. in. to a pound ?
25. A man having a triangular gore of land, one side of which was 256
rods long, and the perpendicular distance from this side to the opposite
corner, 72 rods, exchanged it for a square farm of equal area ; what was
the side of his farm ?
Miscellaneous Examples. 311
26. An importer bought 1565 yards of silk, at 5s. Gd. per yard ; paid
£7 12s. for freight, 25 per cent duties, and remitted a bill on London at
9£ per cent premium ; how must he sell it per yard on 6 months, jn order
to make 12^ per cent, allowing 7 per cent interest ?
27. A merchant sent his agent in London 425 bales of cotton weighing
356 pounds apiece, which cost him 9| cents a pound ; the agent paid f d. a
pound for freight, £43 for cartage, sold it at 8d, a pound, and charged
2h per cent commission. If the merchant sells a bill of exchange for the
amount, at 10|% , will he make or lose by the operation. How much ?
23. "What rate-per cent income will be realized from 8% stock bought
at 95, if paid at par in 20 yr.?
29. Four notes of $500 each are due in 3, 6, 9, and 12 months respec-
tively ; in how many months may they all be paid at one time ?
30. Which is the greater, an income of $500 per annum for 15 years to
come, or the reversion in perpetuity of $500 annuity at the end of 15 years,
interest at 6 per cent ?
31. Which is the better investment, 7% bonds, or a house which rents
for $240 a year, taxes being $30.50, and annual repairs $40 ?
32. What is the average distance between stations on a R. R. that is
149 m. 234 r. 4 yd. 2 ft. long, the number of stations being 18 including
one at each end of the road ?
33. How must goods which, cost 60 cents a yard be marked, that the
merchant may discount 20% from the price and still make 20% ?
34. How many shares of mining stock at 80 must be sold, that the
proceeds invested in Iowa Mid. 1st M. 8's, due in 1900, may yield a profit
of $960 if bought at 108 ?
35. A father left an estate valued at $11740 to 3 sons, whose ages were
15, 13, and 11 respectively, to be so divided that if put at interest at 5%,
the amount should be equal as the sons came of age ; what sum did he
will to each ?
36. Bought $600 worth of books at a discount of 33^% from list prices,
and sold them at regular retail price on 6 mo. credit ; what was the per
cent profit, if money was worth 6% ?
37. What must I pay to insure a factory valued at $21000 at £ % ; and
the machinery valued at $15400 at f % ?
38. Sold a bill of goods amounting to $1875, of which 15% was payable
in cash, 25% in 3 mo., 20% in 4 mo., and the balance in 6 months ; how
much cash would pay the debt at once, when money is 6*% per annum ?
39. A miller had 400 barrels of flour worth $6£ a barrel, 15% ©f it was
destroyed by a freshet ; he sold the remainder at $8.50 a barrel ; how
much did he gain or lose ?
40. Which is the more profitable investment, to buy flour at $8.50 a bar-
rel on a credit of 6 months, or at $8.25 on 2 mo. when money is worth 6%?
312 Miscellaneous Examples.
41. A cylindrical tank 30 ft. in diameter and 15 ft. deep is filled with
oil ; how many gallons does it contain and what is its value at 4$ cents a
gallon ?
42. A merchant's retail price yields a profit of 25% ; if he discounts
10% at wholesale, what per cent does he gain at wholesale?
43. Bought Chesapeake & Ohio 1st pf. R. R. Stock for 26^, the same
Stock sold last year for 32£ ; how much would a man lose who bought
$5000 worth last year ?
44. At what price must 6 % bonds payable in 10 years be bought to
realize 8£% on the investment?
45. What is the per cent income in 1884 on Chic. R. I. & Pac. 6's coup.,
payable at par in 1917, bought at 123£ ?
46. Divide $1860 among A, B, and C, so that for every $5 given to A,
B may receive $4, and for every $3 given to B, C may receive $1.
47. Divide § into two parts, so that one of them is greater than the
other by f .
48. A mine is worth $50000 ; a person sold T 3 <r of his share for $3750 •
what part of the mine did he own ?
49. A can do as much work in 2 days, as B can do in 3 days, together
they did a certain job in 12 days; in -what time would A alone have
done it ? In what time would B ?
50. A piece of land is 95£ r. long, and 58| r. wide ; how many house
lots of equal size, the largest possible, can be made from it ?
51. When stock originally worth $4000, sells for $4250, what is the
per cent premium ?
52. In 1870 the population of Chicago was 298977, which was 1905
more than f the population of Brooklyn. What was the population of
Brooklyn at that time ?
53. The population of Brooklyn in 1880 was 566663, that of Chicago
503185 ; what was the % gain of each ?
54. The population of New York in 1870 was 942292 ; in 1880 it was
1206299 ; what per cent was the gain ?
55. What principal on interest from March 1, 1880 to Nov. 1, 1884, at
6%, will amount to $4401.60?
56. A merchant sells a quantity of goods at such a price that | of the
selling price will cover the cost ; what is his gain per cent ?
57. The crown of a certain king consisted of gold and silver in the
ratio of 2 : 1 ; what was the per cent of each ?
58. A bookseller has 150 books to pack in two boxes, whose dimensions
are as follows : the larger one 4| feet., 2 ft. 8 in., and 2 ft. ; the smaller
4 ft., 2£ ft., and 1| ft.; in the smaller he can pack 50 books ; how many
will remain unpacked when he has filled both boxes, the books being
of the same size ?
Miscellaneous Examples. 313
59. American gold coin contains 1 oz. alloy to 9 oz. pure gold ; what
quantity of each will a ton of double eagles contain ?
60. Divide the number 7980 into 3 parts in the proportion of 5, 7, and 9.
61. An Iron Manufacturing Co. made an assessment of 6% on its
capital stock, par value $50 ; how much must a man pay who owned
18000 shares of stock ?
62. A father dividing his estate between 2 sons, gave the younger
$2800, which was 75% of the share of the elder ; what was the amount of
his estate ?
63. 25260 is 20% more than what number?
64. Sold 2 droves of cattle for $11360 a piece ; on one I gained 12^%,
on the other lost 8% ; required the cost of each drove, and the net gain %
on the transaction.
65. Sold goods for $450 and made 25% ; what per cent should I Rave
made had I sold them for $6)0 ?
66. Paid $8.40 apiece for dictionaries ; becoming shop-worn, deducted
25% from the marked price, and yet made 10% profit; required the
marked price?
67. What length of paper f yd. wide will cover a wall 15 ft. 8 in. by
11 ft. 3 in.?
68. Find the circumference of a wheel whose diameter is 4 ft. 8 in.;
how many times will it turn round in 10£ miles ?
69. A dealer bought 6 hectars of land for $1050, and divided it into lots
of 8 ars each ; what must be the price per lot to gain 30% ?
70. A note of $600 was given Jan. 1, at 6% interest, on which a pay-
ment of $225 was made July 3. Oct. 15, the note was bought at 3 %
discount on its value at that time ; how much was paid for it ?
71. | of C's money and f of D's equal $900 ; and f of D's is twice f of
C's money ; what sum has each ?
72. In how many days will $75 at 7 T 3 ¥ % int. gain 80 cents ?
73. A note of $800 dated Jan. 1, 1881, had an indorsement June 4,
1881, of $250, and Oct. 9, '81, $120 ; what was due Apr. 26, '82, interest
being 6% ?
74. A man owes $12000, of which \ is due in 5 mo., \ in 9 mo., and the
remainder in 15 mo.; what is the present worth of the debt?
75. The true discount of a debt of $1215 due in 10 mo. 20 d. is $90 ;
what is the rate ?
76. What is the interest in United States money on £167 8s. 3d , at
7 T 3 ^%, from June 10, '81, to May 2, '82 ?
77. Sold a cow so that -f of the gain was equal to T ^ the cost ; what
was the gain % ?
314 Miscellaneous Examples.
78. A father wills an estate of #19000 as follows : to each of 3 sons he
gives $1000 more than to his daughter, and to his widow $1000 more than
to all the children ; what is the share of each ?
79. A storehouse takes fire in which A has 350 bbl. of flour, worth $8.25
a bbl.; B has 275 bbl., worth $9 a bbl.; and C has 2500 bushels of corn,
worth $1.10 a bu.; the damaged flour and grain are sold all together for
•$3100 : how shall this be divided between A, B, and C ; what is each man's
actual loss, and his loss per cent ?
80. What is the difference in value of two pieces of land one of
which is 87 ft. by 42 ft., the other 57 ft. square, both being worth $1.75 a
square foot?
81. Find the cash balance of the following account:
Jones Bros, in account with Loeser & Co.
Dr. Apr. 10, 1884, to mdse. $150; Apr. 30, $400; May 16, $90; May
24, $100 ; June 1, $300 ; June 10, $340; June 26, $200.
Or. Apr. 12, 1884, cash $250 ; May 1, $180 ; June 7, $400 ; June 25,
$564. If the acct. is settled July 1, 1884, what will be the true balance
allowing each item to draw interest from its date, at 6 per cent ?
82. The duty on a quantity of coffee in bags containing 185 lbs. each,
value 14 cts. a pound, was $3591.75; the duty at 30%, tare 5% ; how
many bags were imported ?
83. The taxable property of a village is $860000, the number of polls
at $1.50 each is 620 ; a Union School -house is to be built, worth $22860.25;
allowing 3 % for collecting, what will be the tax rate ?
84. What tax will a man be required to pay whose property is valued
at $16420, and who pays for 2 polls ?
85. A Milwaukee grain dealer invested as follows : 800 bu. red wheat,
at $1.30; 500 bu. white, at $1.60; and 300 bu. spring wheat, at $1.20.
The whole was shipped to his agent in New York, who sold the first, at
15$> advance; the second, at 20% advance; and the third at $1.15 a
bushel; his expenses were $112.25, his commission 3%; what were the
net proceeds ?
86. In the above speculation, what per cent was the grain dealer's
gain?
87. A merchant sells goods at different times as follows: May 2, a bill
of $800 on 4 mo.; May 15, a bill of $1200 on 6 mo. ; June 1, a bill of $1500
on 8 mo. ; and June 15, $800 for cash ; he then agrees to take a note for
the whole, at 60 days with interest ; what should be the date of the note ?
88. March 4, 1884, a note for $1000, at 6% interest, was given, on
which the following indorsements were afterwards made: May 1, 1884,
$75; July 17, 1884, $15.50; Dec. 1, 1884, $30.50; Dec. 31, 1884, $400;
Jan. 31, 1835, $250 ; what was due Aug. 18, 1885 ?
Appendix.
315
TABLE I.
THE AMOUNT OF AN ANNUITY OF $1, AT COMP. INT., FROM 1 YR. TO 50.
Yr.
1
3 per ct.
%% per ct.
4 per ct.
5 per ct.
6 per ct.
7 perct.
Yr.
1.000000
1.000000
1.000000
1.000000
1.000000
1.000000
1
2
2.030000
2.035000
2.040000
2.050000
2.060000
2.070000
2
3
3.090900
3.106225
3.121600
3.152500
3.183600
3.214900
3
4
4.183627
4.214943
4.240464
4.310125
4.374616
4.439943
4
5
5.309136
5.362466
5.416322
5.525631
5.637093
. 5.750739
5
6
6.468410
6.550152
6.632975
6.801913
6.975319
7.153291
6
7
7.662402
7.779408
7.898294
8.142003
8.393838
8.654021
7
8
8.892336
9.051687
9.214226
9.549109
9.S97468
10.259803
8
9
10.159106
10.368496
10.582795
11.026564
11.491316
11.977989
9
10
11.463879
11.731393
12.006107
12.577893
13.180795
13.816448
10
11
12.807796
13.141992
13.486351
14.206787
14.971643
15.783599
11
12
14.192029
14.601962
15.025805
15.917127
16.869941
17.888451
12
13
15.617790
16.113030
16.626838
17.712983
18.882138
20.140643
13
14
17.086324
17.676986
18.291911
19.598632
21.015066
22.550488
14
15
18.598914
19.295681
20.023588
21.578564
23.275971
25.129022
15
16
20.156881
20.971030
21.824531
23.657492
25.672528
27.888054
16
17
21.761588
22.705016
23.697512
25.840366
28.212880
30.840217
17
18
23.414436
24.499691
25.645413
88.132886
30.905653
33.999033
18
19
25.416868
26.357180
27.671229
30.539004
83.759992
37.378965
19
20
26.870374
28.279682
29.778078
33.065954
30.785592
40.995492
20
21
28.676486
30.269471
31.969202
35:719252
39.992727
44.865177
21
22
30.536780
32.328902
34.247970
38.505214
43.392290
49.005739
22
23
32.452884
34.460414
36.617889 •
41.4:30475
46.995828
53.436141
23
24
34.426470
36.666528
39.082604
44.501999
50.815577
58.176671
24
25
36.459264
38.949857
41.645908
47.727099
54.864512
63.249030
25
26
38 553042
41.313102
44.311745
51.113454
59.156383
68676470
26
27
40.709634
43.759060
47.084214
54.66'.n26
63.705706
74.483823
27
28
42.930928
46.290627
49.967583
58.402583
68.528112
80.697691
28
29
45.218850
48.910799
52.966286
68.822719
73.639798
87.346529
29
30
47.575416
51.622677
56.084938
66.438847
79.058186
94.460786
30
31
50.002678
54.429471
59.328335
70.760790
84.801677
102.073041
31
32
52.502759
57.334502
62.701469
75.298829
90.889778
110.218154
32
33
55.077841
60.341210
66.209527
80.063771
97343165
118.933425
33
34
57.7:30177
63.453152
69.857909
85.066959
104.183755
128.258765
34
33
60.462082
66.674013
73.652225
90.320307
111.434780
138.236878
35
36
63.275944
70.007603
77.598314
95.836323
119.120867
148.913460
36
37
66.174223
73.457869
81.702246
101.628139
127.268119
160.337400
37
38
69.159449
77.028895
85.970336
107.709546
135.904206
172.561020
38
39
72.234233
80.724906
90.409150
114.095023
145.058458
185.640292
39
40
75.401260
84.550278
95.025516
120.790774
154.761966
199.635112
40
41
• 78.663296
88.509537
99.826536
127.839763
165.047684
214.609570
41
42
82.023196
92.607371
104.819598
135.231751
175.950545
230.632240
42
43
85.483892
96.848629
110.012.382
142.993:339
187.507577
247.776496
43
44
89.048409
101.238331
115.412877
151.143006
199.758032
266.120851
44
45
92.719861
105.781673
121.029392
159.700156
212.743514
285.749311
45
46
96.501457
110.484031
126.870568
168.685164
226.508125
306.751763
46
47
100.396501
115.350973
132.945390
178.119422
241.098612
329.224386
47
48
104.408396
120.388257
139.263206
188.025393
256.564529
353.270093
48
49
I 10S.540648
125.601846
145.833734
198.426663
272.958401
378.999000
49
50
! 112.796867
130.997910
152.667084
209. 34? 996
290.335905
406.528929
50
316
Annuities,
TABLE II.
THE PEESEXT WORTH OF AN ANNUITY OP $1, PROM 1 YEAR TO 50.
Yr.
1
3 per ct.
3 l / 3 perct.
4 per ct.
5 per ct.
6 per ct.
7 per ct.
Yr.
0.97087
0.96618
0.96154
0.95238
0.94339
0.934579
1
2
1.91347
1.89969
1.88609
1.85941
1.83339
1.808017
2
3
2.82801
2.80164
2.77509
2.72325
2.67301
2.624314
3
4
3.71710
3.67308
3.62990
3.54595
3.46511
3.387207
4
5
4.57971
4.51505
4.45182
4.32948
4.21236
4.100195
5
6
5.41719
5.32855
5.24214
5.07569
4.91732
4.766537
6
7
6.23028
6.11454
6.00205
5.78637
5.58238
5.389286
7
8
7.01969
6.87396
6.73274
6.46321
6.20979
5.971295
8
9
7.78611
7.60769
7.43533
7.10782
6.80169
6.515228
9
10
8.53020
8.31661
8.11090
7.72173
7.36000
7.023577
10
11
9.25262
9.00155
8.76048
8.30641
7.88687
7.498669
11
12
9.95400
9.66333
9.38507
8.86325
8.38384
7.942671
12
13
10.(53495
10.30274
9.68565
9.39357
8.85268
8.357635
13
14
11.29607
10.92052
10.56312
9.89864
9.29498
8.745452
14
15
11.93794
11.51741
11.11839
10.37966
9.71225
9.107898
15
16
12.56110
1-2.09412
11.65230
10.83777
10.10589
9.446632
16
17
13.16612
12 65132
12.16567
11.27407
10.47726
9.763206
17
IS
13.75351
13.18968
12.65930
11.68959
10.82760
10.059070
18
19
14.32380
13.70984
13.13394
12.08532
11.15812
10.335578
19
20
14.87747
14.21240
13.59033
12.46221
11.46992
10.593997
20
21
15.41502
14.69797
14.02916
12.82115
11.76408
10.835527
21
22
15.93692
15.16712
14.45112
13.1(5300
12.04158
11.061241
22
23
16.44361
15.62041
14.85684
13.48857 •
12.30338
11.272187
23
24
16.93554
16.05837
15.24696
13.79864
12.55036
11.469334
24
25
17.41315
16.48151
15.62208
14.09394
12.78336
11.653583
25
26
17.87684
16.89035
15.98277
14.37518
13.00317
11.825779
26
27
18.32703
17.28536
16.32959
14.64303
13.21053
11.986709
27
28
18.76411
17.66702
16.66306
14.89813
13.40616
12.137111
28
29
19.18845
18.03577
16.98371
15.14107
13.59072
12.277674
29
30
19.60044
18.39205
17.29203
15.37245
13.76483
12.409041
30
31
20.00043
18.73628
17.58849
15.59281
13.92909
12.531814
31
32
20.38877
19.06887
17.87355
15.80268
14.08404
12.646555
32
33
20.76579
19.39021
18.14765
16.00255
14.23023
12.753790
33
34
21.13184
19.70068
18.41120
16.19290
14.36814
12.854009
34
35
21.48722
20.00066
18.66461
16.37419
14.49825
12.947672
35
36
21.83225
20.29049
18.90828
16.54685
14.62099
13.035208
36
37
22.16724
20.57053
19.14258
16.71129
14.73678
13.117017
37
38
22.49246
20.84109
19.36786
16.86789
14.84602
13.193473
38
39
22.80822
21.10250
19.58448
17.01704
14.94907
13.264928
39
40
23.11477
21.35507
19.79277
17.15909
15.04630
13.331709
40
41
23.41240
21.59910
19.99305
17.29437
15.13802
13.394120
41
42
23.70136
21.83488
20.18563
17.42321
15.22454
13.452449
42
43
23.98190
22.06269
20.37079
17.54591
15.30617
13.506962
43
44
24.25427
22.28279
20.54884
17.66277
15.38318
13.557908
44
45
24.51871
22.49545
20.72004
17.77407
15.45583
13.605522
45
46
24.77545
22.70092
20 88465
17.88007
15.52437
13.650020
46
47
25.02471
22.89943
21.04294
17.98102
15.58903
13.691608
47
48
25.26671
23.09124
21.19513
18.07716
15.65003
13.730474
48
49
25.50166
23.27656
21.34147
18.16872
15.70757
13.766799
49
50
! 25.72976
23.45562
21.48218
18.25593
15.76186
13.800746
50
Appendix.
317
TABLE III.
AMOUNT OF $1 AT COMPOUND INT., FROM 1 YEAR TO 50.
Yr.
3 per ct. \SY 2 perct.
4 per ct.
5 per ct.
6 per ct.
7 per ct.
8 per ct.
Tr.
1
1.030000 1.035000
1.040000
1.050000
1.060000
1.070000
1.080000
1
2
1.060900 1 1.071225
1.081600
1.102500
1.123600
1.144900
1.166400
.2
3
1.09272? 1.108718
1.124864
1.157625
1.191016
1.225043
1.259712
3
4
1.125509 '< 1.147523
1.169859
1.215506
1.262477
1.310796
1.360489
4
5
1.159274 1.187686
1.216653
1.276282 |
1.338226
1.402552
1.469328
5
6
1.194052
1.229255
1.265319
1.340096
1.418519
1.500730
1.586874
6
7
1.229874
1.272279
1.315932
1.407100
1.503630
1.605781
1.713824
7
8
1.266770
1 .316809
1.368569
1.477455
1.593848
1.718186
1.85093C
8
9
1.304773
1.362897
1.423312
1.551328 |
1.689479
1.8:38459
1.999005
9
10
1.343916
1.410599
1.480244
1.628895 |
1.790848
1.967151
2 158925
10
11
1.384234
1.459970
1.539454
1.710833
1.898299
2.104852
2.331639
11
12
1.425761
1.511069
1.601032
1.795856
2.012196
2.252192
2.518170
12
13
1.468534
1.563956
1.665073
1.885649
2.132928
2.409845
2.719624
13
14
1.512590
1.618694
1.731676
1.979932
2.260904
2.578534
2.937194
14
15
1.557967
1.675349
1.800943
2.078928
2.896558
2.759031
3.172169
15
16
1.604706
1.733986
1.872981
2.182875
2.540352
2.952164
3.425943
16
17
1.652848
1.794675
1.947900
2.292018
2.692773
3.158815
3.700018
17
18
1.702433
1.857481,
2.025816
2.406619
2.854339
3.379931
3.996019
18
19
1.753506
1.922501
2.106849
2.526950
3.025599
3.616526
4.315701
19
20
1.806111
1.989789
2.191123
2.653298
3.207135
3.869683
4.660957
20
21
1.860295
2.059431
2.278768
2.785963
3.399564
4.140561
5.033834
21
22
1.916103
2 131512
2.369919
2.925261
3.603537
4.430400
5.436540
22
23
1.973586
2.206114
2.464715
3.071524
3.819750
4.740528
5.871464
23
24
2.032794
2.283328
2.i 563304
3.225100
4.048935
5.072365
6.341181
24
25
2.093778
2.363245
2.665836
3.386355
4.291871
5.427431
6.848475
25
26
2.156591
2.445959
2.772470
3.555673
4.549383
5.807351
7-96353
26
27
2.221289
2.531567
2.883369
3.733456
4.822346
6.213868
7.988062
27
28
2.287928
2.620177
2.998703
3.920129
5.111687
6.648836
8.627106
28
29
2.356565
2.711878
3.118651
4.116136
5.418388
7.114255
9.3172751 29
30
2.427262
2.806794
3.243397
4.321942
5.743491
7.612253
10.062657
30
31
2.500080
2.905031
3.373133
4.538039
6.088101
8.145110
10.867669
31
32
2.575083
3.006708
3.508059
4.764941
6.4533S7
8.715268
11.737083
32
33
2.652335
3.111942
3.648381
5.003188
6.840590
9.325.337
12.676049
33
34
2.731905
3.220860
3.794316
5.253343
7.251025
9.978110
13.690134 34
35
2.813862
3.333590
3.946089
5.516015
7.686087
10.676578
14.785344
35
36
2.898278
3.450266
4.103932
5.791816
8.147252
11.423939
15.908172
36
37
2.985227
3*71025
4.268090
6.081407
8.636087
12.223614
17.245626
37
38
3.074783
3.696011
4.438813
6.385477
9.154252
13.079277
18.625276
38
39
3.167027
3.S25372
4.616366
6.704751
9.703507
13.994827
20.115298
39
40
3.262038
3.959260
4.801021
7.039989
10.285718
14.974465
21.724522
40
41
3.359899
4.097834
4.993061
7.391988
10.902861
16.022677
23.462483
41
42
3.460696
4.241258
5.192784
7.761587
11.557033
17.144265
25.339482
42
43
3.564517
4.389702
5.400495
8.149667
12.250455
18.344363
27.366640
43
44
3.671452
4.543342
5.616515
8.557150
12.985482
19.628469
29.555972
44
45
3.781596
4.702358
5.841176
8.985008
13.764611
21.002461
31.920449
45
46
3.895044
4.866941
6.074823
9.434258
14.590487
22.472634
34.474085! 46
47
4.011895
5.037284
6.317816
9.905971
15.465917
24.045718
37.232012 47
48
4.132252
5.213589
6.570528
10.401270
16.393872
25.728918
40.210573 48
49
4.256219
5.396065
6.833349
10.921333
17.377504
27.529943
43.427419! 49
50
4.383906
5.584927
7.106683
11.467400
18.420154
29.457039
46.901613 50
Pages 8, 9.
3. 435,5589,14014.
6. 556.
7. 809.
8. 566.
9. 4805.
10. 6454.
11. 6458.
13. 12225.
i£ 15772.
16. $8592.
iX^es 10,11.
18. 6928 votes, less ;
8636 " greater.
19. $149 ch., $201 w.
20. $181 B, $319 A.
21. 1917 less no. ;
2570 greater.
22. 13, 875, 6716.
23. 8.
24. 4, 2.
#5. 63 y. V. 41 y. P.
26. 58 c. 47 a-b. 23 inf
5 Off.
27. 682 more.
Art. 11.— 2. 1255440
3. 1562292.
4. 1441073.
5. 1517644.
7. 6950664.
9, 4526818.
10. 5212999.
11. 6047136.
12. 7956585.
14. 67544325.
rages 12, 13.
16. 465507.
17. 712236.
18. 27600.
19. 3458000.
20. 17520000.
21. 124704000.
22. 495.
23. 737.
25. 62680257.
26. 8435406375.
29. 25038.
SO. 57196.
31. 253377.
32. 323352.
55. 5456256.
36. 860209340.
87. 9067243052.
38. 5153209664.
Pages 14, 15.
41. 1873784.
42. 2232321.
43. 33104944.
44. 40858938.
48. 4698.
49. 21760.
50. 182975.
51. 2015898.
Page 17.
3. 9626^.
4. 7707*.
5. 1792.
5. 1312AV
7. 46364.
5. 2580|14|.
11. 1104&-
lift 9042^.
15. 8325 T V
l£ 13400*.
Prices 19, 20.
3. 2, 11, 13.
4. 3,41,397.
5. 2, 2, 3, 5, 41.
6. 2, 5, 281.
7. 3, 5, 5, 43.
8. 2, 2, 2, 2, 2, 2, 2, 2,
3, 5.
5. 2, 2, 643.
JO. 2, 2, 3, 3, 3, 83.
12. 2.
13. 2, 2, 3.
14. 2, 2, 2, 3.
15. 5, 5.
JY/f/es 21-25.
2. m-
Q 1503
«*• -'■SUT-
4. 5 T V
/r 145
O. ^3 T .
0. 236^.
7. 64.
5. $24.
9. 36bbl.
10. 676 bu.
11. 38 § reams.
12. 6 men.
^Lr*. 39.-2. 144.
5. 2.
£ 46.
5. 4.
0. 19.
7. 2.
5. 16.
£>. 2.
10. 12.
Xg. 4 Acres.
13. 3 ft.
X*. 14 ft.
15. 16 yd.
^•*. 45.-2. 210.
3. 100800.
4. 21168.
Answers.
319
5. 3360.
6. 9900.
7. 51408.
8. 34650.
9. 1791700.
10. 1388016.
11. 2520.
W. 5040.
74. 30.
15. 12 in.
i0. 360 peaches.
17. 180 weeks.
18. 2f.
25. $31.68 ;
72 H., 9& A., 88 G.
.Prtflres 45-50.
4. 2540.42 m.
J. 385 00024 Hm.
6. 17232 m.
7. 8960.008 m.
8. 40157.575 m.
9. 370.678307 Km.
15. 836.0524 m.;
83.60524 Dm.
16. 75.842 m.;
7584.2 cm.
17. 18.762 m.;
1876.2 cm.
18. 6175000 cm.;
61750000 mm.
19. 1.58364 Hm.
20. 285300 dm.
21. 153000 Dm.;
153000000 cm.
22. 8634 ca.;
.8634 Ha.
23. 75000000 sq. mm.;
7500 sq. dm.
24. 82.34 A.
25. 1.8438 Ha.
28. 256034.089 cu. cm.
29. 38.450 cu. m.
SO. 253000000000 cu.
mm. ;
253000000 cu. cm.
31. 1.28653 dl.
12.8653 cl.
32. 3500 cl.;
35000 ml.; 3.5 dl.
33. 8000 liters.
34. 800 DL; 80 HI.
35. 238.47 dg.;
2384.7 eg.;
2.3847 Dg.;
23847 mg.
36. 0.025384 dg.;
0.0025384 g.
37. 2158 g. ; 215800 eg.
38. 0.001 Kg.
39. 31000600 g.
Pages 51, 52.
4. 70.925 bu.
5. 19.295 gal.
6. 223.704 mi.
7. .3047328 oz.
9. 199.53325 A.
10. 8829 cu. ft.
12. 2286 cm.
13. 10972.5 g.
14. 2609.7 cl.
15. 3412.28 A.
16. .4046+ Ha.
17. 60.746+ Ha.
18. 1772.04+ lb.
19. 995.334+ p.
2. 10798.22 m.
4. 93 cm.
5. 0.3872 Km.
6. $362. 16829.
7. 99.053 g.
S. 25.028+ m.
9. $323.
10. 1.44 fr.; 33.84 fr.;
$2.53.
11. $31.70 gain.
12. $38,245 gain.
13. 9 1 sters each ;
7.20 fr.
Pages 55, 56.
2. 1535220 sec.
3. 1296000 sec.
4. 762036 in.
5. 3872448 in.
6. 1401264 grs.
7. 328291b.
8. 790294i sq. ft.
9. 13200 ft.
10. $39600.
11. $380250.
12. 41 far.
13. $2104.70|.
Art. 151.— 16. 1111b
6oz. 11 pwt. 14 gr
17. 386 bu. 2 pk. 6 qt.
18. 4 d. 10 hr. 50 min
34 sec.
19. 5847 c. 74 cu. ft.
20. 857 bbl. 8 gal. 3 qt.
2gi.
21. 658 A. 90 r. 204 yd.
22. 5907 r. 4 qr. 12 sh.
Pages 57, 58.
23. 20 m. 7 ch. 2 r.
24. $60.61.
25. $1790.25.
26. 20 A. 13 sq. r.
260| sq. ft.
27. $1874.04.
30. 200 rods.
31. 1 pk. 5 qt. If pt.
32. f gill.
33. 45 lb. 12.8 oz.
34. 6 d. 6 hr. 46 min.
48 sec.
35. 6 oz. 17 pwt. 3* gr.
36. 9 oz. 15 pwt. 18 gr.
37. 9 hr. 28 min. 4.8 sec.
3S. 6 fur. 30 r. 2 yd.
7.2 in.
39. 5406l T V sq, ft.
40. 64 cu. quar. in.
Page 59.
44. .688+ lb.
45. £.733 + .
46. .0004958+ m.
47. T^hi, or .00382 lb.
48. .05625 gal.
49. .0580357 wk.
50. .0131579 ton.
51. $638.53.
52. $59.25ff
53. .0625 d.
54. .2903.
55. .4187.
56. .3808.
57. .03062.
58. .625.
Pages 60, 61.
2. 241 A. 1 sq. r.
3. 168 bu. 2 qt.
4. 38 mi. 5 fur. 39 r.
2£ ft.
6. 2s. lOd. 3 far.
7. 8 oz. 13 pwt. 6 gr.
8. 3 quarts.
9. 4 d. 21 hr. 33 min.
320
Answers.
10. 13s. 3d.
12. 9 mi. 1 fur. 18 r. 7 ft
10 in.
13. 1 oz. 2 pwt. 6 gr.
U. £1 14s. 9d.
15. j.
17. 6 yr. 6 mo. 5 d.
18. 12 yr. 9 mo. 19 d.
19. 46 yr. 1 mo. 17 d.
21. 484 days.
22. 109 days.
Pages 62, 63.
23. 462 days.
24. 436 days.
25. 374 days.
26. 37 days.
27. 1° 19' 14".
28. 79° 8'.
29. 62° 50' 30".
Art. 158.
2. £74 lis.
3. 143 gal. 2 qt.
4. 580 m. 7 fur.
5. 2 d. 20 hr. 5£ m.
5 sec.
6. 1355° 47' 56".
7. 385 bu. 2 pk. 1 qt.
8. £37 9s. lOd. 2 far.
10. 2 gal. 2 qt. 2| gi.
ii. 3 bu. 2 pk. 1 qt. f pt.
10. 3s. 7d. 3| far.
13. 5° 33' 16|".
U. 91| C.
15. 9s. 2d. 2 far.
16. 7772 T f3fr.
17. 36| doz.
IS. 113i mi.
19. 7.182 Km.
Pages 64, 65.
2. 101° 22'.
3 4° 48'.
4. 13° 37' 42".
5. 74° 1' 2".
7. 3 hr. 13 min. 40 sec.
8. 3 hr. 14 mi. 47| sec.
9. 10 o'clk. 7 m. 35f s.
10. 5 o'clk. 52 m. 26^ s.
11. 1 hr. 15 min. 56 sec.
12. 3hr. 31m. 46 s.;
1 hr. 16 m. 47 s.
13. 1 hr. 6 m. 17 sec.
^Pages 67-69.
2. $101061.
4. 580| ft.
5. 50 r. wide ;
$351 T 9 e, cost.
6. 9 f \ rolls.
7. $30804. 51 f.
8. 194400 sq. in.
10. 80 rods.
11. 46010| sq. ft.
12. 17| rods.
13. $367.00125
Art. 178.
15. 338 sq. in.
16. 29 A. 85 sq. rods.
Pages 70, 71.
2. $94,815.
3. 262.144 cu. m.
4. 237^ loads.
5. 169 U cu. ft.
8. 3456 gal.
9. $10.93i
10. 303.1875 ft.
11. $227.81^.
12. 7.95 ft.
Bages 72, 73.
3. 21 ft.
4. 16 4 ft.
5. $77.34|.
6. $7.48H-
7. 585 cu. ft.
8. 5Hf| cu. ft.
9. $12.60.
/0. $318.93f.
11. 243 boards.
12. 2270| ft.
Art. 190.
1. 73ff perch.
3. 197208 bricks.
4. $1493.85.
Pages 74=, 75.
2. $1794.98.
3. $1258250.
4- $1.12.
5. $4,477 + .
6. $3750.
7. 13^ lots; $6462 g.
9. $334,331
10. $450.
11. $842|.
12. $14.16f.
13. $66.
14. $98.50.
15 r $151.20.
16. $34,375.
17. $210.
15. $799.50.
19. $70420.
20. $2640.
£*. 105 lbs.
23. $163,
«& $2164.
Pages 76, 77.
25. $2.80.
26. 22 planks.
07. 13^ bales.
29. $57860.
30. $120.
31. $895H.
34. $4696.30.
35. $3914.625.
36. $1457.33|.
38. $12020.
39. $0,112 per lb.
41. $26.0658.
42. $192.92.
Ptoses 78-81.
$163,745.
$653.35.
$152.98.
$977.
$241.27.
$1588.75.
Pages 83, 84.
20. .42, or 42%.
21. .53f, or53|%.
22. .46|, or46|%.
23. .2l|, or21f%.
24. .34ff,or34ff%.
25. .27^, or 27&%.
26. .50, or 50%.
07. .23f, or23f%.
30. 471.
3i. 586.25.
$£. 469.84.
33. 313.38.
34. 814.20.
35. 7397.25.
30. 6842.
Answers.
321
37. 6.03£.
38. 49.92 sq. r.
39. $24.25 dif.
40. 26.999 miles.
43. 4f%.
u- m%-
45. 5%.
.46. 6^ 2 3%.
47. m%.
4S. 18|f%.
Pr/</e 85.
49. A°t%-
si. mi%-
52. 10^%.
5,?. 3f%.
55. 16%.
56. \\%.
57. 89ff%.
55. 39 T 3 T %.
55. 77f%.
eo. 8if%.
61. 61£%.
64. 4083J.
65. 12480.
66. 13814f.
67. 2589.
68. 139536.
69.; ioooooo.
70. $546.
71. £49660.
72. 125300.
73. 500000.
74. 360 T V
75. 64.25.
Page 86.
76. $555f.
77. $21000.
79. $85.93|.
52. 21448.
83. 1400.
54. 2760.
85. 4000.
56. 5250.
57. 3240.
88. 600.
59. 7000.
90. $9600 cost;
$5^ perbbl.
92. $32000 cost;
$15 per bbl.
92. $7366 r V
Page 87.
1. 12432if-
2. .59ff|.
3. $69 F V T loss -
4. 17H g. per ct.
5. $27368.42 T V
6. 180.
7. 581.25.
5. 15.12.
9. 26.95 mi.
10. $24.25.
27. 87f|56 gaiD.
12. $0.76*\.
75. .78f| profit %.
14. $30,998+ per A.
75. 18f%.
76. 2516.
77. 12%.
Pages 90, 91.
2. $380.19.
3. $676,962.
4. $184.8413.
6. .3775, or37f%.
7. $7.8125.
5. 25%.
9. 50%.
79. $627.
12. S2.35 T 3 T .
75. $279£.
14. $1210.52i|.
75. .25.
Pages 92, 93.
2. $27.343|.
3. $2707.50.
4. $2713.225
5. $15000 sale;
$14625 owner re'd.
6. $21.0732 com.
$842.93 amt. pur.
7. $621.30.
5. $16743 amt. sale.
9. $26250.
79. $10000.
77. $24477.684 invest.
$887,316 com.
12. $1172.25 com.
75. $5489.53.
U.
15.
10.
17.
IS.
19.
937.172.
$603.75.
$363.48.
$2920.
$11006|.
$425 com.
$4575 pd.
21. $8196.583.
22. $292,875.
23. $12676.92.
24. $1733.
25. \\%.
26. $64,924 com.;
$3181.276 spent.
27. $6819.43.
28. 31363.63i 7 T lbs.
Pages 95, 96.
2. $33.50.
3. $30 gain.
4. $62,002 + .
6. .008.
7. 6|%.
5. .008i.
79. $169331-.
77. $4960.
12. $9090.90 + .
75. $20872.72 T 8 T .
75. $271683.67 + .
76. $4329.897.
77. $26056.70
75. $14234.82 + .
Page 97.
1. $4£ per $1000.
2. $5 ¥ 5 T per $1000.
5. $487.50.
4. $15600.
5. $85478.47.
6. $314.50.
7. $12873.56.
5. $312.50.
9. $14.70.
Pages 99-102.
2. 100%.
5. 39^%.;
$983.6941 F. ;
1573.91^ M.;
786.95if P.;
1180.43HH.
4. 20% =
5. $555.
322
Answers.
6. $70312.50.
Art. 267.
3. $51.
4. $232.
5. $77.20.
6. $548,375.
7. $302.93.
8. $496.13f.
10. $13193.717 + .
Pages 104, 105.
3. $87.32.
4. $805.49.
5. '$902. 79.
6. $669.
7. $1138.66|.
8. $22.77.
5. $26.46.
10. $145.91 + .
11. $144,375 int. ;
$2644.375 amt.
rages 106, 107.
13. $179.62.
H. $17.55.
15. $626.40.
16. $4474.96|.
17. $103,039.
18. $2096.1243.
19. $65,875.
20. $104,498.
21. $104,796.
$60,144.
$163,457.
$119,574.
$2213.76.
$7944.62.
$1234.67.
$988.38.
22.
25
30. $1059.26.
31. $625,567.
32. $355.30;
Nov. 24th. 1887.
Pages 108, 109.
2. $707.53.
3. $40.79.
4. $149.34.
5. $2869.93.
6. $4623.06.
7. $101.
8. $50.98.
9. $425.65.
10. $134.72.
11. $68.04.
12. $195.16.
13. $1024.25.
U. $664.32.
15. $1296.875.
Art. 284.
2. $8,925.
3.
4-
5.
6.
7.
8.
9.
10.
11.
H.
15.
10.
17.
IS.
10.
20.
21.
$5.20.
$4.73.
$7,686.
$677,259.
$791,868.
$1211.33i.
$2551.66 + ,
$400,318.
$637.88.
$31.25.
$6.00.
$100,048.
$35,445.
$40.63.
$26.19.
$251.81.
Pages 110, 111.
24. $8.40.
25. $146.78.
26. $1329.57.
27. $16.90.
28. $60.04.
29. $61.04.
Art. 288.
2. $130,985.
3. $121.32.
4. $104.95.
5. $360,412.
6. $316,898.
7. $162.08.
8. $9.69 at 4% ;
$12.11 at 5% ;
$16.95 at 7%.
9. $17.30 at 4% ;
$21,576 at 5% ;
$30,206 at 7%.
10. $30.30 at 4% ;
$37.88 at 5%;
$53.03 at 1%.
11. 33.66 at 4%;
42.09 at 5% ;
$58.91 at 7%.
12. $63.05 at 4% ;
$78.77 at 5% ;
$110.27 at 7%.
13. $170.48 at 4%;
$213.08 at 5% ;
$298.31 at 7 %.
Pages 112. 113
2.
$3080.
3.
$3083.46^.
4.
$16126.20.
5.
$17902.50.
6.
$18425.625.
Art. 292.
•2.
8%.
3.
6%.
//•
lrh%.
5.
6%.
(J.
6%.
7.
8.
7%.
9.
5%.
10.
10.3+%.
Pages 114, 115.
12.
13. $58333i.
14. $55555 1.
15. $360.
17. $535.71?.
18. $1264.41 +
Pages 115, 116.
19. $179.25.
20. $220.
21. $3456.54.
22. $375.60.
24. .5 yr., or 6 mo.
25. 2.055+ yr.,
or 2 yr. 20 d.
26. 16|yr.,orl6yr.8m.
27. 1.399+ yr.,
or 1 yr. 4 m. 23 d.
28. 1.069 + ,
or 1 yr. 25 d.
30. 8^ yr., or 8 yr. 4 m.
31. 9.52A, or 9 yr. 6 m.
9 a.
82. 28 years.
Pages 118, 119.
2. $498,962.
8. $498.59.
Answers.
323
4. $4149.68.
6. $252,233.
7. $2633.51.
Pages 123, 124.
12. £5 2s. Id. 34 far.
13. £10 18s. 3d.
14. £111 13s. 4d.
2. $328.78.
3. $2090.098.
4. $3390.048.
Pages 126, 127.
6. $4466.987.
7. $3040.4565.
8. $819.65+.
9. $7622.336.
10. $2981.21.
11. $2149,294.
12. $1900.155.
13. $3787.218 + .
14. $1200.
15. $1115.398 + .
16. $100.
rages 127, 128.
2. $871,789, p. w. ;
$78,461, tr. d.
3. $2827.21 + , p. w. ;
$445.29, tr. d.
4. $5995.652, p. w. ;
$899,348, tr. d.
5. $7473.65, p. w. ;
$1177.10, tr. d.
6. $8661, p. w. ;
$1339, tr. d.
7. $177,455, Dif.
8. $2500.
9. $805.66 better, cash,
Pages 129, 130.
2. $836,825.
3. $875.70|.
4. Sept. 2d, maturity ;
12 d., term of dis. ;
$5287.11, Pro. '
5. $3.24, Dif.
6. $859.69.
8. $933.20.
9. $8527.16.
10. $5545.95 + .
Art. 317.
3. $5073.17 + .
4. $8375.63 + .
5. $3307.888 + .
6. $2807.88 + .
rages 133-136.
1. $5,425, B. dis. ;
$344.58, Pro.
2. $5.25, B. dis. ;
$494.75, Pro.
3. $1217.86|.
4. $1215.63^ at 7% ;
S1211.16§ at 5%.
5. $426.71 + .
6. $709.33^.
7. $712.25.
8. $1616.
9. $520, 1st Amt. ;
$515, 2d "
$510, 3d "
$505, 4th "
10. $523,331, 1st Amt.
$517.50, 2d "
$511.66|, 3d "
$505. 83J, 4th "
At5%,$516.66f,lst.
$512.50, 2d.
$508.33^ 3d.
$504.16|,4th.
14. $471,596.
15. Apr. 4, 1883, mat.;
$9,304, Dis. ;
$1153.696, Pro.
16. Mat., July 44th;
$25, Dis. ;
$2475, Pro.
Pages 139-142.
3. 1.84+ mo., or55d.
4. 5 m. 23 d.
7. Jan. 29th.
8. Sept. 1, 1879.
9. 4 months.
10. 62davs.
11. Aug. 10
12. 32 d., or to Aug. 2
Pages 143-146.
14. 67 days.
15. 8 days.
17. $910, Bal.;
Due Apr. 28.
18. $945, Bal. ;
Due July 7th.
19. $510, Bal. ;
Dec. 30, Av. time.
Pages 147-149.
20. $906.54, Bal. ;
Due June 10th.
21. $100, Bal. ;
P'bl. Nov. 14, 1883.
23. $290, Bal. ;
Due Aug. 5th.
24. $435, Bal. ;
Due July 12th.
25. $1780, Cr. Bal. ;
Due Mar. 17th.
26. $140, Bal. ;
Due Dec. 20th, 1879.
27. $100, Cr. Bal. ;
Av. date June 17th.
28. $1190, Bal. ;
Due Aug. 14th, 1883.
Pages 152-154.
31. $121.62, Cash Bal.
32. $670.82, Cash Bal.
33. $677,105, at 8#.
34. $221.33. Cash Bal.
35. $1229.90, Cash Bal.
36. $1462.07, Cash Bal.
37. $199.52, Cash Bal.
38. $199.52, Cash Bal.
39. $201.45, Cash Bal.
40. $1903.81, Cash Bal.
Pages 155-157.
2. $15234.12, Net pro.
3. $12002.45, Net pro.
Art. 366.
5. $14161.44, Net pro.;
Due Jan. 8th.
6. $3484.43, Net pro. ;
Due Nov. 23d.
Pages 161-163.
Art. 382.
2. $400.60ff,A's share;
$549.39f|, B's "
3. $374.46ff , A ;
$425.53 T V B.
4. £5517.24^, A;
$3972.41^, B ;
$3310.34^, C.
324
Answers.
5. $10000, Net cap.
close ;
$6C36f, A's floss;
$3333|, B'gi "
6. $3461^, X's share ;
$2307 ^ Y's "
$173011, Zs "
7. $1500, A's share ;
$1800, B's "
$750, C's
$4500, D's "
8. $1800, share of 1st ;
$1200, " 2d ;
$900, u 3d.
9. $180, B's share.
10. $3125, sh. of 1st ;
$9375, " 2d.
11. $13554, A'sdiv.;
$9036, B's "
14. $347||, A's gain ;
$278 4, B's "
$173|i C's "
$4347^1, A's net cap.
$3478^3, B's "
$2173|i, C's M
15. $4933^, A's net cap.:
$2366-1, B's "
42f% loss.
rages 166, 167.
19. $14207.50, Firm's
net g. ;
$17768.25, C's net
cap. ;
$15691.75, D's net
cap.
£1. $9266.68, A's cr. bal
$8963.93, B's "
23. $419.41^, A's sh. ;
$528.15^, B's "
$652.42 T 7 o 4 s , C's "
24. $878.04ff , A's sh. ;
$526.82ff , B's "
$395.12 ¥ 8 T , C's "
Pages 168, 169.
26. $19541, A's profits ;
;*, B's "
27. $1411^, share of X;
$1411|f, " Y;
$1176^, " Z.
28. $35.00, A's part ;
$30.00, B's "
$22.50, C's "
29. $1875, A's share ;
$10412, B's "
$20831, c's "
30. $3510, A's part ;
$2730, B's «
31. $9721 fj -§, A's part;
$12344* |f, B's "
$9133f $-?-, C's "
32. $7784 , 8 5, A's part;
$7851f|, B's "
33. $25454 T 6 T , A's part;
$40000, B's
$54545-^, C's "
Bages 170,171.
2. $1854.02^1, A's
part;
$1312.08 T f F , B's
part ;
$1083.89^, D's
part ;
28 T 7 T 8 7 per cent.
8. $2171 ; 26+ %.
4. $7907.70, A's part ;
$8933.25, B's "
$9391.20, C's "
64| per cent.
Art. 393.
1. $1650, A's loss ;
$1100, B's "
$550, C's "
2. 13i£ per cent. ;
$2142.85|, A's loss.
3. $1307.14|, Ins. Co.
real loss.
4. 19^f T % loss;
$510.34#3, Co. B's
real loss ;
$2063.92ML Co. C's
real loss ;
$43.77|f i , Co. D's
real loss ;
$4002.85o 4 /3, Co. A's
real loss ;
$5502.85^3,
vessel's real loss.
Pages 173-177.
2. $794, carriage ;
$1062, horses.
3. 5586.
7. £227 12s Id.
8. f .
11. 4605 sheep.
12. 66 years.
13. 1440.
15. $41,205.
16. $3536.25.
17. $14760.
19. $6937.60, sold ;
$1737.60, profit.
20. $85.80.
21. 72%.
22. 3600.
23. $4104.
25. $430.36 + .
26. $1265.06+.
28. $27.30.
29. 9%.
30. 9%.
31. 10+%.
32. 2 years.
S3. 3 yr. 4 mo.
34. $1388.88$.
85. $4390.24^-
36. $1010.61 r 8 &V
37. $3309.84+.
38. $1791.66|.
39. $6474. 66|.
40. $54.38.
41. $325, A ; $175, B ;
$100, C.
42. 33 9 T hours.
44. $203.
45. 250 shares.
46. $85.
47. 14046 5 2 3 times.
48. 22|%.
49. 16 yr. 8 mo.
50. $12380r^.
51. $124.96.
52. $640, A's share ;
$840, B's "
$840, C's "
53. $350.
54. 7 o'clock 51 m. 12 s.
55. 3750='; 2500 = i;
1250 = I.
Answers.
325
56. 19i%;$1933.33i A
$725, B ;
$2390.08*, C
57. i hr., or 15 min.
58. $960, A: $1440, B;
$2160, C.
59. 244. mo., or in 3 mo.
60. s4:02 + .
61. $116.28 + .
62. $30666§.
63. $15.29.
64. 6£%.
65. 2807?| cords.
66. $12000.
JPages 183, 184.
Art. 430.
4. 80A mo.
5. 128 spoons.
6. 3584J Km.
7. lj yd. wide.
8. $359,892 + .
9. $10.50.
$74.
$4830.
12£ tons.
10.
11.
12.
13.
Panes 186, 187.
3. 42davs.
4. 5004 bu.
5. 160 ft,
6. $674.
7. 154 min.
8. 720 pair.
9. Ill lb.
10. $15,774.
11. 32 pp. '
i& 2| days.
2.?. 18 coin.
14. .36.
15. 2 days.
26. 15 ft.
17. 2£ ft.
-4r£. 431.
2. 244, 1st ; 192, 2d ;
288, 3d.
Page 188.
S. 200, A's shares ;
100, B's "
150, Cs "
4. $2200, A's share ;
$2933i,B's "
$3666f, C's »
5. $4150, A'sinvestm
$4950, B's
$5150, C's
$4250, D's
7. 84 fc 1st part ;
169, 2d "
190, 3d "
138i, 4th "
8. $189 ft, B's money
*379-ft, C's "
$75 f \, A's
9. $79.20.
10. $7.20.
11. $71 6f, A's share;
$895 5-, B's "
$5374, C's "
12. $450; A's money;
$800, B's
13. $3363^ = 1st ;
$5045 T 5 T = 2d ;
$10090}? = 3d.
Pages 190, 191.
3. $8642.725.
4. $6853.55|.
5. $9936.71f.
6. $7512.30.
7. $4845.
8. $12367.50.
9. $4208. 134.
10. $843625.
11. $4381.50.
12. $1140.50.
13. $8408.964,.
14. $9641. 93|.
16. $6293.1925.
17. $4430.25.
15. $5684.
19. $9857.793f.
Pages 195, 196.
2. $8484.937^.
3. $17177.60.
4. $73570.96875.
5. $13583.819+ ;
$13513.799 + .
6. $17092.38;
$17421.764+ ;
$17217012.
8. £3134 lis. 7d.
9. £5187 5s. 6d.
10. £1741 16s.
11. $4.80.
12. $3.7534 + .
t 13. £11 15s. 6d., or
$52,565.
14. $4.91.
15. £3832 18s. 5.7d.
16. £2036 7s.-4.8d.;
At $2.97 per yd.
Pages 197, 198.
18. $112.31, dif.
20. 23535 f r.
21. §230.769.
22. $150.32, dif.
23. $391.95.
25. $916.75.
. 7856.08, M.
29. 7399.472, M.
SO. 11946f, M.
32. $1645.
33. $3561.45 + .
34. .63.
35. $532,072.
36. $626,163.
Pages 201, 202+
2. $123.75.
3. $2190.61 + .
4. $10645.937 + .
5. $2175.331, duty ;
$8090.562, cost.
6. $1920.10|.
7. $660,832.
8. $5583.0074.
9. $994.31.
10. $903.60 + .
11. $4278.237 + .
12. $1043.86 + .
13. $584.26.
14. $607.95, duty ;
$6960.064, cost.
15. $4950. duty;
$10363.36, Bill ;
$15313.36, D. & cost.
Pages 208 , 209.
1. $450000000, Issue ;
$22500, Fund.
2. -S33650, proceeds ;
300 shares.
3. $4627.30, tax.
4. $180000, B. notes.
326
Answers.
5. $2936.925, A;
$3788.07f, B ;
$2053.29 + , C.
Art. 489.
2. $351.65, Bal.
Pages 213-215.
5. $412.40, Bal.
6. $201.54, Bal.
7. $259.6H, Bal.
8. $747,561, Bal.
9. $298.00, Bal.
10. $683.12|, Bal.
Bages 224=, 225.
tf. $100100.
4. $5070.
6. $8165.625.
7. $111 T % 5 T per share.
8. $968.87£.
10. $4375.
11. $38200.
13. 9f%.
14. 3|%.
16. 160 shares.
rages 226, 227.
27. 13 2 3 certs, of 1000
bbl.
18. 714£ff shares.
19. 400 shares.
21. $50 per share.
22. $266| per share.
24. $108281^.
25. $33187.50.
26. $35840.
27. $35416|.
28. $63600.
81. .03861 T V
*J~. .UO ff 6 ? .
.&?. 4 per cent. @ 122f ;
$28.83, better.
34. $65.25, diff.
35. $450, rec'd;
4% on cost.
Pages 228, 229.
37. 17 T V%.
39. 3ft %.
44. $96 ¥ 8 T per share.
45. $109f per share.
46. $438|f,
or $87ff per s.
Art. 559.
1. $66f.
2. $100 per share.
Pages 230, 231.
3. 20-yr. bond @ 90.
4. A, 100%;
B, 50% ;
C, 40% ;
A, 1000000 ;
B, 750000 ;
C, 250000 ;
l-i 9 ^ shares.
5. $26933i
6. $32.41.
7. 7 t Vt%-
10. $300.
11. Chem. Bank ;
$107.14f, better.
13. $312.50, gain.
14. 86f acres.
15. $3325.
16. .07f£.
17. $3750.
25.15^%;
12|f%.
19. R R. Stock ;
.00f, better.
20. $150.
21. $7560.
22. 7|%.
JVtflres £32, 233.
05. 33i% dis.
&£. $187*.
25. $196.02.
26. $625.00.
27. 8tf %.
0£. $11200 ;
50 sh. each.
00. $5205.
30. 2C0 shares,
or $20000.
Art. 561
1. 8ff%.
2. $551,994.
3. $1506.18.
4. $1.23 per bu\
5. 481.59 tons.
Pages 234, 235.
6. 634 notes.
7. lift?', 22+%.
8. 4% com.
5. $600.
10. To pay cash ;
$742.50 better.
Art. 565.
2. $979.65.
3. $19.41f.
Pages 239, 240.
2. $266.10.
3. $13236.
4. $64378.07+ C. int.;
$29835 f . rec.
5. $621.36.
6. $880.64.
7. $1612.80 less.
8. $2.20.
9. $14633.40;
$47697.75, End'w't.
10. $805.92.
11. $7544 less.
12. $11617.20.
13. $20817, Bank;
$2817 more.
14. $1289.05 less ;
Pages 242-247.
4. $3924.32 + .
Art. 597.
3. $1001.179 + .
4. $13417.085 + .
6. $4692.537.
7. $3366.37 + .
8. $44632.425.
10. $4212.93 + .
11. $8142.008, at 21 ;
$5847.622, P. w.
13. $50000.
14. $11199.303 + .
15. $43219.424.
Pages 248-250.
2. $2660.974 + .
3. $23739.647 + .
Anstvers.
327
4. $15622622442.
6. 36 yr., and a bal. of
£33309296.
7. 42 yr., and a bal. of
$33667195.
8. 5 yr., and a bal. of
$2311236.22 + .
10. $191005.524.
Art. 605.
11. $27173.596 + .
12. $43477.76.
13. $296048.80.
U. $5174.10.
Pages 254, 255.
0. 54.
3. 729.
4. 16.96 + .
5. .28.
6. .87576 + .
7. 32.7679 + .
8. .0976 + .
9. 785.64.
10. 60.7042 + .
Art. 622.
13. tf.
U. ft.
15. ff.
16. ft.
18. 59 T V+ rods.
29. 42.426 + r. side. ;
11.25 A.
20. 176.
02. 1838.265625.
22. 20 ft.
05. 11.3137+ in.
24. 58.864+ ft.
25. 17.889 rods.
26. 84 ft. wide.
Pages 257, 258.
2. 34.
3. 47 + .
4. 1.208 + .
5. 47.7 + .
6. 6.006 + .
7. 358.9 + .
8. 1.18 + .
9. 5.000006 + .
19. 345.
12. \.
IS. T V
14.
ft*
26. 99.9 + .
17. 51.01 + .
25. 17.51+ in.
29. 108.8+ in.
20. 132.5+ in.
21. 5903.
22. 53.7+ in.
23. 408.
04. 763.
P«</es 259, 260.
3. 36 sq. ft.
4. 7£mi.
5. 1121| sq. in.
6. 34.6+ ft.
9. 575000 cu. ft.
20. 15.64 ft.
11. 4188.16 cu. ft.
12. 1429ilbs.
13. 18| in. diam., 8 in.
deep.
14. 19774^ Kg.
15. 799.41b.
16. $3600.
17. 79.54+ rods.
25. 5.25 cm.
Page 263.
1. 800 sq. ft.
2. $200.
3. $15.91^.
4. $90.
5. 19800 sq. ft.
6. 2200 sq. ft.
7. 8 rods wide ;
40 rods long.
8. 22500 bricks.
10 breadths.
99fiyds.;
11 breadths.
Pages 264, 265.
1. 192 sq. ft.
0. 224 sq. cm.
3. $7.92.
5. 724.56+ A.
6. 249.4+ sq. ft.
8. 10^ rods.
9. 14 yd.
10. 70|H rods.
20. 768 rods.
25. 44 yd.
2^. 138 ft. 11« in.
Z5. 56 T f T rods.
JPagres 266, 267.
4. 113.318+ in.
5. 71.52+ r. per sq.;
63.39+ r. per circle;
8.13+ rods, dif.
6. 30.27+ rods.
7. 1590.435 sq. ft.
8. 57494 sq. ft.
9. 263.8944 feet.
10. 23.888+ sq. rods.
11. 11309.76 sq. r.
20. 30 yd.
13. 141.372 rods;
376.992 rods.
14. 203.717+ Acres.
Art. 655.
16. 200 sq. in.
17. 6.324+ in.
18. 162 sq. in.
19. 58.5362 sq. dm.
Pagrs 26S, 269.
21. 42.315 rods.
00. 49.74 sq. r. cir. ;
39.06 sq. r. square ;
10.68 sq. r. more in c.
Art. 666.
3. 412| sq.ft.
4. 3168 sq. ft.
5. 450 sq. ft.
6. 14.1372 sq. ft. con. ;
17.6715 sq. ft.
entire s.
Pages 270, 271.
8. 47.124 cu. ft.
9. 59.0857+ gal.
10. 18400 cu. ft.
11. 375 cu. cm.
20. 800 cu. dm., or
liters ;
0.8 Kl.
13. 19614 cu. in.
15. 96 sq. ft.
16. 131.9472 sq. ft.
17. 418.3 sq. ft.
18. 3769.92 sq. ft.
328
Answers.
rages 272, 273.
21. 5151.157^ lb.
22. 9.163 ca. ft.
23. 333 cu. ft.
25. $41,469 + .
26. 201062400 sq. m.
27. 31416 sq. cm.
29. 259777100108cu.ini
30. 28.2744 cu. dm.
31. 2982 065625 cu. ft.
32. 3.541+ hhd.
Pages 274, 275.
2. 33.614+ gal.
3. 1059.5286 liters.
4. 658.125 gal.
5. 102.9384 gal.
6. $3.95 per gal.
7. 3.31 bu.
8. 8 in.
Art. 684.
2. 568 r \tons.
3. 241.164 bu.
4. 57.024 bu.
Pages 276, 277.
5. $49.13.
7. 50 ft.
8. 122|ft.
Art. 687.
2. 1152 sq. ft.
3. 294 sq. ft.
4. 72 sq. ft.
6. 13 boards.
7. 9.4 bd. 18 ft. long ;
155H bd. ft.
Art. 689.
8. 22^ cu. ft.
9. 26~cu. ft.
10. 12.726 in.
Pages 278, 279.
1. 18756699.
2. 16330115.
3. 992385222.
4. 11496.
5. $5.27.
6. 714.
7. $3192.
8. 315 eggs.
9. 15680 men.
10. $31233±.
11. 5 bu. 1 pk. 6\ qt.
12. 77.14+ bu.
13. 40791422655.
14. 75.
15. 12 = g. c. a.
16. 63| smaller ;
80£ larger.
17. 1J§ , sum ;
ff,dif.;
a prod. ;
l|f, quot.
IS. 5.
19. $440.
20. 224.67^ bbl.
21. $33^. '"
22. $3.40.
£?. 94.54| planks.
24. $450.
55. 71 hr.
26. 73.84+ ft,
57. 38.416+ ft.
25. 50%.
29. $3675.
Pages 280, 281.
30. $31^, A's part ;
^o9^tj", jj s
$78££, C's «
31. 95f%.
55. 2| cts. gain.
33. $104.65.
34. 77 Ha.
35. $658.35.
#?. $72.
37. 96 ft.
55. 2280.
39. 439^1 , sum ;
87ff, dif.;
46333 T X 5, prod.;
iftff . q u( >t.
40. $12525.
41. $0.74i.
4f. 60|§t%-
4c?. $12432.432 + .
44. $6.73243728.
45. $3.83 ioss.
#. $5329.03 profit.
47. 71 bu.
45. 8.999+ bu.
49. 967 cars.
56). $115.09 loss.
51. $19.89.
55. 88%.
J5. 242| acres.
54. 847170 Phil.
1206299 N. Y.
55. 3364 Ca.
56. 93± sq. ft.
57. 363.73ift.
Pages 282, 283.
58. $745,875.
59. 3 shares.
60. 28*%-
61. 44.204 ft.
62. $12000.
63. .00^.
65. 106.08 cu. m.
66. $450.84.
67. 540 bbls.
68. $2120.60.
69. $2760.69.
70. 1019 in.
71. 2.7 cm.
;.?. 3 mo.
73. 23, r/. c. d.
74. $23809.52.
75. 108 lbs.
76. $3.50 per yd.
77. 107, r/. c. d.
78. $599.34.
75. 113097.6 cu. in.
5#. 64.75, Ha.
81. 39.38 + . HI.
82. $271,845 + .
83. 6.3 in.
84. Wh%.
85. $11609.76.
86. $665.37.
87. $127.73.
Pages 284, 285.
88. *$1 87.20.
,89. Oct. 16th.
90. Dec. 6th, 1883.
91. $1962.01.
92. 44 ft.
93. 8.
94. 9.
95. 6.
95. 3375.
97. 200%.
9S. $2470.75.
Answers.
329
99. 178.731 bu.
100. 49140.
101. 18 ft. wide ;
54 ft. long.
' 102. $595.
103. 5.19 ft.
104. 156 rods.
105. $3405.30, Bank ;
$4905.30, all.
106. 7 + in. = 1 side.
107. 132.9+ meters.
108. 1 yr. 1 mo. 14 d.
109. $2174.585 + .
110. 24dif.
111. 1970.80 sq. r.
112. $8.91 per bbl.
113. 126.589 Km.
114. 78 mi. 211 r.
5.332+ yd.
115. Ufa.
Pages 286, 287*
1. 75635.
0. 586916.
3. 754108.
4. 6783002.
5. 7388520.
6. 1731704.
7. 1010663.
& 948395.
9. 982110.
10. 1183219.
£2. 1199035.
12. 725522.
!«?. 661945.
14. 549253.
15. 1417691.
16. 974687.
17. 1162790.
18. 379261.
19. 1373105.
£0. 1486901.
01. 3193.
22. 1856.
05. 89111.
24. 89189.
05. 88909.
00. 164808.
07. 366185.
05. 665645.
29. 611111.
50. 111109.
51. 89111.
* 50. 164898.
55. 484737.
84. 259331.
55. 4436640650.
36. 1817822786.
37. 2626568694.
38. 1331846875.
39. 2023209268.
40. 1398214650.
41. 1777211634.
42. 4130024886.
43. 1431347492.
44. 3468401325.
45. 223702272.
46. 1538746950.
47. 768264600.
48. 4405321875.
49. 4084589512.
51. 68851 T 3 A 9 *V
52. 51846 T 9 T VV T -
53. 2044181HH.
54. 377582£ffff.
55. 83132|ff|f.
56. 30687ff{ft.
57. 24368fffff-
58. 9677 ¥ V3 5 3<V-
59. 22965||ff|.
00. 107932if£f
61. 9392ff|f.
00. 122599^%,
05. 17610HH-
64. 82092Bfft.
05. 15864S## r .
Art. 692.
1. 18A-0,
2. 2dffr%. •
5. $110.22.
4. $267,682.
5. 33|%.
0. 43f%.
7. 14*%.
8. $2205.88 T V
9. $1275.
10. 1 yr. 3 m. 16 d.
21. $638.37 + .
12. $96.47.
25. $58.62i.
24. 6%.
25. .005.
20. $2743.33i
17. $30.94.
25. $85.01.
29. $54.60.
00. £40 17s. 2d. 2.56
far.
02. $7020, pro. ;
$180, com.
22. $51
Pages 288, 289,
23. $448.
24. $2285.
25. $6000.
00. $1584.
27. $791896.
28. $135.30.
29. $118,625.
30. 6£%.
52. $8251.67^.
32. 3 yr. 4 m. 12 d.
33. $2392.34.
34. $2564.102 + .
35. 3 yr. 10 m. 6 d.
50. $3072.
37. 6£%.
38. $60.
39. $16640.
40. Oct. 10th.
41. £1552 19s. 3.6d.
#. 6 T W%.
45. None.
40. 9%.
47. .00f$.
^r#. 6,95.
1. 36897f fr.
0. 59.56 meters.
5. 127 fields.
4. 1323.2248 HI.;
$7507.98. .
5. 3| m. c.
0. 44 men.
7. 22.7 cm.
8. 0.557 m.,
or 5.57 dm.
9. 7.503 dm.
10. 3.9+ cm.
11. 113.0976 cu. dm.
Pages 290, 291.
3. &.
4. A-
5.'#.
330
Answers.
6.
jmr*
7.
^iff-
S.
*V
9.
tIt.
1<>.
tV
11.
51 bags ;
3f bu. in each.
12.
332 lots; T \5 A. each
Art. 697.
2.
24.
3.
*£ = 15f .
4.
isjA - 402f.
5.
*-740 = 97!!,
6.
6f davs ; A, 10 t. ;
B, 15 t.; C,8t.
7.
5 hr. 20 min. ;
meet at stg. pt.
8.
8 hr. walk ;
22 times No. 1 ;
28 " No. 2 ;
33 " No. 3.
rages 293, 294.
2.
515944.
3.
45327848.
4-
53837066.
5.
675159828.
7.
2916 ; 3025 ; 3364.
8.
2704 ; 3136 ; 3481.
10.
2025 ; 4225 ; 7225 ;
9025.
12.
11025 ; 13225 ;
21025; 18225.
u.
59004.
15.
82852.
10.
29623.
17.
31394.
Art. 709.
5.
June 3.
G.
320 y. 3 m. 8 dys.
7.
Friday, May 16.
Page 300.
2.
$3753.60.
3.
$303300.
4.
$3177.72.
5.
$743.88.
Pages 309-314.
1.
93.
155 T X 3 of eac
8 t V| mo.
4.27 mo.
A, $11317 ;
B, $9053.60
C, $6224.35
D, $6224.35
E, $6224.35
F, $622435.
65 each.
313 horses ;
$61 each.
247 yds. ;
$1151.25 cost.
108 A. left ;
$3 per A.
150 men.
1152597 bbls.
690 lbs. left ;
$0,571 per lb.
$5,618 per head.
32 spoons of each.
49 animals.
10.
11.
12.
13.
14.
15.
16. 48 feet,
17. $21428.57.
18. $480,305.
19. $240.
20. 190 sq. ft.
21. $94.41 Net g.
22. U. S. 3's = 2ff % ;
. B.&0.6's=4Hf#§%.
23. .05 T V
24. 3534.3 lbs.
25. 96 rods.
26. 8s. 101-d. per yd.
27. $10566.43 gain.
28. 8*f#.
29. 71 mo.
30. $500 for 15 yrs. ;
$1378.9162 greater.
31. 7% bonds;
$10061 better.
32. 8.807+ miles.
33. 90*.
34. 172.66 shares.
35. $4200, 1st ;
$3900, 2nd ;
$3640, 3rd.
36. 45+ fo.
37. $264.25.
38. $1838.8745.
39. $290 gain.
40. $8.25 on 2 mo;
81 cts. per bbl.
better.
41. 79315.2 gals.;
$3569.184 val.
42. 12i%.
43. $891,493 loss.
44. $118^ per share.
45. 4,£ T %.
46. $900, A's money :
$720, B's "
$240, C's "
47. a i«w ;
f £ greater.
48. f of the mine.
49. 20 days A;
30 " B;
50. 322 lots.
51. 6^%.
52. 396096 Pop.
53. 43% B;
68% C.
54. 28+ % N. Y.
55. $3438.75.
56. 75%.
57. 66|% Gold;
33J% Silver.
58. 20'books.
59. 26250 oz. gold ;
2916| oz. alloy.
60. 1900, 1st ;
2660, 2nd ;
3420, 3rd.
61. $54000.
62. $65331
63. 21050."
64. $10097|, 1st cost ;
$12347y, 2nd cost
.012+% gain.
65. 80|%.
66. $12.32 marked.
67. 26iyds.
68. 3691 §f$ times;
14.6608 ft. cir.
69. $18.20.
70. $387.88 + .
71. $450, C's money ;
$800, D's "
72. 53 days.
73. $473.45 due.
74. $11560.69.
75. 9%.
76. $53,196.
77. 16|%.
Answers.
331
78.
$1500, daughter's
$1050.85||, C's
82.
486.6 bags.
share ;
salvage ;
83.
H%.
$7500, each son's ;
$1784.1 lgV, A's loss;
84.
$413.50.
$10000, widow.
$1529.24|f, B's "
85.
$2313.72.
$1108.88|f, A's
$1709.15i|. C's "
86.
Wf% gain
salvage ;
80.
$708.75 di'f.
87.
Oct, 31.
$945,761-8, B's
81.
$189.03 Bal.
88.
$287.55.
salvage ;
■#
o
o
*
A Hand-Book of Mythology :
Myths and Legends op Ancient Greece and Rome. Illustrated
from Antique Sculptures. By E. M. Berens. 330 pp. 16mo, cloth.
The author in this volume gives in a very graphic way a lifelike pic-
ture of the deities of classical times as they were conceived and worshiped
by the ancients themselves, and thereby aims to awaken in the minds of
young students a desire to become more intimately acquainted with the
noble productions of classical antiquity.
In the legends which form the second portion of the work, a picture, as
it were, is given of old Greek life; its customs, its superstitions, and its
princely hospitalities at greater length than is usual in works of the kind.
In a chapter devoted to the purpose, some interesting particulars have
been collected respecting the public worship of the ancient Greeks and
Romans, to which is subjoined an account of their principal festivals. ,
The greatest care has been taken that no single passage should occur
throughout the work which could possibly offend the most scrupulous deli-
cacy, for which reason it may safely be placed in the hands ot the young.
RECOMMENDATIONS.
" Fifty years ago compends of mythology were as common as they were useful,
but of late the youthful student has been relegated to the classical dictionary for the
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The volume is not one of mere dry detail, but is enlivened with pictures of classi-
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" The Churchman" New York City. ~
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and Rome is fully recognized by all classical teachers and students, and aiso by the
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is appropriately illustrated from antique sculptures, and arranged to cover the first,
second and third dynasties, the Olympian divinities, Sea Divinities, Minor and
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Romans, the Greek and Roman festivals. Part II. is devoted to the legends of the
ancients, with illustrations. Every page of this book is interesting and instruc-
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printed and tastefully bound."—" Jovrnal of Education," Boston, Mass.
" It is an admirable work for students who d(j§|re- J to find in printed form the
facts of classic mythology."— Rev. L. Clark SeelyeTWUfrSmith College, Northamp-
ton, Mass.
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the requirements of our schools. The author avoids extreme theories and states
clearly the facts with modest limits of interpretation. I think the book will take
well and wear well."— C. F. P. Bancroft, Ph.D., Prin. Phillips Academy, Andover,
Price, by-Maii* Post-paid, $1.00.
CLARK & MAYNARD, Publishers, New York.
ID I /^Jo
Two-Book Series of Arithmetics.
By James B. Thomson, LL.D., author of a Mathematical Course.
1. FIRST LESSONS IN ARITHMETIC, Oral and Written.
Fully and handsomely illustrated. For Primary Schools. 144 pp.
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2. A COMPLETE GRADED ARITHMETIC, Oral and Writ-
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This entirely new series of Arithmetics by Dr. Thomson has been
prepared to meet the demand for a complete course in two books. The
following embrace some of the characteristic features of the books :
>m-
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i la
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the
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Sec
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and
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are placed in the Appendix, to be used at the discretion of the teacher.
Arithmetical puzzles and paradoxes, and problems relating- to subjects
having- a demoralizing tendency, as gambling, etc., are excluded. All that
is obsolete in the former Tables of Weights and Measures is eliminated, and
the part retained is corrected in accordance with present law and usage.
Examples for Practice, Problems for Review, and Test Questions are
abundant in number and variety, and all are different from those in the
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The arrangement of subjects is systematic ; no principle is anticipated,
or used in the. explanation of another, until it has itself been explained.
Subjects intimately connected are grouped together in the order of their
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Teachers and School Officers, who are dissatisfied with the Arith-
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