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I
IS;
I
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(V
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^A
TREATISE
ON
COilMIICIilL ARITIIIIIiTlC
TO WHICH ARE ADDED
PRACTICAL COURSES ON
MENSURATION AND BOOK-KEEPING
DESIGNED FOR
HIGH SCHOOLS AND ACADEIvIIE:
By The Christian Brothers.
]S
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Sanctioned by the Council
of Public Instruction.
MONTREAL
44 COTE STREET, 44.
/n
r Hi
Entered, according to Actof the Parliament of Cann da,
in the year one thousand eight hundred and seventy-two,
by Ephrem Gagnon, in the office of the Minister oi
Agriculture.
#K*f ACE.
Our o^ec , » ,*> ,5«*ii,,»i„„ „f ,y, ^„,.^ ., ^^
P y our H>g-h *<*«(;*, Ml Academies in the Dot^inio.
ol Canada, w* » .Wxlerate-si.ed book containino
™'^".'7*'^f^-*^t*'»tf Poetical Tr,atiseson Com°
av „g, th,.rel,y, fe. lfiw,:,.u«. ,ho expense of scve":
within the read;. «l (fii,. Hi,|io„„j, ^i^^^^^
As decimals l^(sw <fe.^™„ ,,,,, ^ ^.^^,^
we have chos.* M, A,,« ,hem along with the latter
thorelore. they mW*»>"fa»d introduced in numeration
Though we iiM,^ ^^i„ll f^ii^^^j ^^^
system, yet. the,^«,,Awl has not been neglected
Amongst lis »wi»«* ^vficular features, this work
otters the i«iw„to4 «**antage of proposing a far
greater number ^1>««»,^, q„,,,i„„^ ,^^,„ ^° ^^
of he same s,«. ^ ^, ,,,„ „,„„,,^.„, ^^^^ ^^^^^
will hnd in It .Mil *^ W*,.„,a«„„s requisite to qualify
them for the po^^l^W Ml accountants or business men
Some pers<«M, f>f^ ^ ^^^ ^^^^ ^^^^^ pl^^
t'
lii^i^
PREtfAOK. ^
merous examples oF application, having for principal
object to render the pupil iamiliar with figures.
Some desire the answers placed immediately after
the examples, and others desire them omitted. Both
methodshave their advantiig-es and their disadvantages.
In order, therefore, that pupils may receive the advant-
ages of both methods, the answers to nearly one third
oithtj examples in this book are omitted. They will
be found, together with clear solutions of ail the exam-
ples, in a Key to this vvoik, prepared for the use ol
teachers and private learners.
jipal
after
Both
iges
raiit-
:liird
will
sam-
se ot
CONTENTS.
SIMPLE NUMBERS AND DECIMAIvS.
Paob
Definitioiii 9
SigM 10
licman Notation n
Arabic Notation , 13
Numeriition Table ]4
Rule for Notation 14
Rule for Numeration ]5
Daoitnals jg
Appiioiition of the Principles of Nu-
meration 18
Addition 22
I Pa4IC.
Subtraction 28
Multiplication 3fl
Contractions in Multiplication 44
Division ^ .,,, 5(,
Cnntraotions in Dirision sy
lJ>ciiiiiil Currency 53
Hediifliion <if Decimal Currency 65
Praclioal Prohloia* combining the
Fun.lamotital Mules 66
Billi and .-Vo.iuiiints. gg
Forms of Billi) «cd Accounts 7o
PROPERTIES OF NUMBERS.
Bxaot Dirliori and Prime Num-
bers 78
Table of I'rime Numbers 79
Factoring 79
Cancellation gj
Common DiTisor go
Oroiitost Common Divisor „ 83
Least Common Multiple 84
FRACTIONS.
DefinitioM, etc S6
Reduction of Fractiong gg
Addition of Fractions 94
Subtraction of Fractiong 95
Multiplication of Fraotion? gg
DiTinion of Fraetiona ^9
(iroatest Com. Divisor of Fractions! 103
Least Corn. .Multij)lo of Fractions.. 104
Practice by Aliquot I'arts ]05
.viisoellanoous Problems i09
DENOMINATB NUMBERS.
Definitions, etc ijj
Old Canadian Money 114
Knglish Money n^
United States Money 114
Troy Weight jjj
Anothocaries' Woi^'ht
Avoiniu
116
[.r-is Weight j,^
Linear or Lfmg Measure .
fwneh Money ^ „r , "'"^ »i>^asure
^ ^ " "' I '^""•7«"' Long MeMurfc. „.
117
118
I J
I
▼1
CONTENTS.
FRACTIONS.
PaOK.
Definition!:, itce Sfi
Reduction of Fractions 88
Addition of l?ra' ions 94
Snbtraotlon of Fractions 95
Multiplication of Fractions^ ........ 9fl
Pa«r.
Division of Fractions 9!»
flrnatest Coni. Divisor of Fractions. 103
Lea.st Com. Multiple of Fractions.. 104
Practice by Aliquot Parta I0&
Mipcellaneoas Probiama 19V
DI'.NOMINATE NUMBERS.
DeflnUions, Ac 113
Old Canadiftn Money 114
Knglisb Money 114
United Stntes Money 1 1 I
French Money 11')
Troy M'eight Jir)
Apotboonries' Weifiht ll'i
Avoirdupois' Weicjht ll'i
Linear or Loni: Measure 117
Surveyors' Long Measure,.... ...., !!'■!
Squfiro Measure IIS
Surveyors' Square Measure 120
Cubic or Solid Measure 120
Liquid Measure 122
Dry Measure ....- 122
Maasureof Time 12:{
Circular Measure 124
Miscellaneous Tables 126
The Metric System of Vfe\ghtg aod
Measures 126
Reduction of Compound Numbers.. 1.14
Reduction of the Old Canadian Cur-
rency to the Decimal Currency.. 141
Re<]uotion of the Decimal Currency
to the Old Canadiah Currency... 142
Addition of Compound Numbers... H'i
Subtraction of Compound Numbers. 144
Multiplication of Comp. Numbers.. 14tl
Multiplication of Compound Num-
bers by Aliquot Part" 143
Division of Compound Numbers... 15.'<
Longitude and Time 15&
Duodecimals 150
Multiplication of Duodecimals 1S7
Division of Duodecimals.... 158
Miscellaneous Examples 169
RATIO, PROPORTION, AND PERCENTAGE.
Ratio 1»3
Proportion 1''4
Simple Propiirtion , Ifi5
Compound Proportion 108
Percentage 171
Misc-llaiieous Examples in Per-
centage 17.'>
Bituplo Interest ~ 1^^
Partial Payments - IS4
Frobiems in Iirtofest 186
Promiscuous Examj los in Simple
Interest '■'''
Oompound Interast > 191
PromlMory w ♦!».••>»»......■..•.....»• ivw
Forms of Notos...MM'«.c ~ ••••• IM
Profit and Loss 1U7
Commission and Brokerage 200
Firo and Marino Insurance 20.'5
Assessment of Taxes 209
Custom-House Business 207
Discount and Present Worths 209
Bank Discount ^ 212
Promiscuous Examples in Disoount 21fi
Stocks - 218
Partnership 223
i'^xohan^e 228
Foreign Exchange 230
Equation of Payments 233
'nvolufli
KvnUith]
Square f
CuUd no
^rithmol
Qnotnetri
M«n«ur«r
MiicolUn
Account*
Omtttl A
DtCnitUnt
il(M«uratl<
ficos .,
P"mifco«i
•al Hurlii
Mensaraiici
ttcDfral l'r»i
Doo«i,»: ^f.H^
Iwfru(;fion«
liny Book,,,,
Jnurnal .„.,
•^gw
Forms of JJ.il
Proceiis of C)
Order of (;|,,i
Pfsftfical Rx.
D(ni«j,K B«'(|
Dai, l>fw-l,
JonrnaJ
Trial Ualadci
Statement
Cash Bo-ilr ,„
Bill Book
OofflBisaiofl H
Piaa.
«',»
ictions. 103
ctioiu. 104
106
1««
btoaad
125
mbers.. IM
an Cur-
•rency« 141
irrency
■eney... 142
ibers... 142
iinberp. 144
mber?.. 14t(
I Num-
143
ibcrs... 16."<
15ft
156
als 1S7
168
■ •«M ••••■ JIVv
1«7
200
5 20;5
205
, 207
th 209
212
>i8oount 2](!
21S
223
228
230
233
''ONTUNTS,
MlSCELLANli;0US.
.^"'^""'n ^fi*rnnU^"Z l.r
'nvolufion,,, '''''
R»''^iUrm,.J.'.',',",' 24i
Squnri- Root'"'.'.','.* ^^'
Co»(o Root,,.. ""
••••••••••••
242
245
24«
**'•*«"•"«';•; K«'.mpi„..z'::::' 254
2«5
•••••■.• ..... 2fi<j
••M*M..n<. 298
Oootnetrlral Pr„^,„,^
Miicoltanooiiii |
^a-^h JJdIance
-Account fif.Saleo
Table of Foroit^n .Monpv<
Examples on Kxt-hanije..
VII
.. 275
,. 27M
. 2<'2
Arbiirnfion of Exohango ....'.'.' 287
Arb.trnHon of .Merchanrli.o .'.' 21)0
- Iert<:-
ures,.
JSIO
Table of Foreign U'oighfs A M
ures
SupplefDont to Progression;".'.'.;;;;;; 29J
Mil IniuraunB
niuraooe
'^nnuiHes
298
Thermome't;'™,;;;;;:;:::.."*"' :]fj
Kqulralonts of M.tria Mtui^ni'.'. 3I|
MENSURATION.
'•"miicono,
•«l Surfafj**
Bx«»p>;
<■» m fcciilin-
•'•■•oraiiwj of ci^Ji
»r Surface*.
914
317
325
•'>27
PromJpcuoug Rxamplw in Circular
f^urfaoos.,..,. _
Definitions of Solids
•nstiration of .-otitis
Miscellaneous I.:xa,npIe;i'n8orrd';;
lablo of Chords... .
SS4
3.37
34*
355
SM
BOOK-KF^EPING.
;-«rtptiri, ,,r p,,„,, , y^
Oen?r«l I'nncif.j©. J
?""'-' '•:«r«r,-8r;T I .;;; j
in»fru<fion« „.. „
Day Book Z'.'.Z'""'' 7
J«ur»il „ '""" • '
•^g-r :';:'::::::"' !
J«rtt,g of Oalanc, BhnttZZ s
Pro«e«» of CMbjj „ i,
Order of C|„*ir,g ; ^'
pr^cfiMi B«<.rr„M„;" ;;;;••; f.
D..t,«i,K E«t«v,_hbt I J „..; 3,
Jo^rniuT. ; 31
Trial B«ia,.«';':a";;;-;;;;;;;;;;- ,^^
Ca*h Bo-.k ^^
Bill «w4..., 48
48
M
Aocminf, Sales
Pra-'f.ieal Kxercise's."
'>"UBLK
KNTRr,— .srt in,
19
Coma»if.ioii ^»imUt^
Rem.irkf
Journal Pay l;ook7.".*.;; "
Trial Balance and I'nVenfory"
Invoice B'lok
Sale,'! Book ""[
Commigsion Sales Book
Account Sales
Check-Book ;,";;;;
Receipts, Notes, ic".*.**',".'.".*
Letter Book ~
Practical Exercises...;;;;"*;;;
t)otjBLR i'-N7RY,— sbt'iv;;;;;;
Remarks ""*
Routine. '
Domestic Invoice Book!!;;;.;.;;;*;"
Foreign Invoice Book...
8»lat Book.........^ """" "*""
u
51
M
5e
n
05
«7
•»
11
U
u
11
u
84
00
»•
»1
93
M
^ •;•.
Tin
J0NTRNT8.
Paok,
<'n'h nook ,...„.. „ 104
U'll li.M lOS
IrTPtit.iry 11 ok 110
Jcmal ni
B i'»noo ^heot m
Si>G',R Kntrt lift
Rr-j-arkj I in
bkj Bok 117
PiOR.
Cash Book « V.'«
UJ-or 121
Statement , 124
Chanoinq Sixqlk to D0CBf.K Ex-
TIIY I2A
l'rncti>:al Ezerci<o.'< I2T
flint-! as to Kefourcus und Liabil-
ities > 131
COMMEiiClALAIIlTHMETIC
J)EPINITIONS.
*» 'ViS-^'^^J^*' i' *^' ««^«"o« of numbers.
?■ M ^"^.^ " *"""• °'' • "»"^'« thin-
i..ci« of wt'e" ^"'"'^'y' •« *"^ ^"^^-^ *h'^t will acl.it of
6. JJ°o;berfl in general, are either abstract or concrete
u aVpa'SSS!!.? r;:ru?r'?"„n' "^'^'->-™
■ The, .r, diviJcd into IT.^iaLj*""'-^'"' •"""'J'^"^
«raa aeci„.U fraction., X'.^uZl'^Y.' ""'' "^ "'"<«' "^
>». Concrete Wumbers m .mmbo™ u^d .itk .■
»•» paruoular thiog or qatDtit, Tbu. J[^ «terM06 to
10
D1FINITI0N8.
I I
They are also subdivided into threo olassefl :
poinds^^'"'' '''"'^' '^"**'"° ""^ «°bdivi8ion8, as «> yards, deven
/fJ"i;//I''T"''V''^i:*''^*°°^'"P*"'*'^^'*^ ^'C''"*' subdivisions, as
fioe dollars twenty Jive cents. =«""«, »s
3rd. And la.stly, those which contain decimal subdiviMong onJv ao
twtntyfioe cents ($0.25). ^' *'
O. A Simple Number is either hd abstract or a concrete
number of but one denomination; as, two, <en dollars, ;?>m hats.
10. A Compound Number is a collection of concrete units
whose subdivisions are not decimals, but represent several deno-
mmations, taken collectively; as, «x pounds /our shillin-a nine
pence, three ftctfivc inches, etc. "*
11 . A Power is the product arising from multiplying a num-
ber or quar.tity by itself, or repeating it any number of times aa
a tactor.
.^ 12. A Root is a factor repeated to produce a power.
13. A Demonstration is the prooeeg of reasoning by whioi
r truth or principle is established.
14. An Operation is the process of finding, from given auan.
titles, others that are required. ^
15. A Problem is a question requiring an operation.
16. A Rule is a direction for performing an operatioa.
17. Analysis, in Arithmetic, is the process of investigstiiu
principles, and solving problems, independently of set rules!
\H. The Principal or Fundamental Operations of Arith-
metic arc, Notation and .Nuuieration, Addition, Subtraction
Multiplication, and Division. '
SIGNS.
19. A Sign is a ^mbol employed to indicate the relations of
numbers, or quantities, or operations to be performed upon them.
(.) is the decimal sign indicating that the number after it is a
oecimaL
I lueaos dollar.
». ir*aiii«gimpI,auiBb«rt- 10. »fA«< ». aoompound nuiaberT-ll. WkM
. r"--- — ■■•----- .•••'^- • — '<" 'r««« w a aemoasirauon T — 14. Wkai
wotatiow.
'J'hns
-h the sign oi addition, is renrt plu,
be added to 8.
tob;M!£Sd^rr^'^'--^-^«-Thus.8
11
7 siprnifips that 7 is to
7 signifies that 7 is
^4, „ „, i. , , - 1+,,^'^ x^ . f n: i;"- '-uf
fi>niirf,^,b.fi)rctlio».i„Jir,rj I .! P«.n""I'««. ba« b»m mr-
Thn,, [(8 XT) + U1 i T"^'i*''e°'««'l«<*cbrackeu.
= 70; 70 +V= M-' "^ *'»»-'"8 X 7 -= »«; S6 + ll
..d u tdtifjr- ^'"'' ' = * ■"'•"• *« »'■» »f » •» 4,
>»,".»..». IJ, M read, 6 l» '« 9 as 8 is to 12,
NOTATION AND NUMERATION.
e.p**. "b"""" " '"^ ■"^'"' -' '«^'"» ■""■"«™ when
.ifhs^T™™""'' "' ''°""'°" •" '" «»'-"»" ""- "■• ««a«
ROMAN NOTATION.
nun.bers, viz : ' ""^''"^'^ *^''*'» °^P^*^1 !«"«" to ^express
^ ^ * t D M
l^r.,
Un,
fifty. u °^ , , "»• «>•
hundred, hundred, thowand.
r»
IS
HOTATION.
I
It will be seen from the following Table, that al! numbers may
be expressed by the mo of these letters, cither by re|>etition8 or
ooDioinatioris.
U\ Eyery repefifion of n letter repeats if^ valne: thus II
represents two; ITI, represents thrrr ; XX, (wentf/, etc. ' '
2n(i. Wnen a letter of any value is placed after one of greater
valud, it ad(I« its own value to
the .greater; but when placed
before, its value is to be subtracted ; thus, VII represents seoen ;
XI represents eleven; while IX represents nine, or one les, thai
ten ; jLL, forty, etc.
3rd. A bar or dash (-) placed over a letter, increases its value
» thousand-fold; thus V denotes Jive thomami ; TV, four thou-
$and; X, ten thotuand, eto.
I
II
Ill
IV ,
V ,
VI
VII
VIII....
IX
X
XI
XII....
X II...
XIV....
XV
XVI. .
XVII..
xvni.
XIX....
XX
XXL...
XXII..
XXtll.
XXIV.
XXV...
u
((
i(
((
((
li
((
18 Ono.
Two.
Three.
Four,
Five,
Six.
Seven.
Eight.
Nine,
Ten,
" Eleven.
" Twelve.
" Thirteen.
" Fourteen.
" Fifteen.
" Sixteen.
Seventeen,
Eighteen.
Nineteen.
Twenty.
Twenty -one.
Twenty-two.
Twenty-three.
Twenty-four.
Tweaty.five.
WAMLM.
XXVtl i,
XXIX. "
XXX .. '
XXXVI "
XL ••
XLIX •'
L
LX '
LXX .. '
LXXXT "
XC. .
XOIV
c
coc
CD....
D
DC...
CM....
M
MC...
MD...
MM... "
MMM. -
X -
M «
.'(
><
>(
It
«
<l
((
1(
(I
Twenty.sev«n.
Twenty-nine.
' Thirty.
' Thirty-gix.
■ Forty.
' Forty-nin*.
' Sixty.
Seventy.
Eightv-ont.
Ninety.
Ninety-four.
One iiundred.
Three hundred.
Four hundred.
Five hundred.
Six hundred.
Nint- hiindi id.
One thousand.
Eleven hundred.
Fifteen hundred.
Two thousand.
Three thousand.
Ten thousand.
<W milllM.
irabers may
>etition8 or
1 thU8, II,
to.
of greater
ica placed
ints seoen ;
I hat than
58 its value
four thou-
le.
(1.
red.
cA
id.
i
'.d.
1(1.
[red.
Ired.
id.
[ind.
1
1. Six.
2. Right.
.^. Ten.
^- Thirteen.
6. Fifteen.
"5. Seyenteea.
7. Nineteen.
8. Twentj-five
NOTATION.
BXBRCrSES IW ROMAN NOTATION.
B«pre8. tf.e following nu.nhers by letterBt
An». VI.
13
ajx.
9. Thirty.
10. Forty-^ix.
11. Fiflf-four.
12. Sixt>.
13. Sixty-eight.
1*- Righty-four.
15. iVinety-nirie.
18 ^ "J".'l""'*r^ ^''d nineteen.
}8. Jight hundre<J an.l .«eventy.five.
19. Nme hundred and .ixty-five.
20. Pour hundred and fJ.rtv-one.
22 Siv"[ "f'T^ *?*^ eiglity-seven.
22. Su hundred and ninety-five.
M. One thousand six hunrired and fifty
24. 0«e thounand eight hundre<i and fony.
ARABIC NOTATION.
explt rfu'nbi^^f.^f *°° ""P'"^'^ ^^ ^^^-^--^ or figure.,, to
1 2 ^ .i '''
f^iV'V.c from thp T nf.-n r i J ^ -^"®y ^'"'^ sometiuios caller,
ct>A^' is called „, /I "^'^u""' '''"°*^ «^.^'"'fi^« /"9"-- Th
26 In ordt ? i T'' ^'"''^"^^ ^' '^"^ "^ value of its own
Thus, the fir«^eZsen^Th.-^^u" ^^' P^''' '* ^'"''"P'^^
third,, the A.,./ X the fourth C *^^ r^"**' *^« ''"' '^
each succeeding. fiuVe to th«,jy/r'-^^^^^^^^ ^"^^ ^^^ o--'.
the unit of which Trt^nfoM^hl . '""/'"^"^ *^ ^ distinct orde,
the riaht. '^ '^^ ^''•"^ ''f » '^"it of the order f
pen"druptV.!';,:ttL''irtr™^"'-'p''""^^^*^^ e^^- ^e
14
•nniKRAtioK.
S'nr«!. ?nr/ ^T"*^ ^^ * ^"'" "««<^ inoorabin.tion with other
fiK'ures and deKendin- upon the place the Qcmre oecutj^s ThI
Cipher be,V3me8 significant when 'eonneoted with other ti^eu;s ollt
by filhng a place which otherwise, would be vucan7(No 28) ^'^'
hand^JrJn/l*^', '''I '"?P'' ^*'"« ^^ *•'« first. figure on the -eft
iureofthrlrthn';;?' ^*r ^ "r^^^^ 'l^o»"and«f because iti..
andfts local valn^^" ' v^^'' """P *^ "*'"« ^•^' ^^« ^^ird H^ure i« 4,
eirnple value of h/fiT-' ^°»"?.'' '? « «g»re of the 2nd o?d.r ; the
NUMBRiTION TABLE.
i
«M '-S
O H
*> «t-i .2
3 g K
'si
o
3 "
c 2 c
e
o
T a
•^ o
CE ~
s :=;
S D «
a
o
^.2
45 ® o
a « =
a
o
o ^
2 °
0:3
a
cs
us
O
B
3
O
cog
1 2 7, 8 9 4, 2 3 7, 8 6 7, 5 2 3, 6 7
a> «♦, <«
fc> o c
a ^-^
W'^ r-*" i=; ki « -= = 5 s
a •-
s,!' s^^ 5s^' s- •^i-f SsS
^ RULE FOR NOTATION.
28. To write in tigureg any number without difficulty
of I"u;!t;on"iitn',the?i?L""S°'''l"'^^^^ *^« « '« *^« -der
in the order of hund^s of iniS" i^f *''^^**"' k^^ thousands, the 6
places. Thus ^^'^'^ "^^ "'"'^ •«'^ P"* ciphers in the vacant
4 006 020 ftOO
1.
3.
3.
4.
6.
8.
1.
2.
3.
4.
5-
6.
as. Wkt^i»tkaritU/m-
U»**Jiamf
= « a
NITVKUriOIf.
RULE FOB NUMERATION.
»». To r^ad numbers represented by figures
JJ'^tn at th. right hand, and point off Z 7' -
of three placet each. The first .Cw ■ .; ^^'"''* *"'« P«^A
thousands; the third, .£ lovs 1^/"/ "^.?"^"«' '^«^''«>»rf,
mK TRILLIONS, &c. yA* w ^',; /t.lT'^' ^''^^^^-^^J '^«
i5?*. The number 345 678 907 654 \7^ ""' '''"''fiacres.
«n»aner: three hnndred ami fortvL f •,',' '""^ '■" 'he followmg
r/S^T^* l[iilioi.«, nine hldre7a^7,,^"j^»«?,,«« ''""^''^d anf
-d fi%-four thousand,, three hunl^f ^^rweSj-^'unl' '""'^^
EXERCISES IN NUMERATION OF SIMPLE NUMBERS.
400
6004
80067
670005
9006014
92100121
7.
8.
9.
10.
11.
12.
800800003
87974015
35000918
30150900
70S000549
4050300
28764105
1000500
3008727
605054045
78592835
106405021
EXERCISES IN NOTATION AND NUMERATION OP
SIMPLE NUMBERS
1. Twentj-eeren, forty-eight, si^^ty-five
3 or S'lS r 1 f '^"^' ^''' ^-d-d-
4. Thre hu dred a,5'Skv"' ^'""^'^'^ *"'^ ^wenty-four.
6. Four hur. 'ed and nfarnnV'"*- ^"l^'^''^'^ ^"'^ '^^o-
6. One thousand Z. one Ke hllnl ^T^''^^ *"^ "'°«-
7. Eight tliou^and one lu/r.S ^aid S *"'^i '^'■^*-
8. N.ne hundred and sevenS Sfotrntfi'v /"^^-r i^^"^'^"^.
9. SercD hundred and eiditPPn H?^. . , " ^""'^reJ and two.
CD
CMfV
DCCXXX
CMXLLY
XlX
MM
39
What u the ruU/or num^ratitn t
mn
1^
li
DBCIMALS.
DECIMALS.
» th?' ^^?^'^^"»a^S arc meant, parts ten times, ., hun-lred times
t thousand tnnes. etc, smaller than the unit ., which are TnS
cessivelj ten tin.es smaller than the other '
**f^. A whole number and deeimaln in « <^;, i " ■
constitute a Mixed Number ' '""'' ^•■^P--'""-
«i^i huSr^s,r;'^s^ j;;^"':::^ "I'^r d^^^^V' ''"^ ;^^^'"'^'
and eight thuu.sandth6. •*'"^' '^"'^'' '"^'•^ a»J decimal two hundred
NUMERATION TAHLE
»Oa WHOLE Nl'MBElis AND DBCtMAI.S.
ISOK.VDINQ rROGKRSBION.
1>E8CKNDIN0 PtOORWSlOf.
8.
9 3.
sandths. ionihs. ioiths.
•As 18 easily seen, decimals," with regard to their order folh.™
inver.oly the systen> of numeration of whole nuXs the ? Ij
n^ times .nullor than the unit, wherea. ^e„ is tre unit cpe^ted
Tit a^nll^'l'ff'^^^P'"^^'^'^ '^' hundredth pa toTh«
unit, and a hundred, the unit repeated hundred ti.u.s &o r
wit iT^ m:^:/S"S^ ''■ '^"' ""•"•^ -• ^••^ "> -^-^ --^ - 32.
DMOIMAIM.
It au Huule tin: jtii-ii^ • ■
the teiuli ^.,,,'^, ■,7'*'*^ '»to ten enual nans p..„i •
point ; tic,riim/l(fr''J^ '*T**'"' "/'''''• "^hich place th. l ,
6. Three ^W^Jfki'fi, Lp L ' , ^""^''■*''^'''«-
«»^#^t»tt, a„,j a,, huadredth..
18
THE PRINCIPLES OF NUMERATION.
P. Twol,„„rl,.o.l an.l Mvc.tv. n,,,! nino lunulrcl-thoimndths.
10. One thousand an.l six, and five ten-thouPandth*
1. Joi.r tliousan.l and seven, and three hundred-thou^andtlw.
.o* ^.''^^■"'n^ «*"'! twent/.two millionth^.
3. hji^hty-two, an.l thirty-BJx hundred-n.illionths.
14. higi.t lmndre.1 and fifteen, and sixteen thonsandthi.
15. Iwenty-seven, and one hundred and two biUionths.
lb. Twenty thousand and ten, and thirty milliontha.
BJU-HMS ORALLY AKD WR.Ti: IX WORD„ THK rOLLOWjNO IflXn
mruBKRa ajtd sisolk decimal*.
1.
2.
3.
4.
1.
3.
3.
4.
6.90
9.908
641.400
703.2004
0.004
0.000607
0.005
0.00OT0O7
Mijted number*.
6. 354.0064
6. 352.06046
7. 76.26007
8. 375.60050(
Singlt decim^ila.
0.4072
0.401950
0.9540626
0.075003
9
10
11
12
9.
10.
11.
11
41.004064
452.010778
7657.008007
1898.04
0.69804445
0.736050210
0.000500019
0.00000501
•PPLicATioN OP thk: pkinciples of numeration
A8 LAID DOWN IN N08. 27 A 31.
it fo^owt°''°"^'"° '"^ *^^ principles laid down in No8. 27 & 31,
1st. That, to render a who/e number, ten, a hundred, a thousand
times greater, we must write at the right-hand side of he number
one, two, three nau-hts or ciphers (1). numoer,
tl. Jfi "fL*?' "?'"^'' ^*^ ""'^'' ''""'''"^'^ 260 in adding a cipher after
the b, that ,s, ten Un»e« greater than the first, since the units becomi
tens, and the ten«, hundreds; or, in otherwJrds, thefl'ur of tbeTst
order becomes a figure or the second order, and that onhe second
we obtarSn ' ??»re of the third order. If we ^d another cTphet
we obtain 2600 which is a hundred time, greater than the first num^
ber since the 260 units have become 26 hundreds. ^
Thus, 26..S5 beoome/i tea Umes greater if written a«3.6. tixM tk«
tenths become unit*, the units tens, 4c. ' **
fraatar Y- 3«. Do. A uhoi. N«Mi^.r witA a d^Mmal •mumIV ^■*'** '^^
Uiiy T''"',?"'"' "'ti "" '"»■'*' "«»t.iD.(i, «qa»U ton. a hondrwl d.^ A.
1.
!«»
2"
3'»
4"
*" «WO»LM or NDMERATION.
•"'.', two, throo, &J., jg„™'- "• "'" »a from the right-hand side
Thus, in the nuiDher 99*; . if
place of the units. ^ """ °"= ^main to talte the
numbers beco,,;, O.0O8 8,"d o o02fi'« ""f ■ 'T""' '^'«^; ZTZ
&sr*^'"''-4re^s:S"brsri^hrj^ir
1.
1"
3"
50
PRACTICAL EXERCISES
Render the whole number 38
10
100
1000
lOOOO
100000
«* 1000000^
times greater.
Afu.
Ans.
dns.
Ant.
Ans.
Ant.
380.
38000.
3000000.
V,'i
so
THK PBOPRRTIBS OF NUMKllATION.
8. Render the mixed niimber 42. 1 064231
1«»
2"
40
«°
60
10^
100
1000
10000
100000
1 000000
>■ times greater.
3 Render tiie mixed number 4.20
1
1»
20
3»
40
5"
10
100
1000
10000
100000
times vreater.
6° 1000000 j
4. Render the decimal 0.05
2«>
3"
4»
60
10^
100
1000
10000
lOOOOO
tiniea greater.
fio 1000000
5. liender the whole mini her 6705415
l*
2"
30
101
100
1000
10000
100000 I
1000000 J
• times greater.
©. Render the mixed number 7610438.06
10
30
6«
lO'i
100
1000
10000
100000
1000000
timef smaller.
7. Render the mixed number 5.45
1»
JO
40
6*
101
100
1000
10000
190000
•• IfMOOO
tiracR smaller.
Ann.
An«.
Aug.
An:i.
Ang.
Ans.
Ant.
Ans.
'■ns.
Ans.
Ans.
Ant.
Ans.
Ans,
Ans.
Ans.
Ans.
Ans.
4210.64231
421064.231
42106423.1
iS.
42000.
M
60.
Ans.
Ans,
Ans.
^n*.67054150000.
Ans.
Ans.
Ant.
Ans.
Ant.
Ant.
Ant.
Ant.
Ant.
Ana.
Ant.
Ant,
76104.38M
76.10438M
•.•dS4f
Ant.
2*
4*
»• /
«" JO
10. Jl
14.
19.
1«.
17.
IS.
19,
80
81.
8a
84.
85.
8«,
87.
88.
8».
80.
31.
»8
88.
•4.
ISMKifci;.< iiJtaba!8{MM«lii"j'J;yi
«.
'*«"'«'' '»" rl.cimal 0.05
KM
100
1 0(10
1 0000 r 'injefi «ri,a|ler
» 00000 I
'OO'^OOO j
81
»• ''"'"iT r.H. mucd n„„.ber 206.007
An§,
Ana.
Aug.
A}ig.
An 8.
Ans.
0.000006
2*
101
/oo
J 000
1 0000
'00000 ,
'ifiw fMialUr.
^J" i 000000 J
A7)8.
Ans.
Ana.
Ana.
Ans.
101
100
1 000
J 0000 f ""•«"< "tnaller.
'00000 I
'000000 J
19,
14
19.
1<I.
17.
IH.
l»,
90
81,
93,
99.
84.
89.
80.
87.
8a
89.
80.
31.
38
««.
84.
44
4*
44
44
46
44
44
44
165.
.'<867.
2004,16
040.4
74.
746.
^ »..'{.')
76874.
6.46H
0.46
I^IO
CO.--,
i'.678B
Ann.
Anx.
A nn.
A?l!i,
Ann.
Ann.
0-00206007
146.2.309
100
lOOO
IIH)
1000
loooo
loo
10000000
1000
1000
1000
1 000
lO'jOO
10 time.f -/reater
4,0000007 ](;o
0.0007 jo';;
I4M0 ,o(,j,^,
10
«74,^f;7 10000000
l^'«^e4 1000
Mfl 1 0000000
n't ^'^OOOO
"•'''a 1 0000
II
(1
u
t(
<(
a
li
((
(I
«
'^mailer.
greaier.
it
PMiallor.
^^"f. 1650.
^"*"- .38.67
Ans.
An.s.Umo.
it
n
li
li
it
grcatt-r.
enialler.
greater.
' i
ii
Mjiallfr.
it
greater.
siJialler.
greater.
H»>ialler.
a
greater.
H»na]ler.
greater.
f'tnaJJer,
'e«t«r.
Alls.
An..'.
Ans.
Ans.
Ans.
Ans.
Atui,
A71N.
An.i.
Ans.
An,'<.
Ans.
Ans.
An.'i.
Ans,
Ana.
Ans.
Ans.
Afia.
Ana.
0,074
4.50.
0.00005
6060.0867
22
ADDITlOir.
ADDITION.
OPBRATIUN.
428
635
874
193 7
ber^of- 1^"*?^""?"/' " P"x-« of un.tinj: together wreral num-
Sum t Amount • ^ "* ^« ^-^ * -'^''« nu,„ber called th.
de,H>!!!i,.!;!- f "'• "' '^' "'"•' '^'"' '''"" ^^^^ ^*- ^^« "-
ForinHtance, .lollar- cur, be tt<l.Jed to .lodarH, pounds to Donnds and
t:xampU of an Addition with whole numbera.
^^WhatiatheBumofUi. three following numbers: 428, 635, and
..nuI!*.Oh!f ■"""'".*'' ■[.'■•■'"8«'^ 'l>» n">ober«, so that all th«
flret ad.l the oolnmu ..t «n«V* ,• thug, 8 and fire aiti 13. and 4
arel7 un,t, .^ I te„ a„d 7 units. Wo writ, tho 7 "iniU
under the column ot uniui. and e<urg or add the 1 ten to fbn
column ot tons ; thue, I Hdd.U t,. 'f m»k« S and 3 »,. •
and 7 are 13 tens - 1 hundred and 3 i" ' W, IZ^L
3 lens under the oolumn of tens, and oarr ih. 1 h«dn,d U
ntfh?' •^I?^''^'!," -5' addition by the figures of the first colu.nn
at the nght-h:ind side, 80 that iii whole numbers, we may carry
the tens proceeding from the addition of the units to the colunm
ot the tens, the hundreds proceeding from the tens to the column
of the hundreds &c.; and also in decimals, carry the tenths
proceeding from the hundredths to the column of the tenths and
the units proceeding from the addition of the tenths to the ooluma
of the units, and so on.
41. From the preceding illustrations we deduce the following:
Rule.— 1. Write the numbers to be added so that all the unite
oftM tame order shall stand in the same column; that is, unite
under units, tens undpr tens, etc.
II. Beginning at un^ add downward, or upward, each column
eeparateUj, and u>rUe 'h -., nd.-r,ath, if it be Us. than ten.
,1.: /V^ *"? "^"".^ "•'"'" ^* '«•» ^ ^'-^ ^^«» ^««, ^rite
the umt figure only, af.{ .../„ 'h, ten or te.: to the next oolLmn..
IV. Write the whole sum of the laet cobunn.
w uiMiNMm to «• immmmMdt^ 41. Wka$ w tk« tm m-m i nUe/m- mddHim t
5)^V
" ' 'fi: - i' ^ ^y ] "\ ^~i""-' — —
m^
r^ . by a pointy ,, ^,„,^ drriZr' ^1'"' '^'. "//-m th.
//t« number
areciths, 4682 uni* , l> i .T"
"""» 7'. l.,m.lr,.,W„, and
Orit, CATION.
»S79.26
46 8 2
i) 7 3
78 56
^n*. 1 6 6 9 I . c o
which is road in the following
05
75
HO
86
hundr«dlha'JTi*;";„^/r« '". «nri 5 are (5
write the 5 hundr,d!h! *. ''"'"''•<"''»>«• VVe
than two. "•'*'''' '"^^ ^ .^''•^'ater nuniber of parts
Ana.
OPSRATlOjr.
128.24
349 00
5(1 >5
I49.d4
__967^
"1645715
PliOOF-.
?flt. Part.
123.24
349.00
472.24
2n.i. Part.
5G.25
149.34
967.32
1 172.91
Addition of
partial io/uia.
1172.91
__47l\^24
1645715
which k read 1645 unita 15 hunc^redthl
USE op ADDiTrnv iJi'i-
number.: the whol^^Tstt t rthT Z^ '"^^^'^ -- ^^-voral
pan-a. are given. The selli g p'^^ ^S^ P"°« -'^ other ex-
pr^t are given, <fec. ° ^ ^^^° "»« buying price and
?. We know that the rP^./u,.'^,^ ^^ ,., • -
»n addition, when we must find / T^k^ ^^ ** P'"''^*^"" ''^'quires
*:!:^^f several othe^r^ number equal to the sL or
24
ADDITION.
PRACTICE IN ADDITION.
I.
600 f 850 + 501 + 49 + 904 +
604 + 810 + 333
3.
4.
6.
6.
7.
759 + 216 + 655.
Ans. 4433 units.
1226 +3004 + 4004 + 5105.
Ant ] ^cmc
19223 + 125979 + 189023 + 100610 + :5300. Am. 4.38135."
15879 + 15957 -^ lOOlUl + 8107S9 + 975020 . lOOUO.
?uwn<?* "^.nM"*" '*'•' ^ ^* ' ^'^ + "^"^ ^ '012. 4hs. 1390.
110200 + 9104 + 4610 + 10110 + 95303 + 8888.
100989 + 100001454 + 77777707 + lOllOOOO + 100000090.
^oo;n. ?i„^.J" 1^0^^+ 132 + 20000020 + 109909 . 8888888
I L'^ 11^^"^^- ^ns. 80317134.
9. 49 + 97 + 68 + 45 + 64 f- 68 + 3S • 97 + 75 -*- 03 + 49 -
in ^L'^ ^t" 59 + 87 + 65 + 43 + 21 + 10. Am. 1238.
u \tl\: ^l:^ '^+ 67 + 86 + 3y ,. 47 + 74 t 98 + 57.
Aa' ^L"*" *?. "^ ^* "^ 46 + 67 + 86 + 64 + 3G + 95 + 34 + 66
t ^7^ ^t'^ ^f +65 + 67 + 66 + 77 + 59 + 96 + 69 + 49 + 95
+ 67 + 27 + 45 + 36 + 97.
i^Q ^^.t '^^ "*■ "^^ + ■'^'^ + -^23 + 695 + 987 + 429 + 678 + 542
+ 249 + 75 + 99 + 88 + 8') + 98 + 36 + 674 + 99 + 89 + 69 +
429 + 98 + 103 + 138 + 274 + 39lT + e» + bJ +
■ I?; ^tt ^^.^ "'' "^"^'^ + -^^0 + 694 + 678 + 534 + 864 + 684 + 468
875 + 708 + 1075 + 3548 + 739.
14. Express byfigurtHaiid add up the followini? uutuber.,: eighteen
units, + ninety-five, +cae iiuudredand one, +oaeluDdrf.l ^ud twenty-
thre^e, + three liundred and ten, + six hundred. Attn. 1247 '
Ij. l^«quired the sum of six hundred unit*H, + eight hundred and
any, + five hundred and one, + forty-aiae, + nine hundred and four,
+ seven hundred and fifty-nine, + two hMndred a.wl fifteen, and five
hundred and hfty-fivc
16. Express by figures one hundred and ninetv-five, i two hundred
and eleven, + one hundred and ten, + one hundred and nioety-nine,
t eight hundred and one, + f«ven hundred and Beveniy-eercn. +
Bine hundred and one. ^„g^ 31(jj
17. Express by figuren two thousand nine hutidre,! and ninety-
■even, + twenty-three thousand six hundred and fiftoen, + twelve
thousand 8IX hundred and ten, + one thousand and fifteen, and make
up the sum.
18. Required the euni of nineteen thousand two liundred and twenty-
tlireeuniu?, ; one hundred and twenty-five thou-iand nine hundred
and eeventy-nine, - one hundretl and ei-hty nine tliouarod aad
twenty three. + one hundred thousand six kundrei^ wid t«D, + three
thousand and three hundred.
19. Required the nnni of fift<.en tboB^r^ eight hundred ands«veB«'.
nmt uniui T fifteen thousand nine hundred an.i (iftv-sMtn, -f-.one
J»(-ndred thousand one hundred and one, + eigUl hundr«i and ten
Wiousand beven hundred and ninety nine, + nine hundred and wveatv-
tive thousand, + one hundred thousand and ten ? Ang. 2017746 "
Ant>iTTo?r.
n
'i^^'l and thirtv-tw. . :..::_°"**''...V>o»«and and fifteen, + on. hun
2i.40.()n 4- 104.8 + 100.-..025 + 7.;J87ri7
22. 0.4 + 0.20 + o.O.O. , ,,0, ^ o:'2ro +'^.^1' VS*"'''^"
23. COo + 0.00012 + lio ^ ,1 •..;'"*• V-^^"*** ten-thousandths.
2 . G.% + ;^.99 ^ g 7 \ Jfi.V^''^^^ +0.0001005 + 1
+ 'SSO. ^ ' ■'■' + ■'.■i> + 7.77 + 3.7S+ 9 0-
26. 4.95 + 9.54 ^ « ,,, ^».. 1 1 7.929 tl„„„.„dTh8:
tw™t.v.(i,, lhoa,"tl., "1 «"''''• f ""' ."■»-an,i .l,r <.„„?,' .nd
, ^0. Kequirfd the «„ni of f„„r L».k "P' ^"»- 1167.:i2:-..
hundrt.,! f.„.,i 1. '.''"" '«»"", -r twenty tlmu««i,dt|„, +
Jjii-ce hundred ten-llmu,indth«' * „„„ 1. ', "rV ■""■"»"iiiii«, +
^ • Required the mm of four hn„,7. "'; ''8l"«n liundreiltli,.
'''"3^^=' + "'"etren thou^saldthr **""^'^^-^^0"«'*ndth«. + eiglu bill
^- h„ndreatn?h'3,;:^^ ;-ndred.tho««.ndch^ ,
sand hundmUh,, 4- thirlMnl^tJ hundred tenths, + one thou-
e>^'ht Imndredth. -f- ele«!f u "' '""."T^****' + ^''^"ty miliicnthri
-nd ni ,,,„ ,^ili^^;^^- hu„,ired-thou«»„dth^ . ^hrie thoi'.knd
^4. Kequired th« sum of nn. .i i ^""'- 40.174529.
thousandths ^ two thSandCdS"'^ tenth., -f- f.„r hun.l ed
4- twenty thou,.and miIJioath« Tten tr ''"•"*" ''""-Jml tenths,
faousandth., + one thoS 'and fl.V r'^lr **";' ''^^'^^ '^""^reV'
thousaad raiilionthB ? *'' ^^^ *«^"-«n»ll'onths + one hundred
•»o- What iH tht? ■»>?. ^r u,„ ,.,,. ■
seven miliionths: one hn Jrl) f'""!.'''^ nuna>er« ; twenty-five an.i
jwandth«, on;rndr:f:if:tf:r;flt '-^'-^ -^d'rc!!;;:^^
dnfdthH; »erenteen, and three h»n?5^ ' /"'' ^''^''ty-nine hun
tkouwndths? *"'"" ^""dred and forty .i^ht hu^j^J
viiM. 3(;.^.63«487.
'I
I ki
ADDITIOn,
PBACTICAL PROBLEMS OR QUESTIONS IN ADDITION
1 56
2 3 8
* 2 7 6 4 3 Ans.
2. I bought some merchandise for the sum of S94.'; fi*;. i
must I sell them to gain $25.20 ? «^45.65 ; how much
$ \T5T5 ' equate" h;7it?03t";.l S It r wK" -^^ \P"°'
25 .20 245.66 + 26.20 = $^70 85 LlUng pri^e "" ^'"" ' ''" "•
» 2 7 . 8 bAns.
thano1.MtlriSj2"o^rt «4.75; onTueadaj, $1.15 more
spent duringSseXedtsT '^'" '" ^""'^^^ = ^^^^ "'«°»^ ^*«
the'^7''8'p?nr4;7^ +"*[ IfAV-KnT f Tuesday and Sunday. On Tuesday.
«69;l'rj;l{,;r7liS' t^'f-^'^^' the butcher, ^16 ; th^^ shoe-maker,
famiV owe i^ 111 ? ' *»J f«'' houHe-rent, 145; how much does th^
6.' Th"e"'^;j;.Sn"of Mo' '" t*' ^?^ ^"' '^ '^ ^^''^-fold ?
Quebec, 64^, Se^Rifers sto' f'"^ '•^•^.O;? -»'«» that of
Levis, 6300: Screl 5250 Shirhl ?.' h,3^^T^^'^ ^^^'^'^ P^^'^t-
Pulat.c>„ of tLos;:ev:n-io;n''r'"^'^' '''' = ^^"^^ '^i'- .^^'^ P^'
$45ooV}^t:':orn^!7/5S'';^^^^
owes $92. How much did he'o^e'l'fir* '/•''' '%:^'t^\r
^>eforetheeng^ageme„t? re„.a,„mg. How many had Vo v
86iSmi;Th72rd"mo^;*i;rtL«?r«^^^^^^^ ^'^- -"'^■■-
there in the army? ' ^ *''* •^'^- '^^^^^ ^T '"^''^^ "'«» "<"
„ui:;.I\«ori'^^'^^^-/>^- o, weigh 390 poun1reach??hr;;- .
nc gmined »176. How much did h» sell thora for? An$. $486.
ABDinOM.
27
10. How miiQv v^u.r>i piurv^^j !• •''-•»"' ' An$. .^7240 hush.
.ujr^i n84,e.iS;;;?£iS^^^^^^^ which oc
"• .^ Powon who WM bova ia lijl dlS^ ifJu °^ ^^"^ Christian era ?
year did ahe di« ? ' **"*' *•<* •* '!»• «ge of 37. In what
tkio ^^^ ^'' o^^he Dominion of P«n.^. • "*"*• *3174.55. '
Jh« Province of Ontario iSnL'^V* computed a« follows-
bee, 210000 .quaremfea the pZr"';';^'' ^^•^'ovince af Quei
»»nat 18 the whole area? aJ^^ \oilli^ ^"*''« ""'les.
!»• A tanner bouirht 25 hide« fnr *%. ^»». 4J7360 square mile*,
g-epared them, he e^old tLm for Ju2 67°^'*^^^^'' ' ^'^" J'^-^ng
How,auehd,dhe«ellthemfor? ^" '"""" '^•'i ^^'^ t»ad paid^
20. A «„-*„ . ^„,_ $277.40.
''"• -*■ certain sun, of moner wm h;-;^ ^ "**"• *277.40.
'^ved$65;thT2nJT6-in "r^^, ^hree persons :
tk.lst.,rece^ „^.^^^
J32. more than the geeond
^M the sum divided f
^i*. i8t. $65; 2nd $91 3fl.
21. A merchant in fl«Hm» Jf^^'.^^^M^' ^^o'e sum ^279 70
1143.40 bj the ba gaijf hoVm^^^^^^ "'""""^ '' $6218 So", lost
. 22. At the censul of im tT " *'^ P*^ f"'' '''
1409430 inhabitant that iri^^ Papulation of Upper Canada wa«
fOOOOOj New Bra„a«^^J Is^om/ ""h r^' '''''^' ^-^tit
tbere in those four ProvinnJ.lu ^"'^ "'^"^ inhabitants were
o*' Canada? '^"'''""''' ''^'°»» «on'POHe the pre<«nt Dominion
23. The battle of Marathon took niai"/:.r;^*^.^?^® '"^^^itants.
9"/ ^pf*!:' '''"°^ *^»t period to 1868^? "^ ^'5^'" ^^"«'- How
24. Eighteen tanned honw-hideswelh ^«fi ^Z'" ^'^'^^ ^^"s.
324 pounas ,n being tanned WJa7H55 thl^""'^''- l^'^ ^^'^^ '<>«»
26. A number ia such thaf ;<"!!•• *f , '^"^ ^^"^ weight?
5976. What is the nut ber ? ''^'™'""''^ ^^ ^^^^ th"^ remains but
io. Kawwooi is worth ^n 'r« . *'*««. 1246'?
*2.45. What is the price !f k n ^^Ti^"*^' *^''" P«-^P*red .t aulrnenta
, 27. The populatiuTof EnJon.""^ ''• ^''^'''^ ^^ooU An^^^To
that of Nort'i Anieirc;l3^8a8''Z':>f1 ' Vh^'*'"' '"•-^''•"^« -
that of Asia, 5H8700000 • thltlr a r . ^""*** America, 22007823 •
20600000 : That of A u!:.U,:?^'^/4f"«^. WO.^5000; thaiofO.eapr.a
What IS the whole pop'uiltrcU^'o^rhe^g'loreV"' of Polynesia. ;r90o1:
Ant. 1020360878 inhabitant..
•" SDBTRAOTION.
SUBTRACTION.
between two numbers of the eame kind.
,1,/ ^•^"■'^J """'^\'' ^"* ^^'^t ^'''«^ '■« t« be diminished, is called
tt fc:i;"' ^'^ ^'"'^"^^' - ^^-^ -'-»^ « ^ ^e -btracted,
cerordl^erTnte!'""^'""''"""^^^^ ''^ remainder, ex-
tk^J'fl^ ^r'"^"" «"6W »/;/i.7. each figure in the mbtmhend i$ leu
than the figure alove if in the minuend.
Ex. From 547 take 324.
ortv.kriov.
Minuend 6 4 7
Subtrahend 3 2 4
Remainder 2T3
w» writo in hundreds'
>«I9, Mid 3 uniti, or 2
AvAi.Y^rs-Wowrit* the leaa number under the
Rreuier, ,.., tb«t uuiu of tbe same order shall (taad in
the same column; thoD, wo begin nt th« right and
f)rnoec<l a« foliown : 4 unit* fiorn 7 unit^ ieare 3 units
whuih we write in unit.' piaoe. Two tens from 4 tens
loave two ten<. which w., writo in tons' place. Three
hi.ndred»(ro.n5hnndrc,itf lenre 2 hundred*, which
pirtoe. Henoe we hare for tho remainder, 2 hundreds, 2
fiXAMPLKS Pon PRAOTICB.
(1.)
Minuend 457
Subtrahend 325
Remainder 132
From
Take
11. 3692 —
12. 7634 —
13. 8742 —
14. 41763 —
15. 7839 —
16. 3724 —
17. 2945 —
18. 69524 —
19. .56247 —
20. 72365 —
Cask IL-
greater than
(6.)
648
2.34
1212 =
Ana.
3132 =
Ang.
5331 =
Ans.
11522 =
Ans.
5427 :--
Ang.
2502 =--
An.'i.
832 =
A na.
47321 -
Ans.
15123 =
Ans.
1243-
Am.
(2.)
273
13J
m
a.)
376
264
2480
4502
3411
3024!
24 1 2
1222
2113
22203
41124
71122
(3.)
936
7U
222
(8.)
857
622
(4.)
666
423
262
(9.)
498
176
974
631
343
(10.)
645
642
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
1243
48673
34272
79832 ■
15475
1576«-
982S76 •
217951 •
760142-
391657-
-To subtract when any figure in
the figure above it in the minuend,
- 2I3=itn»...
- 163.30= Ant...
- 13051 = v4n«...
- 67411 = Ans...
- 4050 = Ans. . .
- 4327 = Ans...
-120341 = Ans...
- 5430 = Ans. . .
-570031 ^Ans...
- 141322 = A«,..,.
the subtrahend w
47.
JS; ^^» ""bkr-otion ?_ Ueflne minuend.- subtrahend.- 4i. A.,, fc H.
(6.)
974
Ml
343
(10.)
145
642
-SOBTEAOTION.
». Find the difference between 853029 a»d 3^16.
29
OPKKATION.
METHOD BY HoaHOWlNU.
M^ \?"'^'- '^' «™'^'«^' ''i'l' ""i^- under
wesar.?f"'>^T""'°« "tth" right-hand
Proceed ?'r»l7K"'!^ r-l'iee below. Wo than
above. ^ but ?h' "*" ^ '"^^ ^'•"'» »h« 2 tons
equals JO hundreds, learini; 9 above tha oi-
pher anladd the 1 hunl^od equ,!l to ij
ten.., to the 2 ton., makin - 12 ten.- 7 ten«
f fj; ni 9 I.ares 5. which we write In hu^dVeii'n? ' 'l"V "'^'"^^ ''^' ""'•' "°der ;
' th-;usand from the 3 thousands 2 thn,",n^ ^ *"■" ^®'^*- ^^ ''• h'^ve taken
wh,ch we write under. We cS take 6 I 1^"^" '"^ J """S^t from 2 leave, 2^
so from the 8 hundred-thousSwe take 1 h ; 5*""^"^^' ^'""^ ^ tea-thousands
ton-thousands, ,.nd adding them tl the 5 ten »h '^■'^"''»"'^' "^'^'^'^ «q"al- 10
« ten-thousands fr.n, 15 ton-thou?ands l«a« q ?* '"u"' '"'''*« ^^ ton-thous.nds:
und.r Having taken J hu.dredXu^S fL^'^V ''''2'^f^^' '^'''^^^^ ^« ^"te
h mdrel-thousands are left; 3 hundred hnn,"'; ^ ^"'''''«'' t^o sands, 7
leave 4 hundred-thousand,, which we wJft^uM?,'^' 'Tu ^ '^""I'-oJ-thousaids
or reinamder, to b.' 492554. ° '"*^"^' "'"^ t^"'" SnJ the dirwence
Minuend
Subtraliend
fieniainder
•3
a "
e 9
S° •
H 6 3 2 y
3 6 0475
47nrT54
OPKKATION.
8 53029
3_6_0^4 7 5
4 9 2 r5~4
METHOD BY ADDING lU.
S:to2t^--^^-s-^;^-^p:^i?;:\a
5 ten,. But havng .iJdded i, UL °' f""^'" ^^ tens leave
« mousand, to the minuend wn sKmII k„ ' ''^ °^^° added 10 hunflr«,il
unless we add 1 thousand to the of ,h ^h ■' * ':?'".»'°J«'- 1 thous.ond tooJaTi'
tte°.oM"" >^ t^>-\VotandT£e"'ir?en'^"''""J' t^'-tbo^usI^dT ' 6 ie^
t^nrmakSr/hunlLVi^' '" ''^ --i.-^ ^ "rPen-^e
4 hun^,,a J,^J2f ed-t ousands and subtract theVf^m'tl^'^th^f '^'^■
before. ■^»>"«' w. flad the remainder to be 492554;' the simr?
*L-i"' trrr '"""r'-"^ "^ ^^^'^ "- '^"--«
c Wkt^ i, tk >- y : ■ — — .
«' ^'^^i't^m^for^traciumt
m
#1'
It r '
80 IITBTBAOTIOIt.
IT. Commmnng at the right-hand, take each figure of the mh-
^rahendfrom the figure above it, and write the rZlt und'rneTth
III. If any figure in the subtrahend be greater than the corre*.
oondmg figure abooeri add 10 to that upper figure beforTsl
imS; " " "^ "" '^' '""'' Wt-hanrfigure Iftl ll
PaOOF OF SUBTRACTION.
4S. We make the Proof of Subtraction in a.JJin:,. the re-
.nainder to the subtrahend, their sum will bo o(,ual to tlie minuend.
«t the work la correct, '
Ex. From 35678 take 27899.
Rem.
Proof
356 78
2 7 8 9 9
7 7 7 9
3 5 6 7 8
Akaitsis — ToproTethij operation, we ada
the remainder 7779 to theaubtmhend 27899. and
obtain 35(578, whiohsnmisequalto the minuend
or greater number. Henoe we coaolude that the
operation u correct.
This method of proof depends on the principle, that the greater
0/ any two numbers %s equal to the less added to the differlr,c». ■
Use of subtraction.— ^«6^rac<ion serve$ to find the qain or
u)i> on goods; what we still owe on a turn of money of which
we have already paid a part; in general to find the 'sufilus of a
nvmber over another; the difference between two numbers, dec.
We know that the solution of a problem requires a subtraction
when wemustfind the difference between two numbers, or the excess
of a number over another; and when it is required to find one of
two numbers forming a total, that total or amount, and one of
the numbers, being given, ''
EXAMPLES FOR PRACTICE.
(1.)
Minuend 76518
Subtrahend 49359
(2.)
57813
.38675
19138
Proof 57813
(3.)
13042
9176
(4.)
250143
176158
Remainder 27159
.3866
Proof 13042
73986
Proof 76518
Proof 250143
48. Uvm d* yon prore tubtraetion f
6.
i.
7.
8.
9.
10.
II.
12.
13.
14.
16.
16.
ly.
18.
19.
'M.
tl.
a.
as.
24.
26.
26.
2t.
29.
36.
31.
39.
33.
34.
36.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
.'0.
JI.
J2.
53.
a.
(
u
u
«
«
U
u
u
u
u
u
u
it
u
a
it
ti
«
It
it
u
a
a
«
ti
a
n
a
it
a
«<
»-SU
m
6. I Frpip
7.
8.
9.
10.
II.
12.
13.
14.
16.
It.
ir.
18.
19.
^.
tl.
32.
33.
24.
26.
26.
ar.
29.
36.
31.
39.
33.
34.
36.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
;'0.
51.
J2.
53.
»<.
(I
«
it
u
(4
(4
U
it
u
a
M
U
il
a
M
H
it
u
u
ti
M
u
u
u
u
it
it
it
it
it
it
it
n
n
a
it
ti
it
ti
It
n
it
ti
11
ti
«
it
«4
.#00
46U9
l^iW'-,40
mm
.mma
mmm
mmm
mmm
fWBTEAOTlOIf.
take
mwm
mmm
w>^mm
fMmm
(I
«
it
it
tl
(I
((
it
It
It
(t
It
It
.(
tt
it
a
tl
tt
if
ft
it
II
ft
tl
it
It
tl
ft
it
tt
ft
It
rt"
tV
iV
ft
ft'
ti'
it
&
tV
&
iV
ft'
.1*
351
15574
16134
30409
97J25
179127
471097
198576
55595
608578
4137976
988827
154379
737898
14550045
49876579
4007.S049
91791994
4590489
64834795
9068073
1300476
27740761
15007.34
3740056
6475904
74375676
97050654
277451794
9737.350
476294474
49.5647562
676489672
475207454
45612495
798435496
1&4289778
93457897
i>8047775
71904267
677469579
276499619
203405604
93235945
7456,:$yaa5
39787496
746855472
^78809709
17073969
1977988S
31
»«. ^49
33895
63772
160131
14-7415
268973
3';882!i
388374
48I2'00
130I449«
16835321
20792702
83110009
2969.35925
62608006
185463520
689840100
939476
126030680
3902S9G89
805265.154
484533172
77.3277878
753019798
2693,v5?«I
91272751
18180721)2
88437502
474868620
411088255
77671553
668807729
58P006779
360796512
377406:75
176507908
881264755
93767519
^078f.U81
*o83&.J74
4006736236
*6e722070S
!• H
31
ilTBTTl.AOTION.
\P
SUBTHACTiON OF I)ECr\fALS.
f^r. From «(;.? take 6;).3r)4.
OI'ERATlo.V.
•^6.700
i 7 . 3 4 C
Rttt E - T ir • nuiab«r.
6.
6.
7.
8.
9.
10.
1].
i2.
13.
14,
15,
16.
17.
18.
19.
20.
21.
22.
33.
24.
25.
26.
27.
28,
at.
at.
EXAMPLES B-oa PftACTIOl.
From
Take
Ans.
1.3581
From
28.98S08
«
«
It
«
«
M
M
90.49
109.191
5409.0r.5
764907.05
'^97450.07
4(JiJ742.6
!?70079.04
400048. 2i;i6
409004.9099
670075. yo04
49.1019
610011.050 '
71079.0013 <
79073.07 «
12G001.0001 *>
191279.9709 '-
40IG45.1005 <i
700007.0238 ««
411978.10359 «
960945.00005 «<
0.0707 "
0.0006 «
0.90019 '-
Q.QQ89 «
0.0904 M
6.7009 M
O.Odtl «
take
(4.)
1.0062
0.43
0~57G2
i(
39.69
49.073
4045.997
87929.795
98776.095
76908.075
1987.-9.958
9372.016
100.137
4053.509
35.708
31971.9999
7482.1736
7398.1204
98996.9088
60056.0099
498.6709
79797.0098
36730.09871 '
600979.00007
0.000007
0.0000076
0.7300007
e.0070S76
0.00289709
A 190007
0.004600008
An»- 50.90
" 60.118
" 1363.0.58
" 676977.255
" 388834.425
" 671289. 0S2
" 39067(;.i;)76
" 408904.7729
" 5G6022.39I4
'' 5780:);<.o.)01
" 63.''.!)(;..'^277
" 71671.9496
** 27004.0913
" 14122.19610
" 401146.4296
" 375248.00688
" 35996.5.99998
«
(I
«
u
0.070093
0.0005926
0.1701893
0.00 1 8325
0.08760291
0.610893
0.004599991
33.
34.
36.
3S.
•r iimier th«
J^lit'L' htnnd
thv II. ht of
<ay tlrisnU
»» in i«h(iie
t IB thf i«-
iber.
/Au/ the
null point
(4.)
1.0062
0.43
0.67C2
18
58
•).5
15
<2
)76
■29
'U
01
77
96
I.^
10
1)6
)88
»y8
)o926
K325
60281
33.
34.
36.
36.
M
«
1<
■VBTBAOnoM.
•.077f take
0.900 «
0.19100 "
0.4500 M
0.09839 «
0.01011001 I Ant
0.0019904
0.09900036
0.00660046
.09600969
«
«
0.0
PRACTICAL PB0BLEM8 IN SCBTBACnON
field whinh koJ . A» •
3S
0.0677H999
0.898009fi •
0.091 <>9.965
0.44449956
0.00338041
..in r '" "'""' ""^ -«« «'«« ™ »,d for «638. ^ba. ,. ,,.
op*:ratio».
$26 2 8
$2 3 fi
$268
ing tho coat Drioe S2<fin fv .V °°'^''^"''°' '"""bfraot-
*^" ^'M. $268 gain.
-hL^oZT.'l^Vsru'oT"'''"''"* '■«'«"=' ■'"' W8J5.76 good.
OPiriATIOW.
$5174.10
$4825.76
$
bV.n« pri«. I6174.1Q. wVoSfSo,/""" '^^
^n». $348.36 low.
. -^ 3 4 8. g6 -----.„„.
•' A merchant bought flnni. f«, •cao- . ■*»«. S348.36 low.
«68r,3: how much didTgJS^^"''^*^^' •°'* •**" «»«> whole of it for
fi Si"*.*?"" difference between 70401 and fiOi9 . ^''*- *^227.
6. What ,3 the difference between fi^V^o aV. » -*»«• ^3459.
6. I owe.i J1628 : 1 mid «q7] • f,"i ^^V","* ^**^8- ^'W- 30952.
^ 7. The greater of twriuilera is nn"^"'^ .^° J "^'^ ^^^ ^
what is the smaller » °«»»fera is 1302, and their dUFennce is Dsi .
8 A merchant sold in one dav '?9';7i in _u '^"*- *21.
s-by o,«„d . p.,a. „r »Af 'i,'.r:;rd?i tK IS -^
■"any year. ti„, ,i^, ,«„;« /»-nd„d by Cha,„pl.i„ i„ ,5„3 ^ ^„
n. iiie area of the Provinnf ^.f /» • ^'"' 262 years,
that of the Provuice of oXno iSOOn^n" '' '' ^^'^^"<^ »quare^u Ss •
mi es does the fonner exceed Se latte ' '^' "^ = 'i^'"" "'^y «1--
12. A father was 28 years old .* Vj,L u--.i. . '*"*• 30000 sq. m
J*. What namh«r mn^ u jj . jt^ais oia , ^7,, 57 „.
.»'^ Jr*"' """"'*' "■"" •- 'JJ-l .0 4 unit. 5 l^JX! n*.,.
•» ^«J». 1769.
9%
•VBTKAOTION.
"♦• What number inuat be ad.l«d .« -4 .. , " '^'^'•^'' "'*•"
hiindre-lthfl? °^ ■*^'^*' '*» ^ Hiousttndtl.H, to hare 12
London 28(J,SU1 • how mn^V Yi^^ inhabitants and that of
that of Paris ? ' ^^^ '""^'^ ^^•'^ '*'* population of London exce^
„ 21. Alfred the Great .lied in 901 at th« "*' l^to^^ inHabitant«.
24 years: in what^e^i tt helln ''" •*" "' "' ^j » '^^^ of
. f ^- Oharlemagne was hnm in -7^9 i. •^'••' ^^^^
he, lat. at his coronation as king- 2nd il . ^T "'"^ ^^
age did he die; and 4th how m J, ^"P^^-orj ^rd. at what
until 1869? UmU? oY ^u" *^»P^ fr^^*" hi. death
at $1 1 7000 and adjud|ed fo ^e pH' gT ^"*'^^ knocked^dm t
■n the museum of the louvre ^uTred?h^^ *^« P'«c«i ^
l8t. and the last bidding ? «^"»«d 'he difference between the
24. The population of Montreal in iTan . •. , ^'»'- fHTOOO.
'tant8; in 1861, it wa« 57715 In 'l856 f^^^r?^"'''*",^ "^ ^000 inhab,
'" 1868, about 136000. What i« thf i ^^' !•" ^^^^' ^0000 5 aad
1851 to 1868? *^''"^*'"«''^*«eofthepopulationVroM
25. A farmer reaoed 1689 h»ak^i , ,' ^^^^^ '"habitants.
oat« He sold his CigLS John 89? h^r!' ".""^ ?'^'' '-^»^«'» of
bushels oats, and the rema3«,. t , hu^shels of wheat and 478
97 iT„ 1 r *i^^ '""' "' *°^ second ?
-..Id have $75 lel{; how mVh have J^ ' ^'^' «^ *J0I6.80, and
28. A merchant sold ti ifian It <• , ^"*' ^^582.30.
dit it cost ? °"°" "^ ■" '"J P«"i i' «300 lore. How mSok
hJL S.'^f""'" "M in.Mted in the jeu nia u "*?' *'^'^°-
b.fo« th. „„.ntio, o( prioUns, -iich .X 1«1 ', ''i':,''i'i« ;^^''»
PRACTICAL PROBLBMai cOMBmmO ADDITION aT
SUBTRACTION.
-ond^.':?ilKrt7V^8^^ !!;«.<'--^or change; on
of $43.2? .ndUi^'mo 76 fo°\«lPr * «*" of SSS-.o/anotl.:,
•MMMns to him in cash » .«» -r •llT"^ «pen«w, and then there
M» hu Moounto right ?
■UBTRAOTION.
Xl.t;a^Srw\"ir :ii". !r..^ '-"» "-^ ««•<» •' b, had
ri
I««> Si'.'J, 4»,'i« f 7».H6 4. 68,46 4. «« J. 128 80 -U f.A ar, <
aft
not paid
7:^.16 -.|J30.
nhimlil bo left
Ant. $0.50 Hgainat
y,l^ •*»l».l>» «. 9IM.6O ; diffarenofl 160.60 — 160
bow ;„i;;'';;*i:2n t' •"**••' ^^' *" '"'^'^" 2*' *°^ ^^--^^^^^r 6 ;
^- A Htntleumn having 11128, lost i«a8 And b~.„» •it!^?
triMch |„j,| 1,^ rM,uvn]w'^ ' «P«nt $172: how
;J. Tf.e water, of the'^St. Lawrence eorer an area of 5G500n*»n"*
>i..''e«, twoof.tstributaric'fl, the Saguenav and St Man. ^""*
<ii^ on. an ar«l of 27000 nq/.are rn?fe" and *he othef 21oSo' T'"'
m,!*!,. Ih^ ,„uch doea the area of the St Lawrence exceed fh'^^
<i 1 ■ ^ns. 017UOU fniiare m »a
i4%r u J"'"^»'5'>70.30; for the 2nd., $3674.60; for the "/rd
-ii .^" u" r*" '""" »'»"' '"' ^'»" *»«"• Christ, lie left Eainl
■.t'l;t^;"'i'«.'trf'"fV''''°"-''u''"''' •■"' ^-j -mS
u YL» » " •'^••' '*°^ '^^'"« Christ. What age was he IaL »>..»
hel«ftK^pt, 2nd. at hiB death; and 3rd. how log from tht rJriod
«rk3« death to the jear 1871 of the Christian era? ^
' j4n#. l«t. 80 years; 2nd. 120 years; 3rd. 3222 years
E Wtif ?k ?7u^u*^' the 3rd., he gamed $685.30 ; the 4th.
Wa^rS Ivn ^***'' »»«g*'"«d $4320.95 ; and the 6tl ., he los
•gau, 1.1000, I).-U.r.i5ainorlo«e, andhowmuch? Ans. $169.651oe8
10 A ow«« a .u,.. of fC90, plus $5.5.20 for intere^. He reimbursed
-d,ffi««tum« $87.50, $210.00, $318.45; how much doe^ he Stll
♦«4 ?/7J;^it2;:^8\r?Jir.'s^'rT' .*»•!-" Jliiitt
a Bank lin* /y « nnn A if- t 1®* *^°*"^' »° «*"''««» he gave
'M\
!
</
%
I'l'
M!
,' ll
'-ill
M
MULTIPLIOATION.
m
16. A spfoulatwr bought 217 cords of wood for I1085 R. '•
much does he ow«yatT '^ "**^ •^"•' ^" *^2. H.<vr
" « ' 1!;°:, r'^^ *• *TH°°c:sr. r """^ ^r,"?! '"
R«qi'ired th. prio. of ,!,. s i^^'A''" T' °^° '"""' <' "'W-
l><>»e C0.1 »4.{o 7 ^^ kMwing <h«l ihe ulr bih,
I>" ihop Wore hi/lM ,,',,~h.„ S •" ■"" '•■" i'*'f "h" I", bi^l i.
hospital.. Having Lked 3500 mLTh™ ^•''*r "^''«*'^ *° '«»^« "'
AIM. Io730 niMi.
MULTIPLICATION.
OA. Ihe multiplicand and mnltini;-. „p- „!!-» «^-^
because they ;,.orfa« or m«feth7-pr,;& '^"^'*'
MULTIPLICATION.
MULTIPLICATION TABLE.
^1
i
38
l\^
IHTLTTPLTOATIOIf.
no^^^c'i'12^''^'''""*"^^^'^-^^^^^ ^he multiplier doe.
^^ Multiply 642 bj 7.
OP«RATIOW.
^Multiplicand 542
Multiplier
Product
7
3794
*42^re?L";? ??,«^^^^^^^ "quired to t»k.
' ' ■"« "8 product u 3794
Multiplicand
Multiplier
Product
EXAMPLES FOB PRACTICE.
(6.)
16812
(8.)
68607
3
4
4
5
6
8
7
9
11
9
12
X
X
X
X S =
X 7 =
X 11 =
X 12 =
10. 873
n. 946
12. 4731
13. 5607
14. 6924
16. 8667
16. 27693
17. 61786
18. 45678
19. 36397
20. 634576
0a8r TI..
owA 12.
Eof. Multiplj 478
OPERATIOK.
Multiplicand 473
Multiplier 34
Partial ) "TsTI
products. { 2868
Kntire product 30692
' Ant.
Ant.
Arts.
Arts.
Ana.
Ans.
Ans.
Ans.
Ant.
Ans.
Ant.
2619
3784
16924
28035
41544
69256
193851
466074
502458
327573
7614912
21.
22.
23.
24.
25.
26.
27.
28.
76394
&7631
266532
83545G
541378
367542
426985
- 576483
29. 6932574
30. 397466
31. 3745178
71, .«^ ^n»..,
by 64.
8 unita »re 32 onita i P~«««d tfiug. Four time,
the 2 unit, in rpC'oftit?!';"!.'!' ''« ^^^
to the nrodi./,* »P*i.I.- .t """'» and add the 3 t<.«=
^TFTTrPLrOAlHw.
3f
(4.)
8634
6
51804
19 hnndrels, wUieh we writ* in it. «-
obu.ned by this .Dulfiplioation. in WnSf„ $• *7 *' ""*• *»•• «Mt fl«;a«
hpi.er; and. addin,- tho ;,ar<u^' prSut „*?l"^ I"**"'" *« « of the *""
w.nndthewho!,producU478CA2i^5|,";4''^ ">• two mmdp&o^,
N<.TR:,-.When there ure oiphen betwrnin th- ■ •«
plier. paw orer them in the JTr^ioi «nd Sf.iH*!"''!*** '»"•" '^' the ■«!«.
rfraw « fine underneath. ^^ ^*^ '^ '^ther, and
n Multiply tach figure of the multiplicand bw ea^ 4^ .
PROOF OP MULTrPUCATIOlf.
•??; . '^'l^ P'OOf of multiplication is generallT m,,A^ k, *..
Miultiphcition (1) in which onp nf .,," 7 T™'^ "»***« ^J another
the third, or the fourth etc ofon«lm .7 T"'^ ^'^^ ^^^^^
and the other equals t^t^^^Ztrt^^^^^^^^^^^^^
faotor of the operation. Or. "i^r umea, etc., the other
In multiplying the multiplicand by the multinlipr M - - l j
by 1. and to the product addin. the multipSd Tf tt "^
Jhe^same as the product by tho".hole of ntZ^^^::^
USB Of il^hTlPLlCATlON.— Multiplication ,BrvPM tr. . /
numherno man, time, greater ; to takeZ7al7:Z%a:t;:i'
to find the value of several units or part, of £, L L **""**^i.
ihem is known; to bring a number^eZressL T^, T *"** ^-^
mature to another nunZ .x/rmL S Xa ' "-^^ .^r'«^«
of the first, d;c. presnng umts which are subdivisions
Omtrally tee knov) that the solution of a nmhl^
tn. ...,,. oj .e..n,. «.- rcqairea, or that of some parts of the unity .
4U
■I, ^
4.
6.
I.
7.
8.
9.
10.
11.
12.
13.
14.
16.
16.
17.
18.
19.
20.
21.
22.
23.
24.
26.
2C.
27.
28.
29.
30.
31.
32.
33.
34.
36.
36.
37.
38.
39.
40.
41.
41.
43.
44.
Multiply
(1.)
8621
47
60347
344S4
AlU. 406187
976
697
749
8386
7.5.S537
1.^4679
824956
984765
66r)4
97248
€89834
867894
807497875
84966
643966
96824
43208
90480
43
76496
7674
3696
69421
4321
766849
908708
4916
766420H
80097 X
900007 X
4300407 X
460004 *'■
960076 X
690800 X
7006924 X
786530746 x
4i6.'i4Z0Uo X
898302466 x
496307429 x
767489007 x
879407864 X
MtTLTIPLIOATION.
EXAMPLES FOR PRAOTIOK.
(2.)
37216
65
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
186076
223290
An*. 2418976
27
34
46
67
68
79
387
766
789
866
943
996
966
7649
9475
4696
4962
9007
89006
87969
12478
819162
21764
987664
74323
70469
69678
20963
74269
700608
700608
99804
90708
456007
640(JK6
36781)4
987405
94376f>
936704
900076
698765 '
An$.
«
«<
«
«
«
«
it
u
«
ti
II
u
«
«(
((
u
u
It
u
tt
u
«
u
u
tt
tt
tt
tt
tt
tt
tt
tt
tt
tt
tt
if
It
It
tt
(3.)
167034
304
668136
60I1(;20
Ans. 50778336
26362
23698
34464
478002
61240516
10639641
319257972
744482340
6250006
84119520
650513462
864422424
779235449372
6499049.34
6163983100
464686604
214398096
814953.360
3827268
€729276624
95766172
3027622762
1610184434
4267652934
66261288227
69109612052
342637048
160465162304
694872409.'{
€30562104266
3012899647466
46910239216
87086673808
315009635600
3784.341 5654 6<
"•■'■■T^-fs.stovrjVzi
411098671149.525
845888887386840
46.3956449974016
681797676464532
€1449942(1100310
MVLTIPUOATION.
41
a) ■
167034
304
668136
11(20
778336
26352
23698
34464
478002
61240516
10639641
319257972
7444S2340
5250006
84119520
S50513462
364422424
236449372
549904934
153983100
164685604
114398096
14953360
3827258
29276624
95766172
27622752
10184434
57652934
51288227
)9512052
12537048
•5162304
-8724093
2104256
9547466
0239216
6673808
9635600
155546<
icui- ;;;:■}
1149626
^^86840
•974016
464532
ioosie
45.
964907089
X
46.
457907842
X
47.
856407809
X
48.
674396856
X
49.
1864321
X
50.
2465783
X
kl.
72400.36
X
62.
J08007004
X
600789
796807
305407
285679
609649
3686407
4029008
500123
u
ti
a
u
ii
n
673697675093221
364864173860494
261552939723263
192661019425224
1136581433329
9089879711681
29170162964288
46411618686U92
MULTIPLICATION OP DROIMALS.
Et. 1. Find the product of 4.35 by 8.26. ^
ANALT3I8.— We multiply m in whole numben. and poiat off
on me right-hand of the product ai many fignreti for deoimalf
a« there are decimal places in the multiplioand and multiplier.
The reMon for pointing off Jie deoimala in the product la.
that in multiplying 4.35 by 8.26, or by 82« hundredtho, which ii
the same thing, wo take 826 times the hundredth part of 4 36
but we obtain the hundredth part in removing the point two fi-
,-Qaift A l"""' *"''*■'*'' *>' '1" (*^"' "' 2nd-) which will gire 0.04S5;
i6.9310 ilns.there remains then but to repeat 826 times thia hundredth part
to obtain the product required. Ai the number repeated oon-
mak nfth. aan,-"*^ of ten-thomandths, the product will bo composed of deci-
matoofthe same nature; to separate the n hits it ia then necaesi^ to take its
fcSjL'^UmaU^atL'rUi^lir""'" '"P""*"* '*-- "^^ ^"•'
If the factors are decimalg only, we multiply aa usual and cut off
M many decimals m the product as there are in both factors; but if
the product does not contain a sufficient number of figures, we fill up
the vacant places by ciphers, placing one alec for the unite.
Ex. 2. Multiply 0.054 by 0.066.
ANALT8ffl.-MultipIying 54 by 5«, we oktaia 3024: bat as
.J? VI i'^'^^a's «n th« two factors, we place two oiphen
at the left aide of the product and having put the decimal
point, we place another cipher for the units, and thus we find
the number 0.003024, which ia iwad 3 thouaandtha 24 mill-
lontha.
•PBRATIOV.
64
56
324
270
f.003024
(54. Henoe the following
Rule.— I. Multiply as in whole number$, and point of eu
ffMUiiJigures/or decimals, in, the product, as there are decimal,
%n the multiphcand and multiplier.
II. If there are not a« many figure* in the product at tk*re ar^
^cimal places %n the multiplicand and multiplier, supply the d^
Jiciency by prefixing dphtrt. ^ ft- 3
Won.— To multiply ^at&maiM by 10. 100. 1000. eie, (Me. M).
I
42
MULTIPLIOATIOW.
olr/-"" """'" "" "»■"« »■ '» maUipli,..i„„ of whoU
EXAMPLES FOR PRACTICE.
3807.4/)
489.04
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
9.
98.
«75.
66.
976.
696.
4.C5
6.96
3.95
9.475
7.789
2.967
6.694
28.9005
60.705
13001.4
42S1.45
13808.927
5321.807
37.00845
P:JACTICAL PftOBLEMS IN MULTIPLICATION
»*• 137.43
622.3
6001.7*
11042.64
95403.76
41588.88
4403.55
6048.24
1362.75
640.076
6122.154
1109.658
63.39218
1140.702736
41066.32546
521913.456
41175089 9806
93749640.72768
20262510.2547
18098.612388
9 ieekaV"'"'^'''"" '"" *15 per week: how much wil
he eara m
tain the mux wquired « 15 vT« ifl' '''«'?f°'^«'n multiplying by 9 we ob-
2. How much W.J1 126 yard, of cloth coBt at |3.25 a yard ?
drSJir.^yiTcoftf'''^^^''^^^-^^' ^- ^"Ch will 75 h«.
o'^"'*S"'^'- '*«<»!^'"^' ;."!'%?t'L''r™'^^ "^» ^"^ -i" •>.
0.76. w. Ui the ,« ,.,,i^ ^2.£xQ.7i - /l 80™' '""'"P'^^"* *2.40 by
6. What will 6679 bSheirofSheat L/ *; «f ^^^^ ^' *28260.
7. How many pound, olflm.ra^i'- *oo^ '^^"^'^ * b"«^el ?
198 pound, in ew'h bSS^fr *^*'* '" ^^^ ^*"^^«' '^^^^ being
coLSi UaY liSTr"' ***"* '" • ''^^""'^ :i^" 7 ^ ^ pa^sMSif ^ag.
9. A booM haa 296 windovii ^i^a -,o.,u j ^ l*^^-"^*! letters.
•rgu., bow -r,«rxrkori,rrz°.i^„^^r-
MULTIPLIOATION.
43
10. Required how many trees in a nursery composed of 95 rows, if
^ach row contains 1 78 trees ? Ans. 16910 trees.
11. The circumference of the earth is dirided into 360 deerewi
and each degree into 69.6 English miles ; required how many miles
•'ound the earth? i4fM. 25020.
12. Required how many hours in a year of 366 days ? An$. 8760.
13. How many days in 1000 years? Ans. 36600o!
U. A man deposit* $15 every week in aSaTiogsBank ; how much
does he deposit in one year or 62 weeks ? Ang, $1S0.
16. A ream of paper oontains 20 (|«irea; how many quires an
there in 672 reams? /Iim/ 11440.
16. If a cask of wine oontains 213 qnarta; required how many
quarts m 136 casks ? Ant. 28968 quarts.
17. How many eggs are there in 37 doaen ? Ana. 444.
18. How many days has a person aged 84 years lired, reckoning
3«6 days to the year ? An$. 30660 days.
19. How many pens are there in 200 boxes each containing a ltuss
^„1**P«'^«^ _, , ,, , ilm. 28800 pens.
20. How many days elapsed from the birth of J. C. till the Slst.
Dec 1869 inclusively? (Nc , counting leap years.) ^Iim. 682186.
21. Europe produces yearly 3466 pounds of gold; whatis the value
in dollars knowing th»t a pound of ttis precious metal is estimated
•*J}"8.60? iliM. 16966321.
22. A library is composed of 76 shelves and each shelf contains 86
Tolumes; how many pages are there in all the Tolumes supposing
each volume to contain on an a«^erage 420 pages ? An$. 2709000.
23. A speculator has purchased 268 horses and 274 times as many
sheep ; how many sheep has he purchased ? An$. 73432.
24. There are 12 hags of wheat on a trick, each bag containing
3 bushels ; how many pounds are there in the whole load, if the bushel
weighs 50 pounds? Ana. 1800 pounds.
26. A workman earns $8 a week : how much wiU he earn in 7
7e^^„ , ;, ilfw. 12912.
26. How much will 240 pieces of cloth, each oouMining 44 yds. cost,
at $6.40 per yard? An$. $67024.
27. How many pair of shoes can be made in 265 days, in a factory
in which 86 pair can be made in 1 day ?
28. If, at one load, a span of horses can draw 2997 pounds; how
many pounds can they draw in 327 loads ?
29. A field of 7 acres of land yields 46 bushelaoats per acre ; what is
the value of the crops of the 7 acres at $0.40 aJt)U8h. ? Ant. $126.
30. Supposing a sheep gives 6 pounds of wool a year ; how many
pounds will 28 sheep give in 3 years and what sum would it bring at
24 aentu rM>r munH ? J... •■ on ae
31. What is the value of the crop of a field containing 4 acres, if aa
acre yields 62 bush, oats worth 46 cents per hush. ? Ant. 11160 eta.
32. A laborer thrashes 46 sheaves of wheal per day, giving 16
pecks; how many sheaves could 14 laborers thrash in 9 days, and
what would be the quanUtv of crrain obtained ?
A»t». 6670 sheaves and 1890 peeks grain.
«1|
Hi
If-
HA
MUL^IPBIOATIOWi '
CONTRACTIONS IN MULTIPLICATION,
OR MULTIPLICATION BT FA0T0R8.
6. 15, l^,are^eo.posUe numbers; for dL 3 X 2??! ='6'">5'
mufMieKhlr^^lu^rr^" '" '^' l^^«^^^ nun^bers which,
or 2 and 3 and 4 (2% 3 xl = 24)'' * *°^ ^ (* X 6 = 24) ;
whn'"?^^ ^« » «=on>po«ed .« «^nS 4, % i f i' £ \l Z ^*) •' »»>«• the jJt',
i7*. 1. What will 46 acres of land cost, at |367 an acre ?
kr bought. H«o, th. foirow", ^' " ** •*='-' '^^ ««-
fr® ■^^"r'; '^'5''''''''* '** m«/rt>/i«. into tu,o or more fact^
■ZAlfFLJBS FOR PRAOKOB.
2. Multiply 2T45 by 28 ^ 4 x 7
3. Mnltinlr Rf^^Ao u. «< *.^ '1 An*. 7C860.
ilii*. 6618692.
-i««. 2979423.
An$. $9968.
3. Mttltiply 65742 by 36 - 6x7
4. Multiply 78036 by 72 - 3 X 3x 8
6. Multiply 36783 by H.
7.- wJ;t';;ii4l5\rKir,i!i?j.^«.«-^' . .. ^«. i99«8:
8,. What will 64 7>^dBoime^nT'Z.r"\^^ ^^ *"'"^ * ^""^^^l ?
9: In 1 mile there" e 6336 o"nir^Y *' ^^ °*"**' * ^^ ?
miles?- 2nd. in 64 Ss? ' **"'' '""^ •''*^'^««' l«t- i" *«
Xr-= ._. ^'W- let. 28.51200 ;
tf
3N,
t, aa it will
ing togeth-
er, Thus,
6 = 6X
>ers which,
the factors
6 = 24;;
nb«r. Thai,
Ills the jmrtt
>lier
u a
if we mul-
f 6 acres ;
8, w« eri-
I Uie aua-
'/aetan.
ind that
en u$ed.
vw order
(860.
8692.
9423.
9968.
heir
mTLTITLIOATIOll. 46
aAt^Z^^K*^^,^'^^''^^^^^*^^*''^ '»o* ra*"^ hours, Ist. lu
DO. ;/ Jllfili''!!!!""*" ' '-^^^'^ P^""'^" «^ *»'«•- '» «°« day ; how many
pound, wxl ^^wm\s* oon«um«, Ist. in 72 days?- 2nd. in 96 ?
19 A«-«.- >-,i An*. l8t. 897804;
Sni TfVliS^'^r*** '^^^^ •^^^ = what will cost, 1st. 15 acres ?-
2nd. TOiw^jt^.^, 144acre8? A„,. i^,. 7125;
\M\^tl^.fjf^'^^^^^^P^^^^^*^^^^ '^« multiplier i»\0,
1"^' lv09,.^- ((1^.36, l9t,).
^* ^ii^^^fiw; to <Ae multiplicand at many dphera a$
i^JlltrLtH fOR PRAOTIOE (p. 19).
«i ^^f . ¥^'T^ ^/^^* multiplication when there are ciphers at
tf^ r^M^m46f<m^ Mth of the factors.
^- \\' MyWW^'f im by 80.
•PIRATIC'.
80
uaooi)
- ^e reTOlre the raultipHosnd into the faotors 14
«ui. .*'','lv*''*c'""'*?P''" '°'^ *•»« ^""^o" 8 and 10. Now, it
S^^^i.- ' ^' *' '^ ^''®" soTeral faotors be multiplied
!J°T2 **y ^^l' produce che same product aa the given num-
ti 2. "'*<,''" ^*"'"' 1* X «- "2. ">d 112 X 100 =.
^^^.rfWr* H900 X 10-112000, the same reiolt as In ^he
<M>- i^i'fftff tlitf rtiywdinp' illTiatration we derive the following
a^?^'7^^Ji^ '''O^^MntJiguret of the multiplier under
*t*^'^ of ^,iem^lfl^a^J, and multiply them together: To their
product, urmf^mmy dpher, a, there are on the right of both
n^^%3^m^\4m^m!dtipiier. if j »*
mm^
MAMPLIS for PttAOTIOX.
M^STOoooo
13069S0000
600800
4. MuUjpU'^l^pJ^lly 700500.
J. Mutipfy mm$ by 7007000.
6. MutjpUrj^^y^^kji^iijy ^0302000.
1045560
T84170
785215660000000
An: 427606215000.
Ana. 21515743249000.
iiiM. 814249517400000.
j-ll * J 5}?f }r'**3''^l»t millioofl find four thousand, by three hun-
-J. ^^ 8541220000000.
-i/ii* rIlX?ff^*^ '**'"''*"'' ■•'«°t*'o«''»nd and six hundred, by
^«^i^*ftP*WWiIuttd«d and sixty. Ana. 660114005776000.
M»»ft<trT
f,< Iff both r
art tifhm-t ut M# rigkt-hand of the
4€
•TOLTiyLIOAnOH.
h»Vk- f "'"P'^' ten billions nin«tT-«K #K. "*."*' '^ 00022000000.
12. Multmlj thirty millions nin«fr*L . ^"'' ^0;)y7J 760000.^
«« hundred thousand and °K ^'^^^^""aml and eight hundred, bj
^*. 1. Multiplj 7439 bj 328.
OPBBATION. a.
^ ' "^'"^ ^"f*"'^'-' ^•''e the trne product by 328?^d ^'"^""^ •'
RuVT 7?";"r'"*"" ''^ ^«"^« *b« following
t^al product, will be the prodS^r^uM. "^ '^' '^veralpL
2. Mult,py6626b7 668.
3. Mult^phr 3786 by 721.
i U^W ^^^^^ by 2432.
6. Mu tiply 236428 by 549 ft
«. Jfu tiply 397821 by 25126
7. MutpIyiU6084by2481«
8. Multiply 5723606 by 4249784
Mamples rom peaotio*.
Aru. 3706768.
An». 2728985.
Ant. 12984152904.
^««M. 28441220644.
- • ' ' V
MTTLTr.'TJOATION.
4T
biundred and
240J0000.
te thoiiHatMl
22000000.
>t hundred,
'i 760000.
landred, bj
7264000.
** th4 mut.
the malti-
)art8, 32 (en*
' which the
lotor of the
20, is equal
aultiply by
)ro'luct for
Now, as
hat by the
obtaining
iroducts of
Itiplier f
a larger
ralpar.
6768.
^985,
!904.
544.
!n the
to the
f-rs if
BXAMPLKs FOR pkaotioe (p. 20 and 21).
Cask Nl.~T,> .fed thr maHipUcatinn ofdecivinU when it w
:Sl;S" -^ .Aa' all the decimal places of ie pr..lu.t Zm ^
S.6628
687.5
OPBUATIOK.
32814 =
- 6.562
X
5
4594-
^6.56
X
.7
+ 2
52.'! =
:6.5
X
.08
+ 5
39-
•6.
X
.006 + 3
37.972 Product.
♦k «*''"'" — ^* "Terre the order oT
the figures of the multiplier and write
them undor the multiplioand ; and, sinoe
thousandths is the lowest decimal figur*
to be retained in the product, we place
the uni«' (igure of the mnltinlier under
tho thousandths' figure of the multipli-
oand. Then, the unit of the product U
any ligiireot the iiiultiplu:iui(I by the fig-
ure of the muUiplier that iHlls under it
will be thousandths. When there are
figures in the multiplicand on the rlKht
of that immediatelv abovn th- «<,„,- „p >?*^"''®*, .'■",. ° '""'tiplicand on the right
fig-e being exSe'JruSLfc Sders" th^n^hS^a ^d^'*"^' "^ '\'' '"^^
lected. except for the Bumose of firwiin^ Jk * '°'>^. 'no"8atidths, may be neg-
figure from their product^ ^^^^'^'^i what must b« oarried to the thou««dtli'
63. From this illustration we deduce the following
RULK.— I Write the multiplier, with the order of its finurm
reversed, and wU. the units' place under that figure if hem^
phcnnd which ts the lowest decimal to be retained intheprTdv^
/^n,!!" ^Y'^ *^' P/f^f fj'^f figure of the multiplier by the
figures above and to the left of it in the multiplicand increasiZ
each purtud product bv as many units as would have been ccZ7d
Aom the rejected part of the multiplicand, and one more 2^
the highest figure m the rejected part of any product is 5, or grZTr
than 5 and write these partial products with the lowest fiTe
of each in the same column. j'-y'*re
III. Add the partial products, and from the right-hand of the
result point off the required number of decimal figures. ^
NoTB.— 1. Should the number of decimal niaoea in tha miiif!«ii-..,j u .
th^n^the number requ,r,.d in the product. s^rpl/tV'd'eS'n^^ran^ex^nl
. l'^:rXt:t:Til^^,r^^,;^i^^^^ product it
plication should commenQe at least two places to the right,
v.. When the number ot units in the highest order of the rpiecfftrl nort r.f ,i.
'If
48
*i
■fTTLTIPLlOATIOll.
EXAMPLES FOR PRAOTroB.
tai
plactiH
OPKKATION.
472.350
_646:{.46
283411)0
188940
14170
2834
189
23
3040.256
orKK.inoN.
.^.657.389
3246.360,0
182869""
10972
2194
146
T
_^ 1^
I.9C189
9 »* , . I.9C189
3. Multiply 751.2037 bv 3H ri9«
i- he^;;fir ^^^-^^^ ^^ 0-«0^K retaini., only t^Ji^^.
in th ^"'t'P'y 1.7323152 by 3962 57302 ,-» ^"*' ^-^l 9.^095.
«n the product. "^ o»o4.o7d02, wtamiug 8 decimal places
1. The hide of an ox costs «fi i <; . *
»«-l*+»2+(|0,8xfl«$l.63)
^«». $2.38 gain, ^
board,
MULTIPLICATION.
^'^^!t^t':^^^i ti:^- -^ *'«^ «>^ other «pe„..: ^
bojv rn„.h will th. rnercluf^t r e/i r?" ''* *"'''' «"'^/ ^'i" ^^^^^^
«'»••» at «1.20; L'4.s at ftmn ^^t "^^ ^oo^^as follows.- l2o vol.
HniJo„r.re.p.ctivel,.andh:lVnfrtVeUr^^ have Pete?
1». A merchant f-on^Jais'Siecfs'IJli'^''*'",' ^"^^^ ' ^'"^ *"• *600.
'^'«, •».] 12 pieces of I. acHjot . ««:i! °^''"''. *•»*"' co»tai,ur.g 37
jar
'(>. if HC<>ir cost §28 a hoMP « r. *'°'^" altogether ?
•* rna.h .Mh. C(>w and C*e t t?h ^' ™"'^'' andalarn. y times
'^^•vilithe farmcoHtthaosTor L^^^^^^^^^^^ ^^'^ J^ow „,uS
1 1. A H'f.oro.ale ,,r„c.r bouiht 4^ ? , '^''"'^' ^^ '^^ «anie rate ?
WI ; h. «.Id ,4 »rarre?Hof tS at $Sf 'V^'""^" '''^ ^^'-^^ ^
bu^hfl. of i,«ed ; it i« requ red t'knowtni ^*'""*''^ ^''<^*« ^"d 11
how i„.f,j bush. 0/ .eed will 7 tTJ , "'*"-^ P"""^'« of flax and
ftl l^-.-^.. per U,h. ? An,. 2534 pounlsflaf 77 k^?"^ ^"^ ^'^^ ^''^''^J
I.{. In a Wa,ry, there are 27S Jotf ' 7^!"^ -• '''^'' ' ^'^-^^-Sa.
U T' ^/'.'* ('<>""dH of butter wha eZ wm^'f.^ ^?' ''''^'' «» ^n
io^«)).nghii»!.utter»t?0.18anou„dy i ^he da.rj^.n.an make
it. A [arrner desire, to manuTl « m A"*' ^^'■^'^'^^^
mauur. worth $4 the bundrTdSh? S ''^ ' ^^ f '•^ «^ '^nd with
»upp««f,g h0 requires 2 hundrj wi f. ^'"' ^^ "'""»'« ]. is Held
. '-'. A cabinetmaker earns dailTS'^if^"*^^ /^ '^n,. mo.HO '
tlMWion*, f 0.65 each- hown^m^K ^ ^ hinyfiie. !f!120 : and his
d«.r#Jpe„.e«ofth?;h'olefrm7;beir4V^^^^ by every week, tie
f^«i*2, .Arm 4 times as much as the Lt^ ''^^ ^^ '^« ^'"ount of
»i»e retnaiiider in cash • how m.fl bank , tuck- $1938, and nays
.r *'«' .-t >-''*^'*' b^-'^W a cc^tat ll ?»^ ^ ^^ ^ ' ^»'- ^^S
fM0 7«f;c.r pound ; had he bou"h?S*^ ofivorjat the rate of
^!u '';? '"•'^^^^doneeig uh SSwlSr."^^^^^ '^'^ °"-^^ ^««Jd
H. The repair, and super it'enZ.^ t '^"^•^' P'^^ ^«' ^''^ '^orj ?
«&y3 per in le ; the cxr.f rfl« r • •*• ^'^ * fajlroad tract co.st yearly
»«••<'*! /Ofljf 7 - ./ — P^'^stinifB for a track 132
-y. A pJu,„b«rfurni«hM ti,— b 1 . . ^n*. $136045.
tit ^'"^ \ 2 inches r^oXe'rlarf'r ''^- V^.' ^'^''"^^^
tM4i wa (he third, 8 iDchesat «0%fi .1 '"':, ''°^P**' ^ '"^^es at
I •"»'aeeati|)0.y6per)'ard. The first kind jp
■i..i
•i
60
DiyrsioN.
;;j:?'«i::ri-™sv;r5.x,«..-s:
^'M. $244.
DIVISION.
nu^wS^^SJdL'^^^^^ --T tia.ea one
the factors, the product and tJ«'n*if ^^ P'°^ °^ fi"<ii"g one of
To divide 12 by 3 i!t V "' ^^'''' ^^'-^^ ^"^^^^ Thus
Sj.given i2forp7od!;c" or"t:Vad"r'? "^'"''' being ,„ultiplied bv
plied, to obtain*12 iu th'e p^cSua ^ ''^^'*' ""'"'*«' "^ ™"« be nmlli^
an/tect".;^^^^^^^^^^^^ '^e .nown factor, Divisor.
•nd mu«t be less than the divii>l ^ "^"^ ^^'^ «euial«Uer.
^*. 1. How many twnw ,e 7 contained in 994?
OPBRATION.
Divisor 7 ) 994 Dividend
142 Quotient.
>d •'•4 moi«
bor fi>r )„•.
*li4.64.
•tJpio.r)*'
? expenses J
► dozeu of
n?
'• $244.
times one
ng one of
n. Thus,
Itiplied by
be iiiulti.
Divisor.
nuiubei
iuder.
2.
> quotioat
• on the
MO them
d; then,
7 is oon-
remain-
he 7, ita
) of the
qjual 29
aining ;
laininjf,
liike 14
ljure of
'i divi-
'Heath
(tieot?
DiTmow. II
'•^ 'M prL^l tV ''T';*' 'tV^^'^-iing any figure, r.n,ukr
before''^ '^' "'*' ''^'^ «/ '*« ^»'»'**«<', ««'/ ^t'^tofe «
equii to the dividt^Tht' woTk Is ZU^J ^'^ '""'^ ^^^'^^^ »-
pliSnTcM)"*''"* "' P"«^ '°"'''- f~» di-W« Wnt the ™^r.. „r «alti.
BXAMPLK8 roi PftAOTIOS.
1. DiTide 8164 bj «.
OPKgATIOV.
Dirisor 6 ) 8164 Diridt^L
(3.)
5 ) 714326
142866
1. Divide
8. Divide
9. Divide
10. Divide
11. Divide
12. Divide
13. Divide
1359 QuotiMU
S ) 893rM
rsoor.
1869 QuoUeok
6 Divisor.
8164 Dividend.
6376 by ft.
5692 br C.
38776 bj 8.
174321 bj 9.
1643784 b7 12.
46216796 by 11.
63412632 bv 12.
t ) Nfllt
lamfi
(6.)
4 ) 662846
QaoMenti.
127.0.
932.
12347.
19369.
136982.
4201436.
14.
1ft.
16.
17.
\x.
19.
Divide
rv;_.- J
Divide
Divide
Divide
Divide
10. Divide
2271582 hy 7.
I i. 15721 2 by 6.
4056360 by 9.
12980400 by 8
4208479,5 by 6
4607060 by 12.
^023620 bf M.
6.
2.
C.
t.
4.
BITmON.
FRACTICAL PROBLEMS.
1. Fine jurda of silk velvet at,ai *T'> u
J«fti? '^*"''" ^^^^ *^2; how much did it cost •
Alf AI,T«I8.— If the Drioa nfm^w.^l
7ald obtain $72; thep^w 72 TA^r!!;^ ^°u'"'; '" '^^"'«P'ri"g it by 9 wt
of a 7»rd. Then/in dirE 2e nro C^T u^'T^i *''*'" f^*»" " »nd the pri«
of • r»rd , 72 ^ i = ^w §8 j?r ''^. ''•"" ''"*«'• *•• "e obtain the E
wtain thu prioe of m yard. ^ ' "'"°' '" diT'ding 72 by «, w«
.hilii=p? """'"«• "•*• • ■'■>"•' i 1"- m».y JollT, in 8890
^4. Ho, „.„y barrels of «„„,„„. ^,_ „,„ ^bof/if-,^,
6. If 12 inches make onp fnnt . i. . ^ .'^"*- ^^ barrels.
$1152? "^ ^""o »t> a cor.i ; how many oorde will be had for
10. A person wishes to distrihnu ifiQ „ i "?."'• ^^^ cords.
^«.";«»1'.^" ^'•^ ''''«'• P™<»- Of <ii-i«.on i, wHtten. the ope^tion i« termed
£;3r.
Divide 4738 by 34.
OPBBATIOK.
^•Th*"'- ^^^'<*- Quotient.
2nd. partial dividend
3rd. partial dividend
34 ) 4738
34
NAi,Tsia._Taking 47 aun-
- — f ^1* ^"^ *^* «'^t partial divi-
l X 3911. ^?°?',!'« ""y 135 is oont.in«d in
fh' ""If- ^•'^ > "« '^te in
the quotient; 34 x 1—34.
which we write undtr dTe 47;
« — 34 « 13, to which brin/rine
down the next figur, of the di?
I??"f,5'"«*> '" 3. we form 133;
34 in 133, 3 timei. The 3 we
Remainder. JT^/'^'" *^« S'^^wnt ; 34 x »
u. u . r ..i "'"''*' ''^ write under
which bringing down tfcan«»f «»,..- f*i. i- . ,^"« *"; 133 — 102 -, ai II
133
U)2
318
306
l2
«6
vino7i,
..^:^^^rr-t.lt^2---
''^*«* •• '*• ml* «• iWwtfa »»f„ 14, 4j^j^^ ,
1911
•'«^^
iid it cost •
? it by 9, we
«nd the price
btflin the prjoe
yard wiil eoat
'« 72 bj «, w«
krfl in 8890
8 dollars,
ildren; how
i#. $9958.
bought for
5 barrels.
164 inches?
'erage sum
ns. $2:n.
ing 4 cento
Ans. 66.
did he re-
Iw. $62.
be had for
'2 cords,
ong 4 bojs
Ans. 24.
>o is termed
g 47 aun-
irtial diFi-
ontained in
e write in
' - H
ir the 47;
h bringing
of the di-
form 133:
rhe 3 we
.34 X »
>te under
« 31, t*
in 318, 9
ite under
Bft ondi-
mpletiiiff
^lidend.
tfrrmton. ••
II. Take for ihtprtt pt^rtial dividend the yn»f *««.A^ ^
^ the. ««( «™, „/rt, dh{A,nd,/0T the .u^d p.,rli,a. divi.
7' J/^^^y jx^rtial di^iaerui will not eonfain the divi^,or place
J.Ji' /'*"■' '' ? '""^'Wtr o/Ver AVWinj „« th, figure, of the
PROOV.— It is the same aa in short diviBion.
DIVISION ACCORDINO TO THK FRENCH MBTHOD.
Ex. Divide 11812 by 72.
OPIRATION.
Dirideod 11812 (J^2 Divi.-^cir.
!!. iGi^"" Quotient.
461
432
292
288
4 Remainder.
Omkbtatioh.— We lee by ti.. ex-
ample m the margin, that the dirisor
M placed on the right of tlio dividend
and the quotient below it. This mode
JiTei the work a more compact and
■eat appearance, and posieisieR the
adTantiigo of haying tho ligares of the
quotient near tho dlTisor, by which
means, tho practical aiffijulty of mul-
tiplying the (lirigor by a figure placed
at a distance from it, ij reraored.
ABBREVIATION OF LONG DIVISION.
«7 By the following method, we avoid writing the products
in ic... r division, as m the example of Case II, above.
Ex. 1. Divide 8764 bj .365.
Analtsis.— In this operation, wo say : 3 is
«)ntaiacd2time«in8; we write 2 at the quo-
OPEIUTIOV.
365 ) 876.4 ( 24
146 4
... 4 remainder.
tient and multiply the dirisor saying : 2 "
times 5 are 10, which sabtracted from I«
(because wo iiioroaae the « by 10), laarcs tf
irhich ■■)itr»«t<yl Ai^ IV I. A """J^ oarry one; 2 times 6 are 12 and 1 i« l.V -
WBicn Hbtraoted fMm IT laayei 4 and carry 1 ; again 2 times S aia A and t # '-
■»* ■
64
onrnioii.
I
'. which, subtracted from 8 !«•«. i i. .
^RULB.-I. Obtain tUjir,>fy„eo/. He j^^^, <,«..«*,
remainder. ^ <iividm.d, and xorite underneath thi
the former, till the work i$ finished ' ''^ proceed a, with
the SnT"her;i;Tt!lf ^^ all the figure, of
firstly in tenths by adding a ciX? »[' Tl'^J'^Z'^T^^^^^^^^^^]
^e division J but then, af we cannot have anf °^ "' i*"*^ «°»^'°"e
point at the quotient. When m»^LTJ ?J T*** "«'*«» replace a
rema.nderi8;educedintohund^dt^bvri^^^•^''^'^^^^ *»»« »«^d
but place no more points at Jhe quoLL .u!'^^^
^he order ih^y occupy. (Nos. 27\nd VSV "" '*'"«*'«*'«^ bj
Ex. Divide 679 bj 28.
OPBRATION.
28 ) 679 (24.25
119
.70
140
pher at the right-hand rf if "i ^ """"« " «»-
the quotient fnd th" p/oiwd ^ L'f ''''*^'' '»'« •»
hundredths by the ^l\^\t°t "*"* ■nnUr t»
qwtl.nt of 679 by 28 a. .h?°'i°'' u ^•''°« ''• -wMiTSTtVl «**•***?* "*^'»«
.Had there h^^IinlZl\Z!'^l *''• ?"»'• " *^* *"««*
'h«, we oan carry the *n!^^"*""*"' "• "•"W h*v» .dd.rf «
rry the approximation to any order ^13 "^tT"^ •*»*"•
'^e first place a cipher an?« • '^i^''^*"'* " •'"•"w than the Ai^i^
are n integers or^^.t^X"* Th^n' r '^T* ^ •'"''>^^*^'^'
^•^ths, hundr^ths, *e. cNo. T),' an'd;r:cVdt;a'r: ''^'"^ *^
^- C>iven6to be divided by 25,. hat ^„ Bet., operation.
OPKRATION.
25 ) 6.0 ( 0.24
1 00
in J?a"SoUonTa?:5"^we'rr *1«i«"»«. we«y: »
the quotient. S' ^ JIH^^VjP*.'"- -^d • point Jl
fay placing a oil'her at thVrirtr-hanVr',!? '"" *•""»
26 ,n 80 J, contained 2 and ?0 tonS/ '*' V»d "7 •'
pher, and say : 26 h lOO IntZ'^T}'''^ hnndredths by Uie !d5?Mo»"!:r ^»
2.
3.
4.
5.
6.
7.
8,
S».
11.
12.
13.
U.
16.
DIT18I0N.
form th« 8«Qoa4
we write at fh*
n the second pM-
be added to t^
t in the unktl
lotimt Jigun,
nderneath the
8 next figure
oceed as with
the figures of
lia remainder,
ind continue
ta, we place a
the aecond
other cipher;
iodioatad bj
I rtmaiat 7*
rritlnj a af.'
^» point a»
Bat w then
a aonber t»
iphnr. Mai.
Ithataothin*
utheeoiTC^
■on oipk»r.
le diriflor,.
thacther»
ndend ti*.
ktionf
we»ajr: »
1* point at
>n tenth*
' ud lar ;
on of a «u
therefore,
66
Use of my isicm.— Division seruM t^ Ai^A. i
« *o» ^ny Unu, a numUr i, contained into aZLTuSnk t
"hal »am6,r muMi a given number be muHi„lZl?rZ^' '"■'"'"''*
Siven number. Division serve, aZ rJni'ttZ^fT"'''T
EXAMPLES FOR PRAOTrOE.
i. Find how many timea ie 72 coataiaei ia 2S50Q.
^ . Divid'd.
I>'v.8or. 72 ) 23596 ( 327 Quotient.
216
~T99
144
666
604
62
Bomaiiider.
Paoos- By MULTIPUOATIOM.
^27 QuoticDt.
72 Divisor.
654
2289
23544
. ^ Keniainder
23596 Diviiiend.
2.
3.
4.
5.
6.
7.
8.
9.
10.
ii.
12.
13.
14.
i6.
27939
38582
406683
743241
964992
173469
497699
218579
ox J ^00
41126
432606
845002
8«7632
sum
16
18
20
26
30
o6
40
42
47
49
60
63
69
CO
Quotients.
1746
2143
20284
31833
12442
13006
8662
14703
ftem.
3
8
3
16
2
21
19
n
4
16
5
23
66
41
56
DnrisioN.
1^
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51. I
52
53,
54.
55.
56.
57.
68.
5y. i
«0.
4968
940025
445124
4728
39006
1679407
4306404
167008
7466029
6717890
64
68
70
75
79
80
86
87
90
98
(juotieata.
77
6358
493
60663
82844
To ealculate with two decimals in the quotient.
67980
432101
470896
680094
666648
767642
124674
964321
7246579
7H90645
9120128
687621
3466604
4268901
2486930
*l0712d
81267904
69267421
8IMJ640IO
6947:^0210
468904008
389006753
86742807
707070709
654380316
987664321
8606000041
61247680241
742.^8961401
9649646664
8674289646
4247698734
63 .' 241)0086
45t)»010ti007
378942UU4$
96
69
72
67
441
386
126
216
<12
367
637
4691
1279
1467
7614
7614
617*
7186
7908
9087
7064
d004
8906
4260
49060
49068
6004:
74086
48647
42867
74651
S4672
59866
300462
9S7684
Quotients.
708.12
6262.33
10150.66
1511.67
989.47
4464.44
21500.39
146.68
2909.96
539.41
9639.21
76463.74
48601.64
166979.03
20129.09
826721.74
225106.64
44867.62
162037.95
4i0
61
64
3
69
47
4f
66
%9
98
H«m.
48
23
16
46
163
380
78
196
328
187
153
1422
240
435
4532
6126
3592
6794
184
7462
6768
2684
5914
4120
37440
39106
49042
13310
11893
32712
48424
88056
46810
186360
88764
s.
\
4.
6
6.
6.
7.
i
8.
9.
1
10.
DITmiOR.
DTVISrON OF D8CIMAI>8.
M». 1. Divide 3.466 by 2.4.
M
OFBRATION.
1.4)5.466(1.44 An$.
24
IM
N
H
M». 2. Diride 0.626 by 7.6.
AifAi.T9T».--W« diTld. M i. vrhftle nura-
n Jk*"?!. *'^'"' *'*• <*'^'»'"' »ud quoU»nt
r / . '^° f*«»*»". »'bioh. being multi-
plied together, produce the d.Tidend. w«
to «*• uabcr te th« pndNet « (tfridewL
OPfiRATIOK.
TfM ) 626.00 ( 0.07.
626 00
.dend«oeed tfco.e in the d,W, w Lake
fe.m equal b7 npnexing two ciphers to the
2^ AL'V* '"'^"» P">o«eded in the divUioQ
oVT ^' '.P;1*' '"'^ ''°*^ *• quotient to be
9.t7, or ff unit 7 hundredths.
«7. Prom the preoediog illuBtrations we deduce the following
Rui,« I.-Z?tt;irf«- «* »n «,^fe numherM, and point off as manv
2^.e of the divisor; hut if thw$ ar0 mt as many, mmply th, de-
fiotmey bi/ prefixing ciphtrs. '' '^^
Or,
Rule }l~lf the dividend and divie^ hawe not the ,amt
number of decimal,, annex cipher, at the right^de of the term
^l^Unur^bL ''"'^' "*''*'•" '"^ '•^^'^''^ tothepointra, in
»OTB l.-To diride deoimali bjr !•, 100, ItOO, .i*. (jr.. jy^,
^mooF.-The proof i. the .ame a« in diyision of whole aam-
■XAMPLB8 FOR PRACTICE.
s.
79.1
4.
67.8032
6.
2.3421
€.
0.338
7.
14.
8.
0.21318
S.
10.86
10.
0.1728
2.6
U.4
42.2
0.16
Quotients
31.64
4.174
0.055
0.7852
8.34
17.
0.0776
0.012
140.
N
tu
8
0610
400
«7. What i, «^ rule /or tht dMtion of dediMta f
58
DivwroN.
To calculate ^hh five decimals in t) • *•
'*"' '" tue quotient.
Quotients.
1.62745
1.19201
8.23846
«. 78318
1.62197
0.189IH
0.13680
PRACTICAL PROBLEMS
Ham.
34
740
18478
6984
296
1998
528
960
17178
34
240
4
1. If 4.') yards of cloth co8t SI 2^ fn i
»4 . .70 ? * oo per d»j ; ,„ ij^^ ^
in«4T7n ■~^''P»ny"'M«*,«2 8S fi, • . ^'«»- 18 days,
in f 47.70, u many davn wni k *'*•''*' «« pnoe of a day's UKn,
j: One Of" ^''rS^;*''^ t"!r"""ir* "^ " -"u" '/oS* ,
Other factor ? »« *• /& and their product 4222 fS PinH ft
^M. 182 milM.
BTTMIOII.
59
int.
'.8.
5
Kam.
34
740
18478
6984
296
1998
528
960
17178
34
240
4
yard cost 7
t by 46, we
otors 45 and
f » yard =
•«». 12.76.
iJl he eaFD
18 days.
■ oontained
70 by 2.65,
. 18 days.
umbers ia
»• 7777.
re 70344 7
Find the
redths.
that per
)76?
r*69?
can be
r. 215.
pages?
*. 80.
bought
ards?
^" will
». 32.
I work,
r. 23.
howlkr
nilM.
<»it.«mf6yp. ii^i'J^it^^^Ysilj,^^^^ r^**^ '° • kiln which
ihe value uf ii^^ijiS? Sfo \?^ " ''^^"^^ <«>' ^^^e operatioa and
of 10.28 per ^ff^Lf^S'.^ '« *«*>™««d at $231.14, aUhe rate
prf^%*A^7*^ '"" ""'^^ b^ahelsof coal have b^
ength»8abowt#/S^ ftirr^uirjr^ <'" F^'^^'^a, the meat
die yearly, 4wJ^, ^TTour .i/eTrrll^^ l^ow many person.
for6every44<«?i«rifi.y ^ "*^"'» ^^ •»•»•/ minutt
^^^S^^i^^lTONS IN DIVISION,
<ftf lityrsiON BY f AOTOM.
^*- 1 • ftM^fri^^l^^umiy ««>ng 28 person.
.r«A.:<ft«. ^^**«.-Th. raptor. ^ 28 ar. 4 «.d r We d" •.
««^W^^^^»^^W^^^ <>/ ^^ facto., an.
7 ) 39?
I
■lii'
'•*?«»m/ quotient. ""'^' ^^' ^' ?««<»■««/ will beZ
2.
3.
4.
5.
6.
BXAMPLE8 FOR PaxOTlOB.
Divide 4536 by 14* a x 7
Divide 9774 bj 18 =r 3 v «
Divide 14560 Jj 35 =Vx*V
Dividel26375br76 -3 V fi r
- Dir de «9384 Ht 49 --.3x6x6.
». Diride 57456 br 72' "'-"^ '^' ^*«'^"-
«. Divide 246792 by «4 ""'"^ '*•" **^'""-
». Divide 2962876% 1^5"?^ ^^.^*«'«'»-
<"o Dj U6, Being It* factor*.
iliM. 324.
An». 643.
^n#. 41 «.
-4««. 1686.
^»»«. 1662.
^»». 79a
Ant. 2938.
^fM. 2370S.
,4
6
3 = 12
3 = 9Q
103
, „. . «IA"»L«S rOB PRAOTtOi.
• 4,j:f ^"^ '"'• »-« «.. '«- . .„. ., .„, ,„, .,. ^
-T — '. niin the "*•—
nt loill he the
Ant. 334.
An$. 643.
Ana. 41 «.
Ans. 1686.
it.*. 1663,
An$. 79a
ln«. 2938.
M. 23701.
DITIBIOII.
fl
I the
opm.
^Qd 7, and
■Diridlag lo
T« A quotient
•maiiuler of
in diridond,
part of tho
Tho 3Stf4
•rising froa
« unita %t%
io Talus M
lave a quo-
. it muat bo
>s makM«
7, wo hkTo
be uQita of
S3; there'-
» dividend,
oom dirid-
> true r*.
aU tht
the
tnfe rl::^:lT '^ ''' "-« »^« ^-tor, 3, 4, .nd 7, and find th.
thetrS^;f:;,LS^ '^ ''^ -^-^ ^^^ ^^-^ 3, 6, a„d 6"r,i^ta
i^^e^S^' '^ ''' --S»^e ^-tor, 2, 6, and .""aJd^Ld
V- -ii^c^^^^^ '''' "'^"' ^^« ^-- ^' '' *^ -d ,t';/Ld
«-e Sdtf ^ '^ ^^^' -^"^ '^e ^--« 3, 6, and 9, a;?.r^'.!^/tb.
C TT ******* *•
(No.3?,i;t7^'''*"'^"«'*«'«"»"»^^%10, 100, 1000, etc
1. Divide 87 by 10.
2. Divide 5813 bj 100.
3. Divide 7009 bj 1000.
J- Pl'^iJe 510040 bj 10000.
6. Divide 200371 by 100
BXAMPLB8 FOB MAOTld.
Atu. 2003^
£». 1. Diride 85726 by 4600.
46100 ) 857126 ( 19^yy^.
45
407
405
226 ReiDUQder.
»r the entire quotient Isi^^JL
III. Place the entire <i.W.-- „-,^^^ ^i ,
63
BiraioM.
J^lv'SiSS^i'-rSooo.. "--ems*.
¥' •■''^reZTc^'i^f.f^!'^'' point « ma», .fa«, ,„ ,;..
OOKMOir OFM„IO».
M.647.8)6„.«,63( 28.684
-"^iF^rs"-
llii^ = product bj 2. -f. 1
204 50 '
1«^ = product bj 8, + 6.
J*i| = product bj 6, +3.
l|8 = productb7 8,+4.
» = product bj 4, + I.
470 94 176
204 SolsTO
188 37 904
9660
8428
12H20
37904^
744160
418962
325208
figures the aboT« Biftr»,.u •„ *? """'nod Wo flnt MMrt.in i.
of the divisor wUh the jn«7^^ "t"^ ?'««« •?
quotient fiL'urTwSi h. „Ai " P^'* "^ "»• cirTidend it irP"?°« "•« •""re part
"?^?Uontain>. fij °",:''^" J •'^d « there itre to be 'wXet''"/ 7''' '^°'*">
diTisor, oountine them fmm 1 ^ 7* "^-^de «t fint bv fi« « '^ <>f deoimals, |t
and r.jecti4tliVfi^Tre« ?«'•'*' 'T'* '"»»^<». the "kK JL,»«"''?' ''^ *»»• given
le abb»«iia»,4 T"7?r'"*«d with
anarejectiii»thefiiriirB<.^T" "**•■<*« the ri^ht th... • °' '"• «»ven
vifior bj iU anoii.»f « ^^' ®" *•«» "ght. In in., H»i • "*' ""°« ^^^ 23.647
the abbKnii»;»9 ._a ^^'"■"'ea with the oommnn .i~*u-j ' P ^')-
'raJ«to<MM^,
i:
wrm»t^
«8
•>«m«rt8, 14. WoS!^ *••'***•' '^""''•"^ <»' <iiri«c. wh.B — - ^,
"^conj dedm^j place. ^ "•""^i'fi-^ extending the quotient to the
■*«. 9876.54321. *
DKCIMAL CURRENCY.
94
DKOnCAL OTTHUNOT.
The *,:W coins are tl.e fifty^ent piece, the twenty-fivc-cent
p.ec. the ten-oent piece, and the five-cent piece ^
loJ^gLT'^lJooi^edl'"* "'*'"*'■••■* P'**"' "»-«»« 'till in olroulatlon. i. no
The copper coins are the twoKjent piece and the cent.
nilt The Coins of the United Stat« arc of gold, silver, and
e^IleXi^^^^^^^ -«'«- »^^i^-.le. quarter-
a„d^h:i^il"'" '" "^^ '^""' ^»>^-<*°"-' qunner-dollar, din.e,
Th^„.cA./coina are the 5^nt,3^nt,2-cent, and 1 -cent pieces.
weight of gold and 1 part •# « XJ ^Tl^Mn i ' ? . ~'" ~""**'' *» ?"•*« ^y
TABLB OF TH« DNITID 8TAT«a OTBEINOT.
}J Sn^"^^"!^ ! r*' '^^ let. ore
10 dollar. « i^K,' " li?
Ja^aPd\r;;Stir.;^^'/r;^^
centt, and mi/t'.. «wuaw are kept in dollarg,
Dimes, o^nts, and miUa. bcioff tr^tinnm nf - j«ii
from th. doJIw kj lb. CiiKlJ T.f fc i ■;', '"'•'^""^i
are written I-V236. nunarea thirtj-five luills,
To exprrjB any number of centa I<mm th^n i n - • l
placed brtween the fignre exp^JriLlThat nu™Sl "J^.^ T^'^-* ^'
point; thus, 8 cent. ^writSL^^or oS ^'''"^'^
JSoTKB. — 1. BuBin»M men fraaaaaUv w^t. —.k.
doUar ; thu., ,3 ,4 i, a,^ wn'ZS^^y^^Tj^,':^^?^^^ '"^*^-" ^ '
2. In buiiueas tr»rn«otionj, whan tKiL./ ».„■» * "»^ ao"»"
EXAMPLOS FOR PRACTIOK.
Write fifteen dollaru twenty-three oe«i;«.
Write eeven dollars sb. centa.
loiiaFa niue oeo;^
o oeais.
Write ten d-"==-
Ang. ^15.23,
6
6
7
H.
9.
10,
Ama. 15.008.
DKrr.MAL CDRRBNOT.
Write five dollars eight mills.
Vvrite tiiirty cents.
Write one huiiiircil cents.
Write one tlion.-anil mills.
Write one cent five mills.
1 1 ^"^'^ :;eventeen dollars four mills.
11. Write $6 and 7 cents.
12. Write 3 eagles -t .iollars 3 dimes 3 mills.
REDUCTIOX OF DECIMAL CUriRB>07
«0. Reduction is the procons of chuntrin" a .iumi.>, of r -..
II. Tochmg,. dollars ,o mill.,, „nnex Ihre,- cipher,.
HI. lo change cml$ to mill,, annex on,, cipher.
Conversely, * '
U ^n-'!'"^^" ^^.<^^^'«^« '•««<« 'o rfo^^ara, r/twWe 6« 100.- <Aa<
^,po>ntof two Jigures/rnm the right ^ "", «rta«
TTT ^''''^"["d'' mills to dollars, point off three fynret.
All. lo change mills to cents, point off one figure,
EXAMPLES POH PHAOTIOE.
!• In $7 how many milln ?
-^7000 mlllr^" *' '^"*' "" '""« '"""' "^ '° «' »»«"« *" ' time. 1000 ndlk
2. In 3"j6 cents how many dollars ?
Analysis.— In $1 there aro 100 oents. therefore i nctu«. u
•quale the n«n.bor 01 dollar, ^^ onit-tl^ """'" "''""*'
3. Change $464 to cents.
4. CJiange 612 cente to dollars.
6. Reduce $3.10 to mills.
6. Reduce 35 cents to mill*.
7. Reduce 704.5 mills to dollars.
«. Change 10426 cents to dollars,
y. tieduce $4005 to mills.
!''• In 20GI liiillg h<.\v many ceuitJ ?
Ana. 46400 cts.
Ana. $6.12.
dnllart in cr».'« onrf
MM* to dnlUirit—
. -~J«™.«r..-fvs«K-»»Ta.-i-.':.'3^V'
S6
PRAfTrCALPK-ORLEMS COM
PRAOTTOAL PROULBMH.
1- A broker bo
RULEs'^"^'' 'i'HE FUNDAMENTAL
2. m
-ugiit stocks lor .•3);^729.90, and
ii'w much (lid he gain?
sold tlieni for
An.9. $43«.2;{.j
wa^e- ain.miit to?^^'*^^*' """^"'** "'' •p.'.'.iju, wnai will 12 mouths'
co.r; ^ '*""' "' ""•'"•be™e» cost $0.9376, »hal will I ,„„.
h»w ,n»,,y of each 't H S .."..; 'j' ""'^ ">/ ««;«« "
«^ c..„., eacl, . how ,na,7of e;o-h'w;;d ZZ^^J^ An, 15
a i:,,n.ri,f u Y, •" '^^'^" '^'nd did he te
gain by ti,e bargain ?'' *•''■ '^''** '* °«^'; how much did I
. '• ^^'"^'ifi"!?! J ;^5 bushels of wheat at !Rnfi9oK . ;^"«-;^^235.
-t *().:^7.-. a pound, and he ?ema ni^ • ^1""*^^ ^'^ P*^"'"^'^ ^<" coffee
he receive ? ' '^ ^ejuainder in cash ; how much ca.sh did
^- I'' a gentleman's incom*. ho i^'mnn . , .'^"*- *66.586.
<5l:iO; andto he8eco;7J2TI^^^ *« the «rst he gare
the third receive? ' *^ '^'' ^''*" '^ *^« ^"1: how mucli did
10. A lumber merchant boucrht «8n ln„. f m "*"'' ^^^O.
what i,s the price of each 10^?' '*^'^°'' *^« «"'» o*" *'^644.80,
li. With a Bank note of Siinnn i -j ., ■^"*'- •'^S.se.
my shoe„.ak.r's of srfand m^'o, se'rfnt 7s8?5"h ''" ^*' *'^«'
lar.M have I left ? ^ ^"' °* *^'5 5 liow many dol-
12. If a hat cost $4.25. how mi,ol> .„iii a j '^"'- '^202.
cost ? ^ ' '*°* '""<5^' ^^'" five dozen of similar hate
^3. Anarmv comnosed of fi2]fifi ,„»„ ^ .i_ -^ns. $255.
13708 men lesfafterTleenial^ern^ '"' °^ ^ battle, has
in the army? engagement; how many men are there yet
15. Uow much £ I sellllod ''?'';!'''' ^'^^^ *'^^ ^ ? ^- ^-^«-
in giving ,^18 comnZtn ? ^ '"^ ""'' "^' ^^^^ '^ ^^^ «76
1 1>. Jo.oph bought 73 casks of t^vrun at S'^iQ fl « , ^",*- *^^^-
again for §,-,2 ; what is hi« nn 'fit ? ^ *^ "*® ^'-''''' ^'"^ ^^'d them
17. A IJauker is to receive .'Sl^^'fin i^ »u ■ -• --•
an.ouutingto^aHOO, and he se^tud Z S^^lo^^'T"'' './^^ «^^»
Hit of the third? second, to |.4.^20 j what will be the
'1
Ana. $3830.
"ozen of similar
amount of the third?
oue'-cit?''" '"■" ''"'''' ""''■''' »-^ »""«'» -ill
^ 19. I bought 150 applea for «1 0^ u ^'"' '^'^^^'S*^-
- ' -■ """ ^ ""7 lor
20. A banker received dnrin.r »j.^ a * '^"*' 2656.
H2769. Ho paid out duriL tt wi vear ^P^^T"*^ "^^^ '^«''^»»
niuch he lias fell supposing le had «ii-4|^?^ •V96843 ; required how
of the year ? *^^ * *** ***^ '-^^^^ « bis »aA» at the b^nniac
OMENTAL
them for
43H.2;{.).
2 iiiuuths'
IS. $426.
5?1H?
IJ 1 quart
Ji0.062o.
md geese,
le geese at
ins. 15.
3 of it at
ich did I
$1235.
i received
H of coffee
cash did
66.586.
iseH$4.20
t he gave
luoh did
$120.
.S644.80i
.«5.36.
)f $348 ;
any dol-
$202.
far hatfe
$256.
ttle, has
lere yet
8392.
U.80.
;aiQ $76
$380.
Id them
5949.
he firat
be the
5830.
similar
3.80.
'iij for
I66d.
during
fourth,
(1 how
pafd 52 Tu ;?K TY *. ^"'*'"'' ^^ '^^'^^^'^ **f bft'-'^y ♦«' which I had
^^22. Frank was bora m 1857, in what year will he be 21 year-
the age of the non when the father will be 75 year, old?' ^^.4
24. An omnibus able to seat 18 per-on. ,nakes 12 trm^ oer .lav
how many travellers will it carry io one vear ot 365 day^s .^on SL
that there are always 1 8 persons at each irip ? T..' 7f?40
2o. If we can buy a yard of tiannel for $1.76 ; how many yards of
the sarne quality can be got for .$626.56 ? ' A J Si
lJr.m^,^ZTV''\r'!'''^ ?"/^^ ^ '^'^"^'•^*'' the" distance
bemg i«y uide^. he ^^Iks during 5 days at the rate of 27 miled ner
V ^q^'red what distance he has yeUo go? ^n,. ^fmiles^
remains vet'.'?!;r "'"A '^PT*^'" ^''' ^^«^'^^'^ «»*-'' «24 all^ th'ere
remams j et * {6.40 ; what is that sum ? Ans. $2004 40
28 I bought 15 yards of linen at $0.25 a yard, 37lJ lo, "^-'oU at
29 Ahfu'^T^'i^ '•«1»«'-«d/lie amount of my Bill? ^. $123.81.
earn p'; dly ? " '^*^' '^ '^^ *^* """'^ = ''^^^ ™"°i' '^'l' J»<»
• ealio?*I lo!t^"» n' * ^"7' ?'''^'' contaming 28 gallo1.r Jt^ 'lo^.^b
SefiSn d 1 if '"' ^y. '^^kage and sold the remainder for |l.20
per gahori ; did I lose or gain and how much ? Ans. Gained $4.20.
«»i ofl?l3"s" Y:^l'^ ^T^ *"'* *'^'^ *"^ '"*^'"g repairs for he
L^t I fell 'it ? '* ' «t 80 as to gain $60o1 foriiow much
32. What sum of money is required to pay 34 wu-l^^n^fleh* of
whom has worked during 28 day^ at$0.80^^r<iay ? A^i^i^ei 60
33. I bought 97 barrels ofcodfish at $5 a barrel, I gave 17 barrels
rail'i^n^f^tU^^— '"'^-^^^^ - '-± ^J^
34. Louis bought 500 acres of land for the ..ZTmsU Re
•fterwards sold it ,n lots as follows: 127 acres, at *47 : 21 'aero:
Jt$96; and the remainder, at $37; how much di, I he .a,n llv h.
35. Henry receives 45 cents to buy 6 pounds brea i a. ! ceuH' ^
pound,and2copiesat3cea^api.«e; what is his change ?
36. The overcoat of Wilfrid costs 3 times as much as the hat cf
alett rr b^lLr «- -- ^^- theothef ; h^w^L^^^^^^^
38. A milliner bought silk ,n a shop tor .3« oentT thread fJr2(i
cents, needles for 9 G'»nte ...i.j ..,,fu.n/^r iZ-^^ T' , ■»
■itfl hftH ?•> /^.n/.. I^ft u " -'W'a''^r !Hc«ai»,- afier paying herb
^8 wiaf ll ?•' .'•«'^'"«°^ money had she? !j,,«. $1.55.
t.W6 ? " '^•'^Klend when thc^ divisor is 3061 and thequoUent
At, A i^.,^ „ . 4iM 198,966.
"^ntH ; what proflt does h« ,„ake or. I 76 pounds ? 4*m. $5 25
LfH^i^- i 5>f.^, ' ^-.g;^
MAOnOAL raoB
n
48. How much will 3550 laths cost at 22 ceuM ner hT.^'ri ?
$13^0^?"'' '"*"^ '"■'^' °** '^^^ ^' *^-=^5 * ««'d did I buy for
co^t^^f2^r;sr ^' ^^-^^^ ^- ™"^ i,w^
53. A cabiaet-.naker km earned $45 in a certain number of dav.
35tdT'^" ^rS^^" '^ "- -^^ ^vear« old, wlrJ^hrXLi was
mother^"' "" ' "^*' ""'' '^^ "''"*' *S^^ ^^ »^« f^*^^'^»^
thfratfo7'^?75rrH"'"'rfa'"\''^^'^'^''^»' ^ bouglu 'tfo ^f^J^s 'at
ttie rate of «l7o0 each, and 19 shares of Bank Stock at $103 iJr
57 In celling cloth for $610, a merchant gained a« ^mch^^frthe
cloth cost hun, lesH $5)0 ; what was the cost? i^ *656
58 Althou,rh I wa« robbed of $25, yet after havin«^id $546
which I owed, I haTe $17 left; how mui mowy hi J? ^ * *^
BILLS AND AOOOUNTe. ff
BILLS AND ACCOUNTS.
82. A Bill, in business transactions, is a written statement of
articles bought or sold, together with the prices of e,ich. and the
whole cost.
N0TK8.-I. The party who buje, or who receives money, goods, or serrieM.
83. An Account is a registry of debts and credits.
friJ^rH'.rV/'' account should always contain the names of both parties in th«
if L^Zi'°i' °"*y '"*^« "?^y T «'le. which may be either debit or credit: or
It may haTe two sides, debit and credit. . « u.i. , ur
84. The Balance of an Account is the Jifference between
the amount of the debit and credit .«iues.
85. An Account Current is a full copy of an account giv-
ing each Item of both debit and credit sides to date. '
/«e^"'~"^° -ooount current hiiTing only one side is sometimes eaUeu a BiU mf
86. An Invoice is a full statement in detail of goods sent to
a purchaser or agent at the time the goods are forwarded, giving
the marks and coatenta of each package, the charges paid? and
how sent.
87. The Footing of a Bill is the total amounr, or cost of all
the Items.
r^^T^T^" ^^^^ •creditor receives the amount of a bill or an account cur-
Z :, » If ^°ri^1?^' '^ ^ ^ PT'^.'^J'. »»riting r.t the bottom of the bill or »«.
oouni "lleceivedPaymem" and sigi:ing his name. If tho payment be trade
aooount by writing the creditor's name first and his own t,ame under it. as in
rorm I. ' '"
2. Bills and aocounts are sometimes paid by the debtor -iving to the creditor
a promisfory note for the amount. n e, <-" i/iouiun-
In the following bills and accounts the abbreviations are :
Dr. for debit or debtor.
Or. for credit or creditor.
yd. for yard.
elos. for docen.
bbl. for barrel.
bush, lor bushel.
lb. for pound.
cwt. for hundred weight.
82. What w a Bill ?-
M-r««i.» ^fl*^*i^"7~ What i, meant by debtor and creditor?- i^v « BUI <rf
Par«l.t-83. W*a«w«m Account?- 84. The Balance of an Account T-8»
70
Mr. G. Murray,
rorms of bills and aooountb.
(Form 1.)
Kingston, Sept. 8, 1870.
Bought of E. P. Healet & Co.
15
24
16
34
8
4
2
32 yards Ca.ssimere, . . .
Blue Cloth, m
Flanuel, (co
Drilling, ^
Fine Muslin, /®
Gin<;hani, (®
doz. Shirt Bosoms, m
Wool Hose, ^
ra> $1.70
3.25
.67
.12
.18
.30
5.60
3.25
*, fi
54
48
16
40
75
08
Received Pavment,
E. P. Hbaley & Co,
per N. Ryan.
|158|45
Mr a. Seymour,
(Form 2.)
Montreal, Sept. 17, 1870.
Bought of T. McGiiBRVY & Co.
May ej 4
June 10
July 21
<<
24
Aug. 3
«' 12
Sept. 2
15
3
4
7
15
10
150
boxes Oranges, ^ $ 3.55
" Raisins, rs> 2.90
cheats Black Tga, ^ 25.00
' Green Tea, /® 28.50
' Imperial Tea, ^ 45.10
bbls. Coffee Sugar, /© 27.20
sacks Coffee, ^ I8.6O
bushels Corn Meal, /© .85
Credited by Cash,
Beoeivtd Payment,
T. Moaauv Y k Oo.
B*^
FORMS OF BILLS AND AOOOUNTa 71
(Foam 3.)
Quebec, June 2, 1870.
Mr. D. Johnson,
Bought of Byrne, O'Brien & Co.
No.
2
7
U
10
40lpair Gaiters, ^.^2.30
75 " Rubbers, i^o 72
;; C^fi; Boots ra> 3!S0
' ^'"«k " (3) 2.65
tooperage and Cartage,
Insurance,
108
67
$ 92
54
410
177
4
1
00
00
40
55
37
30
L. Jackson & Co.,
Bj " Canadian Express Line."
(Form 4.)
Toronto, 0«t. 6, 1870.
$739
62
To W. Price & Son. Dr.
1870.
i u ?Lk„„J*--^ ^ 18.50 1757
Aug. 9
36 chests Green Tea, . . ./a 31.80f| 1144
Or.
1870.
'"'^ ?j|^f l^.^ ^*''*^' Bro^'cioth, . . . .® $5.10
" 27 - 76 " Black Cloth, . . . ® 4 67
Aug. 4 ;| 280 « Red Flannel; . . . ® ""Ta
< 24 gross Silk Buttons, . . . <© .43
Balance due W. P. A Son
•ot
0.1
50
80
$3966
$102000
35025
201 60
10 32
30
$1682
17
Received Payment,
jf2384{ll
W. Pwoi t Son.
s^^SSlSSSS.
''^'::f^:I'Pfiyli-
It
FOEM8 OF BILLS AND ACCOUNTS.
'O O C5 O SM
_^ •^ tO fO 00
CC *^ O 00
O
QQ
I
<o o esi 05 1-
I 22 ''O 05 o <-<
II 0» t- kC •»»
II -.
&H- - 2 5
<o o
OS eo
C<» *» 00 Tj* 00 o «o
c^ e^ <—• n I— I
ۥ^3 ^
100 ,_^
sS-'S
nz.
c
en
-Id
CI
o
00
M
**6i AND AOOOTTNTB.
*ft#^'-'a*J^ 1^ m MADK OUT, A8 INDIOAIB).
71
On Form 1.
b v«»i*;.;,ijg5iij«;flour, at24ct8. Footineoftb
to Mr. A. Lame,
t22cts. ; 121ba.
r the bill, $11.17.
On Form 1.
infflton sold to T. Le«, Feb. 10, 1870, and
■ed the amount of the bill : 15 lbs. butter,
20 ct8. ; 750 lbs. maple sugar, at 9 ota. •
Footing of the bill, $176.13.
On Form 2.
Irish liuen, i#lr #w' i ^'^'^ l^^' ^\ ^^ *'*"' ' ^*^- ^i ^6 7^^-
at 16ot«. *^'^;' 2<Wyd8. inuahn, at U oto.; .330 yd., dowlas,
Footing of the bill, $160.69.
(hi Form 4.
^'eb. 20 40DaU- «!iL^SS^ ** «3.75; 28 pair buskins, at 86 cts. ;
$115 120 SiT^l^'^ ^^ ^*"- ^^^«i^ 2, 67 pair gaiters, a
credit/Feb'^2^,^-'jE!^5^^^^^^ ,9"^ f^jf -' thf follo;ing
account wj,ffl?*^'"* «• ^^ * Co., March^2jJ, when \he
settled hvkZirX "^'' ^"^ ^'*'»- Ontario Flour, at $7.20 ; and
What wt Vilf iSfe ^"8- i' '»»• bal. then due L. A. C. 4 Co
vrnat was tt^ei^^j^^rtle note? Ana. $163.28.
On Form 2. .
tobacco' a'tTloS'^^li'^*'^^* ^»""«e= M«ch 1, 1870, 18 lbs.
!^^ "ilbn't;^]"^ ^fLf''*-^ 72 lb. tobacco leaf; at
mol4Wtt3g,d|t3^7^, April 6, credited by cash, $18. What
bftlince waa dwtW!'%yjl^] g?
}i , ''
4n«. $36.66.
r4
BILLS AMD AOOOUNTB.
On Form 3.
7. Sold, May 2, 1870, by L. T. Nolan, dealer in fruits to R ft
Lemome Toronto: 32 bbl«. Montreal 4p^es,ZarkeiT\T tf^t
Ana. *380.10.
On Form 1.
^^L^-^'^^'^^^^^^^^'i^^<i,so\d to S. Montienr Mav S ism.
20 lbs. K.0 coffee, at 24 ct8. .-'sO Iba. W. I "S Jt 7 cYa ' 7^ [h.
thTbiS; $39.89! ' ^^- P''"'° *''"^'^^"' •* ^1 ct..-Footing o5
0» Form 5.
li**llin"?7?'*^n' g'^<f^Tp'•o«to, «old to W. Morrin & Co.: June
i\\ \'J\^ ^^""^"^ *'*'^^^°'' ^^ 93 cts. ; 308 gal. old rum at$l 9rt!
610 gal. Holland gin, at $1.05 ; Aug. 5, 207 gfi. rum at *I 75 ??4
gal. cognac, at $2.10; Sept. 22, 401 gal. Scotcl dn rT*! is ' n^
Ana. $1965.86.
On Form 4.
9Q*"; ^^''.f • ^/n^^'^^"' K'ngston* ^old to J. Kelly: June 16 1870
23 yds. eslk, at 96 cts. : 16 yd. ribbon, at 45 otR • 1 9 Jwl ' r "'
18 ct^. ; July 10, 4 yds! blue doth, a?'$3 60 • 3 ids ^broadHn !"' *f
$4.60; 9yd8. doeskin, at $1.25- 1 cravat Vl '-in -a *"^^trH^^'' **
boote,at.ii.60 5 ^ doz^ol^t kLoTt^^lIt^^^^^ L^'
.^sVo^^lTV^? 'f'T^ '''^''' -' -^"'^20, by 3 bwl green apples al
4^.20; 16 bushels potatoes, at 22 cts. ; Aug. 20 bv canh *7%n
What balance was due P. I. G. Au^ 24. thill' ^iT ^' *^"^"'
settled? ' ^' ' ^"®° *^® account was
Ana. $91.21.
On Form 2.
On /'•rm 3.
8^01
blLLM ANI> AOnOUNTS.
71
5, 1 879 1
; 75 lbs.
3. liutter
>otiDg of
tilop
at
m
C0(
the " Maine Express Line." Amount of Inmce, $^11)3.01.
On Form 4.
. » ■ i?^w •'; F^" * Brothers, St. John, N. B., p,.1,1, June 1, 1870,
toI>. N. WaL^h, 15260 lbs. pork, at 5} cts. ; 72.15 lbs. cheese, at
8, cts. ; July H, llo2l bushels corn, at 50 cts. ;.Julv 10, 15(50 bbls.
Hour at $G.12,Ji. On the above are the followin;? credits : June 25,
by lloOlbs. cotton, at (Ji cts; June 30, by cash, $750: July 12,
H2,jh lbs. maple sugar, at 7 cts. ; 6450 gallons, molasses, at 37i cts.
1 , Vo 9 *™""°' *^*' ^^'^'^ requisite to balance the account on
'^^^y ^^f ^ns. 1121)53.78.
0)1 Form. 2.
A ^^' P\ ?;n^'^'-' t' ^''"^l'* ?!" '^- ^^^"'Phy * ^°-' publishers, Montreal :
Aug. 4, 1870, iii Juneau's Mental Arithmetic, at 15 cts. ; 50 Smith's
Practical Arithmetic, at 37 cts. j 2 doz. Miller's lieador, at H.50 :
Aug. 12, 60 lleiiry'8 Grammar, at 7 cts. ; :iG Kerney'a Compendium
oi History, at 72 cts.; Sept. 1, 30 Walkingame's Priinarv Ah^ebra, at
18 cts.; Sept. 1, credited by 50 Commercial Arithmetic'.. I' the Chris-
tian Brothers, at 40 cts. What balance was due A. M. & Co., Sept. 2 ?
Ans. $54, 27.
On Form 5.
15. S. N. Kelly bought ofH. Hamel & Co., Quebec, Feb. 3, 1870
IB yds. cambric, at 14 cts. ; 60 yds. calico, at 42 cts. ; 39 vds. cassi'-
";\^^*^^t/''i./^f,y«^10 37 yds. cotton, at 35 cts. ; 'e yds. velvet,
a H.70; May 2 .^Oyds. uien, at $2.65 ; May 4, 24 yds. merino, at
a"" X r N. Kelly's credits are ; April 1, 50 lbs. cotiee, at 25 ct-. •
April 9,_7 cords of maple, at $3.50 : May 20, draft on Halifax, $78
t""%«"' ii/.^i' "''' *^-^^- ^^*' balance was due Hamel & Co.
June 26, 1870? ^««. $196.12.
Let the pupils make out Bills or Accounts, as the case may be, in
properform, from the following.
5 ^.^.-O^^IhT ??'''*" ,''*'^'\'''T^'T'''°'*^*« '^"^'" Gossehn, July
6, 870, and I. Kane, his clerk, collected the amount of the bill •
3b bs. map e sugar, at 13 ci^. ; 16 lbs. coilee, at 15 ct.s. ; 13 lbs tea
aty8et«.: 13 lbs. chocolate, at 61 ct<*. : ■- >b". --in-4 a ] 7 r^
47 lbs. cheese, at 9 cts.; 12 lbs. peppe,, .. 19 ct^.f 20 tbs. but^eV
at lb cts. ; 2 gal. vinegar, at 68 cts. Footing of the bill, .$40.S '
17. I'orwarded per the Eastern Line, June 3, 1870, by B. Ellis &
S'ol'e S'^^'l^5i^""'''^C-^n^«\ ''^^''' womeVstockings
IMo. 6, at 90 ets. ; 16 doa. napkias, No. iO. at 47 ote. : 24 pair men's
'■' nlJ!
76
■ILLS AND AOOOUOTS.
V(^
g'.OV
packing, $1.60. ' ^ ""'* ^^"^ '•^'^«'; <- cu. ; charges for
IH. Sold by J. M O'Roillv nr * , ., Amount . 51101.95.
thier- *27w ill ^ "eilly, Montreal, inr 10 Im7(i tr. a 7i
tuier. ^7a ibfl. coffee, at .S6 cts • I'i7(i iho i ' , ' ^ A' C^au-
oam, at II ota . ifjAVi ', ^^'" 'bs. lard, at 13 cts • hnn ik-
160 bushels oat8, at io cts il '^> *^^'- *g^'«' •' '2 ^♦V •
Julia Meredith, andt/e bS pai'd alz^^"^ ?f*'"'^"«' ^ Mrs.
•doz.; 2 doz. silver table TO L t^'^'i'^" **^ f '^'^'•^^' "'^^.TS
spoons at $18.60 a doz.. if] "/^'ffut^^^^ ^'^''^ tea-
doz.j 1 gold guard chain at * I- fi -p '"'^'^ ^""^«''' »t $7.60 a
20 P. Barfy 4 Son Kinlta ;old toT'^u^ 'K^^^' ^394.76.
M follows: 2ioave8white"W'52l« ;,!.""' ^*''«*' «» '870,
flour, jt $7 80, 9ilbs:l^""^,"itf6i^.*lVlh, ''"'•' ^^''- "^"-^
- lbs. black pepper, at 42 ct« 9ft iku',. '^^- ''*''''"^ «^ !•> otM .
ps. at 70 cSf 6 bush bean: aflUO^" Ui' fh 't ''' ' ' ^^^'^^^
I gal. molasses, 60 cts. ' * '^"t]; ^f ^ ^'^^l ^*con, at 16 cts. ;
^ 21. M. Peter Nelson owes D T W. ^^ooj'ng of the bill, $60.83.
6, 1870, 3 gross «hi?t sJud' ^t 85 i^' T^''""??' «« follows: June
stockings, at ,$3.18i; 3 doz.\sL fron/;'i«?'ni^' J^ ^'''' ^"^l^n
ribbon at 25 cts. ; 30 pair si kl lovef I't Jl^Af '. ^"S" ^' ^^i yds.
at $2.85 ; 22i yds ticking at 45 p^I V !• '^^ ' ,* "^^^^ ''"«« towels,
,22. G TurVer & Son §- .btc sold lT"l^ r '^'' ^'i'' '^'"^^ • ^n^
17 pair boots, at«3.00: March 'l«iq ^' \- ^''■'^"' ^^^ch 6, 1.4o.
80 pair hose, ;t$L20%3 pair IVe^^P^^^^^^ %fl-«8; A'pril 9
A. 1-t^reen, the following as credl^VnWifi 97 «^*^. "''^'''^'^ «<"
20 cts. ; 10 Third Keaderf atTs 9o ." Affn . o^'^"""^ ^otdetB, at
at *4. 75 ; 1 9 Golden Cnuat at *^ J?^ • i'p^. ^''"."'"''' I>"^'-'onanes,
ot«. Tlie balance due Q T% Son whfij^ ^^""''•^J*" ^"^'^^^^ -t 37
amounted to $44.05. ' "^^'^^ ^'^ Pa«<l, May 16, 1 70,
Pelt^lr/S^Lt^'J? *^^"«^«' Kingston, Ju. M ..;o ,^ ,. o'
^^^^'^^^S^t::; r$V4 15.. bV^nlr^ L ;
82cts.j 326bush.v,heatt"at $T'6?i*i^»; ^i* ^""^^^'^ co'". a
500 bush, rye, at $1.06. *'-^2i .300 bush om.s, at 91 cf ;
24. Joseph R. Simon, bought of C T S ^'^'fe ^'"' ^^^^^-'^S-
1870 a^fol-ows: 5 yds: blac\ cth at ^3 ?o''. f^"'' V" 20.
•O.50 Trimmings, $3.75 . s v^. Jlli^ f.'^^t 1 «atin waistcoc,
gray fringe, at esVts*. 3 ^eJatf Jfj^^^ ^'f "' •* '9 ct,.,- ri .Js
eassimere, at$2?5- 71 vhI „f ^°' *' ^^ cts. j 3 y-' /„,
9 yds. „i„w a.„„ei, „ 80 to." ? t«™L J? ;rr?'.''"?' ' "•- >
i iu<ia.B ™.inl?' ,• ^' '^ P'^«« muslin, each 37 vds *r«!i^^ 'j*"
!»*«.« pnnt«i calico, ..ah 47 yd.., ^ 82 •i\^y^',* ^^J,* * ^^^'^
at
•ILLS AWD AOOODIfTi. fj
£ljrii;il?%""r' ^^L^Or-l'., »t 70ct8. ayarl; July 10, 11 piece*
|H..I It, ,mft WM,. .vi.at balance was ,|„e P M & \, \,;;* -J^ Y '
^rsi;:r Tzr o'f/ >, . . ^i^.: ^ni. S^"
r»:r/''««'<--n.aK No.' 22, at\?12'50 Vr |;;.:?fdo;'w«
2S-in., at .?l.7.5;
P.ar h;u. No. M at $27 per doz. : .5 urnlfreflal
l«7j' iV'"'^^^{ «• W.lliarn^ Quebec, by H S. Con" ily .[.in^,
.'^*!'.S'/'i!''' 'r- ' '•"''«l Mo^- al, to J. B. Po«ton. a« follow.
doz.
Oct
pewter-polJHhed biti^, at
w, 1870, 4H pair t.,„g^, at .1", ^ ctn.'; ?
S^ck n«*rii,ck*t Vr!; l-^rV \ ' h'^'' -shoemakers' awls, at
rm-Sc^K I V^ i ; • ,' ^'* P^''J^ets .4 1,1. Hcrews, at 95 ctH ner
^x i, . ^'"'^*'' rcce.yci yf J ,j p^„,^^ account- N.w s 9
7'J' fh**P^l=bi^tt'ki ;?::acr2r'pi^^- i
ete,T%? ' ''»«*"^"P*'-'«»«J04? chaVi for packing; car^
. »i ». .t,u . Sent. 25^ 3.^ yh. Bheetiru, at 1 1 cts. ; 3 yards
♦'i ydH. bioadcloin, at $4..S7A; Oct. 29. 20 Wdf
tL^^r^f ^""'' '**.'^ ' ^**.V ^^ yi'' n^eriQo, at 70*ct.
the foi
mmp crwl.t. N.v. 1, by 22 lbs. butt
On this bill
cherry wyrxl, «t k:iM
l»l>or, attl.so. Wl,
J)
. . --.er ut 20 cl^^
'«c. 4, by cash, «1 6.00; Dec, d.
■MOtlMWMMItMr
fiat i uiace wmiIiu N. P. M. k
are
cords
days
<vO., Dec. 30
•2I.T62
■■:!
®9Ksif«'- -'*mtikm^mmmtt.ii
*• FBOPBRTIM OF IflTNBIllfl.
PROPERTIES OP NUMBERS.
EXACT DIVISORS AND PRIME NUMBIBRS.
HH. An Exact Divisor of a number 13 one th^t A' -a •
»W. Ail niuubfrB are either even or odd.
00. \n Even Number is a number of whioh 9 ;= «
divixor ; as 2. 6, 8, 24. ^ *° ^^^^f
»1. An Odd Number is a number of which 2 ;« n«f
divisor ; as 1, 3, 7, 16. ^^ °" ^ '^ "o* »n exact
Every number must be either pmn. or r^mposite.
»'« \ Prime Number is one which can not h« ..nc^i J
««pararH into two or more integral f .ctors? as ? 357''^ ''
N0TM.-I. All prime number! except 2 aw odd number.
»5. Tile Power of a number i, the product obtained hv
^ »«. The Exponent of a power is a flexure written nf tu
nght^of a number, and a little above it, to show hrmanv iml'
t IS taken as a factor ; thus, in the expression 5 ^Th^ezUent
M 2, and the whole is read 5 second power. exponent
Prom thes« principles,
*«•• priBM <o «mA o«A«r ?_ 9 { HTAfl, i, ^^^li^ number ?— Jf A«» „re num.
1
2
3
5
7
11
13
17
19
23
'2»
31
37
41
43
47
53
or
FAOTORINQ
We derive the following properties :
r. Two is an exact divisor of all even ^cmborH.
11. Three is an ox ict divisor of every number the sum of' whoso
diijits It will exactly divide.
in. Four is an exact divisor when it will exactly divide tho
tens and units of a number.
jV. Five is an exact divisor of every number whose unit figure
f 0.
V. Six is an exact divisor of every even number, tho sum of
whofe dicjits it will exactly divide, or that 3 will exactly divide.
VT. Eight is an exact divisor when it will exactly divide the
hundreds, tens, and units of a number.
VII. M'ne is an exact divisor when it will pxaotlf divide the
sum of the digits of a number.
TY^^if^'" '• *° ^^^^^ divisor when occupies the units' place.
IX. Etevm is an exact divisor of every number who.se sum of
the digits, standing in the even places is equal to the sum of the
digits standing in the odd places.
TABLK OF PftlME NUilBEUH FROM I TO 1109.
!l
1
59
139
233
337 439
557
653
769
8S3
1013
2
61
149
239
347
443
563
659
773
887
1049
3
67
151
241
349
449
569
661 j 7.-i7
907
1021
5
71
157
251
353
457
571
673 797
911
1031
7
73
1G3
257
359
461
577
677
.-^09
919
1033
11
7y
167
263
367
463 1 587
683
811
929
1039
13
83
173
269
373
467
593
691
821
937
1049
17
89
179
271
n'd
479
599
701
823
941
1051
19
97
181
277
383
487
601
709
827
947
1061
23
101
191
281
3S9
491
607
719
829
953
1063
2tf
103
11)3
283
3D7
iii9 613 i
727
839
967
1069
31
107
197
293
401
503
617
733
853
971
1087
37
109
199
307
409
509
619
739
857
977
1091
41
113
211
311
419
521
631
743
859
983
1093
43
127
223
313
421
523
641
751
863
991
1097
47
131
227
317
431
541
643
757
877
997
1103
53
137 229
331
433
547
647
761
881
1009
1109
FACTORING.
3*7. Gas,-. _. — To resolve <t numhrr into its prin
lef actors,.
•'Jo*"-— The prooe«8of faotoring nurabers depends upon tb«
) foUowlag p(to<
Wkm it S mntantnUtUor f—S T— 4 »— 6 T— • I— 8 T— « ?— !• T— 11 /
so
rAOTOKme.
J:j!fry^^^^^^^^ ^^If'^^- "^ ^^"^t number,
«>»t'"n> of ,u prime factors. °»a»ber are its prime factors, or 8om(
^^■■- What are the prime /actors of 15% ?
oombi-
tho^?s'm?;l^fhf Jt,^-^,2 the least prime (actor, and
Proof. Tl . product of .11 tK. ''"^/"^^^/^^^^^^ n'j«„-.^.
aumber. ^ '^ '" *^" P"'"^ ^^^tors mil be the given
EXAMPLES FOR PRAOTIOE.
Required the prime factors of
6. 1140. Am.
7. 3420. Am.
8. 2445. Ana.
9- 2431. Am.
10. 2205. Am.
1. 28
i. 36.
3. 86.
4. 144.
5. 360.
.4n/.. 1, 2, 7.
Ann.
Arts
»o.
H. 12673.
12. 12496.
13. 21504.
14. 1.3981.
15. 17199.
Ans.
Ana.
Ana.
Ans.
Am.
more innnhern.
?Zl '^-^"fi'"'"^P^--M,or> common u. ,„.
•r
Ex.
What are the prime factors common to 84, 126, , ,d 210 ?
OPBRATlOlf.
2|8_4, 126, 210
3|i2r~637
7
it
2,
3,
105.
3^
6.
ANALT8I8 We find 2 1^ !.»
divisor of all the numbers it^^ fu" ^'^■'*°'
a oommon tn-'tor • Tio ' '^ *• ''»ereforo,
the flrstlJ^f quotit "t«?rciTof ttr" ?l
set of quotientl. therefore 3 LJ 7 ''°?'^
common factore'of tl, nui" Th! '"'°
no exact divinnr nf >>,.. "uraoers. There is
prime factors. ^'- "«^ '«« common
98. (F^// 1» «/i(? rule #0 »w»ri/«« « _„ZI ^ T~ ■-- ■
CANOSLLATIOM.
81
EXAMPLES POE PRAOTIOl.
Required the prime factors ooramoo to
1. 12, and 24.
2. 48, 96, and 120.
3. 42, 6;^, and 105.
4. 225, 4;«, and 540.
5. 48, 72, and 9G.
6. 140, 210, and 280.
7. 252, 336, and 420.
8. 960, 1568, and 5824.
t>. 330, 495, and 165.
10. 2340, 11934, 12987, and 1485J.
Ans. 2, 2, and 3.
An$. 3 and 7.
Ans. 2, 5, and 7.
CANCELLATION.
lOl. Cancellation is the process of rejecting eouai far-for,
fr«.bers sustaining to each other the ^relation^rdiviS
Ex. 1.
Divide 112 by 56.
U2
66
OPERATION.
Ll^J.X ^ X 2
^ X ^ X %ir%~
= ! = «•
Analtsio.— The factors of
the dividend are 7, 2, 2 2
and 2, The faotora of th«
divisor are 7. 2, 2, and 2.
Kejeoting the common fac-
tors 7, 2, 2. and 2, we obtai.
i for the quotient.
2. When a factor is oancellod. I is supposed to take it. place
14^-^18 'xT'^''^'^'"''""*"^' ^ '^ ^ ^=» X 5 by the product of
Dividend, t
Divisor,
OPERATION.
5 \
■< ^^ X 5 25
Ifil X IS - "F = ^^•
Oi».— -W e hare perform-
ed this division without
factoring the dividend and
divisor, by rejecting th«
factors that are common t«
both dividend and divisor,
and writing the remaining
raotoM in their proper places.
103 RULE.-I Wnte the dividend above and the. divisor
below a horizontal line. aivtsor
II. Cancel all the factor, common to ..th dividend and diiftmn:
III. Divide the product of the remaining factors of the divid^mA
hy the product of the remaining factors o^the d':^^^:^
result will he the quotient. '
Ml. Wht w cancellation T- 102. What m Ifc.TiliT/bi^'i^iii^a^i^
4*
Sf
f
i.
i4
li
11
Ans. j\.
Ans. 17|.
Ans. Vil
Ana. 4.
Ans. 6.
Ans. 15.
•■ DIVISORS 01" KUMBIBS.
EXAMPLES FOR PRACTIOC
3. 16 X 24 X 48 -^ 32 X 36 X 38 =
4. 12 X 7 X 6 -f- 2 X 4 X 3.
£. 16 X 6 X 10 X 18 -=- 8 X 6 X 2 X 12.
f . 84 X 12 X 18 -r- 21 X 24 X i).
"• 72 X 18 X 16 -^ 24 X 16 X 9.
'i. '^2 X 9 X 12 X 5^ 3 xll X 6 X 4.
3. 76 X 34 X 96 ^ 17 X 51 X 32.
JO. 25 X 7 X 14 X 36 •^ 4 X 10 < 21 X 64.
n. 184 X 145 X 80 -^ 23 X 29 X SO.
}q* ?o ^ f \!!> X 15 X 18 - 7 X 54 X 7 X 3 X <J.
u" J^"" fl."^ ^®?o^ ^^o^ 70 -f 3 X 14 X 9 X 6 X 20 X 6.
14. 213 X 84 X 190 x 264 -r- 30 x 66 x 36.
DIVISORS OF NUMBERS.
103. A Common Divisor or Measure of two or more
°"iaT '!,^"y """iber that will exactly divide each of them.
i«4. 1 he Greatest Common Divisor of two or more num.
beis IS the greatest exact divisor of each of them.
105, Gknkral pRI^x-IPl,Es.-L One is a dwiaor of all integers.
II. Every number is a divisor of itself.
m. Every prime factor of a number is a divisor of that number.
A.IT: w-*^ ^"■"J.'f "/(^^T/jwo or more pnme factors of a nuwr
ber 18 a divisor oj that number. r j uj u. jiuuir
V. Every number equals the product of its prime factors.
VI. A number has no divisors except its prime factors and thp
product of every two or more of them' He/ce, the product ,^ aU
the prime factors comvwn to two or nu>re numbers is their crr/atest
tommon divisor. '» '"cir ^reafesi
COMMON DIVISOR.
106. To find a common divisor of two or more numbers.
B.T. Required a common divisor of 9, 15, and 21,
OPKRATION.
9 = 3x3
16 = 3 X 5
21 = 3 x 7
A.VALTais.— Wo resolve each of the given
numbers into two factors, one of which is
common to all of thorn. In the operation 3
IS the common factor, and is therefore a
common divisor of the numbers.
lOT. Rule. — ■ Resolve the given numbers into tk
eir prime
factors, then xf any factor be common to all, it will be a common
mvMor.
m. What w a eommuB iiymr 1- 104. What it tA« gceatMt ooinmon diTisor T
ORfiATIgT COMMON DIYIBOR.
83
EXAMPLES FOR PRAOTIOB.
Piad the common divisors of the following numbers i
1. 10, 15, and 25.
2. 15, 18, 24, and 36.
3. 3, 9, 18, and 24.
4. 21. 77, 35, and 42.
Ans. 5.
Ana. 3.
5. 28, 14, 42, and .S6.
6. 10, 35, 50, and 75.
7. 4, 12, 16, and 28.
8. 82. 118, 48, and 146.
Ans. 7.
Ans. 6.
108.
numbers.
GREATEST COxMMON DIVISOR.
To find the greatest common divisor of two or more
Ex. What is the greatest common divisor of 168, 210, and 252^?
FIRST METHOD.
OPBRATION.
168 210
84'
252
105
126
28
36
42
Analtsis — First find the y^vime
factors common to the numbers, (IW),
which are 3, 3, and 7. Therefore the
greatest common divisor is 2 v 3
X 7 =.42. (105, VI).
109. Rule. — Find the prime factors common to all the v um-
bers (99), and their product will br the greatest common divisor.
The prime
factors of
SECOND MliTHODo
OPERATION.
168 = ?, X 2 X 2 X 3 X 7
210 = 2 X 3 X 6 X 7
252 = 2x2x3x3x7
AHAtvsts.— The prima
factors common to the
three numbers are 2, 3,
and 7.Therefore the great-
est common divisor is 2x3
X 7 = 42. (105, VI.)
IIO. Rule. — Resolve the numbers inio their prime factors,
and find the product of the common prime factors.
THIRD METHOD.
ill. PftixoiPLEs.— I. If the less of two numbers i» a divisor o
the greater, it is their greatest common dhrisor.
II. .1 divisor oj a number is a divisor of any number of times
that number.
III. A common divisor of two numbers is a divisor of their sum,
and also of their difference.
IV. The greatest common divisor of the diference of tw^> num-
bers and one of them, is the greatest common, divisor of the tioo
numbers.
109. What it the rule to find the grtattH eommon divitor.flrtt method t— Stcond
MMhod t — Third mMhod t
'.t*W
f-rl
5-i
Ml
84
LBA8T OOMMOW MULTIPLE.
Ex. Required the greatest common divisor of 117 and 1366.
fhli! ' ^"^ ''^ * '^'^'sor of 13t)5, it will be
their greatest common divisor. J3y trfa^ I17
« found not to bo a divisor of 1365 sinj
there is a remainder, 78
of 7b and ?i 7 ^ *^' «:^*'"«' ""'^'"on d'^isor
r II IV^ R'f"**. ^'f°' °^ "7 and 1365.
OBa.— A knowledge of the PrinoiDles mn »jn
u ^°™'~T''« greatest common divisor of fhro^ „,
by findmg the greatest common diSr of two of ^^^^^ °«" be found
^ommon d.v^or of this greatest common divlsoraid°r^/'"'' ^^""^ ^^^ S'-*^'»^*«t
The laat common divisor will be the g-atr^oro.^tTst^^f^S'thrn'umU:
common divisor of 117 and 1365.
EXAMPLES FOR PRAOTiOB.
Find the greatest common divisors of the following numbers ■
72andIfiB A^^ ^. .. 6 lumoers.
1. 72 and 168.
p. 175 and 455.
3. 169 and 866,
4. 84, 126, and 210.
5- 12, 18, 24, and 30.
6. 385, 462, and 154.
7. 12, 16, and 18.
5. 210, 350, and 770.
9- 70, 105, and 216.
Ans. 24.
Ans. 35.
Ans. 1.
Am. 42.
Am. 6
10.
II.
12.
13.
14.
15.
16, 20, and 24. 4,^^ a
78, 234, and 468. *
2041 and 8476.
286, 429, and 716.
1649 and 5423.
,^ 92, 116, and 124.
?"S.P'/^2^'^"dl386.
17. 49373 and 1477;j
18. 3013, 2231, and 2047.
LEAST COaiMON MULTIPLE.
,.n o*;.±°„??"^«^„?^«^<^ipIe ^^ a number exact). A'..:.;u. u.
2)J_
2)_j
2) i
2) .'
as.
LEAST COMMON MULTIPL*.
PIBST METHOD. '
OPERATION. . ' f V. iu t
SECOND MJ^THOD
lae second I, :<^c..rAi-r^„ the facfnr 9
«r. 6 in a line undorneath a. before W , ^.^^ '!°"*°'*' ^»« *^« "n Ji^hled'SiVm"
•wr, ti 1 the dirisor and r-.»,r j "'^- "J continue 'a divida ht, „ ^"."'^'^ "um-
' 1
1;
it
86
r&AOTIOM.
IS
118. Rule. -I. Divide hy the smallest prime number that is
'mi-xacfdioisoro/twoor more of the nmnhers, and write the
quotients and the undivided numbers underneath.
II. Proceed with the restating numbers in like manner, until
ffiere is no exact divisor of any two of them.
III. The product of the divisors and the resulting numbers will
be the least common multiple, sought.
lasuo™ Jfi^^e"""'"' '" P""' '' ''"'' °'^'"-' *'»-'' F^'J""* « **"'
EXAMPLES FOR PUAUTICK.
Required the least common multiples of the following numbers :
1. 24, 36, and 20.
2. 7, 14, 21, and 15.
3. 14, 19,38, and 57.
8, 12, 16, and 20.
32, 34, and 36.
20, 36, 48, and 50.
9, 18, 27, and 54.
12, 16, 42, and 60.
Ans. 360.
Ans. 210.
Ans. 798.
9. 10, 45, 75, and 90. 4ns. 450.
10. 12, 15, 18, and 35. Ans. VZiiO.
11. 25, GO, 100, ami 125.
12. 22, 12, 44, ami 11.
13. 18, 27, 36, and 40.
14. 270, 189, 297, and 243.
15. 64, 84, 96, and 216.
16. 84, 100, 224, and 300.
FRACTIONS.
11». A Fraction is one or more of the equal parts of a unit.
130. Two integers are required to write a fraction one to
express the number of parts into which the whole number is
divided, and the other to express the number of these parts taken.
If an apple be divided into 2 equal parts, one of the narts is o«]UA
one half; if divided into A equalVt^ on^ of the prrt^f ca ,e5 o^
third, two of the parts two thirds; if divided into 4 equal nartl oZ
01 the parts is called onejourth, etc. ; if divided into fLuT^^t.
one of the parts is called one fifth, etc. ^ ^ '
The parts are expressed by tigures ; thus,
i
One half is written
One third »*
Two thirds "
One fourth "
'i
h
Three fourths is written
One fifth «
Four fifths ««
Five sevenths «
J£pi".t^^r,^ix'^„,Xr3:r*>Arr,.":r:
'
rRAOTIONft
/..wffhellleT^^'i^^^^ the one
munfof thirnf ."^f **^' """'^^^' '^' V^'''' ^°d shows how
124 S f^i^'l^"" ^' ^*^P'-«^^sed by the fraction.
T Ti" ^T'^^f^'going definitions, it follows
divided the\iti!^^.!^''x'-''"^'^^"^'^^^^ ""it or quantify
of i;i:^'^i;:''^^«3^'^? ^--•- " f y^r^-> the part or fractional unit. I
i. thi da.onuu«^;3X^S'r '*' ''";^ "P'-^^^-'d or numbered is 5. Si|
is the nuu.er*tar^iT„t1 n^ " '?'''""' ^ ' ''^"^' '"*^'«- ^''-«
^.^Pt. "'^''^^'''"^^^^^^ - '^'->>^^> ^W,W, and
*74^J-.'''''*'^"''^^'^>^^'^'^^ '« distinguished as P.o;,e. and
as l^^-^^^^^^^^^i^'^ i« o°e whose terms are integral ;
f ^'^' ^ f ^»f|^^«tion'- fraction of a fraction ; a«
1«^ -^ i4ftft^#ractiOn is one having a fraction or a
mixed number ;ip,<j^,li«,rtf both of its terms: as f L^ H
*«« A ffit|Ci^ts]Sfeniber is an integer and a fraction unii^A
in the same e^jnii/j^j^j., ^ 5^ » ""** '^ iraction united
y-iU iuSatr^:^'lSF5£'*^^^ '-- 122. .^ej^r^iTelenominat^iT^ri^.
fraction?- I. y. HV*,?,^*^!,iT;:^ "'r'^^rl'-J^*^- '^'"" « « «impl«
131. ^ 0«iW«»w»d.iw«uiwy^^ >. 1" ^T ' *^- ^" improper iniction f-
-,«««« WWWttWi- 11J8. ^ complex fraction f— 133. ^ nixsd mub-
^'ll
. l^M
ii
■il
ji
68
REDUCTION OF FRAOTIONS.
1»4. Since fractions are expressions indicating the division of
one number by another, it follows,
1st. That if the nvmerator he multiplied, or the denominator
number ""^ """*^'''' '^'•^''"'■^''^^ *'* multiplied hy the same
2nd That, if the numerator he divided, or the denominator
mm£ ""^ numher, the fraction is divided hy the same
3rd. That if the numerator and denominator he hoth multi-
plied, or hoth divided, by the same number, the fraction will not
oe changed %n value.
REDUCTION OP FRACTIONS.
135. The Reduction of a fraction is the process of changini;
Mb terms, or its form, without altering its value.
136. Case l.~Tunducea whole or mixed number to an
equivalent improper fraction.
Ex. 1. Reduce 12 yards to fifths.
OPERATION.
5 X 12 = ^, Ans.
iJt^"^' ^V^\'~^^Jipi^ '*« wAofc number by the aiven denowu
E.v. 2. To reduce 15| to fourths. *
ANALTSis.-ln 1 there are 4 fourths; therefore, 4
times the number of whole ones equals the number of
.*?*• ^^^^"-Multiply the whole nvmhr by the denominator
ANALYsjs.-In 1 yard there are 6 fifth?, and in
\Z yar.i8 there are 12 times 6 fifths = 6 0.
OeiRATION.
16J
4
1. Reduce
2. Reduce
3. Reduce
9 to thirds. Am. ^.
12 to eighths. Am. »^.
25 to fwurthe.
4. Reduce 36 to fiftlie.
EXAMPLES FOR PRACTICE.
136, What
whole nnmher
Mtm^toaR
Reduce 16 to ninths. Ans.^^.
Reiiuce 70 to tentlifc;.
Reduce 52 to fifteenths.
Reduce 35 to sevenths,
^^^ ^Reduce 81 to elevenths.
♦• redaction fa/ra^tionf— 137. What i. ti^ w,i« /■ Z — :
eqwvaimt imj»roftr/rattumt '^ rMuemg a
6,
7.
8.
9.
10.
Reduc
11.
12.
13.
14.
16.
16.
17.
18.
37|.
2"-i 7
1 'A V <i
I34«
1 30.
nU'iil wh
Ex. Ii
Of
V = 37
140
the quoti
Reduce
1 18
2. 2/.
3. ifl.
4. 2-04.
5. «^.
6. 1//.
7. i-OyOJ).
141. I
Note.— A
•re prime to
Ex. Rei
OPE
2)11
»)H
ST
3)
12) if
140. What
t
RTinnoTTor* o? rn actio vs.
11.
12.
13.
14.
15.
16.
17.
18.
Reriuce the following mixed nu.nbers to improper frac
89
4yJ.
I3lif
1H4«.
96 iV
.18.
Ans. i§-8.
Ans. ^S-t.
i4n«.
121,4
3 •
19.
20.
21.
22.
23.
24,
25.
26.
25^.
I72^V
260^.
171f
331^.
net-.
Ans. iffA.
Ans. M^.
I»». Case II.— To reduce an improper ^fr^tcH^m to an egutp.
'I' flit whok or miaed numher. ^
Ex. In ^ of a yard, lnow many yards?
OPERATIOK.
V = 37 ^ 8 = 4j, Ant.
ANALTsra—Since 8 eighths make 1 yard,
there will be a» many yards in 37 eighths of »
yard a? il oontaiiu times 8, or 4| yards
1.
2.
3.
4.
6.
6.
7.
8.
9.
EXAMPLES FOB PRACTICE.
Reduce the following iniproper fractions to whole or mixed numbers :
Ans. 14^f^.
Ans. 17 If.
Am. 12.
Ans. .3
s. (
Ans
Ans. 6^
24^.
I_0QO
10.
II.
12.
13.
14.
15.
16,
17.
18.
10, ■jj
nir-
"7.8
7)11 •
1U2
18 •
¥/.
2;<2()i
141. Case TII.-_7b reduce fractions to their lowest terms.
Ji'^Tt eaS'oThlV" ''^ '"""' "''■"*' ^^«° ^'^ ''"'"^rator and denouainator
Ex. Reduce If to its lowest terms.
OPKKATION.
* ) if - A
Or,
12)11= ^
Analysis. -Dividing both terms of the frac-
tion by the .^arae number does not alter the
value of tho traction (l;U, 3rd.)j honco, we
divide both terms of .^J by 2, both terms of the
result, 4 « '— T 1..-L--- ....
.J I . l>y 2, both' terras of this result by 3
and obtain | for tho final result. As 3 and 7
are prime to each other, the lowest terms of
Inst ead of drndipg by the factors 2, 2, and.
HO. What M the rule /or redvctM n»^.»....i^~.f— ^.— . TT"
■ \,
%-\i
pi
90
I
! k
RSDUCTION OF FRAOTrONS.
Dmde both terms hy their greatest common divisor.
1.
2.
3.
4.
5.
6.
7.
8.
EXAMPLES FOR PRACTICE.
Reduce the following fraction8 to their lowest term, :
SiT-
27
lite
n-
m-
m-
143
A-
Ans.
Ans' ^.
Ans. g.
Ans. 3?j.
17.
18.
IS.
20.
21.
22.
23.
24.
2H8
fNv
fft#.
.Tn + o*
4n» f.
/1ms. I
Case lY.—To reduce a fraction to a decimal
Ex. Reduce % to its equivalent decimal.
7 _
>
FIRST OPERATION.
= f"So- = AVV = 0.875, Ans.
SECOND OPERATION.
8) 7.000
0.875
annex tlui
ANALY3I8.— We firit .,. .^
same number of ciphers to both
ticinvj! (;" the fraction; this does not
»''«V'"'\ ''^'"°' ('-'^.ard.) J we then
<irn'M 'oth resuliitig terras by 8
tftii 0.,; .ifioant figure of the denom-'
isfttfi;,-, io obtnin the decimal de-
asixr-Mfcor, 1000. Omitting the de-
aoMiiiiator, and prefixing the sign,
wo have the equivalent decimal 0.875
pr,t;£irby tn^e^Sh^ ^*«''«' -'^^ ^^'^^ '"e rosult,
result by [he de-^omSr.S. ^ "' *° "^^ numerator. 7. and dividing the
cipL^:nnS'' ""^ ^--«^^^«- - ^/"' W.- a, .^... are
have"ree7S5rnt'i'r irr tafblYnn^fi^ °^ ^--''» «g--
there is still a remainder. ^' ^ annexed to the decimal to indicate that
KXAMPLES FOR PRACTICE.
Reduce the following fractions to equivalent decimals
1.
2.
3.
4.
6. f -4*13. 0.714 +
Ans. 0.5.
^ns. 0.75.
/In^. 0.8.
7.
8.
10- T^.
ilna. 0.04.
Ana. 0.86.
11,
12.
13.
14.
15.
ilns. 0.3.S3 +
H '^-rl'priiz^:^:^:^^^^^^ '— * ^^./^t^t^
I
twi.i«
». ,v^.
■BPTTOTTON OF FKAPTIOrfi.
t4li. Cahe y.— ro reduce a ikcimul to a fraetion.
Ex. J. ili^Iuc. 0.875 to an equivalent fraction.
OCKKATfO*.
11
Analysis.— Writing the deoimal figureg,
^M76, oyer tho ootnmtin doiioininator, lOOH, wo
i- Honco, the
»■"" iVdh
deLmim^!'^'^^"''' -^' '^""'^'i''''*'. ««^ »"y>/'^.'/ th. proper
I
Ex. 2. U«<Juce 0.54 to a fraction.
OPERATION.
.51 = i* = ¥- L« - 1
10 -- .30 ~ 15'
147. RfJhM,— Omitting the dteimo! point, write the dennmU
fiutor und^the ^^mal, and reduce he fraction to its lowest
BXAMPLB8 FOB PItACTICE.
K«'luce the following decimals to equivalent fractions:
1. 0.0«.
2. U.75.
3. 0,12.
4. 0.125.
r>. 0.024.
<5, o.e.'is,
7. 0.0008.
8. 0.6H.
Am. A.
^«''- TlViJ-
9. 0.000125.
10. 0.8|.
11. 4.00075.
12. O.OC'I.
13. 0.57}.
14. 0.1 GJ.
15. 5.62JJ.
4 3
.4n». i
1.4H. Ca«H5 VI. — yo reduce a compound fraction to a sirnole
one, ^ ^ r
Ex. t li«»lMC<r I of f to a .simple fraction.
orKHA'tUfK, A.VALTsis.— By multiplying the donominator
] X ^ sz l^, Ans. '^^ r ^y ."*' ^^^ 'lenoininator of j, it is evident we
wo obUin J ot ^ = ^5^., gjuce the parts into whi(-h
the number h divided nve 3 times as ranny, and
eonsoqu«."<rty mij J Me Urge tu before; and, since i of « = r, j „f 5 „n, j,g
twias^j ^ ^^. r 2r 7
i^ar. 2. U<*lnc* | of J of J ot ^ of | of 3'| to a simple fraction.
OPERATION.
X r X -=: X
11
5?«
rri i4n«.
14«, 147. ff)Utf Ma«na«y0/- raUnvt/t^ u liammui to ajractumt
f 1
HI
<M
'^l
IMAGE EVALUATION
TEST TARGET (MT-S)
^/y.
f
//
%
if/ j^:t9
<v
/_
K,
^
1.0
1.1
1^128
• 50 l*^"
IL25 ■ 1.4
— 6"
2.5
2.2
2.0
in
1.6
=1
V]
<p
/i
^>.
<^
■J
Sciences
Corporation
23 WEST MAIN STREET
WEBSTER, N.Y. 14S80
(716) 872-4503
>^^
'%■: ,
93
■•DUOtlOH or FRAOTTONS,
II MMIpl^ the remming numerator, together for „ new n,^
merator. una the remaining de„om{natore /oL nJZJo^iZZ
EXAMPLES FOR PRACTICE.
1. Whatis Joff of|?
2
3,
4.
6.
6.
7.
What is i of|of|?
Whatis Jof^ofjof f?
Required the value of « of 1 of A of 21
WiS.^h"'"' f * ".^f V'<^ 'oV.unp{e fraction.
What 19 the value of | of i of 5 of f' nf 24 ?
Reduce A of J of A I a !nnp!efra^tily^ '
8. Reduce ^ of X of M of 9| to a whole number.
1 n' wu *' • ' '^^ ^^'"« of J of 2i of 1 A ?
10. What IS the value of A of # of A of ii of «3 ?
12. Required the value of J of 7^ of 1t% of ^ of :"(.
150. Casi VII..
nator.
Am. ^.
Ans. ^.
Ans. ^^.
Ans. 2^.
Ana. |.
Ans. ^.
-To reduce fraction, to a common dmomi-
a CGI
»^m„o„1,ro?,;iLr' *'°°'''"'''"''™'°'«l™' -'-• having a
l«"lRaT OPERATION.
2
3
3
4
4
6
X 4
4
3
3
3
3
6
6
6
5
4
4
40
60
45
6t!
48
60
ANALTSia.-The product of the denomi-
nators is evidently a common multiple of the
denominators. Multiplying both terma of
the fraction § by 4 and 5, and of | Ly 3 and
5, and of 4 by 3 and 4, does not change the
ralueof the fractions (134, 3rcl.), and to-
duces them to equivalent fractions having a
common denominator. Hence, the
SECOND OPERATION.
i' *' *» = *8, M, n-
15». RiiLE.~Multipl^ the terniH of each fraction by all the
, I a,
. 2 ai
. f a>
7.
8. ;
9. ;
10. J
11. ;
12. 1
13. }
14 *
lo. 1
quotient.
ReduoA
1.
2.
16«.
s
BKBUOTION OF FRACTIOl^g.
93
EXAMPLES FOR PRACTICE.
Reduce the following fractions to their comrT,on denominator —
i Am S. J»« 1A in . . . '
i and f
2. ^ and a.
3. f and |.
7. 7j. ^, and ^•
3 ft «
/Ins
18 2
5 4) 2T'
■"i (I
lot 1(7-
1 II li 1
4. ^ and f,
ind .
and
5. ^ and ^7..
i47l.f. •?§. 25_
6 '8
Ans. 4i|),
8.
9.
10.
11.
12.
13.
14.
IT-
^««- ^. f§) If."
2
' ,f ' ''3
4 7
V< II'
5, ail'
I
1
3'
and ^.
and .'^.
and I or
^"«-Hi, r,M, ^
2 3 1 ;< ,-!
^•
Ans. f2|, ^ ^^8^, 11^.
ir. H/i'oTe; and iil ^"*- A^^' A^A, Ifll-
JI54. Ca.E VITI._ro r.^«c^/mc.'/on, ^0 their least common
(fcnominafor. common
155. The Least Common Denominatni- ^p f„
fractions is the least denominator to"rcrtheVara"be"r
duced, and it must be the least common multiplj of their denom-
ve.r. Reduce l J, and ^ to their least common denominator.
AHALr»iB.~Wt find tb« loaatcom-
mon denominator, by (i.i^, to be 24.
We then take such a part of it aa i«
OPERATION.
637
2)6; 8' V2'
2)37
3)3,
2 X 2 X 3 X 2 = 24-]
f = 12
2,
1.
Ans.
expressed by each of the fractions sep-
«ately for their reapectiye new nu-
merators.Xhus, to g^t a new numer-
ator for |, we take | of 24, the least
oommon denominator, by dividing it
by 6, and multiplying .he qMotientby
6. He proceed in like manner with
each ot the fractions, and write the
numerators thus obtnined over the
least common denominator. Hence, the
; - - -.-■ "-""• -• -^ "'" ine imst common mult
dmominators, for the least common denominator " -
11. Urnde this common denominator by each of th,> ^;, 1
nomi:vUors, and multiply each numerator huthi ^^'''^'h-
quotient. The productf Millie theZTZutors. "'""^^"^-^
EXAMPLEH FOR PRACTICE.
Reduce the followinL- frufitinns fo thfir Ifaat »
2. I, ^,V audi .«. ^r-»tii^J§-
^2 - U
■ -5« T, - „ """""uior. iienee,the
!»>«». RULE.— I. Find the least common multinle nf t\. •
nominators, for the least cnr»m^.. .7...!, ".!^""'^'' of the given
156.
W^.t.i>^ ru„y«. re4.<,i^J-;~;;^^
n
m
^m
94
ADinriON OF PRA0TION8.
Ii' ib
I
3. I I I, and ^.
4. H- i, f ?. and f
^ /k, A, ^X, and 2f;
6. I I 6, and ,V-
I- ih ^, I, and h
7' TT> 'i) and 51.
9- A- e»"5, and 7i.
10. 5/^, 7, 7 1, and 8.
12. i !), 7, 5, and 4.
J^- Br T^j, T^, and ^^.
Jt- M, 7^5, -li, and A-
15- 1^, A; ^f, and i«.
^«s nU' im. tVa, im-
4mo 2J 20 00 28
--X/IA. ^, yjj, ^^, Ijj.
^n»- m, hm m, ^'
ADDITION OF FRACTIONS.
NoTES.—l, Fractions, to bo added c subtracteil, must be abstract or of iik«
denomination, and must have a common denominator.
2. Only units of the same kind, whether fractional or integral can be added
^together. i
Ea:. 1, What is the sum of |, f, and ^j?
s
^T^.
OPERATION.
9+20+14
24
— 43
Hf, Ans.
Analysis.— M'e first reduce the given fractions to a common denominator.
And as the resulting fractions, ^Pj., |o, and i.| have the same fractional uuit!
we add them by uniting their numerators into one sum, making 43 __ i ^
the answer. **
Ev. 2. Add 7 1, 8^j, and I J.
OPBRATION.
7 + 8 + 1 =. 16
I + A + S - _lf
17|, Ans.
Analysis.— The sum of tne integers,
7, 8, and 1, is 16; the sum of the frac-
tions, f , ^5^,, and 1, is Ig. Hence, the
sum of both fractions and integers ie
16 4-1^= 17|. Hjnoethe
157. Rule. I. To add fractions. — When necessary, reduce
the /ructions to their least convnon denominator ; then add tht
numerators and j)lace the sur.i over the common denominator.
II. To add mixed numbers.— ^rft/ the integers and fractiont
aeparately^ and then add their sums.
Note. — All fractional results should be reduced to their lowest terms, and if
improper fraotions, to whole or mixed numbers.
11.
16T. What M «A« general rule /or addin fractiont ?
w.
SUBTRACTION OF ^XAnTjONS.
KXA.VPLE8 FOR PRACTICE.
95
1.
2.
3.
4.
5.
6.
t
i .
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
Whatisthr ^muufl 3^ ami 3?
Wliat IS the sum ui'i, 7.. anil ' •!
What IS the sum (A-1,X, * and 1 "
Add h /„ I an,| g^' ^' '' ' * •
FindthesumofJ, I, §, and||.
Finu the sum of i, » ii arui 29
Awll^^' •'- - -^""
'^'J^ V'^. ^2^. and 2A.
A;d4i, l.,aad4A.^'
Adddofi, 4of^, andr ^
Addf of^, iof^ofl, ami^.
Add 254, 327^, and 25^. '
t^'\ 5. I Ar A, and H.*
ti>KlthesumofI7|, 18^, and US.
Ad.Uuf/rof|2toYof|! '^
Add3^ol5i, 2^ol-7i, am]^,^4.
/In.s. 2|J.
Ans. 2/5.
.ln«. 2Ifg.
4n^. 10^.
/Ins. IfJ.
Ans. I161f^.
4n.s. Iff.
Ans. 40^.
SUBTRACTION OF FRACTIONS.
^^. 1. From I take %.
Ex. 2. From 24f take I6<.
ANALTsis.-We reduce the given fm-
tions '0 a common denominator, and have
j-^ and /^ which express fractional unita
oi the same value, ^hen 9 twelfths less 8
twelfths equal 1 twelfth = ^, the answer.
FinST OPERATION.
24^ = 2414
16i=._16|f
7|| Am.
A.VALYsrs.-We fir.t reduce tho fractional parts
and i. toacommond.n.„.i„„t.r,35. sL'e "e
cannot take 2,8 f,o,n 15, we add
1
SECOND OPBRATI«N.
24^ =. i|i = ass
w = m-
we hi:: fcV^r ^"^''^'^-^' an^subtT^t g
we have 7|2 for the entire remainder.
duce, he mixed number^Sp^peTfr™:
t.on.0. and these tractions to acoKnX
Si?""/- ^l" ^''''" subtract the liL
frMt.o,. from the groater. and, reduoio*
.r
M
Mk
til m
f6
>t*<^w->'--
MTTLTTPLIOATION OF FRAOTlonB.
158 RuLB. I. To subtract fractions. - fT/ien necfsmry, re>
duce the fractions to theh least common denominator. Subtract
the numerator of the subtrahend from the numerator of the min-
uend and place the di/erence of the new numerators over the com.
mon denominator,
II. To 8ubt,act mixed numbers.— /e-Y?«ce the fractional parts
too, comrrwn denominator, and thai subtract the fractional and
integral parts separateh/. Ov,-Reduce the mixed numbers to
improper fractions, then to a common denominator, and subtract
the less fraction from the greater.
i7i =
Ans.
An^.
I.
2.
3.
4.
6.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16. 19^ -'m= Ans. 15
33. From 'i offtake J of ^.
34. From I of I take | of i.
35. From ^ of } take f of ^.
36. From « of ^j; take i of ^
EXAMPLE.S FOR PRACTICK
Ans. i
21
If- -„
4 - iH =
lof - 4-
^h - H =
8^
65.
Ans. i§.
Ana. ^f.
Ans. 10 J.
Ans. 5^.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
71^ - 13^ =.
75 - 1\.
\r
^2 _
'i —
Ans.
Ans.
^729
ff?T'
^'"M - ;^A =
^s - 2|.
165J - 77f =
h^ - ^^^ =
Ul - HI
n - 2f =
47 - Ij^.
1015
12-7
Iff-
••^^ =
93i.
63^1 - 342iJ =
25f -
13'i
17|
Ans. 24^.
Ans. 87^^..
Ans. 3^.
4ns. 4|f.
Ans. 5|f
/4?i.s-. 291 f.
/Iras. j^.
4n.<?. |§.
Ans. j^j.
lbs., and ai
37. From | of f of 3^ take J of 1^.
38. What i.« the value of i of 3 — i of 2.
39. From 72 lbs. there were taken at one time i
another, 28,^ lbs.; what quantity remains? Ans. 25i^ lbs.
40. irom *15, $3i were given to A, $44 to B, $2i to C, and the
remainder to D; what did 1) receive? '
MULTIPLICATION OF FRACTIONS.
15». Case I. — To mnlliply a fraction hj an integer.
Ex. Multiply I by 3.
FIRST OPERATION.
J X 3 = V = 21
ANALT8I8. — In the first operation, wo inaltiply
th« numerator of the fractiou by the integer, 3,
and obtain 2^ for the answer. It U9 erident that
8EC01
THlli
7
3
by diviilinj^
fraction is c
before, whil
Mnltlp
fraciiim h
NOTK.— I
fraction, ind
too.
finil afr't
E.V. Mil
FIRS]
SKCON
24 xf
THIUI)
^V
— )
1
Multiply
eand denott
Note, — In I
fraction, \ndioi
lei. c.
NUTK. — To I
fraction.
Ex. Mult
FIRST C
BfiCONO
.1 !
168. Whet t» :kl rate /or tvAtriMf - 7./' oeliovg f
I
1^ ^
12aV
;^^.
MULTIPLrCATfON OF rftACTlCNS.
SECOND OPERATIOV.
97
ih
THIIin OI'KIJATIO.v
i| 1 3 ~ "3
3
rtie frncfion ^ is multiplied by ra,riti,,lvin,r iu
"■""orntor by 3, «ince tho par J t.ken 'il fre 3
tune<as,„a,„y as before, whilo tho ,a t's "1
-^ch.. . „.,of the fraction i.di^d'n.;;^
lB,^tnI nf '.r",'^ operation, wo divide tho d.noru-
ootam ^i for thn answer, as before. If i^, .,vi.
by dividi,,^ ite den min:.tor bv slt'V^"' ""' ^'"^'''"' ' '« '"-''tipliod by 3
fraction i» divided are onivl as m^r f ''"■'' '"'" ^'"'°'" '^^^ ""it of L
before, while tho par,. ta4n re JirfbVie'ir:"^' "'"''• " '"^^' *'
or I'll
JE.T, Multiply 24 by 4,
FIKST OFEIiATION-.
2^ X if = i|Q ^ 20.
SECOND OPERATION.
24 X f :- 4 X 5 = 20.
THIHI) OI'EIJATION.
7 X ^ = 20.
AxALT8ia.-In the first operation, we first
-.1 .ply the integer. 24, by "the ..nnerator of
the- fr.cn :,n, then divide the product by the
den.tu.nator, Mnd obtain 20 for tho a,.,-wer
lu the second operati-m, we divide tho in-
teger, H by tho denominator of tho fraction
and obt,un; of 24 „ 4, which multiplied by
S. the numerator of the fraction, gives a of 24
»■ z\). uenoe, °
frJ:siSicS:Siizt-a-:K:srti^'s^^ - a
lei. Case lll--To.udtlpl!jafrn.cnonbyafracnon.
fra^^Uon:~'° -"'"P'^ » ^-ction by a fraction is to find a fractional part of .
Ex. Multiply ^ by |.
FIRST OPERATION.
A X ^ = n
1
8-
SECOND OPKKATION.
I
1^ "" ^ - 3'
Analt«!8.-To multiply 5^ by ^ is tot^ke 4
of the irulfphoand, 3 Now, to^ obtain 4 I
^j, wo simply multip-ly tho nameratorg tog^.
er for a new numerator, and the denomina-
tors together for a new denoninator nso)
Ther»for«, ^ *'
fcTJLTIPLIOATION OF fRAOTIONS.
Multiph/ing one fraction hy (mother i$ the same a» reducing
compound fr< I ctions to simple ones.
From tht! foregoing we deduce the following general
103. RuhE. — I. Rechice all integers and mixed imnihers to
improper fnictions.
II. Miilllplij together the vunierntors for a new numenitor, and
the dtuiDiniiiitorsfor a new denominator.
NoTKs.— 1. Cancel allfiiotms common to numerators and denomiiiatorit,
2. The word of between fractions is equiyalent to the sign of multiplication.
KXAMPLKS FOR PRACTICE.
i X 7 ==
J X 4.
^ X 8 =
I.
2.
3.
4.
5. {\ X 6
6. 12 X 1.
7. 13 X f =
8. 1« X ^.g.
9. 11 X 1^ -
10. 21 X \.
12. \ X
1.3. ■
14.
oij.
\ 1
8
Ana.
Ann.
Ans. 1
An».
Ans
Ann. ^
Ans. ■jf'y
16. 3| X 1 =
h\\
17. v^ X 15
18. m X 1| =
ly. !> X m.
20. 7i X Hi =
21. Ux,7^.
22. « X 71* =
23.
24.
25.
26.
27.
2H.
2y.
30.
i'^llolli
1? w (ll
■Ig X .'j.
12| X IIS =
4i X ^
i X J X
i) V 2
Iff ^ 7
I X li X ii X v
lit X I X 2 X 5^
,7 y 4 3 y 54 -
3 _
5 -
V 5
I
Ans. 2\.
Ang. 2i.
4ns. 60^.
Ans. 63|^.
/4ns. U7i.
Ans. ^.
Ans. |.
15. l\ X 21- = /Ins. 5^,
31. Find the value of 2^ times ,
32. Kinti the value off of If offg of »
33. VViiat is tjie product of ^ of j of J by 11 ?
34. What is the product of 12^ by 5^ times 6|?
PRACTICAL PROBLEMS.
Ana.l.
Ans. 3^.
NoTC. -In buflineBs transiictions it is customaiy to add 1 cent when the fraotion
iseqnal to or gie!it€r than a hailof a cent, and to omit it when it is less than the
half of a cent. ThL' fraction is retained in the following answer''.
1.
2.
3.
4.
5.
Required the cost of
(;} lbs. of ham, at 12^ cts. per lb.
T^ yds. of tape, at .''>| cts. per yard.
1)5 quarts ol plutiif, at 7| cts. per qt.
.'iG lbs, of chalk, at | of a cent per lb.
T^ yards of nuislin, at 9 J cts. per yard.
6. 7 A lbs. of beel', ut .0 cts. per lb
7. 6^ bush, of apples, at 74^ cts. per bush.
8. 12^ bush, of oats, at 62^ cts. per bush.
Ans. f 0.85^.
Ans. |!0.75JJ.
Ans. .'5!0.74|.
Ans. .'i!4.84J.
IW. What it tht rule/W the muUijAieation of fraotion* t
9.
10.
11.
12.
13.
U.
16.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
34.
35.
36.
37.
38.
39.
40.
DIYIBION OF FRAOTljNS.
79 bush, ol'salt, at J of a dollar per liusb.
6i quarts of nuts, at [)% cts. per quart.
2| yurdrt of cloth, at J ,,f a .iullar per yd.
y barrels of vinegar, at $6 J per bid.
15 lbs. of almonds, at U.^ cts. per ib.
8 J yds. of cloth, at S*n per yard.
15 yds. of ribbon, at 2(ii cu^. per yd.
7| lbs. of coffee, at ^ of a dollar per lb.
8S cords ol' woo(J, at .:<2| per cord.
12 cords of wood, at $i;,37i per cord.
42 budh. of apples, at (13^ cts. per bush.
11 cwt. of sugar, at ^'J'l per cwt.
7 J do«. of eggs, at 12i cts. perdoB.
llf bble of salmon, at ^^* per bbl.
I2| bush, of potatoes, at 37^ cts. per bush.
22f yds. of seiicia, at 87^ cts. per yard.
7 J cords of maple, at $5J per cord.
4i bush, of rye, at $1.75 per bush.
10| yds. of calico, at 15| cts. per yd.
35| lbs. of raisins, at l,s| cts. per lb.
7| yds. of cloth, at $3^ per yd.
75 J bush, of wheat, at *ld per bush.
9 doz. of adzes, at $10^ per doz.
6| bush, of turnips, at 37 ^ cts. per bush.
23| cords of wood, at |3^ per cord.
75ii lbs. of sugar, at 7| cts. per Ib.
212| lbs. of beef, at 7^ cts. per lb.
3| tuns of hay, at $12^ per ton.
14| bbls of vinegar, at $IU| per bbl.
6^ gal. of molasses, at 2oJ els. per gal.
18 handkerchiefs, at J of a dollar each*.
134 lbs. offish, at 'J| ois. per lb.
9»
Ana. ?6'Ji,
Ans $2.27}^,
Ana. $1.42^.
Ana. $3.99.
Ans. «;221 J.
Ana. $26.58.
Alls. $0.96;t
.ina.
Ana. *41f^.
Ans. 1.74^.
Ana. f 25||.
Ans. $i}5|.
Ans. $5.85J.
Ans. *1.52.|».
^^1
i till
111
DIVISIOiV OF FRACTIONS.
163. Case 1.— To divide a/raction bjf an integer.
Ex. Divide f| by 6.
FIRST OPKKATION.
f I - 6 =
A-
8E0OND ePERATION.
f I - 6 = H ^ A.
Analysis.- In the fim operation, we
divide the tidinorator of the fraction by 6,
and write the quotient, 2,over thedenoin-
inatnr.
In the seeond operation, wa tnuU'pl? »he
denctuinnt'.r of the fraotion bv the .livi.sor,
t), and wriir the pioduot under tlio numer-
•tor, 12. Henoe,
/•.«f/l?7 '^' numemtor or multiplying the denominator of a
fmctxm by any number divides the fraction by that nmnber (1S4)
IM
DIVWI05 or FRAOnOMB.
■ •4. Cask U.— To divide an integer bt/ a fraction.
tiw. /fow many times wilJ 24 oofitain ^ ?
riRHT OPKUATION.
J4-?- ^= 168 ^ 6 = 28.
• f'JCONl) OPKUATION.
24-4-^ = 4x7 = 28.
OPK RATION.
3 • i - ; X I = f^.
/ANALTHis — The integer 24 will co«-
tain j at) many timoa a.« there are *«•-
«»'/(» in 24, equal 168 .-uvcuthn. Now,
it' 24 contains 1 seventh 168 timt's, it
will contain ^ at many timoa u« 168 will
contain (i, or 28
tt^ J t" the aei'ond operation, we divide
HW*ft " .«r by the numerator of the fraction, am multij^ly the quotient by the
•*w^i».m,'.r, which produces the anme re.-.mt aa in the tirst operation. Uonce,
thruluiq hji a f, action ajtisists in multlplijing by the dtnomi-
miw, and dividing by the. numrrator uf the' dioiior.
I<I5. Ca.-e III. — To divide a fraction hy a fraction.
AV |;ivi,J(. 5 by J.
Analysis.— We inrert the terms of the
diTiaur, ,nd then proofed a« in multiplication
of tractions ( 1 62). The reason ol this pruceas
J . will bo seen, if we consider that the divisor
9f M *w wpression denoting that 2 ia to bo divi.led by 3. JVow, rog.ardin' 2 as
«• »M«|«r, we divide the fraction J by it, by multiplying the denomi'Lator ;
"*' » X 2 ~ I'ff* ®"' '^ ' divisor. 2. is 3 times as largo aa it ought to be,
iW*"^ It w«t to be diTided by li, aa aeen in the original fraction; therefore the
Y J*f' tV '^ * »3 large as it should be, and must be multiplied by 3 ; thus
a I '
|# = f»' thean-wer By this operation we have multiplied the denomi-
MlAy 6f |h« dividend by the numerator of the divisor, and the numerator of the
mfitUffid hy the denoininatoi of the divisor.
Vftm the foregoing we derive the following general
Ion. RULK. — I. Reduce integers and mixed numbers to im-
ffff/pf-r fractions.
It Invert the term* of the divisor, and proceed as in multi-
plif/tlifm of fractions (163).
««i!!r'***Tl' ''''* liviJend and divisor may be reduced to a common denorai-
^v*,ftr>d the numerator of the dividend bo divided by the numerator of the
mtf*»,i} (biS Will g ve the same result as tho rule.
^' ^P1>*f e»ncellation where practicable.
EXAMPLES VOH PBACTIOE.
Ann. |.
Ans. tj.
4. 23 -f i.
6. J - ^
Ans. H{.
31.
ttt,, WhatU Affjjoi.eral rule /or dividing fraetioni f
8. aVV f.
9. 2i^l^
10. ^ 4- I?
DIVISION or l-BAOTIONS.
^«*- m- 1 19. J ^ ^
/ln«. 3.
11. 7
12. J« -. I
i:ii =
Ans.
':l
13. 7
i
14. § - KIT.
15. 63 -I- X =
5^.
16. 3i
17. i^ ^ 2S
18. i^ -- 49.
/Ins. 21.
6
An8. 117.
i20. ill -^51.
21. i - ^
ins,
7 _
1 J
— JiJL —
22. hi -f- 08
23. g| *
24. 15
2o. li)
in«,
101
:w=
I'ft
26. M - 19
27. 93 ^ 47
i:^ if.- '?
JJ =
Ans. 3J^.
31. Divide J of J by | of}.
I X I = A
A
29. 81f -f 91 = 4n#. yj^jl
A.N4tT«w._The dividend, re-
duced to a siiuplo fraotion, is 7 .
the divif'or, reduced in like man-
"'-''■' '* (h i ^^^ ^2 '^•'■iJed by 2
18 ISf, tho quotii'nt reijuivod. 0?
wo may apply the general rul«
directly by inrorting both factow
rill, , . "i the dirisor.
The Moond method of solution has the twofol 1 udTan^igesof givinc- the an.w-
by a single ope.at.on, and of affording greater facility for cancellSn "
W = IHJ, Am.
Or.
i X I X J X I = 18}.
33. Divide J of ^ by X of A.
34. D.vide|offb/|?f}.'^
35. I>|videf of7^jby^j-ofl7f
.^(.. t)ivide^(yof4by|of3i.
37. Divide I of II of A by } of jf of j.
38. Divide|^f5iof7by§of3>;. '
39. D,vide|offof|byiof^o't-A.
40. Divide i of I of 3G by 1} off.
41. What ia tiie value of ^?
8i
8i - ^
66
9
OP£RATIOM.
28
26 _ ^^
" 3 - V
3
13
~ V X £5 = — , ^ns.
28
Ana. If
-in.*. 11 J.
0»8.— This example
IS only another form
forcxpressingdivision
of fractions; it is call-
ed a complex f motion.
We simply reduce the
upper number or div-
idend to an
fraction, and the lower number, or dirisor te ui imn,. J ^^""^ !° "" ''"P'oper
divide as before. amsor, te an improper fraotion, ancf thVn
42. What is the value of"?
43. Wliat is the value of ^?
44. What is the value of-^?
Ans. 6^,
m
^^'^ BIVI810N OF KUAOTIONB.
45. What ia tl)« value of'
?
Am. 1.
46. What is the value uf - ^ --?
? .,t ;ii
47. What ia the value of ,-— r- ?
5nf^
48. What is the value of t-JL^ 7
4iolg
4a. Ueduce -i-*^ ^
,~v — --—i- to ItM sinmk'.-*t Curtu.
Ana. {|.
60. KeduceL^J - 1' to its fliinple^it form.
'• ^ rr ^tV
PRACTICAL PHOIJLHMS.
1. If f of an acre of land sell for .f63, what will an acre sell for at
tk« HHine rate ? v4n.s-. $U7.
2. At $1 per bushel, l-,ow many bushels of onions can K" lu»ught
for*12? Ans.\6.
3. How many times will IGJ gallons of vinegar fill a vessel that
holds .{gallons? Am. j^.
4. At j^ of a cent each, how many apples can be bon;rht tor 84
cents? /Ins. II.
■ ). If 15 pounds of raisins can be obtained for *3f, what will 1
pound cost? An-f. $0.2 1«.
tJ. A butcher expended $56f for sheep, giving $1J per head; how
many sheep did he buy ? Arts. 47.
7. At $5 per yard of broadcloth, what part of a yard can be bought
for f of a dollar ? Ans. A..
H. If I pay 5"^ cents for riding 1 mile, how many miles can I ride
for 1134 cents? Ans. 20.
9. How many pounds of tea, at$li per pound, can be obtained
for$13i? Ans. 12.
10. li'j men consume | of 'Jf pounds of meat in a day, how much
does each man consume ? Ans. | of a lb.
11. A man bought 37| yards of calico for $5.61, how much did it
cost per yard? /In.s. $0.15.
12. Huw many tons of coal, at $5| per ton, can bebou^ihi for $57 ?
13. A horse eats jj of a bushel of oats in a day, in how- 1 nan v days
will he eat 15| bushels? Ans'. 42.
14. A merchant bought 97 sheep for *1002|, how much did he
give per head? " Ans. i^\.04.
15. If a boy earn } of a dollar a day, how many days will it take
him to earn ^9|? Ans. 26.
10. I'(.ter paid $513| for a farm, giving $2 1| per acre ; of how many
acres did the farm consist ? Ans. 25.
17. If $2f is paid tor 5^ pounds of grapes, how much is that pei
pound? Ana. $0.50.
18.
per ton
19. ,
20. ,
il. I
get for
22. I
> yards
2;{. I
21. I
would a
2:>. A
•31 per
20. a
ooTer a
27. H
each b(jt
2H. If
chased f
29. H
• 4 .vards
30. A
e*ch, aiK
did he ga
GRE.
167.
tions is t
them, gi\
liiH.
fractions.
Ex. W
Greatest ci
Least com
ANALTBia.
least coiumo
tors 112, HO.
fifth*, their g
fifths; then I
1^ aa the an
167. Wm
low
6
I nde
18. H
per ton ?
QREATBST COMMON DIVrsOR Or rRA0TION8.
*nyton<,ofUyc.nbepure»,aH.<l for
vw ni
108
Aff'Ir/lr^i'Jr'-"^.:^'^^— t
^ork lor $37jyj ?
11).
for $A r ' * '""*^ P**"" '^'*"«". '"- n.ucl. b.er can be bouSJ
-'• 't 2^ apples are worth il »«,,»= t ^^'- 2* cal.
get for 1 cent ?^ """ '** *^'"^«' "'f"*' pa-t o( an apple can ' ou
f.vSdi'c^sy^^'"'-^''""-^*-'i. how ...uch lea, iU.utl L
would 8| b«.i.el.s Huppl'^rl'L';;: ,;^ ■; -? ''^^' '-- '"-; horee.
J^'. A young man, iiuvin.r.^jo ,rav,. i % i • ^"*- ^•
•31 per ream; how much Tui he' l^.v ? ^ ' ""'"7 '''"" P^P^^ at
^o. Uow many tieet of caroct •'■''/;.,.( ;„ • i.. .;;"•'• ^ reams,
corer a floor ,4i f.ec m lenXl?, uj e^ in w iti;" .'" '''''''''' '«
29. Huw much more than Fi vnrJc ^<- * ^"*- 27.
'i yards ,.f calico co.st at U ct!.'a ^td ? ^^' ^* ' ''l- ** >'*^^^' ^i"
An$. $4.
GKEATBST COMMON DIVISOR OP FRACTIONS.
167. The Greatest Common Divisor nP,
tions ,s the greatest number which w re/.cl ^ '-^''^ ?'"
them, giving a whole number for a quotient. ^ ^'^' '''^ °''
E». What is the greatest conunon dirisor of^, 1|, .^ ^ ,
OPEKATION.
3i If, }| = y, y, ^^ ^ ^^ ^^
Greatest comn^on dirisor of the numerators = 4 ) Ore«.-»^
Least common denominator of the fractions = 35 \ d'rZl^i;::,
l^^^^stP^^^^^^^^ ,.na, Che
tors 112. HO. nn'i -'J *.- h" V """°<i tne greatest oommon diriaor nf »i.- -..*.:"
^y;j.. their greato"st ^omoTon fc/'u'no'^ 4 'iVho'./°'ii'-Pr«««"'*^'4'-
fafths J then fore we write the 4 oyer th, ult\omm^«^ '""^'' ^' * "«irty.
^ ai the answer. " "••* •ornmen denemmuwr, 3*, luia baire
; t
ii jtf
'.■'f'
i'-*'
-"I;
WT.
»»* « tA« gntiU^t remmoD dJrigor •/ f*n0tm^l
Siv'i
104
fe».»^Wii
LKART COMMON MULTIPLE OF FRACTIONS.
169. Rule. — Reduce the fractions, if nece$»ary, to thdr b/ut
common denominator. The greatest common divisor of (f/w numer-
ators, written over the least common denominator ^ will aim (h$
ifreatett common divisor required.
EXAMPLES FOR PRACTICE.
Kequired the greatent common divisor of
1. 'i, U, and |.
2. t. I, andl|.
3. ^l I, and If.
*• f a, if, and f
Ans. ^g.
Ans. ^l^.
5. 3|, 5/5, and 2^..
6. 2i. 4, ff, and 4.
7. Hi, 12|, and<4.
8. -^i 4, iftx, and 2f
An0. 1$,
LKAST COMMON MULTIPLE OF PKACTIOm
ITO. The Least Common Blaitiple of two or more frdAitUm§
18 the least number which can be exactly divided by each of ihmUf
giving a whole number tor a quotient.
ITl. To find the least common mnltiple of two ormorefrnAtU/m,
Ex. What is the least common multiple of 7 J, 5^,, aad 3j[| ?
OPBRATION.
Least comnioo mult, of the numer. = 63 ^ | Leatst wmiwrn
Greatest com. div. of the denom. = T ~ *^' | multip. t^^itrnX*
Analysis.— Haying reduced the fraotiii » to their simplest form, we |$m4 it^
least common multiple of tho numerators, 63, 21, and 63, 10 be fiS. Wv», mm
the 63, 21, and 63 are, from the nature of a fraction, divideiiit, of whicfe itt*jf
respective denominators, 8, 4, and 16, are tho divisors (118), the leaj-t 'i»mmm
multi{ilo of the fractions is not63, a whole number, but so luany fracdi/i«J yi^f^
of tho greatest cotumon divisor of the denominators. This common ^fin^r W9
find to be 4, which, written as tiie denominator of the 63, gives «/ = 16 j «« ftf^
leaet number that ono be exactlj divided by the given fraotiong,
17 m». Rule. — Reduce the fractions, if necessary, (/) their hfg,
est terms. Then find the least common multiple of the numMraUrfti^
which, written over the greatest common divisor of the d^mmi'
nators, will give the least common multiple required. Or,
Reduce the fraetioru, if necessary, to their least comm/m dmm^
inator. Then find the least common multiple of the nutmratttfi^
mnd write U over the least common denominator,
169. What it therule/or Jinding the gre^itewt oommon diwUnr 0/ frnetiitmf^'
ITO. Whit in th« leaet common multiple offraetiom t— 172. What it tlu W<#/*r
^md%%y tht Ua»< "MimoM m^Atipie of frm«ti<m* t
R«qui
1 ^ "
2. S 15
n V 55
3- f , h
PRA(
17»
part as ^
4, and 6
NOTK.—
must be a
50 cents
33^ cents
2a cents
20 cents
16j| cents
174.
price of a
Ex. At
OPEI
)
An
175 f
as the pric
1. What
pound ?
2. What
3. At ^
4. At KJ
6. Wiiat
6. At.i«3.
173. Whati
thf cn$t 0/ em^
a doi/ar t
^»«a»«»i»teia ^iW ija ^ii irf;'
ANALTSfS BY ALIQUOT PABTS.
105
KXAMPLBS FOR PRACTIOE.
Required the leant common muKipla of
Ans. 8^.
Ana. 24.
1 A- I and 2X,
2 n I - 1.4'
f,|f, and^
^- I, f and f
5. 5i, ^2^, and I i.
6- IH,^,eA,and2||
7. fl, i, and ^jj.
^- A. «, t)l, T^, and 2i
i4nt. lOi.
Alts. 3|.
*' /ff' Mj A> *n<i f .
PRACTICE, OR ANALYSIS BY ALIQUOT PARTS.
4, and G are aliqlVpartt^^^^^^^^ ''"^"^''>'= ^»»-> 2, 3,
-^rberiho&iC/ "^^ '' '^ '''^'^'- - • -«•<* -»»>.. whi.. . faetor
AI.IQUOT PART8 OF ONE DOLLAR.
50 cents =^ of 1 dollar.
fh cents = i of t dollar.
2a cents = i of 1 dollar.
fO cents = ^ of 1 aul!ar.
Ib|cent8 = ^of I dollar.
}23caits = iof 1 dollar.
10 cents = ,V. on dollar.
Hg cents =^ of 1 dollar.
t'i cents = ^ig of 1 dollar.
cents = ^ of 1 dollar.
e^. M .21 ce„« a j,ar,i, „.],»., „i|| 4I6 yards of „,u.li„ co,.T
OPERATION.
8) 416
Ans. $52
EXAMPLES FOR PKACTICE.
^1. What will b. the cost of 724 pounds of coffee at ... cts. a
2. What cost 376 yards of calico, at 25 cts. per yf/" ^'''^''^'
j6_At.*3.1Gi each,^hat wniti'hitfco.^P"^'-' ^«'- «1«6*-
173. W*a<M rtn aliquot part of » n>jmh«r» itk »r . • i ' -^
■:I:I
. l!
PRACTICAL QUESTIONS BY ANALYSIS.
, QUESTIONS
INVOLVING THE RELATION OP PRICE, COST, AND QUANTITT.
170. Case I. — The price and the quantity being given, to
find the cost.
Analysis.— The cost of 5 units must be 6 times the price ot 1 unit ; of 6 unita,
tj tiineg the price of 1 unit ; of 4 of a unit, ^ tim^s the price of 1 unit, etc. IIuuos,
tho
ITT. Rule. — Multiply the price of one by the quantity.
ITH. Case II. — The cost and the quantity being given, to
find the price.
Analysis. — By Case I, the cost is the product of the price multiplied by the
quantity. Mow, having <he cost, which is a product, and the quantity, which is
one of two factors, we have the product and one of two faetors given, to find tha
other factor. Hence, the
ITtt. Rule. — Divide' the cost by the quantity.
ISO. Case III. — The price and the oost being given, to find
the quantity.
Analysis.— iieaaoDing as in Case II, we find that the «ost is th* produot of
two factori, and tke price is one of tha factors, iienoe, tha
1^1. Rule. — Divide the cost by the price.
183. Case IV.— The quantity, and the price of 100 or 1000,
being given, to find the cost.
Analysis.— If tha price of 100 units be multiplied by tha number of units in a
given quantity, the product will be lUu times the required result, haoause the
multiplier used is 100 times the true multiplier. For a similar reason, it will
be the same if the given price be 1000 units. The true value will be obtained
either by dividing the product by lUO or lOOU, as tho case may be, or, by ruJucing
the given quantity to hundreds and deoimuls of a hundred, or to tbuusands and
decimals of a thousand. Hence, the
183. Rule. — I. Reduce the given quantity to hundredt and
decimals of a hundred, or to thousands and decimals of a thoneand.
II. Multiply the price by the quantity, and point ujf in ihe re-
sult as in multipiic 'tion of decimals.
184. Case V. — To find the cost of articles sold by the ton
of 2000 pounds.
Analysis. — If the prioa of I ion or 2000 pounds be divided by 2, the quotient
will bo the price of j ton or 1000 pounds. We then have the quantity and the
price of 1 000 to find the eoat. Hence, the
177. What M tht tale for finding the coit of articles, tk« price and the quantity
being given ? — 179. For finding the priee of urtioleg, the eott and the quantity
b'-ing given? — 181. For finding the qurtntity, theprice and the eoit being gi^enf—
IM. For finding Ikt mtt of artielee, the quantity, or tht priee y 101 or lOOO, iinMf
given f
i9ent-
h$m f i
PRAOrrOAL QUESTIONS BY ANAJUTSIS. 107
lh.*2^r '^''}''\\'^^''^<l't^^'P^!<^eof\ ton b}, 2, and. multiply
the qaolmit by the number of pound, expressed a, thousandths.
EXAMPLES FOR PRACTICE IN THE PRECEDING OASES.
fo/s2t7 5o"?^ ^'' ^"*''' ^""'^ '"^"'' ''*""^''' °^^'""" ^'^ ^>« obtained
9 rei 1 V ,• ■^"«- 29 barrels.
_^. it I jurd of calico cost 23 cents, what will 3 U yards cost ?
• pmul/r''''"^ ^^^^ ''"""'' '*'''^' containing 70^ lbs., at $^
^5.^ If board for a family be $342.18| for I je«, how much is ii'p^r
R VT J - Ant. $0,931,
adozenT'"*"^ ^*'" ^^'°*°^' ^"^^'* ^' •*-^*' *^ ^(^iot*-
7. What will 3921 feet of pine boards cost, at $17.25 per Tooo ? '
at $I7| a ton? ""^^^^ ''^^' ''^ "'''"'' *^°^ ^eig^^'ng 162^ Ibfl.,
Ill's Oiin ^ * ^'"''^^^' ^^'^ ™*°^ '^"''^''''' *^*" ^^^^ °*'* ^* ^°*'«^* ^<*
in*Af,-„ . , , 4n«. 75| bushels.
iJl'n^L o v" P''"",'^' ^'^'!: ™^°^ ^^""'^ of codfish, each contain-
12" aT^/?.^ ^V''lT'?*'^*^'^?,*PP^^^''^«^»t*^6i per hundred?
12. At 373ct3. a bushel, what will I ot 456 bushels of j^tatoes cost ?
lOon . ?«Ti "^"^^"^"'^^ ,^^e P'^i'i ^'-^r 48« feet of boards, at .^20.25 per
i?";7.'5j%^rrom"""''"=' "'^-'^^ ''' '"'-^ "'V^fjvr^t;.^^
per barre'r?^ ^"*'^ of Montreal apples cost $97.50, what is the price
^^16. How many acres of land can be bought for *2117.lsi"at '$5|
tAinln^l il^ I***, '^^ ^"f ''^"' ^T'' '"^"y ^*"^^« «f potatoe"*" eacSon-
I « f «> i )i»''hel9, can be purchased for $50.62^ ? Jlng 54
q w\ ."^ of » barrel of rels be worth $6.42, what is a barrel woKh ?
poindsT *"" ' P^'^ ^""^ ^^^ ^^'' ^*" ™***' •' ^'' P" l»""'i'-«d
20 Wha^. cost 1080 lbs. of hay. at $12.75 a ton. a"l'l3«^'ibs'* ol
«.h feed at^^l5.50 a ton ? ^^. ^17.487.
1344 feet of siding, at !^1. 62 i per 100; and 2216 bricks' ir$4rpir
AHS ^4i H4jI
22 A grocer bought 108 gallons of oil for $145.80, and lo^t'l2 gal.
I'ch'didtelL?"^* "''*'' """"'•' •* *'■'' P*' «»l'-5 ^-
1;
4
;?
•I
I
.ir!M
IM. ir4a«M
«*• nl9/»rJln<Ung (A« «oi( ^«r(MiM *y«ft« Im ^SM« »•,?
108
BXAMPLIS ON BILLS AMD AOCN>UNTB.
fffi
23. A lumber dealer bought 106250 feet of lumber at $14.ST6 per
I 000, »nd retailed it out at $1.75 per 100 ; how much was his whole
i^ain ? Ans. $;^;!2.0:^ + .
24. A load of plaster weighing 3.360 ponnde cost $6.71 j^, how much
will a ton cost ?
25. If |6.97i be paid for 0.93 of a hundred pounds of beef, how
much will one hundred pounds cost?
26. A farmer exchanged 42| bushels of barley w(^th ^1^ cts. per
bushel, and 679^ lbs. of hay worth 75 eta. per hundred, for 18780 lbs.
of plaster; how much was the plaster worth per ton?
27. If 42 yards of cassimere cost $147, what will be the cost of
34f yards? i4n». $121.80.
28. What is the value of 12 pieces of black cloth, each piece con-
taining 27'| yards, worth $2J[ a yard ? Ans. $954.50.
29. At .^5 psr bushel, how many bushels of wheat may be bought
for 118.90? Ans. 21^.
30. A farmer sold to a merchant three loads of hay weighing res-
pectively 2739, 2217, and 2884 llj"-> at $8. "') per ton, and 42i; lbs,
of pork, at $5.25 per hundred. He received in exchange 46^ yards c
mwthD at $0.09, 9| yards of carpet ui S4.50, and the balance in m'
a«y ; how much money did he receive ?
Let thepupilB makt out, in proper fornix as the case may 60,
the following:
1. Sold by R. S. Gruham, Monkeal, to E. Dudley, as follows :
1870, Jan. 3, 109^ yds. calico, at 18^ cts. ; Feb 11, 430 yds. muslin,
at islets. ; March 2, 37i yds. sheeting, at 23^ cte. ; May 16, 75|
yds. Irish linen, at 4K eta. ; 43^ yds. lace, at 7K| cts.
Footing of the bill, $161,007 -t- .
S. T. E. Clark bought of F. Larose & Co., Quebec : 1870, June 10,
731 gal. Irish wliisky, at 86 cts. ; 108^ gal. fine old rum, at $2.12^;
67^ gal. Holland gin, at $1.45; Aug. 14, 89^ gal. old cognac, at
$2.67i; 107 gal. brandy, at$1.37i; Sept. 7, 201^ gal. Scotch gin,
at f 1.20. T. E. Clark gave in pait payment, Sept. 11,4 chests green
tm, each 67 4 lbs., at 56 cts. per lb. What balance was due F. L. A
Co., Sept. 12, when the bill was made out? Ans. $867,714.
3. J. N. Webster, butcher, Kingston, sold to A. O'Regan, Oct. 6,
1870 : A illet of veal, weight 16| lbs., at 10^ cts. ; a loin of lamb,
weight 74 lbs., ui 17^ cts. ; a leg of mutton, weight 13| lbs., at 6|
cts. ; a leg of pork, weight 164 lbs., at 9^ cts. ; a pig, weight 24ilbs.,
at 124 cts. ; a buttock of Ijeef, weight 374 ^^^-i ^^ 7^ cts.
Footing of the bill, $11,314.
4. E. Lemay & Co. bought of Messrs. A. Roche & Son, Toronto,
Sept. 3, 1870 : 123| lbs. eutn lac, at $1.15: 65| lbs. quinquina, at
$14.10 : 1074 lbs. rhubarb, at $2.40 ; 1 20i^ lbs. sassafras, at lU cts. :
356i Iba. mastic, at 21 1 cte. Footing of the bill, $1415.911.
6. Sold by B. H. Porter, Ottawa, to Miss D. Valcour, Aug. 20,
1870: 27f yds. Dresden lace, at $3.09; 194 jda. Flanders lace, at
$1.62^; 83^ yds. gauEe, at 454 ets. ; 364 Y^^- muslin, at 18^ ots. ;
iO pair kid gloves, at 32 cts. ; 25{ dosen napkins, at $6. 1 2^.
Footing of th9 bill, $335.3«|
>*^ .■•sfW3fc'*^<toft ■ -^i
!U Ibe.
at
MISOBLLANIOUS PROHLUMS.
lot
«. Inroice<J per Canadian Expresn, by 8. Blanchard & Co., Qnebec.
.o J. IJutler, Kingston, July 6, 1870: 25 aack
bush
at 04 ctH. per bush. ; 32 sackn pease, .Vo. 4
tares, N',x 3. each 2^
H7i ctH. per bush. ; 20 Hacks oats, No. (], cacli 'M biinh
each 3 bush., at
at 56^ cts.
each 2^ bu.h._, at $1.37 J per
2i bush,, at 85 ctn
per bu.-h.
per bush. ; 8 sacks malt, No. 5,
bush. ; 16 sacks beans, No. 7, each
Insurance and cartage, $3.40 Amcn.t of Invoice, $'i:21.5o.
& O'Npil M f f Co., wholesale n.ercharu., Halifax, sold to Lenoir
AONeil, Montreal, as follows: May 19, isTO, 85 nieces Norwich
tlT'i^'Tf' ^«^P'.^«^« Liverpool cottons,' at ^7.6 ; June 5
1 5i yds. Antwerp sheeting, at 24| cts.; 698^ yds. Amions' velvet, a
Jl .feO ; Au^^ 8, 375J yds. Yorkshire drab, at 65 cts. ; 872^ yds aI
iV^fir^S w'l^'tri^^"' at $7.50; Aug. 12, by draft. at3day'a
sight, for $oOO. What balance wae due T. McC. & Co., Sept. 3 when
the account was settled ? ^^g fl^^^j Ji^*°
fi tfiS^-^^""^^^'?»«eofMontrea1, soldtoMrs. F. Stepbens, 'April
6, 1870, and Ed. Noonan, hie clerk, collected the amount of the b^
39i yds. camb et, at 31 ^ cts.; 47J yds. shalloon, at 32 cts. , 271 yds
90i cts. ,_34i yds. calin.anco, at 37^ cts. A„-,i. of the bill, m.i)2^h
.1 «."7'ir''^^''",?.n''"; ^V^^''''' '°^^ ^^ '^««^''^- <^- Cooper & Co., Sur-
el as follows : 1870, April 5, 12^ doz. palm sack, at $li.42 ; May 12,
Port wme, red, 6oi gal., at $1 68 ; 42^ gal. Claret, at J2.17J ; June
at%6i1t:.Twt'?-''M^^^^^ ***^«'«- 3^H'al. Rhenisi; wine
at Oba cts. , July 8, 25^ gal. Slierry wine, at .$1.33. Received in nar
payrnent July 9 150 bush, oats, at 67^ cts., and $60 in cas 1. vTa
was the balance due to L R. & Son, July 10 ? Ans. *240..i3
l42" T.ii^^'T. '•^''"^^''''f^'^'^'r*^''^^'' Montreal, as follows:
ibjo, June 18, 4^ pieces n.uslin, each 37^ vds., at $2.15; 7 J r,iecea
chintz each 47^ yds., at 92^ cts. ; July '2; 4^ 'pieces Holland hnen
ton^'at'lb cti ^ Whi'"^**' fi?"""'' "' ^1 ""''' ' '^''^ >'^i- Lowell cot:
ton, at 18a ct^- What was the amount due, Aug. 3, to T. & G ?
Ana. *1 335.47
MISCELLANEOUS PROBLEMS.
,»indT^** "^'^ ^' '^^"^ *'°''' °^ ^^* P*"""*^' Of honey, at I6| cts. per
2. At $4i per yard, how many yards may be bought "br $ni ?'*
3. Reduce W to a mixed number. ^ 4n/l25i?
^Lwnr '' •' ^' ^"'^ • '° «q"'^*'^"* fT^*°"^ having a common
lenominator.
Ans.
^ff.
.lfat^^\V'''"*;'"° "T^r '" 2378i and'tSlf; &Se,^li^i;
A liat IS the greater number? ^^^ 244" U
bought fcrlafctr/ ""*"' "" •""" '"'""" "'/"'"l "-t'l"
J.t^'ii^^J^'^t^J' ^— '"■^» ^-- ^IK^""
ii: 1
11
110
MTSOBLLANBOUS PROBLXMB.
8. What will 15i cords of wood cost at ^ of $9j per cordr
». H.iw many pounds in 4 b:ig8, the first containing
Mcond _680|, the third 296i, and tlie fourth STa,".? 4na. 16
3605,
10. Andrew spent f, J, and \ of his money, am
i, and the fourth BTaj^j?
i had i?54.r)0
ike
h- r-"- 5) 8,' """J s v^i mo iiiuiic^, aim iiaii .to^.oO left t
ow much had he at first? Ans. $8H4.70|^.
11. A servant had J of his savings in one bank, ^ in another, and
the remainder, which was 877, in a third bank; how much money
tad he? ' ^„g jji4Q_ ^
12. Leo had I of g of 7i times $7862, and paid i of i of" it for" a
," ; how much had he remaining ? Ans. $3.3379.
lA-'/o ,,^ bogheads of sugar containing, respectively, 9451 lbs.,
itAJ^^-' ^^'-^^ '^^-^ ^^''ff' a"'J 899|, how many pounds?
i -*•, ^^"''y bought a bale of cloth for $96.87^ ; he disposes of it for
I of the cost, and by so doing, loses $2 on a yard : required the
number of yards in the bale. Ans: 18,4^.
15. What is the value of 376U acres of land, at $7.5J per acre?
_^ lb. If the transportation of 18| tons of iron co.sts $4S.15|, what is
u per tea? Am. $2M-X.
17. A man purchased I of a yard of velvet at the rate of $3.62i per
yard ; what di.l it cost him ? Ans. $3.11 jJ.
I H. Charles has 634 sheep, which is 94 more than i of 3i timea
David 3 number; how many has David ? Ans. 243.
• ^i^i'."^ ™^" travels 4 miles in | of an hour, how far will he travel
m 1 3 hours at the same rate ? Ans. 10 miles.
20. A merchant owned i of a ship, and sold ^ of J of his share for
i^^^'vt^ ^^*' ^^'^' ^*^^*' ^*^ ^^^ "'^''^^^ "'o^''' ^ ■^"«- ^1 ^^00.
il. What will i (,f lOj tons of coal cost, at ^% of $42 per ton ?
. 1^^; }H of * •^'•^8 be multiplied by ^ of itself, and the product di-
Tided by i, what will be the ret^ult? Ans. ^A.
23. Band C own 3144 sheep; how many has each, if B has 11
tunes as many as C ? Ans. B 1834, C 1310.
24. Edward has I of a dollar ; he gives Loui-^ ^ of this amount,
and then divides the remainder equally among three boys : what part
does each of the 3 boys receive ? Ans. f.
V.'3. James obtains from two fields 344 bushels of oats ; if the first
yielded 4 as much as the second, required the yield of each field ?
26. How long will it take a man to travel 553 miles, provided h«
travels 3^ miles per hour, and 9} hours per day ? Ans. 16 days.
27. 1 bought 15 loads of wood, each containing 11| feet, cord meaa.
ure, and divided it equally among 9 persons : what did each receive ?
28. A tree, whose length was 136 feet, was broken into two pieces
>y ailing; | of the length of the longer piece equaled | of the length
•f die .shorter. What was the length of each piece? Ans. 72 and 64 fl.
29. How many bushels of wheat worth 80 cts. a bushel, will my
for f o( a barrel of flour at $7i a barrel ? Ans. 7^ bush.
30. Lought i of g of 5^ yards of blue cloth at the rate of $3.50 per
yard; what is the onst? Am. $8.02 ' .
31. Ill of » barrel of eels costs $5, how much will 2 tubs ofe'ela
«OHt, one containing J of a barrel, and the other f of a barrel ?
32. If,^ of a gal. of porter is worth i of a gal. of ale, and ale is worth
$i per gal., how many gal. of porter will $20 buy? Ans. 24.
".0 left;
MI8r«LLA,X10US PROBLEMS.
wi!Ln;r[;tri"!;:if/^^'-.'«/^!?^ divided
111
remainder, wliich
ave 4, John 1, Peter ,»„, Tl
'■morit;
>« 24 ; what is the wiio!
5 boyg
i*n. lipomas ^^. an.] Paul the
34. What Will be the'co t of Hv J« r ' T-'^"''^-' " """ '''^'i''^'^?
d 121 v,^« ,..• ,' ^" . ^J '3 y<>8- of calico, at i-'a .-t- ..„- ..
nJ I2i yds. ol'nuKl
35. PI
!>. at 1x5 ct
J'lipovns/^ofa,sin|:
per yard ?
;> .>^ c;irM;o, value.]
■3 ots. per vd.
owns
^n«. ^, owns $87000: D $2 0^ J $sm^
-n I of a steamboat, and UnV';.''?'^.' .'J"'' ^' *106»00.
45 0o'TJ.l^.^^-'"'-^-d«;il
«45000. VVha\ p^rt o ZXa-roaTh ' f,T ^''^''^ to Ow;n for
at that rate ? ^ ' "" '^^ stea.nhoat have I left, and what is it worth
i. inUef :n' oWoVJ r;;:,:, TJ " f * •*' ■»,»■ "^ P«'^ "^^
BO pay for the coal ? ^ ' ^^'^ ""^"^ PO""^^ were required
39. I have *800 and wish to lav out S'Urt n<-.> • '^"'- ^'"^^ "^'^•
• pound, and the remainder in tea at 52' ct! 1 '" 'T^l ^' '^ ""^
pounds of tea do I bu y ? ' ^" * P*'""'' ' ''^«' "lany
40. A merchant expended .^840 for drv .. ^« '' ?^^^^^^ ^^'-
house-lots of the same extent ii.t, Lk;m ^i V J , ^^'-' 'argest-sized
•nd .1.0 .he „.,„^e/„;s ^^'s v 'fV.tuol'r'rr 'i;'r''"''
42. A man own ns 135 J acres nf l«n i n 1 ..: ^^r*- ' '*^ '"^s-
to his son; what wL the vl'ue of th/ "^ '-^V*' ^"^ ^
acre? ^*^'^* ^^ the renoainder. at $57.80 per
43 A merchant owns 5 of a factory worth >«!4«nr:n'**'l^^^n'''«'
hie share to A, and i the renmi .W f^ n if ^^^- ^« ^^l'*^ *
ceive from A and S respectiX and . . ^"^T '""^^'^ <^^'' ^ « re-
^ns. From A $25200 p'""' ?.*'' ^'^'^ ^'^ remaining?
44. A drover bou4t 257 sheen L/'''\'^' ^^f^ '' ^'^^ ^^'^^ A-
bought348at$1.87fperLad ?hpn ^frf P/^ ^^^'^ 5 lie aft'erward
$1.75 per head, and^th'L / L^,;,£^;,«<i'^> tf.tlje, whole number at
and how much? ^^^naei &i $^.12^; did he gam or lose,
45. A mother divided a basfc*.fr,f^-„ ^n»- Lost $,{5. s 7 ^
ters; to the first ehe^e 12 o/a,^^^^ three daugi
and to the thir.i as much as to tKfi . . ^""""-^ ' ^* ^''« ^hole,
the third have ? ^^^ '''''''' '"'^ ' ^"^ ' "^any oranges did
46. What IB the smallest sum of monev with ,v5^1*' "^^ '^'■*"g^«-
purchase a number of sheep at -^2' Ta^K V V''''\>' f^^er couW
each,andanumberofyeaiKsa?lAoK"7"'''^'l^^"^'"^« "^^ »4i
could he buy with this moneyl ^ ' ^^''^^ ^""^ ^°^ '"*"7 o-^«acb
-^. Induing .ef^rdi^-^L-S^tl^^
^°s: b!. K Hf brofcoTon^?;? I \ ' ^ ^- ^' 31B^"/:"«
!■■
112
MlgOKLLANXOUS PROBLIMf.
49. The
le A of a farir. j^re sown with corn ; the A with barley and
50. How n.aMv huHhels of oats at 62^ cents perlnlh' 1^ remSed
61. Ifit requir^ 34 days for a mason and his JnZ nK;v^23 cubic
^ 2 IfTrof 'r 'T^T^' ',' ''^'^^^''^™ ^« ".alee ucuLic yard?
n„?r ",,fi.:'f"^?""'''"^'l^^'^"'e8 of Riienish wine cost ,:;j.:U) • how
much will .^482 Lotties come to? j„,. "
the .'^atne
wi ■ 11 1 1 --■-.-"""• •««.'»•. .'§543. 192.
Whal will |.e the pnce of 57^ bushels of rye, if 17,31 bushels of
me (Ilia if.v f-r.wt ^«A3 9 " ^ > . ' ' i j "": "*^"* O'
jiiulity cost $52?
Ans. .$;i0.6G
. 54 A piece of silk vei;et would bring $210 were .Tllm'er""know
•ng^the pnce of a yard to be $7.50, required the fength ^flhe thoTe
• 65 A market woman sold the f of a basket of e.m'^a^"addmt'*28
66. A man has an income such, that ifit were au-Mifented t^'^the
pr.ce he pau for a mahogany writingdesk, thatis-WlT heluld spend
$2 02i per day. What is h.s income ? ^ns. $685. 1 2^*
it tI^^A■''T^' ''^'' "'f ^^* y^'"^ '^f >'"en in 1} hours ; how lon^^will
It take him to weave : Lu. 15 yds. ; 2nd. 2& yds. • 3rd 44 vd« • il^
^r'^'^y'}- ' ''^: n of a yd. ?' 'Ans. l'^28i L!; l^'si^h e'tc
tHe , and the^ of he sum paid for 93 lbs. be 60 cts. ? Ans. $2.25.
5 ). In mixmg 10 lbs. of bismuth with 6 lbs. of pevtor and 4 lbs of
lead we ob.a.n an alloy which melts at the temperature of boiin.
water ;requu-ed Ist what quantity of each metal enters into the m ixt^
«fv f h'K',^"'^- li^bs.; 3rd.3|lbs.; 4th. lllbs.; 5th. 27! lbs
2° » Tk r . ?u ^'r,f ^' ^ ^^- ""^ ?«''*«'•' a»d f lb. of lead]
2 *lb.ofb.smuth,/j,lb. of pewter, and ,1^ lb. of lead, etc.
60. A weaving, mac „ne makes 135 yards of cbth per ,ia; ; how
many yards wl .t make, Ist. in 3 days; 2nd. in ,7^ of a day; rd in
4idays; 4th. m 15 days; 5th. in 32^ days; 6th. in 47^1 days
and 7ih. m 27m days ? Ans. 1 ° 41| ycis. 2^X1 yt eT '
61. It would require 1800 yards of cloth f yds', wide lolfake cloLs
for a regiment 5 but, on delivery, the cloth is found to be too Sarrow
the cbthT'"^°' " "^^^""^ "^ ^"^ ^^^^ ^"""^^ -■ ^^^^ ''' ^''^ -iJ^" of
remn . ^^^ f!f^-V'' ' ^'''''' ^^ broadcloth of equf HenJ^hi .
Z:^1^^ ^..uiredthelengthofa P^-^knotjng tha!
63. The breadth of a painting is but the J. of its height' If ^th«
breadth equa the f of 2 -, yar.ls, what is tS height ?It% yds
^6<. A teacher ofa select school has 60 pupils ; 24 of Sm mv
Rnw „ "k "1 ^f ^'' ^^^- ^ "*" '"'^ remainder, ;^1.75, and the rest $2.?.0.
T^ Tu v^J' ''' '■^^.^''^^ ^"""^ ^'^ P"P'1« '" 8 months ? ^n«. $846.
«„'!v.u"?''^"°n''0'»'e between two watches is | of an hoar-
LI ri^'"'' ^*K ' ** ""'""i"' ^''' ^^y' ^^"« ^^^ other loses 5', in the
same time: m how many day. will they again mark the Mme tu».f
4th.
'^7 6
'"21
DlNOMKCATl NtTMllM.
Ill
" A dealer in poroelam l,oud,t a J,»t '"""'«' ^ *»-64.
-'"••■j:..tE~SS;i;;sB»r
DENOMINATE NUMBERS.
pounds
^ing one bushel ISO are ^o^nav^ of '.'^' '"^"^^""^^ "°i^
fractions '^ ***^' * °^ * yard, etc., denominate
„.f;!l^:-^'°°°^^°ate Numbers express Curr«n«|
An
IVsights,
188. FFia^waijrapI, nu^j^ - ...
■oimnate number T~W/d.aVmJ«j!*^ oompoand aumb«r?-
■88. .i de-
JDominato
s l< ' •'
II •
lU
lUii
flffrl
OURBBNOIW.
OtlRRKNOIM.
1. Df.MivioN OF Canada Monet (77).
li Old Oanabian Monit, ou Halifax Currenct.
TABLE.
d.
§.
$.
£.
4 t'lrthingfl mak* 1 penny,
12 pence «* I Bhilling,
6 shillings " 1 dollar,
4 d( liars ** 1 pound,
d. qr.
t. 1=4.
$ 1 - 12 = 48.
£ 1 « 6 = 60 = 240.
1 = 4 = 20 = 240 = 960.
*•■■» •»•*/ id. rf th« old oaiaag* if equal to 6 eenta of the new.
III. Enqluh Monet.
TABLE.
4 krthingn (far. «» tr.^ make 1 nennr g,
ii P^Cf •• 1 Bbilling ,,'
W •iMdIififp n 1 pound or sovereign £ or sow.
«.
£ 1
1 = 20
d. Jar.
I = 4.
12 = 48.
240 = 960.
I ^"L^t *"*"*'»«« "• generally exprosBed as fraotiona of a peaay: tkui
i m^ mmtAHimm oailed one quarter, \qr.) ^^\d.;Z far. wm Id. '
k^S^J^/' tfc» original abbreTiatioD for shillingg, was formerly written
^^ »^H,»»* and pence, and rf. tbo abbreviation for pence, wm omitted!
^JT**;!*' ^'^^ Wf'tton 3/0. A gtraight line is now used in jplaoe of the/, and
mtfmmgt ace written on the left ot it, and pence on the right. Thus, 3^6, 7j3, eto.
*4jMS*-nT"* ""u"* f ^H •'«"■''"« pound '1 the Dominion of Cani» k
9*^999^, Mttrl fe«Dce the value of an English shilling is 24J oenta.
..«j *tt *?!*••'*■*'*■* *° goneral oiroulation are: the Mvereirn {=., £1\
«Mtt#Wl.»6^ereign^- 10«.), made of gold; the crown (-.5..), tfie fcalf-'
*My*J-^(W)^ the io.-in (- 2..), the shilling, the aix-peace. the^our peno.,
SKfr^UST*?*^' ' ^'^^'P'^^^' "»" haJi-penny, end the far-
fc Ifc* gUtodfad gold eeia of Inland ii 11 parts /jure gold and 1 part '^Uoy
j^^^ ^ ■ »" \f5 • "" / 1 — --»..-. aim u parw (-1, ;^
■W^ a^pyw/ M foaee, la eopper coin, wotgh a pound avoirdupoia.
rr. Unitw Statu Mon£t ( t
f RBNCH MONKT.
Ill
C«l.ada u,„„,/; "l°'«l »■ '»lue to 80.188 Do,„i„i„„ of
TABLE.
}0 roillimes make 1 oentini.,
centimes " I deoime
fr ,^ '°'^**^""«^ '• 1 franc.
_, OOMPAIIED.
•4 «(•«"'■ I centime
1«.
WEIGHTS.
D. C.
I0.00018«.
*0.00I86.
«0.186.
8Calo8 of weight are usedTZn °'"' ^^"^'^ standard. Three
tain, and tho'^Uniid S ates" ^^ .^S'a 'l.^^"^-'^' ^^'^^ «'• -
d"po»s. "'*'' ^^^- • A roy, Apothecaries', and Avoir-
^- Troy Weight.
TABLE.
24 grains (er. ) kiaIt. i
20 pennywdghta * J'"7''''°'^'' ^"*- "«• '*«*•
12 ounce*. « i °""*'5' o«-
I pound, /ft.
'f- 1 = 30= 480."
1 = 12 « 240 = 5760.
WoiBa— 1 ©iaoaond*. eto.. ara ••i.k.j u
A era. w.igh.4^„H« ^o/^^^r* ' '^ •^'^' ""*>««<-« .f a oar.t
-i. in .peaking .f the purity >f Im . ^^ ^
«• A T«v p,«i i. ^, J*]r 3^^^^ ^ ^ ^^^^
( .
116
II. APOVHEOARIEri' WeIOWT.
1S>4. Aiiotbi-c tries' tUTeight is used b^
physicians in niixiti- medioines; but modiciries,
are bought and sold by Avoirdupois weight.
TABLE.
ipothecaries nnd
in the (juuiitity,
20 grains (gr.) make I scruple, sc. or i.
3 acruplcH <• I dram, dr. or s.
1 ounce, oz. or 3
Ik.
I
8 dranifl
12 ounces
1
12
n
41
1 pound, lb. ur lb.
ir.
I
8
i^6
1
3
24
288
fr.
- 20
= 60
= 480
= 5760
m
ril. AV01B.'»DP()I8 WeIQHT.
-«5. Avoirdupois Weight is used tor all the ordinary pur-
poses of weighing.
16 drama (dr.)
16 ounces
25 pounds
4 quarters
20 owt., or 2000 lb«.,
TABLE.
make
n
«
1 ounce, OM.
1 pound, lb,
1 quarter, qr.
1 hundred weight, cwl.
I ton, T.
r.
1
curt.
1
20 :
qr.
I
4
80
lb.
1
25
100
2000
oz.
1
16
400
1600
32000
dv.
16.
256.
6400.
25600
512000.
NoTt — The long or grot* ton, hundred weight, and quarter, were formerly ia
oommon use; but they have now fallen intodiiuse am»ng merchants in Crntid*
The Custom-Eouses continue to use it. Farmera and others weigh still some few
trtioles by the long tan.
LONQ TON TABLB.
28 lbs.
4qr. = 112 1k.
aOewt. = 22n
miike
it
I
quarter, marked qr.
hundred weight, ♦* cwt.
tvn. " T.
OOMP
1 pD«nd
1 OQBOe :
K V 4BLB or WBI0HT8.
'!&*:/. ApothaoMict'. AToirdupoU.
6760 grains, = 7000 vubii.
480 " — A9W t^ ,.
■■ 6760 grains,
480 "
irs
480 " xs 480 " E 43r.6 "
VawtdM, IB 176 pMiBda, = 144 poands.
MKASU'KES.
or ^mounufaSatS^^ dimension, oapaoitj
standard. It majt 'o^r v ZfT^. •"'^^^^'"^ ^ «ome^fixed
•res <>f J^-tenaionf and'Z'L'o" Capacit;:"° °'--«-^^^«-
*'^'^''^*''*' ®^ EXTENSION.
thick,.I;.'^'^^"«^«'» »^- ^'^^ di-nsion«- length, l^eadth and
^ A Sol.d or^BodyhLYhrerd.- ''"'"'''" '^""^'^ ^"^^ breadth.
ihickne.8. "^ ^^''' d.mens.or.s- length, breadth, and
I. Linear or Long Measure.
or Ztce!""'" " ^°"^ Measure, is used in measuring line.
I incV (fn.)ss
12 inch's
3 feet
H yd., or I6i ft.
40 rofis
8 furlongs, or 320 rod.
•^ in Ilea
69J miles (nearly)
attv degrees
TABLE.
0.3363 French inch,
"lake I fo.jt,
1 yard,
I rod,
1 furlong,
I mile,
I league,
it
(t
u
«
«
u
u
yd,
rd,
fur.
mi.
lea.
J degree'on the equator, rfS' or •
1 great circle of the earth. '
mi.
1
1
8 :
rd.
1
40
320 :
¥d.
1
220
1760
A
1 =
3 =
16i=.
660 =
6280 3
in.
12
36
198
7920
63360
.'?•'
F-TH
■■! i;
n«
MBASUBS6.
Sotn.—l. For th« purpon «f mauuriog oloth u4 other goodc soU W ife^
JMrM^'/T'u" *"^'*"^ '°'" '"''^•«' '■°"'*'^»' «'«»»»'»•• "»<» ^i«u*«U« fl*
oia table of oloth measure is practically obsolete.
1 f^i.^° ^Miners' Measure, 12 lines make I Mohj4 inches, 1 hand: *5fo#«,
1 lathom; 120 fathoms, 1 cable-length ; 7i cable-lengths, 1 mUe; X of a <i»«i»,
of the oircumference of the oarth, 1 knot, or geographical mile, equaJ to*M
statute miles. ^ "
3. The length of a degree of latitude varies, being 68.72 miles at the «4uM«ir
B8.9 to 69.05 miles in middle latitudes, and 66.30 to 69.34 miles in the mW
regions. The mean or ayerage length is as stated in the table. A degr-w^
longitude is greatest at the equator, where it is 69.16 mUes, and it «»di*««*
dooreaaes toward the poles, where it is 0.
Table of the old French Linear Measubu.
1 line =
12 lines (<. )
12 inches
6 feet
3 toises
10 perches
84 arpents
1000 French feet
0.089 Engl. inch,
make 1 inch, in.
" I foot, Jt.
1 toise, tu.
1 perch, per
I arpent, arp.
1 league, lea.
«
n
H
1068 Engl. feet.
NOTM.— 1. The French linear measures are in frequent u'« in the Pnefaaa
of Quebec. ^^
i;i'^^''T.^°'^*^^''^°='^^^**'^"«'-f««*''''"* t'je B-renoh league of C«*«<<«
308.16 Engl, ft., or 268^ French ft.
Surveyors' Linear or Long Measure.
I??- ^ Gunter's Chain, used by land survejora, is 4 roth
or be feet long, and consists of 100 links.
7.92 inches
mi.
2.^
4
10
8
fur.
1
8
links
rods, or 66 feet,
chains
ftirlongs
TABLE.
(in.) make
a
it
<«
<t
link, /.
rod, rd.
chain, rh.
furlong, fvr.
a.
1
10
RO
1
4
40
320
1 mile,
I.
1
26
100
1000
8000
nn.
in.
7.W
198.
792.
vno.
II. Square Mbasttrr.
900. A Square is a figure bounded by four equal Ums
perpendicular to each otker. Tt is the Unit 9/ M^ntur* fer '
■■UVBM,
IK
•^
'Kr
II
d
— _
m
•
The squar. in the margin ii called tkrmi fmt
^h^Tm^n' '' " *••''• .''«* °" ^^""^ aide. B "/'S
the smail squaree, within the large square, re-
preaenta X.q^arefoot. or 1 foot fqml. %Z^
thore are 3 square feet in each row, and 3 ro^Js
inil?#«T"' '^T ^r. 3 times 3 square feet
equal to 9 square feet in 3 feet square. Hence
3 ft. = 1 jd.
TABLE.
1 «q»are inch (sg. in.) = 0.8767 French inch
U4 squar. inches make 1 square foot, .^X
ffq. yd.
iiq rd.
30^
40
4
640
square feet
square yards
square roda
roods
acres
<i
I square yard,
1 square rod,
1 rood,
1 acre,
I square mile,
R.
4.
sq.
wit..
R.
. A 1
sq.vii. 1 = 4
I SB 640 = 2560
»q. yd.
sq. rd. I _
1 = 30i =
40= 1210 =
160 = 4840 =
sq.ft. ^
9 Z
10890 =
43560 =
sq. in.
144
I29(;
39204
I5tiSl()0
6272640
.02*00 =3Cm0O =278784°:;' =40,Sl:
TABLE ot THE OLD FRENCH SQUAIiE ,„.;,A,,URES
I square JQcb (.}. in.) . 0.007921 Enel fooi
U q,..r.,„ch« make }.q„ar. foot, 'trfi.
36 feet
9 toiees
100 perches
iotjv arpcnig
it
H
U
(S
1 square toine,
1 square perch,
1 square arpent,
1 sq'uare league,
^"^^S:::it±'^,!^: work a. fbllow, vi.
sq.ft.
■s^. to.
sq. per.
sq. arp.
sy. L.
the square of 100 2quare'feet:'brXKl*t'."^^^^^^^^^ ■• ' ■
glaiingand stone-
r,"a< "J "ii: oquBi'e yards: floorinir rini»;n„«;«™ ?' "■""«• »>'u paper-
the square of 100 Square feet j' brX gC -/Sru^aVrL"*;', "'^i*"^'' '"'"« ''^
by the .quare yard, and by tie .quare of foi squZ f^'Jt^ '^' ^°»'"'' '"^cks.
1 I
f I
»j::^'i,iiiaiae^--.T„'i;;ij£!^_.7.^2.v:?^'"
1^ 1-
ISO
MIASUftBS.
Ih. w.alh:"'*'" '"°«'" "™ °^*'"'»»«'l 'o «-" 1 -quare. being laid i i..h„ to
surveyors' SQUAttE MEASURE.
TABLE.
626 square links (_tq. I.)
16 poles it
10 square chains u
640 acres «
36 square miles (6 miles square) "
make 1 pole, p,
1 square chain, aq. eh.
1 acre, A.
1 square mile, so. rnu
1 township^ '/p^
mUe oflandie also called a""«.-^' ' "^^ «"'°« '"'° ^""««' ^ 8quai«
III. Cubic oe Solid Measure.
-olH u^^^^ Measure is used in estimating the contents of
solids^ or bodies ; as timber, wood, stone, etc.
nf ??*^\ p?»*ents, or Solidity, of a volume, is the nun.ber
of times It contains a given unit of measure. «numDer
tl,P^.™^-^'T"''°5,?''''''*'"P''*^"-«<^"di*y«'-e always taken in
the denominations of linear measure.
If each of the sides of a cube is 1 foot, it is called a cubic foot
fiJn^'' ■|!"V:l^ °'?"'° '•opresents a oubio yard.
Since each of the edges of a cubio yard is .rfeeL
•uch of Its faocB will contain 3 times .3 equal to 9
«qu are feet. If, from one fane of this ou be, wo cut
oflfa p.Goe 1 foot in thiokne... wo evidently hare
9 »oUd/ee(i and as tho whole block is 3 feet
tmck, It must contain -i fimoc o _ ot . i; , « .
Henoe, " " "' '"'*'' ^°^^
1yd.
^flnd the $oM contents of a cube, multiphj its length bmrdth
«md thickness togethc, ^ • t
MEASTntm.
121
1728 cubic inches (eu. in.)
27 culiic leet
40 cubicleet of round timber, or )
f<? " " "hewn '« i
lb cubic feet '
8 cord feet, or i
128 cubic feet t
24| cubic feet
TABT.l.
"lak-o 1 cubic foot, cu.ft.
Ic'ibicjard, cu. yd.
1 ton or load, J\
I cord foot, cd.Jt.
1 coni of wood, Cd.
n
u
u I I perch of stone > p .
( or manonry. | ''^*
1728 ('ubic inches
21(> c, bic feet
1000 French cubic feet
iO(»0 cubic toise-i
TABLE 01- FRENCH MEASURES.
make 1 cubic fool, cu fi
i toise, cu. to.
" 1218. 186432 Engl. oi)b. feet.
■• "J745. 491456 cub. yd.
th^i;;.^S!j::i:'];:^«^--r;-i^ freight b^
.tc.,of s.ffi'e':p„';/,;;r/u:.t. ''"Brir*"°« ^"S'^'''^"-' '^-".
mit.ng their work by oubio me Jb««T Bn«l'l»yers and masons, inesti-
wallsofhouees.eelli^^rflto h,?? I!;- ^*°u *''°^*°ce ^o"" '^e corners of the
•Btire length of thrwdlo^tbeoJwl™''''' '''"'' ''°^' ''^ '^^ y-'. that i' the
ditn^Sra'a^re'^^^m^^'iCu'^^^^^^^^^^ and embankment., take the
eomnutation« are made inlet n 1 SI. Ti"""^ decimals of a foot. The
yards. In civil enginoo W thH /il ^ri'''^^ •"""' "" "**"°''^ *° *'"^'<'
e«a.ationsaBde;,fb..nk"f^tsaVefitli;;tluo^ "'* '" "'''■''' •'^"™''*«« '<>'
~LJ;;^fc^^™rCa5^;^!or^ir;rnn. or tVei,ht,„g. ^ of the solid
that will make 36 foot of hewn or sawed dmhL- " 'T'm^ "' ''^^'''S- '^•'">'' '"^ '°g
by measurement; but its mrket 'a^e k - .^^^ ** ° "''''' ^"^^^
•awed ti.uber. Henee. the cubic content, ,?fi^« f '^""'/" ^^°"^'° ^''^ «'' '>«^" «'
timber, ns estimated for marked are irfentlfaf "^'"°"°'^ '^"'^ *^ ^'^«' "^ '^«'^''
«>ld- by ^hlttir^tVS':::^^^ ''•""^"•'•^- "^^ "- 6--a>'y bought and
aej .td'';ke;lr;'e'itSrnrs*^!st^^^^ '.f^''^' "^ '''^ '-'-" o^ th.
ATolfdupois. ""• '* ^•l"'*' '" ^«gbt to 62i lbs. or 1000 oi.
MEASURES OF CAPACITY,
nifies extent of space. "^ "liferent unit«. Capaaty Big.
two .IMMS. Mtmmre. of L.y^nrf, and Jf««vr« «/ Dry SuhHan^
i V , - .^P
Mil
riiiHi
■"— ''"imTrr"'"-"
122
inBABtniRs.
I. Liquid Measure.
208. Liquid Measure, also called Wine Measure i« nnw
used for measuring all kinds of liquids. ^'^easu.re, is now
TABLE.
4 gills (gi.)
2 pints
4 quarts
31 i gallons
2 barrels
2 hogsheads
2 pipes, or 4 hogsheads
make
tt
1 pint,
I quart,
1 gallon,
barrel,
hogshead,
pipe,
tun,
tun.
1
66/.
hhd, I
pi' i = 2
1=2 = 4
= 2 = 4 = 8
gat.
1
63
126
252
[j =
(ft.
1 ^
4 =
126 ^
252 =
504 =
1008 =
Ft-
I
2
8
252
604
1008
2016
pt.
qt.
s^al.
bhl.
Mid.
pi.
tun.
gi-
4.
8.
32.
1003.
2016.
4032.
.'-■064.
2o1;*S''«»«'°Tk*"^''°'u*'y!''®^*"''"5 "'"letimes, howerer. in casks of 6 10
20 gala. etc. The beer barrel contains 36 gallon,, anl the hothead! 54 gallon.:
II. Dry Measure.
aOSI. Dry Measure is used in naeasuring articles not liaaid
M gram, salt, fruit, roots, &c. ^ '
2 pints (pt.)
4 quarts
2 gallons
4 pecks
36 bushels
1
Imsh.
1
M
pk.
1
4
144
TABLE.
make
u
n
u
II
gal.
I
2
8
288
1 quart,
qt.
1 gallon,
gal.
1 peck,
vk.
hush.
I bushel,
1 chaldron,
ch.
qt
pt.
1
2.
4
8.
8
16.
32
64.
= 1162
= 2304.
»a.-»«j«i<iS(ji!lo»;. *,^v
viAsuftsa.
MEASURE OP TIME.
60 seconda (sec.)
60 minutes
24 hours
7 days
4 weeks
365 days
366 days
12 calendar months
100 years
Table.
make
tt
1 minute,
1 hour,
I day,
I week,
1 lunar month,
1 common year,
1 leap year,
I year,
1 century.
N«. of months
The calendar year is divided as follows :-
2
3
4
6
6
T
8
9
10
II
12
Seasons.
Winter,
Spring,
Summer,
Autumn,
Winter,
Names c •• months.
I January,
( Hebriiary,
(March,
SJune,
July,
August,
( September,
< October,
(November,
t)ecember,
AbbroTiations.
Jan.
Feb.
Mar.
Apr..
May.
lun.
July.
Aug.
Sept.
Oct.
Nov.
Dec.
min.
k.
da.
wk.
IIIO.
yr.
yr-
C.
No. of dajrg,
31.
28 or 29.
31.
30.
31.
30.
31.
31.
30.
31.
30.
31.
— ^*"""> uec. 31
iii^22
&SSB^^S!Sss^^^m^:,^ '
124
mBAmiwu.
V •
2. Th« J«<io»» Ttar, lo oalled «rom th« calendar instltnud by Jnllni CMsar,
•ODtains 3fi5i dayi, as a medium ; three yeara in succession containing 365 dayi,
and the fourth year 366 days; which, aa Roinpared with the true solar year, pro-
dnoes a yearly error of 1 Im. 10^^^ sec, or of 1 whole day in about 120 years.
3. The Giftforian Year, or that instituted by Pope Gregory Xltl, in the year
1682, and which is nnw the Civil or Legal Year in use among the different na-
tions of the enith, cwiitains 365 days for three years in succession, and 368 days
for the fourth, exoptin;/ centenniril years whose number cannot be exactly di-
Tided by 400. The Gregorian year gives an error of only 1 day in 3866 days.
4. The eivU day begins and ends at 12 o'clock, midnight. The dutronomieal
day, u?eu by astronomers in dating events, begins and ends at 12 o'clock, noon.
8. In most business traosaotions 30 days are oalled 1 month.
TABLE
SHOWING THK NUMBIR OF DATS FROM ANT DAT OP 0N« MONTH TO THl
SAME DAT OF ANT OTHER MONTH IN THIC SAME YEAR.
VROll ANT
BAT OP
TO THB 8AM« DAT OF
Jan.
365
Feb.
31
Mar,
69
Apr.
90
May
120
June
151
July
181
Aug.
212
Sept.
243
Oct.
273
Nov.
.304
Deo.
334
January
February
334
365
28
59
89
120
150
181
212
242
273
303
March
300
33/
365
31
61
92
122
153
184
214
245
275
AprU
May
2V6
306
3S4
365
30
61
91
122
153
183
214
244
245
2Vri
304
335
365
31
61
92
123
163
184
214
June
214
245
273
304
334
365
30
61
92
122
1,53
183
July
184
215
243
274
304
335
365
31
62
92
1 \3
153
August
lo3
184
212
243
273
304
334
365
31
M
92
122
September
122
153
181
212
242
273
303
334
365
30
61
91
October
«2
123
151
182
212
243
273
304
335
.^65
31
61
November
61
92
120
161
181
212
242
273
304
3;;4
.■^65
30
. December
31
62
tfO
121
Ul
182
212
243
274
304
335
3<6
For example, to find the number of days from April 4th to November 4th w«
look for April in the left vertical column, and November at the top, and, where
the lines intersect, is 214, the number sought. Again, to find the numberof d' vs
from June lOth to September I6th, we find the difference between June 10th and
September 10th to be 92 days, and add 6 days for the excess of the 16th over the
10th of September, so we have 98 days as th ■ exact difference.
If the end of February be included between the points of a time, a dav must
be added in leap year. j '^ •><,
When the time exceeds one year, there must be added 305 days for each yea*.
CIRCULAR MEASURE
211. Circular Measure, called also Angular Measure, Is
used principally in surveying, navigation, astronomy, and geogra-
phy ; for reckoning latitude and longitude, determining locatfoaa
of places and vessels, and eomputing difference of time.
MI801LLANROIT8 TABL18.
12ft
212. An Angle i$ the differtncc of direction
of two lines which meet at a point; thus, A,
B. (!, is an ;tii.j;le. The lines are called the
sid w of the angle, and the point where they
meet is called tlio ' /
V.
Deo.
i
334
i
303
j
275
i
244
i
214
i
183
i
153
i
122
L
91
.
61
»
30
)
3«&
2i:$. A Circle is a plane figure
bounded by a curved line, all the parts
of which are ecjuallj distant from a point
within called the center.
A circumference is the curve line which
bounds a circle, and always contains 360
degrees.
An arc is any part of the circumference, as C D, D E.
Tho are within the sides of an angle whose vertex is on the
center of a ciicle is the measure of the angle; thus, the arc C V.
IS one fourth of the circumference, and measures the an-'leE B C
which contains 90 degrees. "^ '
TABLE.
60 seconds (")
60 minutes
30 degrees
12 sigoa, or .360°
0.
1
■.
1 =
= 12 =
1
30
360
make 1 minute,
*' 1 degree,
" 1 sign,
" 1 circle,
»
1
60 =
1800 =
21600
9
o
s.
c.
60.
3600.
108000.
1296000.
of S '■m^aT'^X''-"' "if^' ''"^''' '' °"<'-fo"E'»» of » oiroumferenoe. or an m
01 «()u ; aa A U. 60" is called a sextant, or I of a oircle.
12 units
12 dozen
24 sheets
20 quires
MISCELLANEOUS TABLES.
COUNTING.
12 gross make 1 great gross.
20 units •« I 8core.
PAPER.
make 1 dozen,
" 1 gross.
make 1 quire.
** I ream.
2 reams
5 bundles
make 1 biuidle.
" 1 bale.
BOOKS.
A sheet folded in
2 leaves is called a folio. i 16 leaves is called a IGrao.
4 " " aquarto, or4to. I 18 " « an 18mo.
8 <♦ anoctavo, orHvo.i 24 " '< a 24mG
I* " " • 12mo, I 32 " « » 32010.
lU
T«i mTMQ arsTSM.
THE METRIC SYSTEM OP WETOHTS AND MEASURES.
The metric system of woi>ht8 and measures-so called bpcaase
'^^'''%]'^\--^' ^rom ^.hloh the other units of the sptem
whether of length, area solidity, capacity, or weight, are derived
--originated m France m 1790. It was determined and established
as foUows : a very accurate survey of that portion of the terrestrial
meridian or north and south circle, between Dunkirk in the
Wthnf ^T°'"'">''''^^''°'^ ^^'' measurement the exact
hetuatoVtotr' f ^^V'^*"^ "^"^^^'^' ^^ *h« distance from
Dart of ?M, ! "°/*^ P"'"' ^"^ ^^"^Puted. The ten millionth
Ffo 7 i ?'^ V^ denominated a metre, and from this all the
standard units of measure and weight are'derived and deLm ned
t1,r? r' 'iJ '^'^"^ ^'« ^•^^"y ™^de the only le4l sZem
Mooted W 9°' • ''^'r' ^" ''''' Since th'at time, Thas
Deen adopted by Spam, Belgium, and Portugal, to the exclusion
of other weights and measures. In Holland^ other weights Tre
used only m compounding medicines. In 1864, the Iv t'em wis
egahzed in Great Britain ; and its use, either ^s a whole oMn
C/^t P'''''^"' been authorized in Greece. Italy Norway
Sjreden, Mexico, Guatemala, Venezuala, Ecuador UdtedsTates
fn mt^; ^--1' Chili, San Salvador and Argendn RepubHo
In 18b6 the use of the metric system of weights and measures
was authorized by Congress for the whole of the United States
TABLES AaTHORIZED BY CONGRESS OP THE UNITED
STATES.
MEASUHE8 OP LENGTHS.
Metric Denominations and Values.
Myriametre,...
Kilometra,
Hectometre,...
Decametre,. ...
Mkthb,
Decimetre,
Centimetrs,....
Millimetr*, .....
lO.OttO metres,- .
1,000 metres,-..
100 metres,....,
10 metreSi^ .,
1 metre, ,
^^ of a metie,
y^ of a metro,
Equivalents in Denominations in use.
6.2137 miles.
0.62137 miles, or 3280 feet, 10 inches.
328 feet and 1 inch.
3'J3.7 iQehc!».
39.37 inches.
3.937 inches.
0.3937 inch.
U.0394 inch.
TH* Miraia stitkk.
HRASURRS (.p SCRTAOM.
127
Motrio Denominations and Values.
Hectare, ..
A»«,
Centiare,.
EquiyalentH in Denotninationa
in use.
10,000 squaro metres,
100 gquaro metres,
1 square metre, I I55o"8qVa"reinchei'
2.471 aores.
11'.».6 square yarda.
MEASURES OF SOLIDS.
Metric Donominations and Values.
Decaatere,
Stkrb,
I>eoist«r*,„. ...
10 cubio metres,
1 cubifl metre,
BquiTalenta in DenominatioBa in
DM.
13.079 oubio yards.
0.2759 of a cord of wood.
100 cubic deoimetrea,. 3.63144 cubic feet.
Mf:ASURES OF CAPACITT.
Metric Denominations and V»l
ues.
Names.
Kilolitre, or atero,
iieetolitre,.,,
Decalitre,
LtTHB,
Decilitre,
Centilitre, ....
Millilitre,
No.of
litres
1000
100
10
1
1
TU
Cubic Measure.
Bq-iTalents in Denonrioatione
in use.
Drj Measure.
1 cubic metre,
jJjj. of a cubio metre,....
10 cubio decimetres,,.,.
1 cubic decimetre,
^ of a cubio decimetre,
10 cubio centimetres,
1.308 cubio yd
2 bu. 3.35 pk...
y.08 quarts
0.908 quart,..,.
6.1022 cubio in.
0.6102 cubio in.
Liquid or wine
measure.
1 cubic centimetre,. ...„jo.061 oubio in..
284.17 gallons
-'6.417 gdllona.
2.6417 gallons-
1.0567 quarta
0.845 gill
0.338 fluid 01..
0.27 fluid dr...
WEIGHTS.
Metric DenominatioM and Val
ues.
NMaea.
Millier, or tonneau,.
Quintal,
Mjriagramme,
Kilogramme, or kilo.
Hectogramme,
Decagramme, «.,.,
GIkaiqik, ,
Decigramme ,
CantigraBUBe, ......
MilligranaM,.^...,
Number of Weight ofwhat quantity of
grammes, w.-vter at maximum density
Equivalents in De-
nominations in nse.
AToirdupoia weight.
1,000,000
100,000
10,000
1,000
100
10
1
fir
TffTT
••••••(••
1 oubio Miecro,.
1 hectolitre, ...
10 litres,.
1 litre, ^...,
1 tlet'ilitre. ,„,
10 cubic centimetrefi,
1 cubic centimetre
^lyOfa oubiooentimetro,.
10 cubic millimetres
1 aubio millimeb'e,
2204.6
220.46
22.046
2,2046
0.3527
15.432
1.543S
0.1643
0.0164
pounds.
pounds.
pounds.
pounds.
ounces.
ounoe.
gr. Tr. W.
grains.
of a griUn.
•fa grain.
^n
( "i-
m
TfIB MBTRIP STSTKM.
MKAfiiraRS OF ANqLBM.
'M'V; rienominationfi nn,] V;iluo!>.
EquiTalenta in Denomination* in we.
NOMEf^CLATLTRE AND TABLES
W^^^ V;iue,, Timet anf^^"^ "'" ^"''^•''' ^'''P««'^'«'S
T<«^ i* fhe same S m" • ^ - "'^^ ^'■''- '^^'^« ^^^lo fo
• .J^,r,.l ..aie. In iach of X .'^ m"*;-''' r *'' «°"«t^"°ted upon
««i^ i« princVara J '^t'dti;:;:" -^lif -.-Potions of
»r# «lM? »t^/y« which i«.f>,oK/.!,- -^^^ principal units
dirmly fmrr it The two filuo^ ''^Vf ^f™' *"d those deriveu
i^ Mm the menrrr "''"' ""^''' ^'^^''^ «^°"'^
I •!' Tu'"°'P*' unit of lengths.
h M*TRR, ... J ^" ^ '** ^*«^ o^^he metric system, and near) v
' • < one ten-mi, honth part of a quadrani
^the earth's meridian.
.•<■ Equivalent, 39.3708 inches.
n. Am J .i* ?""<^'Pa^ unit of surfaces.
' 1 ^- ^ '"^^''^fe whose side is ten metres. '
( ^. Equivalent, 119.6 square yards.
III. Stbrf I i' a'"'"*:' ^*' ""it of volumes or solids.
»T.RB, .... j 2. A cube whose edge is one metre.
' 'i- i-quivalent, 1.308 cubic yards.
IV, LiTRi,.
7. WK
'AHifR
'» • •
f 9' ^""•''P'' ""'t of capacities.
I -i. A vertsel whose rolume is equal to a cube
1 q T. *''^?«^ ^'%« '« one-tenth of a metre.
Equivalent, .'JOH quart dry measure, or
k 1.0567 quarts wine measure.
/J- Principal unit of weights.
I -2. The weight of acul:>e of pure water whose
ed£r*» ia ni nf .^ .^-i.
o m, e^ge'8-01 Of a metre,
d. 1 he water must be w
4° C, or 39.2° F
eighed in a vacuum
4. Equivalent, 15.432 g^ns,
CO
H
Hi
D
o
TWi MFTRIO 8TRTBM.
12f
CO
Eh
t— (
D
> i
<
Id
O
1.
Q
a
o
o
n
en
u
'
"'to tenths, hundmithfl. and tii.iusaii.ltli.s.
Z^^T^y con.sMj.ri„g as a u.ut' to,. ,i,„e u
time" each of r'hl""' ' •''"r'*"^^ ''"'^-^' ^'"^ '«" ^^»«»'^^»d
wmuM, eacii ol the principal unitf.
The na.nea of derivative units are formed bv
attaching a prefix to the name of the princi-
S.nT* ^\T- "'''!'''' ^''^-^ "'■'^ ^'"'^^'J. vvi.ioh
indicates their relation to the principal uniu
^'M^r'^i""'"' ?"'' thousandth, contracted
M^i. je^am;,/e MiHilitre ^ ^^ of a litre
8 miUilitreH = ^^ of a htre.
^*centr''''i'?l"''p''"- *^"°J'edth, contracte.^
cenu. tux., Centiare = ^^tt of an ar*. • 4
centiare8 = ;j^ofanare. ' ^
3. Decivims, tenth, contracted deci. Ex De-
raeTrr^" = i^ »»etre ; 3 decimetres L ^
a.
•r: tn
* £
III
S s
-2
09
a
* g
oft)
CO '^
c «
c c
i
s.
'1. Deca, ten. Example, Decametre, = 10
metres ; 5 decametres = 50 metres.
2. Hecaton, one hundred, contracted hecto.
7<^r»^'f''''^'''=^^^^'^^«'^' 7 hectolitre*
= 700 litres.
a, I.*,
3 o S ^ 3. Kilioi, one thousand, contracted kilo. Ex
2"^ Kilogramme = 1000 grammes.
*■ iKn' f^" '^^"'^"^^ ^'^•' Mjriastere =
10,000 steres ; 3 myr asteres -. 30,0U0 steres.
^' J'JIm '" ^^''^^"d "'yria, and the o in hecto
I, and kilo, are dropped wh«a prefixed to are.
"^'Ifniri"' f^^f'"^ constructed upon a decimal scale, ten
The facts in the preceding views being mastered, the tables can
be constructed by the pupil at sight. For exampk The „Imc^
of the den.atiy« units are formed by attaching the seven prefi^e^
c -
K * S
11
t ! r
i iJi
I ul
i
; f
I! f
180
THB MRTRTO STSTRM.
in their order to the principal units of the tnblee. The order of
pragres«,on bo,n. ten, tho table of cnpa.itio,, will be written TZ^
lOMillilitres =1 Centilitre,
10 Centilitres = 1 Decilitre.
10 Decilitres = 1 Litre.
10 KiloiitroB
10 Litres
10 Decalitres
10 Iloctolitres
I Mjrrialitre.
- 1 Decalitre.
- 1 riccfolitre.
= 1 Kilolitre.
^.tit' .^'''^'^"' ^'"^^^^^^^^^ are presented to-
gether in a convenient form in the two following tublea :-
TABLE OP SQBMlJLTrPLES AND PHINCIPAL UNITS.
Names of Units.
PREFIX.
BASE.
10 Milli.
Equal
1 Centi-
10 Centi-
Equal
1 Deoi-
10 Deci-
Equal
1 Principal Unit.
10 Principal Units
Equal
IDeoa.
' Metre
Are
• Stere
Litre
Gramme
f Metre
\.'.
■ Stere
Litre
^ Gramme
' Metre
Are
•I Stere
Litre
. Gramme
r Metre
Are
Stere
Litre
{ Gramme
PaoNnifoiATioir.
Mill'-e mee'-ter
Mijl'-e-ftre
Mill'-e-st«r
MiU'-e-li'-ter
Mill'-e-gram
Sent'-emee'-ter
Sent'-e-Are
Sent'-e-stir
Sent'-e-Ii'-ter
Sent'-e-gram
Des'-e-mee'-ter
Dee'-e-ftre
Des'e-st^r
Des'-e-li'-tw
Des'-e-gram
Mee'ter
.\re
St6r
Grana
Stubolr.
»M
.A
.8
.1^
,M
.A
.S
.0
iM
lA
|8
iL
.0
M
A
8
L
O
THl M»TniO BTRTiM.
TABLE OF MULTIPLES.
lai
N'amks of Units.
PKKFIX
10 Deca-
Equal
1 Hectd.
10 Hecto
Equal
1 Kilo
10 Kilo-
Equal
1 Myria
Myria
Pronunciation.
Dek'-ameeter
Dek'-4re
Dek'-a-ptdr
Dek'-a-li'.tep
Dek'-a-gram
Hec'-to-meeter
Hec'-t^re
Hec'-to-stfir
Hec'-to-Ii'-ter
Hec'-to-gram
Kill'-o-mee-ter
Kill'-Are
Kill'-o-stgr
KiJl'-o-li'-ter
Kill'-o-grarn
Mir'-e-a-mee-ter
Mir'-e-are
Mir'-e-a-8t5r
Mir'-e-a-Ii'-ter
Mir'-e-a-gram
M
Q
2
M
G
L
ABBREVIATED NOMENCLATURE.
-.that the na.o. u^XuTfe^t"^^^^^^^^^
tl-ey should be identical in al! kngLti' "" "'' ^*'"' "^^ ^^^^
1
m
182
fmrn wgMtiK arsTicM.
eosraopolitan in its character: it belong to their hn<ma^» «*
more than to ar.v other. The former, however, is nT^',,^
It ,s evider.t to .Ii, that, for business purposes, he Ion 'n^lf
the metric system are inconvenient, and tha to shoCXf
would prove a great advantage. Efforts have been made t" ir Z
duce short names; but these ofForts have invariably s^c^wS
un versal and ezpressive ch.r.cter, which is of inore T^^Z!
to the business world than their shortness. '^P'^nmm
The only true course which seems to be open, is to ubhrmU^*
the names already introduced, in such a way U to retbT^
peculiar characteristics. ^ ^° ^'^^
Tosecure this, the following plan of abbreviation is 8ugge«t^w
First. Let the prefixes be abbreviated thus ; Mvr kil hl^
dec, des, cent, mil. •' ' '' '****♦
Second. Let the initial letter of the names of the five mind^i
units be used instead of the names themselves, thu : XS
use a capital M ; for are, use a capital A; for' stere a capi^lg^r
for litre, a capital L ; and, for gramme, a capital G. ^ ^ '
♦^ ♦^^''*"^- -J?' *^^ °f ?'®' °^ multiples and sub-multiples, Utm%
to these initial capital letters the abbreviated prefixes' thi^^
M, pronounced kill-em' ; Kil S, pronounced kill-ess', &c
By this method of abbreviation, the elements of ' the orlsimi
TABLES WITH ABBREVIATED NOMENCLATUBK,
Written.
10 Mil M,
10 Cent M,
10 Dee M,
10 M,
10 Doc M,
10 Hect M,
10 Kil M,
MyrM,
MBASUBBS OF LENQTHS.
Pronoun««d.
Millem',
Cent-em',
Des-eni',
Em,
Dek enr
Hect
K
em
ill-em'.
make
it
«
it
«
41
Mir-
em'
I Cent M.
1 De8 M.
1 M.
I Dec M.
I Hect M.
1 Eii M.
1 Myr M.
'ten th««
3 to mtfO'
nportaifl^
iS,
¥■■ mnUO STBTHH.
MEASURES OF 8URPACB8.
1S8
f ritten.
10 Mil A,
10 Cent A.
10 Dee A,
10 A,
10 Dec A,
10 Hect A,
10 Kil A,
MyrA,
Prononnoed.
MiJl-a',
Cent-a',
Des-a',
Dck-a',
Hect-a',
Kill-aV
Mir-»'.
make
a
u
u
u
«
1 Cent A.
1 Des A.
1 A.
1 Dec A.
1 Hect A.
1 Kil A-
1 Myr A.
MEASURES or VOLDMIS, OR SOLIDg.
Written.
10 Mil S,
10 Cents,
10 Des S,
10 S,
10 Dec S,
10 Hect S,
10 Kil S,
MyrS,
Written.
10 Mil L,
10 Cent L,
10 Des L,
10 L,
10 Dec L,
10 Hect L,
10 Kil L,
MjrL,
Prononnoed.
Mill-ess'.
Cent-ess',
Des-esa',
Ess,
Dek-ess'.
Hect-ess,
Kill-ess',
Mir-ess'.
MEASURES OF 6APA01TT.
Pronounced.
Mill-ell',
Cent-ell',
Dess-ell',
Ell,
Dek-ell',
Hect-eir,
KiU-ell',
Mir-ell'.
make
1 Cent S.
< t
I Des S.
« .
1 S.
ii
1 Deo 3.
u
1 Hect S.
tt
1 Kil S.
u
1 Myr S.
lake
1 Cent L.
<(
I DesU
u
IL.
u
1 DecL.
<(
1 Hect Lb
i«
1 KilL.
u
1 MyrL.
Written.
10 Mill Q,
10 Cent G,
10 T)cB G,
10 G,
10 Dec G,
10 Hect G,
10 Kil G,
MEASURES OF WEIGHTS.
Pronoaaevd.
M)ll-ge«, make
Cent-<!;ee',
Des-gee',
Gee,
Dek-gee',
Hect-^ee',
Kill-gee',
Mir-gee'.
1 Cent G.
1 Des G,
1 G.
I DecG.
I Hect G.
r Kil G.
1 Myr O.
> I
13;4 RSDUOTION OF COMPOUND NUMBERS.
REDUCTION OF COMPOUND DENOMINATE
NUMBERS.
214. Reduction is the process of chanrrinrr numbers from
one denomination to another, without alterin-; their value.
Keduction IS of two kinds, Descending and Ascending,
-v»>. deduction Descending is changing numbers to lower
denominations without altering their value; as pounds to shil-
lings prds to feet, etc. It is performed by Multiplication.
>5if>. deduction Ascending is changing numbers tohi<^her
denominations without altering their value ; as farthings to pelioe,
inches to feet, etc. It is performed by Division.
REDUCTION DESCENDINQ.
217. Case l.—To reduce a compound number to hvovr de-
nominations.
Ex. Reduce £45 Is. 8d. to pence.
OPERATION.
£45 7a. 8d.
_20
907#.
12_
10892d.
ANALYSis.-Thore ar« 20.. in £i, therefow,
20 times the number of .£ =, the number of
ehilluigs. 20 times 45 = 9ii0«., to which we add
7»., and obtain <J07». There are I2d. in 1« •
therefore, 12 times the number of shillings equ J
th3 number of pence. 12 times 907 = 1088W
to which we add 8d., and obtain 10892(<. Hence
the following
_ 218. RuLK.— I. Mid/i/)li/ the highest denomination of the
given number by that number of the scale which will reduce it to
the next lower denomination, and add to the product the given
number, if any, of that lower denomination.
II. Proceed in like manner with the results obtained in each
lower denomination, until the reduction is brought to the denomr
ination required.
Ana. 848».
EXAMPLES FOR PRAOTIOK.
1. In £35 6s. 8d., how many pence?
2. In £28 VJs. 8|rf,, how many farthings?
^ I" fp-Vl'*"^- ^^^^*- ^^^*'' ^^^ niany grains? ^n». 85894.
4. In IG:>T. iScurt. Aqr. 19/6. l4oz., how many ounces?
6. In 2'm 93 05 29 l:^ gr., how many grains?
6. In I2rd. Hyd. 2ft., how many feet? Ana. 224.
7. Flow manv in/iliaa ji» '? m't A fiiv •-Jl-i-^ l---» «
8. DiGOarp. 7per. Uo. 5ft., how many feet?
214. What IB tedaotioa!— Hoto mant/ kindt of reduction f— 215. What w r«.
da^ot. o^ d em^ending?- 216. Redaotioa'Lcaading?- 218. JFAa/i. ,Wul. /^i
Ea:.
gal.
ii
112
28
MDUOTION or OOMPOTTNT) NFMBRR8.
136
16. How many cubic ih^t in «? <, j , » ^^*' 34080952.
^0. Hov, manj' pints in lOte. S.L*. 7j„, T^' , '
22-. fnT^'S IS 'LtJ* «'"'<"0"vV.H?bu»h.ls e«h,
2fi TT^I ■ ' oo»^ many seconds ? iln/ 489n94a»'
^6. How many minutes in lUC. IS. l* 1' ? "*' ^^20243 '.
27. Reduce 38tt> 6s 33 l», tolrains.
iti».
Case Ih^To redu^ a dmominate fraction to one of
a lower denomination. ^
gal.
JTff
224
112
28
OPBKATIOH.
Ex. Reduce ^J^ of a gallon to the fraction of a gill.
A»ALTsw.-To redaoe gallons to mllg -•
bcM m the scale. And, since the given num
bens a fraction, we indicate the p^oew m"
m multiphoation effractions; and^Xr fi'a^
celling, obtain ,^. the answe . H „ot the
♦ M
tio^f^ihf:u^}7rf^^^^^ ^-f ^^^ ^-9her denomina-
the giL and thr "o^^ .^Sfo^^:'' --..,,«?,, 6e...«.
8XAMPLE8 FOB PRACTIOB.
1. What part of a farthing is ^-U of a £ ? j . ^
i !
|W
136
3.
4.
6.
6.
7.
RlDUOTfOlf or COMPOUND NUMBBRi.
Kec uce ^Jjyj of a lb. Troy to the fraction of a grain.
Kednce 4-ff of a £ to a fraction of a penny. Aus. Id
Keduce s^f^of a cvvt. to the fraction of an ounce.
What part of a puuul i.s ^-^^ of a ton?
What part of a link ia ^ of a rod ? ^„, «/
Keduce -j-^^^ of a furlong to a fraction of a foot. *
W liat part of a pint is ^f ^ of a bushel ? Ans J.et
Keduce f of | of ^/6. to the fraction of an ounce Troy. "^ '
w imt fraction of a yard is f of ^ of a rod ?
.421. Case III.— 7b reduce a denominate fraction to integers
• • of lower denominations.
Ex. What is the value of ^ of a £ ?
8.
.9.
10.
11.
12.
13.
14.
is;
OPKBATION.
£ 8.' d. far.
?). 3 Q
8 6 3^, ^n«
Ahaltsis— 8 of£l is the same u l
^ =» 8«. 6d. 33/ar. Henoe,.Uie
of
22a. livh^.--.Gonsider the numerator of the fraction as so
•S^^;;j^^;/'^^^^«^»rfe«omtna^ion, and divide the^ 4 the
EXAMPLES FOB PaAOTIOK.
1.
2.
3.
4.
6.
6.
7.
8.
9.
10.
11.
12.
' 13.,
14.
15.
what
, What k the value of
,5rOfa£?
I of a bushel ?
I ofaehilhng?
fofaowt.?
I of a yard?
f of a lb. Avoirdupois?
^^ of a day?
|ofl5cwt.? __ ^
I of 2^ po'inds Apothecaries' weight?*
o?6j toTr* ■**"■ ^*- ''■''• ""'• "* ''■''•■^- '"A'j. '».
I of a Sign? iln«. 12'> 5P 25"!
Jromapiecftof velvfetoontaining Syd. 3gr. I cut 2«rf. 2^1
Vtvt VI ihe wnoie piece did 1 take ? ^ '
Ans. 58. 5d. l^^far.
Ans. Ipk. 4qt. ]§pt.
Ans. 3qr. 2/6. 12o«. 7^rfr.
Am. loz. \ldr.
Ans. Ucwt. 85/6 Uoz. &Ur.
«a». Case IV.— £0 reduce a denominate decimal to integers
V lower denominationik
Kt.
OPKBATION.
^0.628125
20
12.562500#.
I^
6.750000rf,
———J
3.000000/ar
*0 12,. 6|./. Aiu.
BW^OTIW OF OOMFOWD N^K„.
ofa£ to shillings and pence.
deduce 0.628125
137
'"g^S and the refluU^f f.. fH"l'^*'«»^>"■
J. to reduce it J/l'Trl"°S rhr "'"^f '^-^^^
«' 'Ae Uft u>iil he the a«,«,er r?;"^/''''";^""'*'''"- ^^« •«'«!J^e-'
£XA':PLfc8 FOR PKAOTIOt
What is the value of
1- 0.45iofȣ?
2. 0.748 of a bushel?
3. 0.765 ofa pound Troy T
4. (-.7525 ofa mile? ^
5. 0.659 ofa week?
6. 0.217«?
7. 0.876 ofa hhd.?
8. 0.865 of an aor«?
9. 7.88126 acres ?
10. 0.626 ofa fathom?
U. 0.78S75 ofa long ton?
12. 0.R46yofadegi^?
* /!»». 9». Id. 21 far
Ant. ipk. iqt. Ipt. SASHgi.
AnM. 6/ur. ord. 4yd. i/t, '^in.
^*«. 13' 1.2".
Ant. 16CV7/ Sqr. 2/M 2.812.
^^'D^OTION A8C1ND1NO
OPKKATION.
24 ) 78692^r
20 ) 'S2THpm. 2L*gr,
12) 163os. lapuft.
13/6. 704.
IWft. 7««. 18^. 20|T., Jim,
A«ALr8is._24fr..ljH;,.. there-
»". jJj of the number of grains ^
«6«2 3278;,v,,..a.a2V.reSlin.
01 the number of ,M,nny weights • tK "
number of ounoei. ^ of 3278 =
138
■IN
ii
I
RtDUOTION OF COMPOUND NHMBBRS.
ih^^!^' ,?"^«-7-I- ?J^i*^^e the given number hy thM numher of
taZ,u ""^ '""^ '"^"'^ '' '". '^' "^^^ ^''0^'' ^'^^^
n^Lf'^l'^'^J'- ^'t '■"r"''" ^^' ^"'''*'^' ^'"'-^ obtained, and so
ZttXti\l' *''"^^^ '^ '^'- denornination required. The last
ZiTJi, ' ""'''''^ remainders annexed in a reversed order'
^nn oe toe answer. '
Ant. £17 2*. 9rf.
Ana. 4ft) 5S IS.
EXAMPLES FOR PRACTIOB,
1. In 16462/or., how many £?
2. In 90720 pence, how many £ ?
3. How many pounds in 4253?
4. In 78692^^., how many pounds Troy wei<'ht ?
•ach ^,P^y«'Cian who averages daily 5 presc^riptions of 20 grains
•ach,^how many pour.ds of medicine will he use ,n one year, or S8o
: M;Jr2?^^^^^^^^ .t4lV.r- '''''•
10 At ai. ^ I' ^u'' '"*"-'' ^"'^'"'^ ^ ^"••'- 19*«- ¥^- ip<.
11 ' nil ^J' ^"^^ "'"^'' ^"""P 0*0 be bo.ight for $;184?
11. How many francs in $176.70 ? >i«„ Qsn
1 J- S,'''' ""^"^ ^"^y' •" 9^^^o ««cond8 ? ' ^"''^-
20. How many tons of round timber in 622080 cu. in'r '
n.^k ^•J' • *' T*"'i2/?. by 24j?. is 6ft. high and 1 },n. thick. How
2» T^r,if • -^^i '''^u' *° ""'^^- ^^'- ••^'«'- ^''^^^ i
Z8. In 161384 mthes, how mtunj milts ?
-easur^T """^ beergallooe M-e then, ia 1*W. i^;. 2^., wi«,
9A- Sii ^^^i?l^'»""* >"«h««' bow many rood« ? "****■ ^^'^•
26. Reduce 20937 minutes to signs. An$ US l«o ^7-
* ' 4iM. 13/6. tio«.
far.
^1
RBDUCTION OF COMPOUND NUMBBIW. I39
2S». Huw many ^re'^ uf Scafu^ «"'! m.nutefi did ,.he change ?
JO. la 13360128 drams, how many tona?
2S7. Case 11.- To reduce a denominate fraction from «
foir^?/- to a higher denomination, ^
Ex. Reduce * of a farthing to the fraction of a £.
OPERATION.
9 ^
liugs.
I
1
1
ANALT«r8.-There are ifar. io
Irf., therefore 1 of the number of
farthings equali the nnmbor of
peme. There are 12rf. in |,
therefore ^ of the number of
There are 2«.. in ^1, therefore , P*°°^^'i"f '"'»»« ""mber of shil-
ber of ^. Hence i/ir 1 1 x ^t 1 ."" "' ^''"°^^ ^l"*"*
H "^ 12 "* 20 *
£
1
2160
Ah$.
the number of 4;
What part of
I. a pound Troy i8 I of a grain T
^. a pound IP f of a scruple?
i>- a rod is I of a foot?
EXAMPLES FOR PRAOTIOB.
' Ans. rhrd.
4. a iDileisSofarod?
5. a hundreJ-weight is f of an ounce .
b. an hour 18^ of 20 seconds?
7. an acre is I of a, square foot?
a. 6 hhd. 18 i of a quart?
9. 4 days is | of a tiiinute? .
10. a cord of wood is a nile 71 A ]nna 9/> i • u i . ,/' t^^W-
11. a rod is 2| of ^ of an inoL?' ^' ^•^' *"«^' ^"'^ "V^- ^'^e?
2. an acre is ^ of -*, of 9^ square rods ? "*"'• '^•
o. Reduce 9.312/«r. to the decimal of a £. An. £o OflQ*
i4. Reduce 517.44/i!. to the decimal of a mile. ^^®^^-
22». Cask III.-- To reduce a impound number to afractum
of a higher denomination.
Ex. Reduce 8.. 6rf. 2/ar. to the fraction of a £.
QPERATJOX.
8«. id. Ifat. = 410/ar. 41
1^ = WO/or. ~ 96^'
A!^Ai,T8M.-:3yr^uetionofd««ia-
>nate numbers (217), we find 8.. M
ijar. «= 410/ar., and that jEI „ 9^
||«ra^ »»ff - til =
I
ilj:
140
RIDUOTION or OOMTOUMD NUMBSBB.
230. RULK. — Reduce the given number to itt loweet denomi-
nation/or the numerator, and a unit of the required denomination
to the tame denomination for the denominator of the required
/raction. ■*
BXAMPLSS FOB PBAOTIOB.
What part of
1. »£is 10». lOd.1
2. R ton 18 icwt. Sqr, 12/6. ?
3. an acre is 2/4. 20/)er. ?
4. a mile is \fur. I2rd. iyd. 2ft. ?
5. a hogaliead of wine is iHgai. 2qt.1
Qj. a square rod is 144/jf. ]i)^in.'l
7. 2civt. iiqr. is icwt. 2qr. 20/6. ?
8. :■{() dayti is Sua. llh. lOmin.l
9. a bushel is 1| pecks?
10. a pound Troy is lOoz. I'Spwt. 8gr. ?
231. Case IV. — To reduce a compound number to a decimal
• . of a higher denomination.
Eit. Reduce 12«. 9d. ifar. to the decimal of a pound.
OPBRATION.
3.00/ar.
An$. ff .
Ans. ^.
. 4
12
20
9.7500rf.
12.812508.
0.640625£. Ana.
AwALTSia.— Since there are 4 farthingfi
in Id., i of the number of farthings equala
the number of pence, i of 3 = o.75<^
which added to 9d. « 9.75d. There are
12ii. in 1«., therefore, ^ of the number of
pence equals the number of shillings, i
Or, 12«. 9d. 3/ar. = 61 r/ar.
£1 = 960/ar.
= £0.640625, Ans.
of 9.76rf.=i0.8126». which added to" t2«."
12.8125.. There are 20«. in £1, therefore,
jljj of the number of shillings equals the
number of pounds, J^ ot 12.8126 =
£0.640625. Hence, the
2i3S. Rule. — Divide the lowest denomination given by that
number in the scale which will reduce it to the next higher denom-
ination, and annex the quotient as a decimal to that higher. Pro-
ceed in the same manner until the whole is reduced to the dcnomr
ination required. Or,
lieduce the given number to a fraction of the required denomir
natwn, and reduce this fraction to a decimal.
EXAMPLES FOB PRACTICE,
What decimal part of
1. a gallon is '6qt. \pt. 2gi. ?
2. a, week ia bda. dh. 46min. iSsec. ?
3. a mile is 5fur. 35rd. 2yd. 2ft. J)tn. ? An*. 0.V3603219 h- mi
4. a Imehel is Zfk. 6ft. \ft. ?
An: 0.9315gal.
RBDITDT105 9W 0ITE1UINOIK8.
141
6. a ponnd Troy is lOox. \2pwt. \^gr. ? Ans. 0.8864581/6.
0. a fathom is ^%ft. ?
7. a ton is UcwLciqr. l6A5lb. ? Ans. 0.H857257'.
8. 14 bushels IS 0.t5 of a peck ?
r.f.\ ^^]'^"f ^^T* '^''■*^- '^^'■- 20/6. tohundred-weightnand tlie decimal
of a hundred-weiglit, .j,,,. .,,f^ 7
1 7]^k£^'^"*'*4 ^2 ^K<^««'-""a' of a pound, 19». 11 |rf., I d.,. ' i)Jd.', " and
1 ^». bia., and find their sum. Ans. £2.710416 1- .
REDUCTION OF THE OLD CANADIAN CrjRRBNCY
TO THE NEW OR DECIMAL CURllBNCY.
£af. Reduce £72 13 9 1 to cents.
OPBRATION. ANAtTSia.— We malHply
£72 X 400 — 9«snn «.«♦„ ^^ ^y *'"• because each
<Ji 00/- r ,« "^ ^^" or 400 cents; next we mul-
»| = 39/or. X 6 -^ 12 = 16^ " tij.ly 13, the number of shil-
£72 IH 9a = 29076T « '''^'''''' ^^ "*^' b«°'^"'''e each
or $290.7f>l, Ant. f'' '!!'"» '' '^'^u-' /° .l** °'"'* '
«. n/fs. lastly, we multiply the num-
anii ro.fk;„_ u c , ,. . , ber (if farthings in the pence
ejaa^ to l*of /cent *'" remainder by 12. because each farthing Ib
farThinl!'^'* farthing ia equal to ^^ of. oent, ie evident from the fact that 48
anrl n^f r ^Tv.? '^ shilling) are equal to 20 rents ; or 12 fnrihings equal 5 cents,
and one farthing equals^ of a cent. Hence, the following ^
;. ^?*' ]^^^^'— I- M'lltiply the pounds by 400, /Ae shillings
oy ^«», and take five-twelflhn of the number expressing how many
farthings there are in the given pence and farthings.
II. Add the three results together, and their sum voill he the
number of cents required,
III. Consider the last two figures as cents, and the result will
be dollars and cents.
■ i
EXAMPLES rOR PRACTICE.
1.
2.
3.
4.
a.
6.
7.
8.
9.
How many dollars and centa in
£4 3 li? 4n«. $16.62X.
27 16 3^? "
27 16 Hi? Ans. $111,381.
69 15 6 ?
14 8i? /ifw.f 2.944.
77 19 4^? ^
17 16 6|? .In.-.. $71.29X.
18 18 lOi? "
9 8 61? iifw. $36.69^.
10. £16 6
11. 97 3
12. 46 17
13. 121
14. 12
15. 1 12
16. 173 13
17. 91 8
18. 19 11
Am. $66,231.
7
9 U
2 ?
11^?
7^? Ans. $187.62^.
Ans. $49,984
9i? '
4 ? Ans. $694.66i
K ?
4| 7 Ans. $78.27|f .
: :!
I I
142
ADDTTIOlf O? PfiMPOnivn IVTTMBWRfi.
mmwnos of the dkcimal ciiruency to the
OLD CANADIAN CURREN(.T.
ear, K«(|„ce *246.88 to the old Canadian ci.rn^ncv.
<»rBRATION.
20
4Md.
4
Analy8I3.~Wo divide 246.88 by 4.
the number of dollnr. in a pound, and
lVr,T\v ^"' •*"" " hundredth, ofa
pound. We multiply 72 by 20 r24\
he nu.nber of .hillin^^ in a pound, and
a 8h llmg. A-am, we multiply 40 bv
12 tijo number of penoe in k' shilling
and the rrsult ,s U. and 80 hundredth
ofa penny Lastly, wo multiply 80 by
4. the number of farthinp. in a nennv
and the resnlM. 3/W,.. anr20 huodSh^,'
or ^ of a farthing. Hence, the
.^Un^' ^^'l'^---fi"''J^ the given number bi, 4, and thnnotient
EXAMPLES FOR PRACTICE.
tiedttce to the old Canadian currency :—
I, $m.W= Ans. £40 11 6 10.$319.13i. -ins. £79 16
2,
4,
9,
mAd
Ana. 97 16 lOJ
Ana. 20 10
-Ins. 142 5
-<Jn». 231
If
Hh\
44
U. 93.S.04i
12. 601.53 =
13. 293.17
14. 39.06^- Ans.
15. 436.99
16. 152.18^= Ans.
17. 846.071
18. 719.11= Ana.
3A
ADDITION OF COMPOUND NUMBERS.
Ana 160 (
9 15
38 11,V
179 16 6}
IV?**^' ^^^/^'^"' Subtraction, Multiplication, and Division of
a# »f«^ployed for like operations in Abstract Numbers. The
mif *M(^ence arises from vuri/mg, instead of uni/orm scales.
miU \I,lf.\" "'' '""^ °'^' ^''- ^^- ^' '^'- lOrf., £8 Us. 6d,
#!n^1*T'^"~^''1"^ '^"''«° "°**8 of the samedenomina-
i .hf v.^^^/"?' '°'"'^°' ""^ fi"'* 'h« «"°> of pence in ?ha
right-hand column to be 29 pence =- 2.. 5rf. We wr te tbl
umn" of'2n- °"'"T "^ ^''""'J '^"'^ """^ 'l^o 2.. to the col-
umn of shilhngs; the sum of which ia fin., = fo i«!.
fo^^H.'^'io *" '^' ^^*- "°«*" t»»e column of shillinss we
^ to 4
4 in »
IH
61
78
17
28
205
"205"
5 8A
6|
ADOITIOK or 0OU9eVND NUMBBR6.
£.'a:. 2. Add^iTyofaXtof ofaahilling.
143
il
OPERATION.
/5ora£ =
^ of a a. -
1 1
9». 4d.
Oa. Hd. 2^/ar.
10«. Orf. 2^/1?:
Or.
10s. Orf. 2^/ar.
ANALT8is.-We first find the ralueol
each fraction in inteafers of less (ienom-
inations (221), and thon add the result-
ing or equivalont compound numbers.
Or, we may reduce the fiven fraotiona
>?„,,^°'.'l"'' "'" '•'• *»">« clenomination
(-219), then add them, and find the vol-
ue of their sum in lower denomination*.
Ueooe, the following
aae. RULE.—I if any 0/ the number, are denominate frao.
t^omoryanyofthedenonunatlomare mu,ed numbers, reduce
the fractions to integers of lower denominations.
.nnh, ^?-' !?' ""'"*'''? '"^ '^°' "'**■'' ^/'^^ ««^^ denomination,
will stand in the same column. "■"'"w
««iV' ^'^''""'> "'^■^^ ''i* ^^'''^^^ ^?^«.m*««<io», add as in simple
numbers, carrying to each succeeding denomination one f^ as
many un^^ as U takes of the denomination added, to make one of
the next higher denomination. ' -^
EXAMPLES FOR PRACTICE.
(1.)
T. cwt. qr. lb. ox. dr.
" ' 27 U J3
15 15 15
13 12
16 15 11
13 U 13
(2.)
71 19 3
14 13 2
14 13 1 U
11 17 3
13 18 2
127 3 2 U 8
yr.
da.
h.
min.
see.
12
10
i;{
42
27
16
102
18
24
36
19
8
21
54
57
23
13
19
49
48
29
18
2li
58
56
^1
1
If!
(3.)
deg. mi. fur. rd. ft. in.
1« 19 7 15 II 1
61 47 6 39
78 32 5 14
17 59 7 36 16
28 56 1 30 16
20i:
10 II
9 9
10
1
8^ 5 17 14^ 8
i=6
d=4
205 9 i 17 15 2
A.
140
320
111
214
100
25
104
(4.)
R- per. so. yd, so. fi.
3 17 27 y
I
2
3
I
2
30
7
15
36
9
14
3
22
6
1
6. What ia the sum of 20/6. iio^. \^piot 23fi-r
l****--. llo*. ^gr., aad lib. Box. n9U>t.2lirr. ? An
2
T
I
3
4
, - , „ , 10/6. 7oz.
7/w/. 21^r.?4n». 34/6. \oz.
1 5/Jtrt,
I'Spiot,
1 1 1
144
«TT.TaAOTicm o, coim,tm„ ^„,t«ki.
^ ' '^^ ^* *» •» I'fr., 6Ifh I Is 33 2» 3^. *^ '
■^^vii.7fur.lch.2on ^^'' '^^i- «/«^- «^A- Ird. 16/
l2<'36M7.8",and57.3M ^ 25.7'Mr 18 2", IS. 3o^2' 15.5",
, 10. Find the sum of A ofa mi?, i r ^^'- *''^- ^"^ ^^' ^^.S".
i«. find th. .„,„ rfi J* i ^»- r?,,"'*- y- .'•?■;?• 1 1.1J.?. m.
.15. A farmer recei^JeoVt. Jhi-^'J f'r/r A"?' *■' '""S '"» ""W..
£Jar. I
SUBTEACTION OP COMPOUND NUMBERS.
Krom £U 6.. 1,W. 1/a,. ,ak. f ,4 15,. ,^ 3^^^_
OPERATION.
der the S" T"f"'« '^« «"btrnhend «-
dtotn=S£t:ro?i;;a^;r"?-
^/or. from l/«r., we add Irf. or 4; ,/ t«
makin. 9,^. ; and id. fJom loTle ve^ 7d ""1-1' ' '^^ '» ">« » '» the sSh ndj
Next.n.weonnnottakeI5,.fromr wf';.^!^^^^^ '^f. ""^ i° the remainder
IrH^^" .u '^'^'"^•^''''•^■''*.''e subtract i^Sfrnm"^^^;" '^" denomination of
•nd wnte the remainder, ^20. under the column of^f' "* '° ""?'• °"""^«".
^.r. 2. From | ofa mile subtract ^ ofa Airlong.
OPERATION.
|m. =4/„r. 1 7rrf4yrf.0/<. I otn.
-y«r. _ ^2 4 2 1 '5
22^
^n». 3 34
4i
82
ANALTBI8.. \ye perform the
'*™f "?"l»«tk)n M in addition of
denominate fractions, (234), and
hen subtract the lesevalu. from
the srealAr,
3/ur. 34rc<. 4iyd?7;»:8|,„.
Jl. *j„„,„-„„„(,j ""'"""Xl <m<ler ,„,-h. „il,„.
EXAMPLES FOR PiUCTIOE.
,;*; f P' ft. in.
^ ^ 35 171.— 140
5 p . ^36^72 32
,,;o. P„„ ,,„, ,^„,. „^^ .,^^ .„,.^3s. ,«. ^^l>r:.^-
i-i. From 5i66/. tak7l nf u^ ^^'^^ ^o°8- """ ' ^'*'
15. Subtract%;65rw:eU:rnr''l'-o ^^--^^^Ml^./ ,^
-- -"""»««• u.ooy week I'mm •> i „ ■*"*• 4oW. Mp-,,/
16. Prom a hoffah^aw r • ™ ^ *^^'<^k8 34 davs ^ '"
OUtj
^liiiM.Tfi^'''
l4lt
MULTIPLIOATION OF COMPOUND NVMBBM.
PRACTICAL PROBLE]rfS IN COMPOUND ADDITION AlfO
SUBTRACTION.
onl'ol'l^^nl^^^^^^^^ two bou^-M^
have I remaining ? '^ ' ^* ''*''" ^^- -^^^ ^i'*''- ? »^ov M««^
di«.nc, how fa. ar. Z', a^rt" 1^ 4r .%ir' ^'".'^ ^j^l"*
, 6. A man agrees to build 1S6 rd an<J inf> if.; ^' ^ ^^**'
time, he builds 36rrf. 2ft. ^ ^iJoihtr^^^^ ** ^
otherUme, lOrrf. l^/^^^kV mu^r'^JH':: kinT^^-bf^^^^ ** •*
7. A hogshead ofir^ne los^bl Kv J^"' '""'^ '""*'"' ^'^^?
including two leap jiws W^ni nf^!!*"^ an average, for5y*«^
mained? ^ ^ ' °°® «'" °^ '"°« a.^^ayj how muci, ,J
«, Suppose a person was boro Fehvniry 2! mt l^'' ^«*'
anmversanee of hfs birthday will he have ffi on Feb 29 \7uTi^
9 How long has a note to run, dated ADril 23 1870 i 1 *.
payable Dec 9, 1874? ^pnJ ^^J, 1870, and im4«
10. From a mass of silver weighin^z lOfilh « i^" '^■T' '^^'
spoons, weighings/ft. llo^^^z^fsUTaUlrdSrLr
14Fr. : a rase. 7/& IIak i^nw 00 *'• > » lansara, oio. Oo^. I3|^
remain.? ' "^' "''*• '*^- ^^^L' ^Tm"*;^?** unv;rouglu 3^
Howlo7gTa;\LTol^rSt,i^:^^^^^^^^^^
How long, if the time is computed by days ? ^^ ^^^' "^ '^'^ «^ *
^n«. let. llyr. 5«io. 25rfa. ; 2nd. 4130 day».
MULTIPLrCATION OP COMPOUND N[mBJ5m
Ex. 1. Multiply £8 9,. M. by 6.
OPERATION.
£ ». d.
8 9 6
6
write tho M. wder the pence, .nd addfhe £,'. Jt
C fr ."i" Of s»>iling8. 6 times «.. are 64*'.~«Zi
2. aro56».-£2 Iti,. Rewrite the 16# uiidS-
the sh.H.ngs and add tho £i with the prodrt^
we wntound« pound.. Tberrfore 6 tia... <|'£*
. 'CSiH. Rule T Wr,;. ti , .
A7j. 9 wu "''''®''^ these leveral parts.
.>p...„oK. -^2 3,. 6rf. per yard ?
£
iT
-tprod„rtistheanLWe'c
•e «. rf.
6 16 9 = value of 3 bbl.
"'^ 6 = price of I yard.
'^ 6 = priceof5yardfl.
£97 n> 2; J
*• ^'''•= price of 45 yds.
^•a^. 3. What cost 643 barrpls ,.f a
■»•' uarrejs of flour, at £2 *>« -rw i.t .
' *-" ^*- 'a- per bbl. ?
OPERATION.
1 bbl. = 2 5 7, X 3 =.
10 bbl. =--2rrrT^, . 4 ==
^''^ i» 4, X 6 = 1367 10 .
Analtsis^S . ^ - ''a'«eof643bbl.
barrel by 3? I'dZt th '^ ''>«/al"« of 3 barrel ie m?, "^ { **"« '^^'''^ »f
•«wer.\eace tt^'''"''"''^'^ P'«<l"°t8. wo'obt^nll'^5^iJ.^;"'"4<»J^J
240. Rule — wu^. ..
ber re,.olve i^^uo .7.; ^^'^.^^^'f ^ ^« °ot a compoaite nam-
•btatned/or the r^uirJrJnii ^^"'^"^ '^ ^«»''«<'*' <Aw
91
3 4 = value of 40 bbl.
i !
148
JIULTIFLIOATION OF OOMPOUND NUMBIRK.
It V '.
if i;
m
IXAMPLES FOE PRAOTIOI.
(1.)
(2.)
(«.)
cwt. qr. lb.
18 3 17
113 2 5
oz.
10
6
12
lb. oz. pwt. gr.
32 8 17 12
8
J61 U
lb S S B
38 10 5 2
427 10 2
14
11
14
(*.)
(5.)
(«.)
mi. fur. rd.
14 6 36
14
9
A. R. p. aq. yd.
7 1 33 21
sq.ft.
7
6
rfeg-. mi. fur.
18 12 6
rd.
1&
8
7. How much cloth will it take for 8 suits of clothes, if each suit
require Syd. \qr. 3na. ? Ana. eiyd. 2qr.
8. A man gives each of his 9 sons 23.1. 3iJ. 19^p., what do they
all receive? An». 2UA. m. Up.
9. Mow long will It take a roan to saw eleven cords of wood, if it
take him 8A. 45mtn. 50sec., to Ha\'? 1 corl ?
10. If 1 share in a certain stock be valued at £13 8». 9irf., what
18 the value of 96 shares? Ana. £1290 \$. Od.
11. If a family consume ligai. 3qt. Ipt. of molasses in one week.
what quantity will they consume in 1 year?
12. If a man be 2da. 5h. 17 win. I9«cc, in walking 1 degree, how
long would 11 take him to walk round the earth, allowing 3651 days
^°^^^wJ -n. . Ana. 2y. 68da. m. 5imin.
Id. What will t>e the value of I dozen gold cups, each cud weiffh-
ing 9ox. V^pwt. »gr., at $212.38 a pound? ^
^A^f' K^ ^^'P "*''^ ^** 2*' ^0" F^J" day, how far will she sail in
^",la^« ^ Ana. 204" 10'.
15. One ton of copper ore will buy 17T. I4cwt. 3qr. Wb. 14o«. o|
iron ore j how much will 451 tons buy ?
^^i K^^'^ ^'" ^"y "^^ ^'^- -^P^r. 208q. yd. Ssq.Ji. of land, how
much wil $4800 buy ? "^ ^ ^Ans. 295^. lOaq yd
17. 11 1 cask of oil contains H{]gal. 2qt. Ipt., how much will 100
casks of the same size contain?
. l^r.' J}'^^ '^ *^® °°^* °^* ^°^^^ ^^f^' 9»'»- '0D& and 2«. 3 Am. wide.
at $0.05 J per loot? ilns. $2 27711.
19. Bought 17 bags of hops, each weighing icwt. ''Aqr. 7/6.7* at
!t)6.«Ti per owt. ; what was t4ie cost ?
20. What cost 27 r. \5cwt. \qr. S^lb. of hemp, at $183.62 per
o? A ^,or,, 4ns. $5098.07 + .
^i. At *li5.75 per acre, what coet 374. 'SR. 35rd. ?
«q5!; Ill^*^ "^^^f ^^^ construction of 17 mi. 6/wr. 36rrf. of railroad, at
$3765.60 per mile? Ana. $67263.03 + .
*o. Dougni a iarm containing 14i/i. 3R. 30ocr., at $97 62* ner
acre ; what was the cost of the fa^t ? Ana. $ 1 4149 62 +
24. At $9.26 per cwL, what cosf 19cw*. 3qr. 14/6. ofixomt
6 d.
4 d.
3 d.
2 d.
lid.
1 d.
lo. =;
8
> 2
14
11
) 2
14
5.)
fur.
6
rd.
18-
8
MIILTIPLICATION OP COMPOU.VD NUMBERS
SOLVED BY ALIQUOT PARTS.
TABLL OP ALIQI'OT PARTS (173).
f'arts of 8 n I
cwt. (1) Parte of I lb. Parts of lo«. Parts of*
ofU2U). Avoirdupois. TroT ^'ansofa
"'• year.
'56 lb.= l
28 ib.= r
16 Jb.= |:
14 lb.= [
Jb.=-i.,
I. i<>
802.
402.
2oz.
loz.
,ij5p;yt.0gr.=|)6 mo„ae=
-^1
Part- ,fiib.
-roy.
" "= 1
Parts of a
[quarter of
281b.
'4oz. _
.Soz. _
2oz. — .
Jo*.10pwt.:=||2(;per.
loz. _. 1 i/>^
— T? loper.
Parts of
1 aere.
Parts of a
month.
= i,
14 lb.= i
7 lb.= i
lb.= |
Parts of loz.
Troy.
Parts of
1 rood.
lOpwt. Ogr. = ^ lOper. =1
/ar^A%,. -^ ''^'"^S 4 pon.uh, ghUUngs, pence ^ni
^- Find th, price Of 944 pen«, at M. per pen.
944 pens at Irf. = 944rf. = £./ 18 8
/?• "^ ?«!?•; i of £3 18 8 = £719-1 ,
!«. - j of irf.; I of £1 19 4 « li {9 J = ^T V\t P!f' f i*
^«- m i» -■ «
i<
IM
MITLTIPLMAnON BT ALIQWOT FARTS.
«um W?y aTeno?- b Jt^^ ^c/ i^ HZ ''«'°«/'"-^*-?*. "e multiply the glr-
it into i AnrK^iS .ttihl ?,7!*" ^^«" P^f j"' * P''""^' we deoompc
the half of id St^hen take the I of /"irs f''V/-' '■''" f»"/'h °f a penn/, or
then irf orS of id., 't^at b.'oSeValf'ol :£ ' iVl L^iTs^ 'whr '' ^LL' tl
■£1 1» 4; the.ua. the- giv ,£2 IS 0, iJr the ansl^er ' '* "^ **
i7*. 2.
What cost ltf38Ib. of Bugar, at 8 id. per lb. T
OPERATION.
16381b. at U. = 1638t. = £81 18
Odrf. = iof2rf.; iof£13 12 = ££_8J= n « u ,, ^J.
£58 3= " "
<<
" 8irf.
pose ii into 6d/2d.,t^d'ilfl'^Ar;rS
^*. 3. Find the price of 252 yards of merino, at 3.. 9^^. per yd.
OPBRATIOX.
252 yards at £1 = £252
3». 4 rf. = 1 of £1
0#. 6 d. = J of 3$. 4d.
Ot.Oid. = ^^of5d.
Ans.
Ea^. 4. What cost 694 cwt. of butter, at £5 II 6^ per cwt ?
OPERATION.
•^694 =priceof694cwt. at£l «
£42 = price at 3*.
5 5 0= '< « 0,.
10 6= « « 0,.
4 d. per yd
5 d. « <«
O^rf. " «
£47 15 r? = «' " 3^
9^rf. " "
694cwt. X £5 = £3470 =
10s. d. = ^o{£l I 347 =
1«. 3 d. = J of 10s. 43 7 6 =
e«. 3 rf. = ^ori«..Srf.i 8 13 6 =
Or Oid.=jofO»..'^rf.j 1 8 11 =
Ans.
«
"694
<<
«
£3870 9 11= " " .< «
EXAMPLES FOB PRACTICE.
" £5 "
" 10 "
" 1 3 •<
" 03"
" _0 OOi"
" £5 iTej"
cwt
«
1.
2.
664 X
if.
Oi =
3. 1984 X %\
i. less X oi
£ $. d.
13 10
3 12 2
S 12 8
5. 1078
d.
01 :=
6. 1683 X 2A
£ ». d.
1 2 6i
7. 2142 X 6|= 61 6 41
8. 1053 X 54= 23 sf
U. 6d. =
©«. 5a. =
MtrWlPLIOATION BT ALIQUOT PARTS.
9.
10.
5728
54 HO
11. 24.S6
12. 2147
I.>. 7028
14. 2708
16. 5491
16. 49.36
IT. 4967
18. 2522
19. 2897
20. 7509
il, 1870
2244
392
576
465 X
425 X
1349 X
28. 7045 X
29. 2426 X
30. 1454 X
31. 3632
32. 6741
22.
?3.
24.
25.
26.
27.
X
X
«. d.
< 71
< a :
■ 6i
: 3j:
S\z
6|
J ^^ =
8| =
lOA
11 =
10J =
11^
9| =
l]\ =
1 8
1 9i =
3 7i =
4 111
5 8 =
J 7
7 4i=
6 5i
9 7 =
2 6|=
■£ *. rf.
173 8
67 17 6
31 6 2i
241 11 9'
33.1893x0 4 IDA
34. 604 X 8 "J
35.2916x0 5 ll|
151
An»w«rt.
•e «. rf.
36. 5.'J48 X 7 ,s^
- 248 10 5
- 868 U 6
X
X
X
X
X
X
X
X
X
X
= 171 11 101
= 179 19 2
■■ 115 11 10
■■ 129 U 2%
75 19 4i
105 3 9
51
84 5
n
382 4 4
892 1 2J
1740 6
863 1.3
8
91
•^7. .3720x0 10 d
38.1509x0 14 6
39. 878x0 11 4.1
40.4571x0 1.3
41. 54 X 1 2 9'
42. 62 X I 7 44
*3- 17x4 3 11
44. 24 X 3 13 ■':
45. 472 X 6 10 34
46. 1958 X lis 8 -
47.2471x5 14 91-
48. 972x3 15 10
49.1077x7 12 .3 =
50.3714x2 13 11%=
i*!. 1415x4 11 10'
52.2150x9 16 1?
53.2175x6 17 10?-
54. 7251 X 8 7 7I
55.6494x6 19 5'L
56.7122x9 13 4^=
-^ 1960 15
^ 1094 6
I _
3113 19 101
61 8 6
71 6 7 '
88 2 6
■■ 3785 9 4
=14179 18 8|
= 8198 13 3
^'0023 18 7i
21083 8 9
l-'818 18 li
45288 17 81
t>!:i860 16 9
Ex.
Required the price 0/ 1581 yards of cloth, at £1
2#. 6rf. = £•
6rf. = ^ of 2s.
iof£\ 2 11
loflU. 5^rf.
Ans
OPERATION,^
158| varde, at £1 2 11
19 15 = price of 158 yd. at 2a. Gd.
__8| =
2 11 perjd.
i
-3
li
SSil/?^^^S:^£'S:iX^ (^~?"«»
ANOTHER METHOD
- I
158
i yards, at £1 2 11.
2a. 6d. = £1
^.Ba
k of 2«. 6d.
Atu
£158
19
3
15
16
6
£181
19
Oi
= price at £1
«
n
per yard.
28. (id. *t u
_0 Us. 5rf. tt u
£i~?~rr " «i
i
H !
] (
!i
it I
M
162
MULTIPLICATION BT ALKJUOT FABT8.
AntALTsrs.— In this method, we Orst find th« nrin* nt isua j
7ard. Thi«is£Io8 15 0; fo; tho price of SS Ts £168 I^hV' ^ P*'
iquarterofa yardbein'^evidentlv 5. it>f thJ^r T I '.^°^' *•"» P"oe of
pnce at £1 por%ar,l bein. ^Fsl fs, h tico at 2 Id ^"-f, t}^'' '^^''>' '^'^
^ 6 U. The sum of these is £181 18 Oi, the whole price,'^» before ' "
1.
2.
3.
4.
6.
6.
7.
187 ^
S28 3
208 5
971 1
675 ]
3714
638 1
EXAMPLES FOR PRACTICE.
£ .f. d.
8. 495
J. 917
10.
11.
12.
13.
14.
515 g
63 g
85?
176 1
15. 785 a
16. 239 I
17. 375 I
18. 759X
19. 774 4
20. U9^
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
17 8
6 6
13 10
15 2
1
3
1
3
3
4
2
3
2
3 15 10
11 8
Ana.
Ann.
£
353
106
7
14
4
5
18
9
18
7
2
'a
8
9|:
10^
4 :
9 :
'6
Ans. 3650
Ana. 917
7
1
4
2
9
8
6 3|
10 10
19 111
15 94
11 6 :
19 lOi :
Ans.
Ana,
Ans,
Ana.
Ans.
Ans.
'25
1630
«.
2
16
11
14
13
1271 14
249 12
6.54
103
Ans. .Sd9
Ana. 1877
16
2
12
7
d.
6
lOi
n
I
2
9
9
6
1
34
5i
Ana. 7416 16 104
Ana. 6736 ft 9}^
perlwtT^"' '' *^' ^°'^* ^^^^'•^'- 2?r. 15Z6. of tobacco, at £5 12 6
£94:
94tw/, X £5 = £470
10s. {)d. .-.: £^.
2». (irf. =^of io*
2qr.= \oncwt.
10/6. -.. ^of27r.
6/6. ■= ^ of 10/6.
47
11
2
'' Us.
" 2s. 6rf.
at £5 12 6
^«* £632
£5 12
f 5 12 6 X 94 = £52815
2 16
U
6
2qr. = ^cwt.
10/6. ,^of2gr.
§/6. = |ofl0/6.
•4«#. . , .J6632 8
OPERATION.
= cost of 94cwt. at £1.
0= cost of {)\cwt. at £5
:r= a il it
15 = << « .<
16 3 = " a 2or.
11 ;^ = " " 10/6.
■ " " 5/6.
8 1^= cost required
ANOTHER METHOD.
^ = ooat of I cwt.
= cost of dlcwt.
3 = " " 2yr.
3 = " " 10/6.
H= " " 6/6.
li«
per cwt
U
U
at £5 I ii S ucr cwt.
<< (< «< U u It
« « U 41 « M
« « « << u M
I.
2.
3.
4.
6.
6.
7.
8.
9.
10.
11.
12.
13.
14.
16.
"94 2 16 at £6 12 c perciT
DIVISION OF OOMPOriNn NDMBEI18.
15S
1. fiBcwt.
2. iHcwt.
3. I'Jcw/.
4. I2'.)cwf.
6. Hlctvf.
7. 2Hr,afr/.
8. 3U\cwt.
9. I Slow,'.
EXAMPIEs Foil PHxcTlCK.
2qr.
'qr.
■Aqr.
Iqr.
'qr.
Iqr.
Mfr.
\qr.
I per cwt
(i
6
8
9
((
a
./n.s-.
£
74
u
u
u
u
Jns. £
Alls. £
Ans. £
Ans. £
ii2
-A -.',9
G20
'(tfj. at £0 17
21/6. !U £4 14
lUh. at £4 11
l(i/6. at £2 12
S/A. at £4 5
17/6. at £2 15
7/6. at £1 IS 10
4/6. at £1 12 7
lA i^r ■"^'- •''■^^/'- at £2 IH 4 " "
1!
14
7
.051 19
nG4 3
4
2J|.
•-'•1+
4 + .
1|.
4 + .
1
1
15. IM.Ji^. 2Mper.at£l 8 7iperacre.
7
Ans. £ 148 10
DIVISION OP COMPOUND NUMBERS.
I £Sel wifgh ?*"''' "^ '"^" "'"'^^ ^'^^■'' ^^^- ^«'*-' ^«^ ™««i^ will
OPERATION,
owt. qr. lb.
fi) 9 1 10
ANAt,Y8i8.-0ne fifth of Qewt. is icvt. audicwt
nmldjr. remaining, to which we add the lor '
and hhve U^r. I fifth of 17.;r. ia 3yr. and 2?r. «
1 q ,s *"'*• l,*!"*'?"^' t<> Which we add the lOlb, and
1 3 12 hav, fi0i6.1 fifth 016,1/6. is im Therefore.)
fifth of ^met. Iqr. Wb. = lewt. 3qr. UCb.
^bers and each succeeding denommation in the same JZ'
%f there be no remainder. mannet,
redLVttlJ'l^u'^t aArci«,tVm^ any denomination,
ZrTnLi 1 ^ !•"'"' denomination, adding in the given nun^
berof that denonnnuttan, if any, and divide as be/ore.
MMv^n/ « T1 '" '^ '^"'^'" *^*'* °^' *^'^ denominations. The
several partial quotients will be the quotient required.
-.S^^io^^ »-^. w. ..,
J;crdttt%lS';[.si£;frsr^^^^^^^^^ ^'^•^--» ",
pie numfceri. »"»w»»twM, Mia thu division then 18 the &ame as in gim-
OPCRATIOV.
€ ) 67 10 = priM of 24 yardi.
* ^ ^ 11 ^ = pri«« of 4 jarcU,
rnr-pricof ijHd.
7
We therefore divide the prior bj
•ne of these faetorg, and the quo-
^nt arising bj the other. Henoe,
Ilh
'I?
IJ!
: I I
i
II I "'
! f i
154
24»5. Rule
in succeessio?} .
Ex. 3, Divide
OPERATION.
£> 8. d.
173) 360 8 4
14
_20
173^) 288 ( I,.
m
115
12
DIVISION or OOMPOUND NUMBBE8.
—Divide hy the factors of the composite nwnber
£360 8 4 by 1 73.
(£2
ANALyaiB.-We dWde the pounds by ITS
and obtain £2 for the quotient, and £14 remain-
ing, which we reduce to shilling., and add the
H». ; and again, .livide by 17.^, and obtain 1«. for
the quotient. Tho remainder. 115*., we redi-o.
to pence, and add the id., and again divide by
I7rf, and obtain 8d. for the quotient. Thus, the
method is the same as by general rule (244).
5^ ,"°"IPS the several quotients, we obUur
*^ I a, for the answer.
173 ) 1384 ( ad.
1384
Ex. 4. Divide £24 3 8 by £3 5^.
OPERATION.
^t^^^L^±J/Sr:__232]Qfar.
£ 3 0«. 5d. Ifar. ~ 2^{)2 far.
8.
Analtsib.— Rednoing both
dividend and divisor to the
lowest don aination mention-
ed meithei, and then iivid-
fng as in simple numbers, we
have 8 for the quotient.
EXAMPLES FOR Pi ACTIOS.
(1.)
T. ctfft. lb.
T) 45 15 25
6 10 76
lb.
9) 143
(2.)
oz.
5
dr.
5
15 14 13
(3.)
hhd. gal. at. pt.
12) 9 28 2
49 2 I
1 dayt '"*° •■ ^ '^'"'^^ ^'^^"'^ ^^^"»»' ^/"'••' ^0^ fer doe« he go in
7. Divide 280 51' 27.766" by 2.754. ^'"- Zs 'iT :^^,','i^'
% When 96 shares of a cfXin sfockt^v^ K^ t^,
what would be the coat of 1 share ? *'
hoi;iV3eU"^rro;i.^:?^«'^ r%^%i,^^ f?r' '^'^
1. Divide 6rr. 19c«,f. 42/6. 14o*. by 123 ' ^^^^''*^'
long woulau cake i.i» to walk 1 degree,- allowing -3654 -dlyrt-o";
13. Divide 916m. 3>r. 30ni. l,fi^^l IfJ!"' ^^^^'«- ^«"*^
14. Howm»aytiinaB«wje5 10 10 oo.tained in £537 10 10 T
LOIfOrrVDl AND TIMI.
166
Ana. 70.
lyk. 7^;:f;;L;":^;e7^'?J\°^*«frt*i" "-'nber of farmers Cbu.
!«. ftvide 3794c». yd. 20c«. ^ 7094c«. m. by 334. ^"'' ^^'
LONGITUDE AND TIMB.
24y Anl , ,.'""*'' P°'«' "-casing the equator at riiht angle™
•rally on the ocean the mlriJu ^^ f^^"*^ <^» ti»'« continent, al.u gen-
" the determiS "leSaT AllntS'lT'"^'^*^^ E"g'«"d
considered to hare noToS^tude ^ '^'' '''''^^ ^^ '^'« ^*»« »'«
w«t of thi. meridian the Z.L£^ '''^^ P'-. -d at place.
BMD. "•MDerorenoonj at those east, the time is after
2. The whde circle of the aartli ^nnn u- t.
aud in one hour parses i of 3M» I iZ "^'^f^' ^^^' th" sua in 24 hours.
One minuto ^ 6D seconds •
1 minute passes iV"^ 1^*^ - M« - i« = Ifi'
•>Mo«, in 1 sMond passes O, on6' .. H' „ i' " , .» „ ' °°""""''
^«no«.^«j^ 14„, g^y^^ the following
COMPARISON OF LONOITDDB AND TIMI.
15 of longitude ss
16* of longitude s
16" of longitude s
1 hour of time.
1 minute of tim*.
1 second of time.
exprtt'i fndeg^^s' 11' tf 'T '^^T''''^ ^^''^'^^^ tu,o places,
their dlfferenc7rtC^^ ^'■"^'^^'^ ^V 15 u^l gioi
II Th, rff ''"^^ f pressed m hours, mmut,,, and seconds.
^;«:;..;t?-^'''T'''^'r''" ""' P^*- ^Pre'^^'t '■» hour'-
I .
IM
MWDSOniAIA
^imkTJ^TJL '^^'^^ >»«>« from oMt to wert, when It b ezMtly II
!?3iil^.tf^;i '"f K*^f 2^ ^^ °'°'°<"^ *» "" P' "-"^ <"^«t, and be/ore f2 at
£■ STttl. at ih^^rll?"^ f 'fforonoo of tiiM betwoeu two plioea. be LbtraJd
JSrlrf ff^hin^ff. ^f'*"!'.*^''*''"'^'''" b« "'« li"« *t the westerly
EXAMPLES I-OE PBAOTIOB.
wL^'iT^l/", '"^t*^!"-^* ^^! ^fi'r"*' »"d Toronto, 79*^ 21' west.
wii#i» ,t w l2ro'olock at Toronto, what is the time at Quebec ?
7>^ 21'
71* 16'
U)^^-^
13
32mi. 2Q$ec
15*. 32w». SOMe.
AHAtTSM.— The difference of longitude i«
»• 5 . Jpmding by 15 and changing to time
flTef 32«r,». 20»e«. for the diflTcreDoo of time
'^*?'i,**' **o P'o^oes; and, aa Quebec is
V* *• "*'™°'"» ^°« '•°>e is later, and we add
the difference of time, which giyes 12A.
32m». 20mo. the tiaa at Quebeo.
iM L% «!f^"'*l*'* ^••'"'^ '•, •' V^' 3«" ''•«*' •"'^ that of Ottawa
«fL2S*i^20^i'w °^y*'^'*'?^>,V'',^.^',^««t, and the longitude
> 'JT , .8 the time at Rome? iln«. 23 wm. 28»ec. past 5 P M
« wiJ-»^'P^"*^ a « „ An8.1h.20min.52,ec.
u iJ /« '* '^, P^*" ^' ^^ Paul'i, Minnesota, longitude 93° 6' west
IJ^^Bjn,. U. 37..V 12.ec. P. M., ^l-£the lon^^^^^^^^^^^^^
ut^i'X'^^ of Jeru»l«» !• 360 32' east, and the longiTude of
tiZi^Jl, \ ""rl' ''*'*"' •* " ^®y<''- ^- ^- a^ Jerusalem, what
^I'JKf M^^'r **f^^J^."i*Vr 1' ^" ^^'t, and when it S 10
-£f^ i' ^' '" ^^**^"' '* •« 8 o «look »3'.«ii. 574*ec. in Chicago •
^^**f loagriude of Chicago ? aZ. 87^^ 34' 45' ^ '
W^longituda of Constantinople k 28» 48' east, and of Kingston,
«^«««dll» 76'> 41' west; when it s 3 o'cl. P. M. at the latter nl*r^«
whM Um^ w it at the former? Ans. 9A. rllmii lesecp T '
«»Lp**Ef*"* ♦*?!"** ^''- 'f ^^ J*'' chronometer that it is 3A. 40min.
S^Lf:;,K-. **°T'^^' '^u'"!* '* ^*- ^'^^^■"' 4°«''<'- by solar
•«»« ©• bo«rd hit vessel j m what longitude is the vessel ?
iln*. 370 26' 16" west.
DUODECIMALS.
^»», Duodecimals are deaominato numbers, the denomina.
»•■•« Which iQcreaae according to the scaU of 12; or denom-
MVLTITLIOATIOIf OF DnODlOTMALS.
1B7
west.
inate fractions, whose denominators are 1, 12, 144, 1728 etc. In
practice, duodecimals are applied to the measurement of extension
the foot being taken as the unit. '
TABLK.
12 fourths, marked (""), make 1 third, marked 1'"
12 thirds " I second, « I»»
12 seconds " 1 prime, or inch, " V
12 primes, or inches, " I foot, « ft.
The marks ♦, ", '", "", are called indices.
251. Duodecimals are added and subtra(-„a in the same
manner as compound numbers.
MULTIPLICATION OF DUODECIMALS.
Ea:. How many square leet in a floor O/i. 7' long and 7/i. 9' wide?
OPKKATION,
74/r
ANALT8I3.— Beginning at tha right, 7' x A' =
«3" =. 5' 3"; writing the 3" one place to the right,
we reserve the 6' to be added to the next nroduot
Then, 9/<. x »' + 5' ^ 86' = 7/t. V, w^ich we
write in the places of feet and primes. ^Jext, mul-
tiplying by 1fu, ne have V x 1ft. = 49' _r 4/t.
V; writing the I' in the place of primes, we resei ve
the 4/t. to be added to the next product. Then, '.^/^
X 7/t. -f- 4ft. = 67ft., which we write in the place
>>, «., r »u J . ■ ,„ Adding the partial products, we hare
3' 3" for the prodact required. Hence, the
_7>.
6ijt.
ufi:
r
^
2' 3"
j7
3' 3"
353. Rule. — I. Write the several terms of the multiplier un-
der the cornsponding terms of the multiplicand.
II. Midtiply each term of the multiplicand hy each term of th*
multiplier separately, beginning with the lowest denomination in
the multiplicand, and the highest in the multiplier^ and write the
first figure of each partial product one place to the right of that of
the^ preceding product, under its corresponding denomination, car-
rying 1 for every 12.
III. Finally, add the several partial products ; thtir sum will
be the required answer.
EXAMPLES FOR PRAOTIOE.
1. How many square (ieet in a piece Of marble 12/1. 7' long, and
i/l. 3' wide ?
Ans. 53ft. 5' 9".
2. What i.« the area of a floor, the length of which is dft. 8' ll"
and width yt. V ? Ans. Uft. 10' 11" 6'". '
3. How many square feet in 10 boards, each \m. 10' lone and
l/l. 8' wide? Ang, 313^. 10' 8".
lij
i
%v
158
OIVIHIOIf OF DTTODIOTMAU.
6in. hliih? ^' "'"^ ^^^■^'' ^"»' ^de, with a clone fence 7/?
of ceiling K/?.^4' ? ^' ^^**-' '^^'h 24/);. .;m., and hii^.h,
Ant. $33.66.
DIVrsiOxN OF DUODECIMALS.
OPKRATION.
•V»-9')8A5;3"(2/<.3', H„,,
11' 3'* '
IV 3"
g. xaereiore, tbo marble slab waa 2/V. 3' in width
ANALTai8.--3A. M contained i,.
dfJiior h^'f^, M>?ltiplying the whole
diTisor bj y*. pveH 7/^ 6' fo, the
produot. which wo subtractfrom he
corresponding denominations of the
dividend, and obcain 11' for a re-
mainder, to which we annex the next
Sr,7"'Sr","f f'"' dividend, and
nave 11 d> 4/if- " oontained in IT,
•J timi's. The divisor beinit multi-
'A
of me ,„„,.«.,, and .,„„., tke .ro.^J/rjfZZv^. """
EXAMPLES FOR PRAOTIOJS.
1. Divide 184/if. 3' by 40rt. II' 4" a .^
2. Divide 4I/i. 8' 7" 6'" bv 1ft 4' a . ; ^-''-o^'
3. A table who6e length M \y V" h.« ^***- .^^''- *' '^"2'"
11" 2'"; what i8 its width? ^ ' »»*« »° *>•«* jf 28«^./^ ;r
and wit /U' V^T?' ^'*" ^^'^^ ^'^^^^ *- - ;^^/'"«' ■^'' '2'",
5 A block of raarble contains 64/?. 2' 5". its ^\dth^&^'f'' a
Its thickness 3fi. V • what Ih its length ? ' ^ ^^n^-^W 'of °^
6. What 18 the wdth of a rectar.miiar r.«„^ u , , '•^- ^ '
9' 6" aiidarea I076,,.i^^^1f//f -Ir^P^^' "'iVli;^^ ^^l?*^^
7. A stick of Umber is IW. 2' u,;.]. ■>/> ,,, ,/^"f- ^Vf ^ ^ •
135c«/f. i0'2"l"'. Wliatisits fe„;fh? ^^^' ^"'^ <^""tams
-4««. 47 feet.
MlSOlLLAIfBOUH SXAMPLIM.
BHSCELLANEOUS FilXAMl'LES.
159
boigh^forVs^'/ef'''''"^"'^'' Low many yanlH of linen may be
f fft'^'flf ^'^'*'"^"'r""^'^' Apothecaries' weija ^'^''•
\ l^^^l'^^^ of wino be bou-l.t f,.r £30 2
of each gallon?
4. What is the value of I5curt
'■^qr.
lOJ, what is the cost
, ,. Am. £1 G (].
I It", of tea, at .■i;9")() per cwt. ?
„f « ^ ?■■.';'" *""'."« '^""- 2?r. I'Jrt. of porf , , M ?ro,^i 2i;a
3.- '.i^-oTr^.ti ?^^? ' '""^ °^"™''- •'£"|' S>'
19 Wl,„. :- Y- , .i". .. . Arts. boAi)b>r</t.
12,
l^iltf ^"'"'^ "^^ ^'^^ ''""- 75'- 'o"g, anTi'cii!
at $04 per^acre'?" '"'"" "' " """" """*' "''' ""'"' ^"'^ '^cA. 50/. v^ide,
13. What part of igcU. Sqt. is 2yt. \pt. 2gi. ? ^"'Anl'n
p\lt^ttu!:"lS2r''''?'' f"^'- V^r^2rd. of road ; aXAom-
Ifi Tf., • :^/**' -^Z"^- ^•^»^- 'before, and 4/ur. 302rrf after
17. Bo"ght 4 barrels of cranberries, ,ach contaimn! 2 L 'k"" '*«
re/A. and 80Z. more than Edward. '^How nn^ch it ea'cht ":?'"
iQ A .^".^•^'■^■«e«ved2I0|/6., E 13S'/6., andLlP8^Z6
rH\J^ "^f » havmg a hogshead of liru'p, sold % of i^ to F rof tb«
^emamder to G, and i of the residue to^ H?w manj g'altons t
20 Find the value in Troy wei.ht of im^l^f; \t 'tt^:,
weight. ' "j„„ ,^1, , 7" — ""'Oiruapu:i
91 w^ , , Ana. 16/6, 5oz. lOptvt. 11.7 + p-r
12^a/ W^7'^^""''■'*V,^' «^"^'' ^ P'*""-^. must te given for
*lf-i9'- of molasses at 37^ cents a gallon ? ^
aJ U wT i^.f ""'"^V" ^^ ^''^ ^q»»'-^ "" tl»e inside, 8 feethieh
•«d 14 feet ,n thioknew; how many perches of mawniy'Je the«f '
'!l
t
l-H
J
*!■
,1 5
I
180
MISCELLANEOUS EXAMPLES.
1 ^^1 7,}^^ •^^?l?i®''* °^ nine copper mines in 18(>8, was 39427' fliSMtf
l^r. 1/6.; ,» 1869, the same nlines yielded 41017'. Sev^tLmi
If copper was worth 20 ct.«. per lb., of l,ow much greater y>i\ul^m til
amount province,! in 1«69, than IHf;8 ? * ^«„ *fiS-VjS
R'-^'lh"''^'.' ?^ « ^-^'^ * «"^t. How m.ich would be gained hyZmm
the whole at 4^ cts. a potnid ?
Ans.^n.ui,
^0. bought a lot 2o roda long and 20 rods wide for * 10000. mi %M
9^ «'n^f 'i'- P""" '^^"^'•'^ ^'^"^- How much was n,v .ai»?
^b. Sold 72 yds. carpeting at ^\.?,1\ a yd., and gained %\%, ftw
much did It cost me per yar,i? ^ aJ.UA^
^11 f. f^^y'nany square yards in the walls of a room 40 t^ jJwr
•il i feet wide and 1 2 feet high ? ^^
28. How many tons of hay, at $0.76 per cwt., must b<? »»«# for
35 con Is of wood at $0.60 per cord foot ?^ Annl if I^
*.i ."'? !?^'^. * ^^'■»"' containing 176^. 3iJ. 2.0rrf., at $75,371 My
acre ; wliat did .t cost ? ^^i,. |'i -^^^u.ZmVr
:??• _^l'^L^i.'^ ^? *'*« expense of plastering a room 40J^".'*lonX mV/,
Its a sq. yd., allowing \Z1^>sq, ft, ft^
Wide, and 22i/2. high, at 18 cents
doors, windows, and base board ? " ' ^Am. $hf7HL
^h AiltV^ '' ^ ^»V^- *^ * P^*°« 30« east of Greenwich |^ iw
l^t'rB„s ^- ''^ " ■'"-'°' ^"'- ^••'^-.t^-.L^
.,/t' ^'"/^!'f,V'*t«ofeq"alsi« contain 159.4. 2/J. 17»«. r<<, 2i5*»
worth 50 cts. per square foot? At^. $lHm^.n.
.ni *i bu.ldmg lots of ground ; the fir.^t contained 4 of I ^«#
acre; the second. 402 rods: the tliir,^ i nr«n o«.». „.,.!. u. l^JT
fof|
34.
l2oz.
35.
the second, 40'| rods; the third, i of an acre; and 'the ImfK
of an acre. How much land in the four lots? Ant. 3R. UpJr
How much beef, at 7rf. per pound, ought I to receive It tllb.
Mo ;. Qn/fnr^"^f "* longitude between London and St. &,
Mo., .9 90- 20' 5 at a certain time each day it is as mucfaS
noon in London as it lacks of noon in St. Louis. What is th" SZ
.nSt.Loui8? 4ns. HA. 59mtn. 20*eo. A, i
db. hixpress in acres and the decimal of an acre the area of dS
square ots, each measuring 5rd. S/l. Sin. on a side. ^ '^ *»
ST. On an acre of ground there were erected 21 buildings occuo*W
on an average Ssq. rd. U28q. ft. ^sq. in. How much of *U mK
remained unoccupied ? Aa^. ^fiper. 9l8a ft Uaa^
38. Reduce ^ of i of 45^/6. to the dec-,oaUf a short"ton. ^' ^'
dy. A person lived in Montreal until he was I8yr. 8mo. tida,m
loronto, 4 as long; in Kingston, % as long as in Toronto, and 4a*<i<w^
Quebec as in Kingston. What was his age ? A. 31yr. 2m^. tm
40. A farmer owninir 19r,>l QW -^ao^ -.3 „^)..„j^ j- • , j 1.^*'^ .
m
in
«4ii
40. A farmer owning 19^4. 3//. 38s^. rd. of land,' divided i
equally among his four sons. How much did each eon recejyj
how mucl! ha.d the father remaining ? '
Am. 364. 2/i. :59|sj. rd. '-ach, and 484. 3ii. Z^8q. rd. x^xnuaing,
41. A steamer, going uom Halifax to Liverpool, t ra versed ll«l
degrees of longrtude d«ly. What length of Ume was it froru om mm
to tM Mzt 7 Am. 23*. 1«M^
II180EL1.ANJEOU6 IXAMPLB8.
161
I': r„^tTavni!!''fi'l?'.; *°" ''''''' ** 20 cents per pound ?
«i<ii8 iieinhbo-fl -„7,-", : j-"*^"^^'l»»'-«»soia :;o square rotls to -nc
WliatiiiddicMvood
he lounu that it contained ocd. Gcdyft V>cu fi
cost him per -lord ? '' '-^*--^-
iSi^t^Sko^;;:;.!;;^;^s^'^^^^^^^-^-«-'^-■-'^^
«fi ]?«,w'"^"*'" ■^'"'^'''* ^"': '""''^^'^ °"'' a"d 54.1 1| ra/. remained
,jLgs;c zr. taC.%rs''f, "^ t'%4"«"' «-■ --
$5.:^ 2, fa yard? ' '^^^""^^'^ ^*^« value of the remainder at
47. Ifagallonofdistilled water weigh 8^6. 5oz, 6.74dr what "is
the weight of 17fi.a/.,39M;,M<,/.? 4n». 14^ 5or'l.r9rfr
meturinVle/rS'' ?" ''''' "'^^ "'" '^ ^'^ °^^^ ^^ ^1^13^^'
24o!' i^nr^n" ''^l** i" ;^ortli <i«. 3d. per bushel, a S-ceni loaf w"e.gh>
Uoz., and allows the baker I^ cts. a loaf for his labor, what Bhoula
pro7t'taraff^^^'^''-'''-P^^'^"^'^^'' ^^^«-^ ^J ^^« --
«;fi;;o. "[-'""s 7'' '^ T^ ''• ^^'■P^'' '^ ''^•^'" 2iyj!. long, 15/?. wide,
61. What 18 the value of a pile of wood that is lOrd. lon^ 4fi.
wide and 1 iyd. high, at $5.75 per cord ? ^n«. $13.3.42 -
>IJ "-''t^:^"'''^ /«"ce ..i/i. high. How much will it cJst to paint the
fence on both sides at 12 ct... per .q. yd. ? Ana. $93,862
o3 A merchant purchased in Manchester 34 bales of cloth for
t-« ly f> per bale ; he dieposed of the clnih at Porto-Rico for 212c«*
.^»ga'; at £1 5 per cwt. Did he lose or gain ? and how much ?
; 04. If a person spends in 6 month, what he earns in 4i months :
now n,a„v dollars can he lay by in a year, supposing he earns $325
m2i months? "^"^ ° Ana $390
00 A man has a piece of land 201 J rods long and 411 rods wide,
which he wishes to lay out into square lots of the greatest possibte
■^ize.^ How many lotp will there be ? .Itw 396
56. If a man can pay his creditors only 48 o«nt8 on a dollar, how
ranch can he pay on a debt of $52.50 ? '
67. How many bricks, ::!tii. long, 4tn. wide, and 2itn. tWck, are
required to build the front ofa house whose wall is 3ok long, 24/t
high, and 2JI. thick, allowing the doors and windows to occupy i the
^,'^''^*}..^7USgat.2it. of melMnet. at 20 eta. ami., 'm^'fm
ou ?«?. 01 It, now uiuHt I m>U tiu wmamder per gal.. wT&a'to reoeirt
X'ul ?' "lot '?f* * , ^"-- «0.263+.
,AA A \ . .7 ^^^ ^""°^ °f ™"™ f**"" «75. how much water must be
tdrted to It that I may seU it at 60 centa per gallon, and gain $15 in
taesaieolit! Am. &Q gai.
■:l F
162
MISOBLLANBOTO EXAMPLKtS
60, Sold 1 25 equal loads of wood, measuring 115Crf. 3cd.Ji. leu. ft.
for V 492.50. What is the quantitj per load, and price per eord ?
„, „ ^»s. 1 la^cu./t. each load, $4.26'i per cord,
bl. How many francs must a merchant in Paris send lo Montreal
m payment lur u doht of $15y8t).862 ?
(>-i. If a man fill J of a cask with brandy, J with wine, and i with
\yaitr. and if it lack 21^ gallons of being full, how manv gallons will
tlwt citsk contain? Ans. lOOgcU.
b.S, U oy Pellmg cloth at lOs. 6rf., ^ of the price is gain, what part
01 the co.st would be gained by selling it at 138. ?
64. A ship's chronometer, set at Greenwich, points to 6A. 45wn'rt.
Msfc. P. M., when the sun is on the meridian. What is the ship's
lori^itude? An8.86"2VE.
ho. A grocer bought 15 barrels of salt, of 4 bushels each, at ^U a
barrel, and retailed it at i of a cent a pint. How much wa^ his whole
S*'"/ , . Ans. $4.60.
Of). James own8 Aj of a field, and Leo the remainder; | of the
difference betweeo their shares is !SA. 3R. l^l^per. What is Leo's
^^'%^\ ,, , . ■ Ans. 20A. .'.R. dlper.
t>/. A gentleman desirous of giving Is. 6d. apiece to some needy
boys, found that he hi^d not money enough in,hia pocket by od. ; he
therefore gave them is. 4d., and had 9rf. left. Required the number
of bojrs. jj J^J^g 7
68. A liquor agent has 50 gallons of wine of superior qnalitv, worth
?7..jO a gallon ; he wishes to reduce its quality by the addition of
water so that he may sell it at $6.25 a gallon. How much water
must he add ? j^^s. 2ligal.
69. A clothier has 960 soldiers' coats to make, each coai contain-
ing 2\yd. of cloth ]li/d. wide, and lined with drilling lyd. wide. How
many yards of lining will be required ?
70. A ship captain, sailing from London to Portland, found, on
taking an observation, that the sun at noon was 3h. 25min. 40«ec.
arieniiaii the London time, as shown by his chronometer. How
many degrees west had he sailed ?
71. My father's garden is 10 J rods long, and Sf rods wide, and sur-
rounded by a fence 7§ feet high ; he has laid out a walk around it,
within the fence, 7^ feet wide on the two sides, and 5^ feet wide on the
ends. How much remains for cultivation ? Ans. 21296*0. /^
72. A bi)y having been sent > a store with 5^ doz. of eggs, was
directed to purchase with them equal quatitities of sugar, coffee
butter and tea; he disposed of his eggs at the rate of 2 for 6 cents,
and paid forthe articles purchased 17, 28, 37^ and 1374 cents per
pound, respectively. What amount ol each did he purchase T
V eord ?
per cord.
10 Montreal
and \ with
L^alions will
f. lOO^a^.
I, wbat part
6A. Aomin.
I the ship'p
I" 21' E.
5h, at$l| a
IS his whole
19. $4.60.
; i of the
at is Leo's
orne needy
by oof. ; lie
be number
Ans. 7.
ility, worth
addition of
luch water
u coiitaiD-
ivide. How
found, on
in. 40sec.
ter. How
iy and 8ur-
iround it,
■ide on the
6sq.ft.
sggs, was
IT, coffee,
6 cents,
cents per
BATIO.
RATIO.
IM
254. Ratio is that relation between two numbers or quan-
tities, wliich is expressed by the quotient arisin<r from the division
of the one by the other. Thus, the ratio of 12 to 4 is 12 -=- 4 v= 3,
255. The Terms of a ratio are the two numl)ors compared.
256. A Couplet is the two tonus of a ratio takoti to»ether.
257. The Antecedent is the first term, or dividend.
258. The Consequent is the second term, or divisor.
25fl. A ratio may be expressed either by two dots (:) between
the terms ; or in the form of a fraction, by innkinj,' the antecedent
the numerator and the consequent the denominator. Thus the
ratio of 8 to 4, may be expressed as 8 : 4, o: as f ,
260. A ratio is either direct or inverse.
261. A Direct Ratio is the quotient of tlie antecedent bv
the consequent, Thus, 8 to 4 is | or 2.
262. An Inverse, or Reciprocal Ratio, is the quotient of .
the consequent by the antecedent. Thus, 8 to 4 is | or i,
263. A Simple Ratio is that having but one autra'Jent and
one consequfnt; it may be either direct or inverse. Thus 6 • 3
ori:i ' ■ '
264. A Compound Ratio is the product of two or more
3 and 8 : 4 is 4
Xf
ratios. Thus, the ratio compounded of 6
= M = 4, or 6 X 8 : 3 X 4 = 4.
265. From the foregoing we deduce the following principle*
of ratio. ^
Ist. Multiplying the comequent divides the ratio ; dividing the
consequent multiplies the ratio.
2iid. Midflplj/ing the antecedent multiplies the ratio; dividing
the oiitccedent divider the rutin.
3rd. Multiplying or dividing both antecedent and couspqneni
by the tame number does vnt niter the ratio.
KXAMPLKS FOR PRACTIOB.
What is ths direct rati<i of
1.
64 to 6?
2.
108 to 18?
3.
7 to 21?
4.
ITtoCS?
i.
Mtoll?
4ns. 9.
6.
7.
Ant. \.
8.
9.
10.
13 to 62?
5:Uo212?
72yd. to ^yd. ?
60w»t. to 4/ar. ?
m. to 2Qg<d. ?
Ant. 120.
■Si
II ^11 i i
!
164
PROPOBTIOII.
Requirtd the inverse ratio of
11. 27 to 81. An». 3
12. 72 to 8.
13. 16 to 48.
14.
15.
IG.
42 to 6.
.02 to 2.503.
256 to :V2.
Ana. ^.
-~ .^ .... ^^,^ 20b to ,yi.
\l' wl''^'* '^ ^^* greater, the ratio of 86 to 240, or of 45 to 72 ?
10. VVlmt is the ratio comDounded of .^.'i In ift. fin tn 7?; anrl
hat
10. VVlmt IS the ratio compounded ol 35 to 40,
to 1 9 ? '
19. Tfthecone-equent be 32 and the ratio 4?, w
cedent? ''
20. Ifthe antecedent be 7^ and the ratio S, what
queat? *'
PROPORTION.
60 to 75, and 21
Aus. Ul.
is the ante-
Ans. 7'.
is the conse-
Ana. 12.
266. Proportion is the equality of ratios. It is indicated
thus, 6 : 3 : : 8 : 4 ; or thus, 6 : 3 r^ 8 : 4, and is read 6 is to 3
as 8 IS to 4 ; or the ratio of 6 to 3 = the ratio of 8 to 4. Hence
every proportion has two couplets and four terms.
267. The Ext-omes are the first and fourth terms.
26H, The Means are the second and third terms.
265>. .^inoo in a proportion, the ratio of the first tothesccon(!
term is equal to the ratio of the third to the fourth term, the pro-
portion, 6 : 3 : : 8 : 4, becomes f = |, multiplying eacb member
by 3 and 4, we have 6x4 = 8x3. Hence,
In every proportion, the product of the means is equal to the
product of th^ exirerues,
270. From the foregoing principles and illustrations, it fol-
lows that, any three terras of a proportion being given, the fourth
may readily be found by the following
271. RiTLE. — I. Divide the product of the extremes by one of
the me. ins, and the quotient will be the other mean. Or^
II. Divide (he product of the means hy one of the extremes^ and
the quotient will be the other extreme.
NoT«.— \V« will denote tke required term of a proportion by the letter «.
EXAMPLES FOR PRACTICE.
Find the value of a? in the proportion.
9 : 16 :: 36 : a,'; a? =
16 X 36
= 64, .In*.
1.
2.
3.
24
7
16
What is the value ui x in each of the following proportions;
4. 42
96
42
X
70
14
; X
10
: 3
. xl
96?
40?
x1
Ans. 56.
Ans. 16.
Ans. 64.
X : 15
^ 3:9? Ana. 5.
6. .17^ $10 :: 366a. -.xbu.'f
7. 2yd. : 8yd. :: $34 . x'}
8. 7.50 : 18 :: xoz. : 7^o«. 7
8IMPLK PROPORTION.
SIMPLE PROPORTION.
165
Jlll^Xtl/Z.l''''' '' " ^q-lityof t.o.i.nple ratio-,
the^Le'rafJ? "^"^' ^^ '^''^ ""''' *^^' ^^^^ ^'^^ ^2 yards co«t »t
yd.
13
$
OPEIIATIOW.
yd- I
: 42 :: 30 :
___42
60
j20^
12) mo
* = $105, Am.
Eldcidation.-To arrange the g.vennumberBin
1 V *on°.u FoP'>''t'on. or "<"<« tht. qwMion, we
miiKe iSdO the i-A.rci term, beeause it is of the same
kind as the required /owiA term; and, as from
the nature of the question the latter raustbe great-
er than the third term, we make the greater of the
other two numbers the leeond term, and the less
tney»r»«; and then, the product of the me» -3 di-
▼ided by the rlren extreme, givws the ^ .oina
THB GAME EXAMPLE BV ANALYSIS.
Yi^^/t ?f i^®'-n y*^^7'" cost ^j of $30 = $2.50; then, if Ivi
8t^$2..0, 42j.d. will cost 42 times $2.60 = $106, the answer, a.
oost
before
Aa^f'v}' f-^^so'/ljeM consume a certain quantity of flour ia 28
days, how long will it take 70 soldiers to consume it ?
OPERATION.
tSolJien. Soldien. dayi.
49 ;: 28
70
days.
7
14
5
= 19|, ^IM.
Elo«idatiok.— SiDoe the reqaired
answer t days, we make the (ivan
dajs the -'i term. Then, as the
flour wiU nut last 70 soldiera lo lone
»« It wiU 4a soldiers, we make 49 mU
diers, the snalUr of the two termi,
the Hi>cund term, and 70 soldiere the
firtt term j and proceed aa in the firei
ezaiuuie, ezoept that we ahertea tiH>
work by eaneeUatioa.
THB SAIIB EXAMPLB IT ANALTSIg.
times 28 dai/ TATf ^^" '^f" \^^ ^""^'^ '^ ^"1 "^^^ 1 «-'^ier4.
IdU days, 70 soldiers will con.sume it in ^^ of 1872 davH = 19^ day*
27». KuLE.— I. Writ§ the givm numben^ that u •/ th§ imm
name or kind a$ the required fourth Urm, or anmer, /^r OU
third if.rtrk nf thm 9i#>/».ui ../.'«•. "^
II. Of the other two numbers, write the larger for the eeesnd
term and the less for the first, when the answer shmdd exceed ih4
third term; but write the lets for the tecond term, and th* larg»
for the JU'tt, whm the amwrnr ehomld be hu than the third tmm.
\%
s
t i f!
I
.1 ( *
166
WMPLE PROPORTION.
III. Multiply the strond and third tenna togethm-, and divitU
*Jieir product by the first; or divide the third term by the ratio «»/"
ihr first term to the second.
N0TK8.— 1. When the first and s.-oond tefus are of diffornnt denfjiainatioE,?
they must bo reduced to the same denomination; and when the thir ; terra n %
co!i)|miin 1 number, it must be roduced to the Soweat donouiinat^om mei^tiooed io
'^'o "u '*"''*'.®'' ^'" ^^. of the same denomimition oa the thinJ term.
2. I'ho pupil should 'perform these questions bf analysis, 3 4 well ae by p»»-
portion, and introduce oanoellatioa when it will i tbreviate iiid wvjration.
EXAMPLES FOR PRAOTIOE.
1. Six laborers earn $7.68; l.ow much wiiJ 10 laborers tHrn? 3«
'a'^^rer^? Ana.%\2M; $46.08
2. Il2.ilyd. of c!'^;!i cost £25 3 3; how much will 198vil coi't?
12t)yd.? 137y.l.?
3. One-half a bu
..«». £11% 15 ^%^ £139 4 3fJ; £1517 4J|.
-"hvii ai «> H coats ^i,S\ eta. ; how much will 16
buphelscost? U buflheic.- T:^, hiuIjplsY 86^ bushels? 90| bushels?
105^ bushels? Am. $14.56; $30.94; $65.62; eu;.
4. TiGlb. of butif-r C6t,v ^^iS.lJb ; how many lb. can be had for
112.61? .125.74? 8o2.b7? -$36.40? An$. 971b.; 1981b.
0. "*
7^cwt.
, wu.u. ^ e*c.
what is the value of I il
a c\v
. If a cwt. of tobacco is worth $39.25 :
wt. ? 561b. ? 931b. 4oz. V 107|lb. ? Ans. $0.3925 ; $294.37^; etc.
6. The I of a cwt. ofen.a;r,r cost?6.48 ; what will be the cost of *ci
:\vt. ? f cwt. '■! ^ cwt. ? ^ cwt. ? An.$. $6.72 ; $7.20 ; etc. -f
7. If 40^ arpenti? of land are worth $215.50 ; what is the value of
}} arpents V 70 nerchM ? 90 toises ? 25^ arpeuts ? 10 per. 4 to. 10 ft. ?
liOi arpents ? Ana. $31.92^^ ; $3.72|J ; $a,53U ; etc.
8. The 1*^ of an acre produce 18. cwt. 1 qr. 12 i)L of hay ; what
quanuiy will 1 Mr« produce ? 8^ acres ? 36^ pert
9. At Is. 8d. per lb., what quantity of coffee can be had for £3 68. ?
^^ }^,^^^H.^ 2i? £14 lOJ? Ans. 39|lb. ; in/^lb.; etc.
16 tons? 3| tons? 18| tons? Ans. $107.45 A ; $24.67 + ; etc.
12. If3|lb. of coflee cost 72 cts., how much must be paid for
74ilb. ? 96ilb. ? 10911b. ? 2lcwt. ? Am. $14.62 f- ; $18.90 ; etc
13. Six cwt. Iqr. lib. of beef cost £13 7 6, what quantitr can be had
tor£8 12 3?£1 8?£17 12 6?
14. For 171 days' work, $26.44 were paid ; how much will be paid
tor 1 day's ? 45^ days' ? 89^ days' ? Ah$. $1 .44 : $65.52 ; etcT
16. The rent of a farm containing 12A. 2R. .30per.is$ : 13.75 ; what
is the rent of another containing 5A. IR.? 16JA. ? 59A. 2R. 20per ■
10|A. ? An». $47.06i + » $145.24
1 fi. Savon KtiaKAlfi ^^'«n<«A -*^«* ©O *TC: . 1- -v-— 1- *ii 10
«.«,w.. ,,,..,-,-,,,, .!i Tl\ra wcsts;c7. ju j UuW UiUt/U Will I in
cost? 18^ bushels? 26J bush
etc.
17. In paying $11| for M28 . v of bowda. irkat quantit
badfor$119j^? $230.60 : %iU,m
Ans. lU54( + ft
>^
'-•W.
18. I can get 336 pens for 3«. id. ; how maajr o«d I get Ir^ S.I t
44T£3 10 14? £0 1 1«4?
2944:
srMFLIC PEOPOBTIOM. |f^
^anuxi had l.e worked 6 dayt more ? ^' ' *'"'' much would he have
h«i /i -^ P"*«''^« cost as ,„uch a7 7 Hnnl« ^ ^"*- ^^82.
be had for H5 peaches? 280 S^^^^^ how „.any applet e.n
ti« creditors to pay ^O.e/on the douL K "P^^' r'"Pr-n»i«ed with
on a debt of $256;^.50 ? "*'^' ^^''^ """c^ ^i" one receive
26. What will be the orice of 21 A tn on ,^"'- ^1640.64.
cost £815 ? P"°® ^* ^^^- 3». 20per. of land, if 36A. 3R.
27. If lOcwt. 2ar Ulh r.e ■^"*- ^187 10
pay for 8cwt. Inr.^U lb ?' '^^'"^*' °^"* ^^04, how much should w.
come M P^-S'"""" «, 40 „.,. ti, k„„j,^_ ,^„ ^„ _,^_^^^_^
<»il each creditor rwei.e ? i^ B t« I P?"^/,'^ '■'^^'*»'' = '^^ ""■"l'
33. If a bowl containing 2 cul.io v,i io .• ^ • "*"*• -^^ ^^ 3. /
niany hours will b- reaum^d t?. «. ^ " ^""^^'^ '" ^^ miautM; how
and 21v,i. deep ? ^"""^ '^ ^'•"P'^ * °'«tern 4yd. long, 3yd. 'wideT
34. One of two pieces of cloth costs &^-i^ ^u .u '^^'- ^ **°"''«-
the ,e„,.b „,eact^„o,i„, rtr:S^?f,t^t^»J^-*„^^^^^
,^ ■• WM„ .t.„,„eo4 «*'.^s.Tk„o.■„g.bat''.re*/;l.
. 38. If the raooa mov-a H" in» ^irm • ^ '*"*• ^^0 ^8 6f
itp'.rforra its revoIuT.on"? " ^^ "» ^P^ ^*^' '« "hat time will
4L''"T'''' ^'^p'- - condition ir; ?lt 'd-*' ' "i"
"".A iif^' ^'**' '"any ehall I receiva?" ' -aou.d receive o per
40. What is the value of 7 b Tin. .<• >'^'- ^«*. 6247.
worth $120 T "*• ^^^■- o^goH knowing that 7oz. are
41. The I of a bushel of prune, ao-t fill k * ^»*- «i«28.67f.
b« bought for lA ' ^' * P*'* ^'^ • bMheloao
m
Ji
te I
IM
COMPOUND PROPORTION.
!l
*^' i,^r**J^'"^ merchandifie for the mm of «5600, Iloat f4.60 ob
every $100 ; how mucli did I disburse? »».o^ o«
4H. A pound uf cin.ianu.ii co.st. $1.10; for how much Hhould 1 re-
tail It to gam at the rate of $-.0 on every $1000 ? Ant. $1.15A
44. Who,, metallic pens are (V^ cts. a doBen, how much will 101
gross cost? 16J gros.Y 25J gros8? Ans. $H 061 ; etc ^
4o. When profitH are :j;5U on every 100 yards of cloth, how many
yardH jnust be sold to raise a profit of $850 ? Am. 1700yd.
48. Two pieces of cloth are respectively 41 and 36 yards • the first
piece costs $46 more than the second ; required the price of each.
AQ wi. u . • .J » 4««. let. $369; 2nd. $324.
49. When wheat is sold at Ts. 6d. the bushel, a loaf of bread
weighs 9 ounees; what should be the weight if wheat i<, but 6s. the
bUBUel J 4njj I 1 1
50. Every soldier in a regiment of 1000 men is to have' a Jatch-
wat;eachcoatw.ll take 4yd. of cloth which is 1 5yd. wide, and is
be l.ned with flannel, 14yd. wide; how many ya'L of fla. nel wiU
V. required to hne the whole ? Ans. 6625yd
61. Jo draw success on my business, I propose to give $5 to thf
poor every time I gain $150; how much willYhave gained when Z
al.^ amount to §100? ^ A^s. IsX'^
62. John can plough a certain field in 6 days, and Maurice in 6
days: what time will both take, working together, to plough the
63. A father earns 68. 6d. per day, his son, Ss. T^d ; in whaUimc
vnH^they have economised £1 iO 3, if they exjend but 58. ^J
5^*.?"'^'>""*'?,T.^^ ' 5*y ^''' P*^'"g * y*^ ''^•ch i8"'60^5ft*ng
and 44ft. wide, if 14258q. ft. cost 5>;!41 ? ^
65. Two gangs composed of 20 and 30 men respectively, did 1600
vards of a certain work in 25 days ; how much would the/have done
had their number been aug nented by 15 ? Ans. 1960 yards.
66. One hundred degreer. of Centigrade are equivalent to 80 degrees
3f Reaumur; to how many degrees of Reaumur will 232 degrees of
Centigrade equal 7 ^^. ig^o ^f Laumur.
COMPOUND PROPORTION.
»74. Compound Proportion h an expression of eqwtlitr
oetween a compound and a simple ratio, or between two compound
8 : 4 I ■ * ^* • 6, li » eompound proportion.
Tfc*t «, 12)>C8 : 6X4 1 : 24 : 6 ; for, 12 X 8 X 8 =« 6x4x14
OOMPOUND FBOPO»TIO»
>st f 4.60 OB
'Ijoiild I re-
t. $1.15^.
h will 10\
06i; etc.
how manv
. 1700yd.
nng2|cwt.,
he smaller
a ; the first
of each,
id. $324.
if of bread
but 68. the
9. IlioZ.
; a watch-
<le, and is
lannel will
6625yd.
$5 to thf
i when my
f. $3000.
urice in 6
)lougli the
A days.
what tinae
ut 5s. per
■ 6 days.
i05ft. long
, did 1500
have done
yards.
80 degrees
degrees of
taumur.
equfilitj
ompound
lit
.n??!';""^" *4'° "raembering the questioi
?!,« «„n5"'."''°« '^'"^^- th. punil ,ho,ad writ.
9
SyATKllgNT.
$• Da.
72 10
* 6
Hr.
8
12
MU'HOD BY PROPORTIOlf.
I
MBTHOD BY ANALYSIS.
If 6 iHen in 10 days of 8 hours each earn «79 i «.— • .u
* ^Lr^k ♦'"^.-'P'0.80; and in 5 days, 5 x $10.80 = $54 Tf in
day,^hey U earn ?2' x 16 76~i$8f.' '"'' '^^ "^^'"« ^' ^^"'^ »
275. Rule.— I. Make that number which U of the Kitne kind
U. 2 hm take the othernumher, in pair,, Sr two of a kind
mid arrange them as in nmple proportion. ^ '
iU.}' ^*'*?.%'»»«^'»><J^ theproduct of the second terms by the
•tthwr Mrthod «r
•i«ticanj.o plain M to im«iMw,rul,. -^'■"*
■XAMPLK8 POl FKAOTIOB.
«1!! 5*^ /^f ?^ ^^^^ P°""^ " 5 how much should be receivad in
promf lu'°^," °"",'l''^, -Wok ""t m. «.60 eaosYnS'.' .
f7«
OOMMUND FmoPOmTIOK.
»««. NruU another wall bott. k. , „. „ a„ d rThlS "
f'H .t require 45 tailors tc u,ak.> :JOJ ccatetn "^ d- v ^ L
mU I* required to make 200 in 27 .lays? ^ ^" i"''^ "!f"^
Jl- »"""^ '?.'''■■'"' •"' 8 hr. each' M laborers were^m'S „ h
a fftbe carriage of 5cwt. 3qr. a distance of if i'J^ ''LZs^"^i%H
J^./« a fort there are provisions enough for 152r8oldierf for* 6
mmth,. If the garrison be augmented bv 1 00 men, whaVdS ration
>wedthflm. ifthevr. uHin i i^ o' ''"«**"'"'/ ranon
«*« »* allowed thflm, if they n
uain ' , .uc
longer ?
l<» 1* f3 1 • • '/ / " "«"! ■„ .uc. longer r
ikliLi r ^!* ^'^"^ ^^^ ^ ^'^''^^'> weighing 7ioz., when vV, at i^ 4s 2d
Sffe^^'i what should a Is. 2d. foafUjh ;hen wheat iest 6d
««•, Kr»6wing that 1500 give $lo interest in H r
|«M *»w/f»kJ r plac- at interest to give me $200 in
TS * work 86 7 mer hd in 28 day.s, or 10 hr. -
^»iv l6J§«oz.
iths, hat'princi-
ar l.$2500.
' n work, to do
h? ..iw. oda.
was Woven with
, . .•',-• ""■'-' s "' « yaiii wiuc , was Woven witl
f4^,^SrL^;u!.i'lJ7^«^^«f^P'«««i-f«* yard wide:
-4fM. .HS^y yards.
171
MROINTAOK.
PKRCENTAGB.
signify 6 oer>ts of eVerv 100 "'f^'^^o^evcry hundred. a„d may
^^ every 100 cents, 6 dollars of every 100 dollars,
ooS.'^'''®*'®''*^'"""'^''- ''" ""^^^'^ '^' Pe'-eentage ig
the pI,Z:,^. "" -'"'"""' - "" P'r«ntage, I iU Oifferenc +
■ijrmDoit.
Decimals.
^%
1%
4fc
5%
6fc
Hfo
10%
l^%
75%
\QOfc
\2b% ^
h7c
1%
%
of a fm„iber
Common fraotions.
\7o
« «
« «
« «
« <(
<< <.
«
«
«
«
.01
.02
.04
.05
.06
.08
.10
.18
.75
" 1.00
" 1.25
" 005
«
of it
« u
it «
« «
« «
« <<
« «
« «
t5^
TffO
«
.0075 " " „
.076 « " =
Tffcr
TffCf
T^f
/a
2
t
1
i
1^
«-^^l. Cask T. — Given, the ha.se and raff //» «*>^«i.
t.x. What 18 6% of 512 yards of cloth?
■JPEKATIOK.
^-'' *> = 4' Th.«for., 6^ of 512jd.
96
,ft,'?™T^% =.06. Therefore. 6«
«f 61 2yd. li. 08 of 5 12 « 30.72yd. ^
Or ^ J«-^2yd.^«. i.^o/!,^4
' 3«.7Jyd.
3fe:J«^Sfota,
ITl
0», 100% = 612ytl.
1% = 6.12y.l.
6% = 30.72j'<l. Ant.
Ptao«NTA(J*.
Or, If lao^ _
= S0.72jrd. Hence the following
511/d., 1% =^ of
a. 11yd,
mally^ and point off a, in dedmah. Or, ^ ^^^^^^ rf««-
A'firf that part of the hate which the rate % U of 100.
BXAMPLE8 FOE PRACTICE.
1. Wh.t « 5fc . < 1462? 4% of 1560? 8% of $630. J5? 7* of
^2. WH.i«., orsrorr r, »/2yi>t^Ll'?-^-,
^^3.^Whati«32^ or.n60.60? 4*^. of 4M^^oP34t?n|Tof
^^4^Whati« 20/. ofOOcwt.? i% off«50? i /Tf " S'sfb jt of
5. What i« 15% of^? 1% of.*80? 2^^^:^'? -rii ^Jfaj, ^g?
much did he spend for each ? 6 7»; '^ r sugar, now
« A u***; f'"" f* «S92.05; T. $986.75; C. |I776.ir,. etc
ml* ^rTi^n*"* v*""^'!' ^^•'^ ^*"«''' o^ '"<'l«««e« for $7125 ; ^adlold
for^wia iJcS 'nr'' '?*.f f ' * i'*^'^''- *"d *he remainder
tor what It cost. How much did he gam ? An». $1567.60.
2^3. Oasb ll.—aiven, the hate and percentage, to find the
rate %.
Bx. What per ceot of $450 w 27 ?
OPKRATIOK.
100
27
460 ) 2700 ( 6^. An$.
000
Of, A ^ 100^ = 65iJ,4fM.
Or, $450 = 10051^
1= 1%
$ 27 = 6^, Aft«.
Ahalt«m.-|450 101005^ of itself. $27 i«
^/ij of $450; therefore, $27 is ^2 7 of 100 <^
•r^of27 times IOO5K = 6j'of$450.
Jtk^oflOOjij = (J5tof$460.
Or, $450 is 100^ of itjelf; therefore, $1 ii
ihi^'^'^^H = 1%. "Hi$i27 i» 27 timw
1^ = 65^ of $460. Ueiicethe
' " ^Zy ■^'—'^'^'^'F'y ^"":» «y the percealage and divide by
P*^d that part 0/ 100 jper unt. which the percentage . o/th*
% 1
% =
ik,t
eued deei-
)0.
15? 75 of
i2; etc.
lib.? 11%
.6; etc.
? 6J,'« of
192, etc.
(? 9*% of
t5; etc.
E20 16 8?
B8 to with-
for tea;
w. How
ry; etc.
; and sold
'emainder
567.60.
Jind the
self. $27 ii
, of 100^,
, of $450.
tharefon,
Bfore, $1 if
27 timM
livide by
tofih*
PMUMINTMn.
BXAMPLBU FOR PBAOTIOl.
ITS
1. At what rate i)er cent. miuhI we place $20 to have f 2 ? |5 to
have*0.2y? *1440 to have $2l.G0 .' xlHO 5 to have £12 16 4^?
|4to liMve$0.30? Arts. 10^; f,^; etc.
2. Wliat. per cent, of 40 in 15? ut 180 perches in ;Miicr. ? of \^\ ifl
"A? ofi IS i? ofy2gal. iH llgal. 2^it.? Ans. 'M^^: ^%; etc.
3. What fK>rc«nt. of 148 i8 24'!? of 30lb. Avoirdupois is Ulb.
4oi.? of 720lb. ie 601b.? of G20jd. in 46iyd. ? of 1401b. is 771b. ?
An$. \(yi%; 37^^; etc.
4. What per cent of $578 iu $26.01? of $250 is $H0 ? of I is A?
of£.H 15 is.'l^. 9d.? Afif. 4i%; *-ic.
6. Whiit per cent, of $3(iO will give 25% of $72? Ans. ^%.
6. Bought a horse for $840, and wold him lor $560; how much did I
Ioa« per ceiit. ? Ans. 'i:\\%.
7. A number increaHed hy 2 equals 14; required the iucreaee per
cent.
J885. Case III. — Givm, the rate per cent, and percentage, to
Jind the hate.
Ex. I lof?t $27, which is 6% of the money I had ; how much had
I at HrHt ?
OPERATION.
$27 4- .06 = $^'.0, Ana.
Or, $27 -^- A = i*60 An».
Or, &% - $ 27.
100% = $460i Afm
Analysis.— If 6%, or .06 «f lome
number \a $27, that numbar Bust b«
$27 -^ .06, or ^, -: $460.
Or, 6% of some number ia $27, 1%
of it ii J of $27 = |, and 1 tin^, or the
whole number, is lOU timet^ 'i » $460.
Henoe the
3S0. llULE. — Divide the percent <ige by the rate % expressed
decimally, or in the form of a common fraction. Or,
Divide the percentage by the rate %, and multiply by 100.
EXAMPLES FOR PRAOTIOE.
1. 36 is 10% of what number? 84 is 7% of what number? $3.60 is
15% of what number? $55.50 is 4^% of what number? 240 is 12i%
of what number? ilna. 350 ; 1200; etc.
2. $66 is 5^% of what sum? 1^ is I ^% of what wum ? J is 30% of
what sum ? /Ih,. $1200 ; etc.
3. £32 8 Bis 7^% of how much? 207 is 60% of how much? $1.82i
12i%ofhow n)uch? Ans. £432 3 4
4. $2.81i Ih 121% of how much ? 3mi. lfur= Iper. i.» (>1%
is 12^
much ? 16i is 2^% of how much ?
-, etc.
Ans. $22.50; etc.
5. Jfthe perceiitage be $.^7.50, ind the rate 2.^%: what is the
Ana. $\ 500.
annually $145.60, which was 33|%of hie aaoual
base?
6. A
fkrmer saved
; required hi« ia«om« ?
^ i I
iij
I i,.
174
pmMmr7A«Hi.
3«7. Case W.—Oivm, the rate per cent, <md «w/yy,#^ «r
difference, to find the bote.
Ex. What nun)ber increased by %% of itself is equal to 477?
OPERATION.
1 4- .OG = 1.06
^77 -f LOG = 450, Ant.
^f' f5 = 477
^S- = 450, ^n».
Analysis— A number increjis*.)! (^ (^'/^
of iwelf, equal- loejjj, or 1.0(5 t4'il«^^<rtiiaife^
by the condition of tbe qu«8UQ«, j^ 4J^ <
hence, once the number equal* 41T .-t. IJW
- 450. «' -•r »^
Or, 65$ of .1 number is ., fi^ = J rf g|»
nun.b e,^„,, fg o^he number, ^^^"u^l^ Z^:::V%A ^
2«« Rule— Divide the amount by 1 plug the rate %, ^mm^
the rate %, expressed decimally, or as a common /ractiol
EXAMPLES FOR PRAOTIOB.
429.47?'^^ '' *''** """'^^'' ''^'''*'' ^*'»'°'^b«d by 59( „f k^if. ^^^
2. What Humber increased by 5^ of itself, gives £7 J 1*^' ^*^
;'; i.Il?,:^.*'lll%''' '^^ •"'^'•^ ^''•" -y neighbor, wiaat^^^^fe^
my neif^hbor possess?
4. The diflerence is $9.48i, and the rate, 12a*
base ? ' '
5 Andrew has £189 9 8, which ib 751J leee than .l
what sum has the latter? An$ £'i^^
$52"3n"'* ''^^ nuniber which, augmented by the 1% 0/
7. A teacher spends 45^ of his inoome, and saves f85fc: miK**
■18 income? » "o, vm«« w'm
8. After taking 1 2% of a pile of wheat, there remain 44 im4i^M<
how many bushels were in the pile? jt^a 7ti^
«^fi89^Krr'? '"«''^*«1'»/ capital by 15^^ of itself, I find Vt^
»5b82.b() ; how much had I at first ? |«w>««wi
10. A shepherd lost, by disease \2% of his flock : how luawy .J,*^
oomposed his pr.n.tive flock, knowing that there rlrnZ TSif^
1. A clerk sp-nds 20^ of6Gj% ...ore than i of bis incouW-^l-A
ic his income, iflie saves $533? '"^vw*», W'MM
12. A gentleman sold two horses at $120 each ; for one Uft^^sA
2b% more, and for the other 25* less tha,. hi« v«l..» • Ji I :^/?^^
13. A man wishing tr. sell a horse, asked 25i;^r;';ilnr!S!
he finally so d It for 15^ less than his asking price,Tnd gSu*d f?£^
H«m much did the horse cost him, .ad wba! iras his m£w «£f
Am. cont, $120 ; wkiiii prt5 !iS;
175
omiifftt #f
MISCELLANEOUS EXAMPLES IN PERCENTAGE.
An
:.s\ ] !. 7! jl.
J-^;»'^Jf ;'<"70cut. Iqr. im.
2. *lg IS 1% „f what nnm^T? .„, 3.,on
3. P.nd H munler which, .!Hr,ini-he,l bv \i^% of itself ^ive. iJS"
nianyremaln? ' ^"''^'' remainder by sickness; how
6. I 8oJd cloth at :£! in q « . j i- , . •^'»«. 819 men.
how mucl, did i, "i!. ^L , ^ ' "'"'"' " ''"' "i* "f ""• <=»»' i
-hat LZ ;aS."t '"' "'''°'" ■' '■'*«"- "- hi "weetlv ™1 +;
baL4'r'hS:tsct:^3fd fo-ii,"^'"' ' """ '^- «^i=o '"''■ tui:\e
Jj. Waatp.. cent, of a „,„„b„ ,ive. 3.J« „f ,,e |*„T,f,lt..
did tbe cargo TOtbim? '"°'' """ "' " '»« "f-'-^i li«' •"»ol,
H. There remains 2^,' vd fl »; >. *• ■• "*"'''• •^J827..'50.
or iy „„a, .™, 0. liX"',,:^';: ,°' ""™' """t;'?i'tV''*
».«; ^.t^M^S or bf ';„,:S'!"" ,'--. .<;.."« tLe'Veattas
habitants ? ** population j what is the number of its in-
16. A fi8h.n,onger had 720bbl. offish, and sold 2Sftlf ^ ^T^"^'
cent, remamed unsold? ' ^«Hbbl. ; what per
{s* Gav- J'^'p'^ ^'^^ «^h"- "'-"V lb. ? .,„, ifSt s'?'
lo. viave to aBenovo enf R,,f.;rf,. 901 i i. . I'THI), boz.
of my entire crop ■^Z^^^^T^f''^'^^ "'^J'^'' ^^^ I'45^
19. What per^cent. of ^0"^ o 1 jve^ ? '"'"'"'"^ ^ '}'''' ^^'
20. Joseph having received^aiiiv V • ,- Ano.'lh%.
A short tinfe after, hl^^l^lJfSTl"^ 'V^^ "']' '" ^^^°k'
remained £1280 17 6- wLt wiV S. o^'^,''^''' ''"'^ ^''"e still
'ji r . . ' wudi was the Giracv ? Ai^i +'9ij'i ik on
?o«fo, oLrirr„r4 L^eur.', rs ■ ,^ ,;''^- ."■ •- -*>* -i^
battle, and 6* 5?S" eLfder di^'n'ni; ^'''' ''^^f. ^" ^''^' ''^^'^ of '
The ditfer«a*betweeri?numbe^onlrH ^^"t^ ''^^ ^'"'^P'^^'^'
wounded WM 164, fcow«»lv Z« . ^^!?'^ ""'^ ^'^^ "»"'l«"- ^fth*.
«i io» J MOW muv BMB compofltd th* army ? ,*«,. 22d00.
17<
PEBetJHTAat.
Lef>' r ^r, ce :* Va^ T^^'^^l *^« ^itj. whieh distance i, 9A %o(
^^. Th. taies orr, rca'm&ah 1!''''"^ ^'^''' the co,ui,at ?
yearly; tiieVonhe^"^"'*'^'''^^"^^"' *'«^""t to $i^
the value of ih.Clorj ? ' " '''' '*'"' '*''' i«' '^^^^'J" 5 '^i-at i.
30 Mv ..Jn.. .<• . : . .""'^" *'^^ Pa»' more than Leo?
jear/aSfZe/aJS 8'^^'" '»^*° 'hVt of last
increase at the rate of 271^? " "> oe in 1879, euppoamg it to
nnt ^^' V ^«'»" of a nursery in two years wb £2?1% ''f ^'^^•
of the second year were 6* ffr«.«f^r *hu« fi! ^/^ *2178 ; the gams
^re thegaia« ofeach year?^ *^^ ^*'** '^"^ y^*-^' *hat
i4n« -twiner s % «n :;
— o— «••■» wi ratjii year i
I4 4j^,2iid.yr.
t 2L% then, 349( of
q^i T I J 1,X^^' gwnsof ide let. year; £1120 1
much remaios i„ the bank?^ ^'^ °^^^** ' '^1 tro'^'o^"^
what per cen? of hi' rlrenuf ,?;afh'ar"t!^t/' *'! ' 1""J"««. W6 ;
remains? T«? 9I 3!^ oroS®' ^""^ "^''^^ P*' cent.
35. Ifanomberbeaugmentedtfli/Jf il/*'^^^^^ ^^*^-
whirrs "KS^'V^'^-^^r •" ^»»^ PU'«haL'%oe,
the whiHkJy ; but he lost Ji^' ^'^ ^^^J^ «» the -ine *i»d 5% on
entire sal JifiS 10 ^hoi1?Jh\^\^*'''.*'' '^««'^«^ *'«>'"»'•«
ehaodiaer ' ""**'^ •^'** ^e pay for each sort of mer-
Maurice? ^'*^'''^*^«*^?«*her $22320, how much has
wiiL\taStf"^5?0o"TtTr 'f ?rn^ ^° ^''^ Ist.'trFtw,
er as fuUom Feb Si' .t l v"*^ ^^ '? "^""'h«' I read in his Ledgl
S,,,;, 1 ^ ' ^ - '^^ S'"" ' *^"'V' J 3* loft« : A n«ua« .lo< „„:.« !
— ^.- ...J . «»^ain, jNov. 4^% gain; what were the net
monthe ?
!-■ - /w .^jo, v^cL. ^ijt iruiii: J^
profile o( hi* businesa during the
:li
nVPLI IJfTlRlBT.
SIMPLE INTEREST.
in
.u*i*'?" 'i**6f®St J8 tbc compensation mado bv the hor«— , t.
the lender for the use of money ^ Dorrower to
22?" J''^ P^inciral is the sum lent.
of 8100 Jl^4 ^/® per. cent, is the interest paid for the loan
%yTyJ '^ ''"' '"""" "^^ *'"^« -hateverfwhioh is ordr
No«._The rate par -at. i. ootnmon.y a,pr„,ed d,oia.ally « hundredth..
§22" I^^ Amount is the sum of the principal and interest
2»3. Simple Interest is the sum paid for th« „J T!?
principal only, durin,. the tin.e of the lof.' ' "** ^^ '^'
It T^nf;,- f ff^ Interest is the rate per cent, established by law
It varies m different countries. ^ ^'
?oX-^''2t:^r,lfZZS^^^^^^ ^e ,aws of tl.
intended by the partie*. ^ ' "'"'^y* "nd«*"tood to be the one
a»5. Usury is a higher rate % than ie allowed by law
N0T.._The law prohibit, u.ury and uiake. it subject to a penalty.
296. '^<>Md the interest on any sum, at an, rate %, for any
number of years and numiks. "
Ex. What is the interest of $780. for 5 v(^'a.t» am< a .l .,.
years), at 7515? What is the amount ? ^ •°*^ ^ ™'*°***'' (^*
OPKKATION.
$780 Prin.
.07 Rate.
154.60 Int. lyr.
5i
1273.00 " 5yr.
13.66 <' 3rao.
$ 286.65, ,^..
780.00 Prin. added.
>Hyr.
ANAtTsrg.-The intereet of ,j,l for I yea- at
— :*o^.'jO. If the interont Of $780 for I year
Or, jj,j of the principal « the interoat for 1
year at 7^, The amount u found by adding
the principal and intermt together.
$1006.65, Amount.
397. Rule —I. Multiply the principal by the rate % »•
pressed decimally, and the product will give the interttt for <>m^
year, ^ ^**
II. Multiply this product by the number o/ year$, and the month*
as a fraction <}J a year, for the interegt required
The amount {» found by adding the principal and interett to-
gether.
NoM.-When part of the time for interest >■ giren ia aeBtha er d^n
.»onth u eonrider.4 « ^ of a year, aad one day*a. ^ of TmouA ^' "^
6*
t I'
1ft
SIlfPLl INTBU0T.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
16.
16.
17.
18.
19.
20.
21.
22.
23.
24.
BXAMPLE8 FOB PRAOTIOl.
What ie the interest of
* lb tor 7 years, at ,9^ •/
J656 for 2 years, at 7^ ?
SlUO for 3 years, at 8^% ?
M7 I'J Z'"'.* y^ar« 6 months at 856?
$76^50 for 2 years 2 months at 5??
|444.44 for ..years, at 6f5«?
I2^2i fl/*"/ * r**'' 2 months, at 75^?
fIfe7I.32for 14 months, at ()56?
What i!^ tlie amount of
181.81 for 8 year« 4 months, at 6%'f
$894 for 20 months, at 65<?
»760 for 6 years 7 months, at .5^^ ?
An$. $54
4n», $8.96.
iln/?. $155.62.
Ana. 1435.
-4n«. $166.86|.
Ans. $45.27.
/Ins. $8,258.
/ln«. $12,892.
^ns. $8.28 + .
Ans. $78,414.
Ans. $656.5125.
Ans. $116.99.
Ans. $60.39.
Ans. §1110.284.
Ans. $8797.25
Ans. $122,715.
a»S. rojind ths interest on any sum, for any time, at any
rate %. *
SIX PER CENT. METHOD.
Jo^flnd .be i.to«. of »I for .„, «„«, ., e*, .!«,, « aaj- oth.,
I .'a.u' ■'' "'''' '*'■■ " '^ ""'' ''''•' " -"""J- Hence,
Sdaj's. Hence the "'""* P^^ ^ay, or 5>U(U for every
Sll>1^. Rule. —I. To find the rate —Galle.jpt^ uo.,^ « nc
«atrht iimftMT,
17f
IL To find the interest :-^„,,y, the pnndpan, eke rate.
27 dryeV "^^'^ '' ^^^ •"^'^«' ^^*«fiO, at 6%, for 3 years 7 months
OPERATION.
Tnt. offl forSyr.
" 7 mo.
*' 27 days.
" 3yr. 7mo. 27da. = $0,219^
Principal, $660
«
« 14
« «< (i
= $0.18
= 0.0.S5
= 0.004^
Analtsw,— The intoiwt <i(
the given principal it 600 timea
the interest of $1 for 3 years 7
"°i',"l«27day8. Ae the int.
?/»'f9rl/''.«$.0«, for 3yr.
It will be $.18 ; and lince the
interest for 2 months ia $.01.
for 7 months it will be as manr
bmesS.OI.M 2 is contained
m 7, or Sjots. ; again, g.nce the
Interest for daya is $.f07, for
2T days, it will be as many
times $.0f 1, ds rt is contained
:-- jn 27 or 4i milU. Adding
I»e.««, ,,44.87-0 ^.TJo'^O^IST'llEu'S
OPERATION.
10.48
0.04
0.001 i
= Int. on II for 8yr.
= " " '* " 8mo.
— «
«
«
«
<4 «
«
<i
II
« <i
9 days.
8yr. 81110.
dda
« « u u
4(
at I^l^
«7jt.
$0.521^ =
|0.086U==
tJ
10.608^=
$750
».608A
6000
46000
312^
$466.312i =» Int. required.
AHALTflii — After findinj? the inferii«t nf m *.- u •
method laid down in the pfo eiin?ra " ,e wL' "f !!° """' ^ «5l5. by the
find the interest at l^; I then mu- ipTy' . VT't ''" 'T' '''■ '^' -^ then
interestonJIfortfaofHventime atrT J .: ,^ '^"'' ^- *"^ obtain th->
_?*?;»?.l•;!r.^:..^|■«^'¥J■ ■■- greater „, l«. .k,„ „! .
IM
h
i -' i'
'.nil
I
I '1
I 'i
SIMPLE rifTMMT.
i.f-Ml.n.1 p„. ,f i,,e,f „ tt. Z; ^imT.".':*"' ';»» "■.'" '"'""• "4
unr
When the ,i,„e i, short, b„,i.«, „e„ „,e the following
>ou,aMA (TheVirZ a^tir^'f 'tT'''"'^
eeed at in the above rule. "iweat at b%,) Th, r, pro-
METHOD BT ALIQUOT PARTS
.09
Rate %,
Interest for 1 year, jSTTglsO
_ 3
Int. for 3 years, #113.8050"
Int. for 6ino. = i of lyr. 18.9675
Int. for2mo. = iof6mo. 6.3225
Int. for I5da. = J of 2mo. 1.5806^
!nt. for 3yr. 8mo. I6da. ?140.6756i, An$.
AK4LVfis.-HaTingfound
the f.pferest for lyr. and
then for 2 jr., the int for
.''mo. la ohtained by finit
taking i of I j0u's int..
tor (imo., ud tboii ji of
this last int. for 2mo. And
^mcolSdaygareloflme.,
or i of 2ino., we take i of
imo.V int. for 15 days.
The int. ag found for tht
fccreral parts of the wholt
time, added together, girt
the interest required.
VnTB wi,« ^i. . tne interest required,
ample is called $140.68 *' *''•' '°**'"«*' »" *•>• »koT« ex-
II. Anrf ^Ae interest /or the months and day, by aliqxmt na^t.
The sum 0/ the partial interests mil he the interest reqXed
METHOD BY MONTFLS.
Ex. What i« the interest of,m.20 for 4yr.7mo. and 15da. at6^^?
f X ^
= $6.7166.
^. The above u th* product of the prin-
olpnl, rate percent., decimally oxpru-eed
in souths ani «1i»«imaU of a mo«th. dir
U«i hy IS <-■ I X i.
^
12) 1.4520 = Int. fori jr.
.1210 XI Int. for 1 mo.
55.6
6050
6060
6050
fCTUMo. lai. 1^ 54 5 ^^
8UIPLE ranBMT.
181
METHOD BY PKOPORTiON.
«f fo .II^'sl " "" '"'"■<'" <"»^2'=»' " ««. for 4 ye.rs 6 „.<.,.tba
Sol. 100 , 6 X 4rr. 6„,„. loja. :: ,52.50 ;«, whence the
■XAMPLDS FOR PI'vACTrOB
«• n BOLTED BV A«T OF THB ^OVE METHODS.
What 18 the interest on
i* t3s22''r2l7 ^^"•^»'>d I6da.. at 651;?
fi. f H3 for 2yr. and I'rnc, at i^% ■?
;• f**.-^,^ '•^r lyr. and 6mo., at 6<fe''
S* f f J'?J ^'"^ ""o. 4da., at 6^ ?' ^
J-|i;-^*^'«^'y-«n'nOmo,at756?
10. i,b Jl ^ for 2yr. 4nio., at l^-'
16. $3^56 for fimo. ir.da., at 5%? *
18. $72.1 2A (nr i\y\. o„J = L ,i*'^
21. $7671.09 for .iyr. Sino. 5da a. <a:?
u. ^tLWr" '°"'» " '»*
W. iS68.8« for Ifimo. and Ma., at 10% ?
Ans.
Arts.
/4 ns
Ana. 156.25.
■ $1347.82 + ,
^ns. $14.84.
i^IlI.177 + .
Ans. $31.46.
Ana. $4,254.
;• -^8 15 2^.
^ns. $5.01 + .
'-!«*•. $16.86 + .
-ins. $;^6.396 + .
Ans. $1:M],S48 + ,
Ans. $20.04|.
Ans. $6,468.
Ans. $75,208;.
^n». £1 1 5I.
/!«». $7.70.
^n«. $459,94 +
Ans. $18.51* + .
Ans. 137.37 + .
Atu. $21.0.39 + .
Am. $2258.70 + .
^na. $10. U|
"^^
182
24.
26.
26.
2T.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
3H.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
oO.
BIMPLI INTEBBST.
$1040 for 6yr. Umo. 29da., at 7 %?
£24 18 8 for lOmo.'aud 20da.. at 7%?
$.')!. 17 for lOino. and 29da., at I %1
e048.12 for 6yr. Imo. 3da., at 7 % ?
$500 for 2yr. Cmio. 12da., at G% ?
f t)09.50 for .Oyr. oino. 4da., ai i< % ?
£92 12 for 2yr. lOiiio., at C^ %1
$G80 for 4yr. lino. 16da., at (I % ?
$2000 for lyr. Smo. lOda., at D ^?
$471.11 for4yr. and 8nio., at 7', %?
$190,016 for ;^n.o. 24da., al
H^'l
£427 8 8 for lyr. 5mo., at 5^%?
$708.20 for 2yr. 2mo. 12da., at ■[%%'{
$640.70 for Brno, and 26da., at 5^ % ?
$730.50 for IBino. and 23da., at (IJ %?
$'j50 for 4yr. 7nio. 9da., al i^4 %?
£81 10 for 2yr. and onio., at 4| % ?
$150.80 for 7ino. and 20da., at 7 J % ?
$1072.40 for 5 yr. lOnio. 5da., at •;.', ^?
$601.20 for 4vr. 2mo. 3da., at 8^ %'>.
$1425.20 for iyr. and lOda., at4.i%?
£319 10 9 for lyr. lOmo., at 4g %?
$742.30 for 4yr. 9mo. 19da., at (>l%'i
$1370.40 for 3yr. 4mo. 27da., al 7.^ 9^?
$160.76 for 2vr. llmo. 4da., at o| %?
$1463.60 for 7yr. 7mo. 22da.. at 6^ % ?
£184 18 8 for lyr. 9mo. 6da., at 3i ^l
What is the amount of
An«. $436,596.
Ans. £1 11 0i + .
^ns. $233.72 + .
Ana. $296.19 + .
Ans. $168.30.
Ant. $164,888 + .
Ans. £34 16 4 + ,
Ans. $26,037 + .
Ana. $:iGI.178 + .
Ans. $6.98 + .
Ans. $213.35 + .
Ans. $102,618 + .
Ans. $350.30 + .
^ns. $727.24 + .
51. $0,146 for 9yr. 9nio. and 9da., at 6 ^ ?
52. $1051.60 for 2yr. lOrao., at 7 % ?
53. $168.13 for 8yr. 5mo. 3da., at (i ^?
54. $100.25 for 2mo. and 29da., at 4 % ?
56. $1,011 for lOyr. lOmo. lOda., at (i ^?
56. $1000 for Syr. 3imo. 29da., at 5^%?
'".7. $168.60 for lyr. omo. and lOda., at 6i%?
6%. $2000 for Imo. 6da., eX&l%?
59. $0.06 for 20yr. lOmo. 15da., at 8 ^?
60. $326.25 for 2yr. 9mo. 12da., at 6^^?
61. $496.95 for 6yr. 5mo. 6da., at 6| %?
62. £109 3 9 for 7yr. 9mo. 18da., at 3|^?
63. $2560.75 for 4yr. 3mo. 26da., at 6^51^?
64. What is the interest of $1660 from April 9,
65. What is the amount of $175.08 from May 7,
».'^l uv.
Jns. $0.23 + .
Ans. $1260.045 + .
^«s. $253,119.
Ana. $101,241.
^ns. $1183.18.
Ans. $2013.12i.
Ans. $384.09 + .
to November 10,
Ans. $50.2S|.
1861, to Septeni-
Ans. S204.2r
66. What is the interest of $176.89i fix)m January 6, 1868, tc July
22, 1869, at 6^^?
«7. What is the amount of $175«.76 from Jun« 29, 1860, to Febru-
ary 12, 1863, at 7 f(?
•nfPU INTBftlM.
183
T, «7J»" '"'•'"""' °' ^' 2 « fro., i'aroh 17, to D«>,aib«
IMS. Ti%l" ""' '"'"*'■ °'»l"8-'9. ffon- Ma; 7, 1868, tojuly IT,
July ..TS,'..'^*?"'""^'' ' ' *°'" S«P««-*^"^ri8«;to
EXACT MBTHOD OF OOMPUTINQ INTEREST.
805. In the preceding methods of computing interest, which
are in general use, we have reckoned 30 days to the n.on h and
12 months to the year which allows to ea^ch year 3 b" instead
oofL^f oor^r'' ""''^ '^'""^' " these calculations are
The following exaet method is used hy business men in oom-
puting interest when the time is short.
p^e^^I'r^*** '*"' "°^ '"•*'' '* " '«" """» • y*'- •■ «■<"««» by the table o>
aO«. KuLE.--Jf«/<i>,/y <Ae interest of the principal for 1 «ear
Inf Tt'^Tn'' "-^ ^"^* *' ^ ^^^'^ '^^ *'"'^^««^' and divide the
product by 3b5, /Ae jao<jm^ will he the interest required
0,^'l8Ti;" 'ViV"'*'*'' of #346.60, from February 5, 1869, to Aug.
llt'imlH"^"^*' ^' '^ *• "^•^26.60, from J^^^^^^
20,
November 20th. ? .^ ^-ofl 2(i'
4: ^^ ^fiSf i""*^ "8* "f*""". from M«7l,ih:, 1868,' to
.. tr"4.,*m'r^ " '* *■ °' »'""'•«■ *»" '""^ »•*- '»«»,
..^ «1'4:i5ris?f,"^» o.- *a u ,. •« ^. ,„,..
ii
...4^
Hi
•4|
I J J.
*^ FAMTAL PATMflMM.
PARTIAL PAYMENTS.
2M»r. Partia' Payments are payn.entB of part (»f » not*,
Bw»«jOroth'rmoihyed obligation, made at different tim.M.
J he payments are acknowledgod by reooipta written by the
Skliwsement '^ ^^*^°"°^*'''" '''^''^''^'""' ''^'°^ "'^ ^*"«<^
,*f^*^'.^^y^«-— I- If *he iDt«r«Mt be paid by days .—Multiply
m pnneipal by the number of day which have. tUumd before any
payment was made. Subtract the /i^$t payment, and multiplu tht
nmnnderby the number of day which passrd between the firit
'*ml »eMndpayrnetU: Subtract the ueamd payment, and mtUiiply
thu fm^nnd^r by the number of day, irhich passed between the
U Ti '^"•^i'"^»»«»»'- Subtract the third payment, eti'..
«.i > '*," ^AeprodMC^A' together, audfind the intertst or i'heir
ntmfr/r one day.
m. If the interest is to be paid by the week or month :~
mm%iufe weeks or months for days, in the above rule.
£je. 1 . How much principul nnd intercBt have 1 1.> pay on the lol-
Kmttg note, due Dec. 29, 181 i .' ^'
^ ^^' Quebec, Sept. 8, 1868.
U^^tlZ^'^'r'^J I prun^r . to pay Jame. Carroll, or order, foar
hmdf^d Md twenty dollars, with interest, at 7 % ? Tlic.n.aa Brown.
On this note were indorsed the following payments :- -
Oct. 1, 1869, received, t22 28
Nov. 20 1869, " :;Voo:
M»7 8, 1871, " 247.87.
OPERATIOK.
FfSTO Sept. 8, 1868, to Oct. 1, 1869, there are 388 days.
" Oct. 1, 1869, to Nov. 20, 1869, '• '• 60 *'
^ Nov. 20, 1869, to May 8, 1871 " " 534 "
" May. 8, 1871, to Dec. 29, 1871, '< " 235 "
,^ .•-.-4r »f *^ *" '^^ ''''^' = »'85682.4« for 1 <Uj.
Balance | 99.86 for 235 days = | 2.3464.74 for 1 d»y.
Whole interest = that nf $,S91993.28 for 1 day
PABnAL PATMKNTB.
186
Inter««flt on $391 '93.23 at 7 % for Irr - «97dSQ KOfti
Hence, the i.t. f.r 1 da, J?2743&T-. 365 = JtsSt f/
Then interest due =$76.1767 + .
HAlance on note » 99,8500.
$ 460.
Principal and interest due $176.0267 + .
Montreal, January 13, 1869.
fJ: v.^'"? T"*^;'' *^*'" '^*^*' f promine to pay Loui. Merrill, or ,
fo^r^hundred and Mj dollars, Vith internal 6^. "r Value re!
A, N. Moreau.
I 325,^.
Kin/?f»ton. July 26, 1866.
tl,rl"/K!!!!"7Tf •^^'■^«**^' ^^ PfomJ^P to pay Lawrence Boyce, or order,
e ece .; '"'^'^'y^'^ •»'' i'^ ^loHare, with interest, at 7 %. Val-
"^^^^"''^ ■ L. R. Whelan & Co.
26^Sy"?T?^S!'°'S' ^""-l^' »8«7,fl2l.l8; M»roh 14, 1868, $72.46; Jul,
^6^by, $13J.65. How much remained d.m Sept 8, 1870 ? ^«*. I4I. U 1-f .
$1737^,.
Toronto, March 6. 1868.
4. On demand, we promise to pay Fisher & Howe, or order one
w«aSM"/;'"MVT'^°"*^'^^*^'*^^^^^^ Sept. 10, 1888, $70. How much
' A*s. $466.763-|-.
1 12 to.
Ottawa, Aug. 18, 1869.
*Jj *Y ""^^"^ received, I promise to pay R. N. Kelly, or order,
twelve hundred at.d forty dollars, on dema.fd, with interest, at G^. '
Joseph Rogers.
1869*'«4r^"rt ^"l'"*f«^,*Ji^^l^'„^^^*' *»''^5 0<"- 28,- 1869, $217.86: Deo. 12.
^ ^"^ ^ ^- Halifax, June 2, 1868.
ri^Lff ;.-'»^fe<^«^«J. Ipfomise to pay N. J. Web.ter, or order, on
demand, three hundred and four pounds six shillings and six pence,
with interest, at 6 %. I q^ ..^^pP,^ '
n^H^^T^M "^v^oiMSf^' ^1 1» «5 Oct «. ISflS, ^62 8 0; Dec.
11, 18M, £»4$} M«^ 2». 1809. £106 9 1|. How much wm due 6«t. 7
i
3;,
IMAGE EVALUATION
TEST TARGET (MT-S)
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4a
1.0
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I^I2.8 12.5
^m mil
IL25 i 1.4
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1.6
Photographic
Sciences
Corporation
23 WIST MAIN STREET
WEBSTER, N.Y. MS80
(716) I.V2-4S03
#
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PR0BLIM8 IN INTXRX8T.
$ 14696.50.
St. John, June 17, 1866.
'(if
■I. I
!i:
7. ln,r value received, we jointly and severally promise to pay
^ilwar.| Hiimmond, or order, on demand, fourteen thousatid .^ix Inm-
dred and ninety-«ix ^^ dollars, with interest, at8 ^. J. P. Rooiu-y.
S. E. Hamilton.
Rj?'^2i'f«'!.*!fn'"'''i?T' ;^?oPio^' ^^^' *4927.80 ; Deo. 7, 1866. $rS4.40 : June 11,
867 I1-J64.40; Feb. 7, 1868, $5685.80; Dee. 19, 1868, .*634.4(i. How much
^rnained due May 1,1869? i«..$2006. 2S6+
8. A farmer gave a mortgage on hie farm for §4875, dated June 1,
'^^^'■*f i'' P^'^ '"^ y^*''^' "''^'^ 7^5^ interest. Six months from date
?«7r*.>*i^-^f ' ^""K^^' ^^^^' ^^^^^5 -^"1^^' ^87«' ^7.50; Jan. 1,
i«n, fiju ; how much was due at the expiration of the given time ?
^fW. i8r,!l.')..Sl+.
probli^:ms in interest.
30». It will be observed that there are Jive parts or terms con-
nected with each of the preceding questions in interest, viz : the
Principal, the Rate %, the Time, the Interest, and the Amount.
1 he investigation of these involves five oases : I. To find the in-
terest; II To find the amount; III. To find the princioal : IV.
lo find the rate 5*; V. To find the time.
The Oases I. and II. have already been solved (296, 298).
SIO. Case IU.~ The interest, time, and rate %, being giv«n,
to Jin d the Principal.
Ex. What principal in .3 years, at 6%, will gain $47.70 interest?
OPERATION.
.06 int. of $1 for lyr.
_3
.18) $47.70 ($265, Ans.
By proportion.
$100 : ar :: $t; X 3 : $47.70.
AjtaIiTSis — We fiad the interest el
$1 for 3 yean. Since it require! 3
years from a principal of $1 to g»in
18 cents, it will require a prinoipalof
as many dollars to gain 147.70 m
$0.18 is contaiued times in $47.70 :
dividing, we obtain $265, the required
prinoipal. Henoe
311. Rule. — Divide the given interest or amount by the in-
terest or amount o/$l for the given time and rate, and the quotient
will be the principal.
EXAMPLES FOB PBACTIOE.
What principal will ia
1. 6yr. .Smo., at t5 %, give $66.26? Jin$ $2*50
2. lyr. 6mo., at 6 %, give $1.2924 int. T Atu. $U46.
PKOBLBMs IN INMMat.
3. Jnio 18da., at 4 %, give $27.60 int. ?
7. 8yr. 8mo 12da t/-^' ^"'.^ ^^^•''16 interest?
187
^»i«. $1800.
Ans. $120.
-4n«. $342.
8. lOvr lO.nn -ynV *' ^'^'" «'147.9485?
''*{;;' ^^^it is f he sum ?
to produce $619.15 ? ^"^ ^^^ *^*^''' »' 7^ eg,
313. Case IV.-
iiionth, is $24 for 90
. $400.
if- sufficient
-The pHndpal, time and int^est beinggiven
tojind the Rate %. '
^-. The i„t,reat of $750 for 4 years is $,80, what is the rate ^.
OPaRATION.
$750
^
r^O.OO) $180.00 (65g,^„,.
_180^
^^' proportion.
«'00 : $750 :: ar X 4 : $]80.
A^Ai.TM8.-Wefindthe5ntereet
on the principal for 4 years at 1 %
bmce the interest of $1 at 1 % fbj
4 years is 4 cts., the interest of $750
will be 750 times a. much, or *30.
Now, If , 'tJO is I %, $180 will be ^3
T'7J' ^ f'f!> '" contained times
m $180 J dividing, we obtain 6, ♦he
required rate ^ , gence the
rate % required. ^ ' ^ *' "'^'^ ''^^ ^"^'^'^'^^ «'^'^^ ^' t^^
EXAMPLES FOR FRACTIOE.
Required the rate per cent, if the interest of
\'l\lt^^V'^T- '2da.i8$1.3..36.
r «i J;; i o ^^'^ ^y**- '^'"o- 'S £3 JO .'-,3.
0. $125 for 3yr. 6mo. is $32..S7A
5' ll5r/'"".^^'"o^'"°- 2'^da- is $274.77.
8. $36 for .Syr. Smo. 19da. is $8,034.
.J. i 1 "^^f^ '■"^'' ^ '""'^ «^ or anj other
double iieeif in 14a years? / ""•t'r
Ana. 9 ^g.
Ans. 1 2 %.
-^ns. 6 %.
Ans. 7 %.
Ans. 7f %.
4n«. 5i 95.
a«m, be on interest,
. .ruu 01 ...10/. oy- whwi % was the dividend ?
to
814. Cass V.
■The principal, interest, and rate %
given, tofttid the Tim*.
being
s .
! "!
1 I
1 ' i
1 1
1 1 :
'ji 1'
188
PROBLUU IN INTimiST.
Mm. Ib what time will $460 gain $64 inUrest, t,t 6 %7
OPEKATIOM.
1460
M
•27.00 ) 154.00 ( 2yr.
54 00
By proportion.
•100 : $450 :: 6 X ;f i
Ana.
$54.
AwALTgia.— W« and th« iatcntt
oil the given principal for 1 y»r.
Since the interest of |1 for 1 jear ij
6 < tBt?, the intercut of 1456 will b*
450 times aa much, or $27. Now, if
it require 1 year for the t^ven pri«-
cipal to gain «!27, it will require aa
many years to }?ain $64 as $27 it
contained times in 554j dividing, wo
obtain 2 years, the required time.
Hence the
315. Ki LJi.~Divi(k ihe given Intere.st bi/ the interest on the
principal for 1 year, and the quotient will he the time reonired in
years and decimals. ^
aBddliJs~(bJ'2?0)i°"''''*'*°'*'" ^"°^*"*''' "y- ""^y »» reduced to «o.tlu
EXAMPLM FOR PRACTIOl.
In what time will
1. $26, at 6 %. give $1.95 interest ?
2. $280, at C. %, give $84 inlereet ?
3. $45.25, at, (i %, give $1.81 interest?
4. $98, at 8 %. o;ain .f 25.48 ?
6. $240, at t; %. uint. to $280 ? An$
6. $70.50, a :) %, give $31. 72^ interest ?
7. $408, at 7%, amt. to $434,18?
8. £120, at 4^ 56, amt. to £140 8 0?
9. $1, or any other sum, double itself, at 5 9{ int. ? Ans ''
10. $2365.24 double itself, at 7 56? ' ^ "^"^
An$. I jr. 3mo,
A7}8. 5 rears.
Ans. 8mo.
2yr. 9 mo. lOda.
Ans. [ 1 mo.
PROMISCUOUS EXAMPLES IN SIMPLE INTEKEST.
What principal will in
1. 6jr. 4mo., at 4 %, gi^'e $2048 int. ?
2. 6mo. 6da., at 6 %, give £136 3 6 int.?
. 3. lyr. 8nio., at 6^ 56, give $97.60 int. ?
4. 9mo. 21da,, at i) %, give £15 15 int.? .4
6. 3yr. 5mo. 18da., at oj^ %, give $288 int. ?
6. Umo. 9da., at 0^%. give £466 2 6 int. ?
7. 4yr. 6mo. 14da., at 5 %, give $150.37^ int. ?
«. 3yr. 6mo. I7da., at 5|%, give $1451.52 int.?
In what time will
9. $(;25, at C %, give $262,50 int. ?
10. £67 10 0, at 4 %, give £24 6 int.?
r •1779, at 6 %, give $296.6C iat. ?
Ant. $9600.
Ans £5237 10.
Ana. $900.
ns. £3H9 13 9 +
Ans. $1682.42.
Ans. £9000.
Ana. $675.
An$. $7267.71.
^n».7yr.
Ans. 9yr.
An$. 3vr. 4ii>r
PROBLKMb IN UtrBUUBT.
188
Aru. 4 jr. 9nio. 12dA.
An*. 2yr. 25dA.
An$. Ijt.
Ana. 6/r. inu.
Ant. HjT.
155. $242, at 4| %. give |55 int. ?
13. £460, at 5^ 9>. give £50 int.?
14. $2178, at 4/, <■/,, give $635.2;-) int. ?
15. £405, at 6%, ,Mve £151 17 6 int.?
16. $481.25, at :> %, give $1 92.51) int. ?
Required the rate %, if the intertHt of
17. $978.20 for lyr. is $18.91. An$. 6 %.
18. £110 12 6 for50da. is £1 16 lOA. Anif. 12*
Id. $1290 for 124da. is $19.99*. yln» 44?
20. 14340 for Hvr. i8 $.'.85.90. An>i a\%.
21. $675 for44mo. i8$l42.31i. Ana bi<jL.
22. 5^7500 for 48da. is $60. Ana. 6 5
23. $11004.75 for Ivr. is $550,231. Ana. 5 J
24. £120 for 6mo. Isda is £32 10 0. Ans. b[\%.
25. The annua) sales of a starch manufacturer amount t.' £2737 10:
supposing that bin profits are o % per year, in huw many years will
they reach £323 18 9? An». 2yr. 4mo. 12da.
26. An individual disposed of the I of hie lund> iii A % and \ at
6%; eT.ry year he draws as much as will pay the harne-sing of a
horse which ha^aess is worth $117.60 j what is ti^- Miiunnt of hia
<u«id8? ^7i«. $2800.
27. What is the interest of $17.18, trona July 29tli., i >i;i. to Sept.
let., 1868, at 6 % ? Ana. «4.214 + .
28. What will be the amount uf £19 15 9, at 1^%, from Feb. 17th.,
1864, to Dec. 30th., 1867 ?
Ana. £26 10 7 +
29. If $1756.75 is placed on interest, June 29»h., 18«6, what will it
amount to Feb. 12ih., 1869, ai 7 ^? Ans. $2078.869 + .
30. What principal, at b %. durinj' lyr. Hnio. 12da. will amount to
£231 12 11|? iin*. £21.3 10 0.
31. On Aug. 15th., 1860, I lent $5269, at 6%; what amount will
t)e due me on May Ist., 1868 ? Ana. $7092.164.
32. An individual buys 65|^ acres of land at the rate of $509.72
per 100 acres: if he pays only at die end ut iJyr. Imo. 15da., the int.
will equal to | of the principal ; what is the rate? Ana. 4 5(.
33. A person placed a certain sum on interest at 4 %, which pro-
duced £427 10, in 3 years ; what is the sura ? Ana. £3562 10.
34. What is the interest on a bill of $257.81, dated March let.,
^865, and payable July 16th., 1867, at 7 ^ ? Ana. $42.86 + .
35. Find the amount of $17041.20, at 4^ ^, for lyr. 7mo. 28d».
36. What sum is that which will give an interest of 1900, in lOyr.,
ai4.i%? iln». $2000.
37. A principal of £112 10 was put on interest, and at the end of
8yr. amounted to £144 ; at what rate was the principal placed?
38. A boy has accumulated a sum of money by his savings, and
wishes to obtain an annual revenue of $140; if the rate is b%, wha.
principal must he have ? Ana. $2800.
39. A merchant borrows the aum of £938 12 3, which is owned by
a minor aged 15yr. 3mo. 20da. He keeps it until the owner is 21
yeurs old ; what sum will be then due, at 6 % simple intere«t T
ill.
ito
PROBLKMB IN IMTUlHt-.
|{
40. What will be the Interest of $326, from June 6th., 1866,
Julj 4th., 1868, ftt7i%? - -■-' -
u.
Ana. $49.02 + .
41. A merchant eayw that his gain, during the nine years he car-
ried on business, equals the price of 3659 yarda of cloth at |2.08 a
yard; what was his annual revenue, supposinK he phiced his t'ain
on.nterestatS^? ^'^ !l,»,. $380,536.
4J. l^rom I85< to 1867, the population of Syracuse augmented 24|5g;
Knowing the Jasiyear'H number of inhabitants to be 102295, tell ne
what was the population in 1857 ? ,1ns. 82000 inhab.
rcot ,}^!^\ ^"'" '"»«t be placed on interest, at 4 %, to amount to
a1 a '" ^^'- *^"'° ^^'^^'^ ^»»«- ^563 2 1^.
44. A man assures me that if he places on interest a sum equiv-
alent to 968 yd. of cloth at $3.18 a yard, he will secure an annual rev-
'"Vr <^y ^•''•^•''^li 5 wJiat must be the rate ? Ans. 6 %.
4o From an investment of $35680 in commercial concerns, I
withdraw a gain of $223 per month ; what is the annual rate of the
IT^^ Ans. n%.
\^' ^J^^P^^'^y^'^ ^»^'^ for £2830 ; the conditions were £mO in
cash, £87 in 6 months, £625 in 10 months, and the remainder in
lyr. 3mo., with interest &tT %; what was the amount paid ?
• ,"\!L';^*"*^*^'°S raised, during the 6 years of his business,
*ooW o'.$29b5.10, desires to know in what time he will receive
$88y.u3 as interest at 5 ^g ? 4„g_ g-r
48. An individual borrowed £3750 at 7 %, and then lent it at 6 5^ •
• .*' ^o .n ^. '°^^ '" ^^^ ^*y«' ''■ th" y^^h f'^r tl^e first transaction, coii-
sists of 360 days, and that of the second, 365 days ?
49. During what time must a certain sum be on interest at 4A % to
P'^^cs I olit? Ans. 17yr. 9mo. lOda.
50. In selhug merchandise at 12s. the yard, 1 make a profit of 61 5fe :
what 18 the price per yard ? Avs. lis. 31 t- d.
61. Ihef ofaeumofmoney i8lentat4SlJ, andthe*,at5^; what
IS the sum, knowing that the annual interest is $28.82 ? Ans. $655.
62. An apparatus for astroncmical purposes cost £49 ; but, as this
sum could not be paid before 3vr. 9nio., the price was augmented A
of Its primitive value ; what was the rate ? Ans. i %.
63. A man placed on interest, at 4 ^, a certain sum of money which
produced m 6 years the funds requisite for the purchase of 368 lbs
of preserved tamarinds, at 46^ cts. a lb. ; what wtw the sum?
64. A merchant has invested in business a capital of $21840 which
produces him 12^% annually 5 but, for sanitary reasons, he retires
from mercantile allairs, and loans his monay at 7^5)^; how much will
^f «V1 ^^^' ^"'^- ^^'^^' ^y ^^^ ^^^^"S^ ^ Ans- 12636.86 J.
. n'^ -n '? ^''*' principal the ^ of which at 6%, and the remainder
at 7 %, will give $4340 interest? Ans. $70000.00.
5b. A speculator desires to purcha.se a tract of land, containing 450
t^u' ?."?? ^^ ^- ^^^ Wire, and, for this purpose, borrows money at
65 >y- ..t tl-.e expiration of -ijf. llmo. 20da., he sells the f of the land
at £fc 10 an acre, and the i-emainder, at £8 2 S the acre ; how much
does he lose by ihe traueaction ?
lu
CUU-
OOMFOUICD INTBBB8T.
COMPOUND INTEREST.
1»1
itl«. Gomponnd Interest i? interest on both principal and
itil. n>t, when tlie Inter is not. piiid when due.
doman" i """ '"^^'^^ '^ ''''-' *'^*'"«" «f """y- but cannot i*v"%
/•;.r. What is tlie compound interest or$390 for 3 years, at r)%7
OPL-RATION.
1390.00
$-iU9.60
$429,976
1390.00
.06 = J_»^50
|40'J750
.05 = 20.476
Principal for I at. jear.
Interest for Ist. jear.
Principal for '2nd. year.
. Interest for 2nd. yeur.
$429.97& Principal for 3rd.' vear.
.05 z= 21.^*9 875 IntereHt fur 3ril. year.
$451.47375 Amount for 3 years.
$390.01)000 Given principal.
$ 61.47375 Compound intsrei^t.
317. EuLE. — I. Fitvl the amount of the given principal at
(he gmn rate /or one year, and make it the pnncipal for the sec-
ond ij ear. -IT J
}l- Fmd the amount of thi« new principal, and make it the
principal for the third year, and so continue to do for the aiven
number of years.
III. Subtract the given principal from the last amount, and
the remainder will be the compound interest.
(a^^u^^r^' ^^«° *!»« ''™o contains yeari, months, and days, find the amount
ond interval, pjoceed.ng in all respect, as when the interest U pajablo year!??
EXAMPLES FOR PRACTICE.
1. What is the compound interest of $970
24 days, at 6 5g ?
2. What is the compound interest of $520
3. What is the amount of ^128 for 3 years
at 6 %. compound interest?
4. What is the compound interest of $340
payahle semi-annually, at 0^?
6. What is the compound inteiMt of $737
-li-annualij, at 7 f( f
for 2 years 9month8 and
Ana. $173,295.
for 3 years, at 5 qg ?
6 niontlis and 18 daye,
Ana. $156,717.
for 2yr., interest being
Ant. $42.67 + .
76 for 2^ years, payable
I
■ k\
'hi
1«2
OOWPOVND IirTKRn*.
6. What will $900 amount to in 1 year, at 7%, compound interest,
payaMo (juarterly ? Ans. $*.)64.67 +
7. VVliut IS the amount of $')00 for lyr., intereat payable every 3
monthH, coiiipuuiiil interest, at 8^?
8. Find I he cuinpoiind interewt of $94H for 3 years 4 months and 18
day^atG^? .Ins. $207,051.
iilH. Compound interest may be computed more expeditiouslv
by the use of the following
TABLE
Shoimng the amount o/$l , or £1, at 3, 4, 6, fi, 7, and 8 per cent.,
compound inltrest, for any number ojf years from 1 to 34.
^^Hh-
Years
1
t
3 percent.
4 per MDt.
6 per oent.
6 per oent.
7 per oent.
S per oent.
^^Hh:;^
1.030000
1.040000
1.050000
1.060000
1.070000
1.080000
2
1.0l>ii900
1.081600
1.102500
1.12;560O
1.144900
1.166400
3
1.092727
1.124864
1.157625
1.191016
1.225043
1.259712
^^^■i .^.'i
^^^^^^^^H 1
4
1.125509
I.169H59
1.215506
1.262477
1.310796
1.360489
^^^Hi ;
6
1.159274
1.216653
1.2762.S2
1.338226
1.402552
1.469328
^^^^H^
6
1.194052
1.265319
1.340096
1.418519
1.500730
1.5S6S74
7
1.229874
1.315932
1.407)00
1.603630
1.605782
1.713824
I
t «
1.26(i770
1.368J69
1.4774,55
1.593848
1.718186
1.850930
;■ i
" 9
1.304773
1.423312
1.651328
1.689479
1.8.38469
1.999005
I'l
10
1.343916
1.480244
1.628895
1.790848
1.967151
2.158925
11
1.384284
1.539454
1.710339
1.898299
2.104852
2.331639
, ■ '*
12
1.425761
1.601032
1.795856
2.012197
2.252192
2.518170
r ;
13
1.468534
1.605074
1.885649
2.132928
2.409845
2.719624
,r\'
14
1.512590
1.731676
1.979932
2.260904
2.5785;H
2.937194
^
15
1.557967
1.800944
2.078928
2.306558
2.759032
3.172169
, '
16
1.604706
1.872981
2.182875
2.640352
2.952164
3.425943
i' " 1
17
1.652848
1.94790L
2.292018
2.692773
3.158815
3.700018
i ! ^ .
18
1.702433
2.025817
2.406619
2.854339
3.379932
3.996020
- ■ i .
19
1.753506
2.106849
2.526950
3.025600
3.616528
4.315701
^^^^^^H
:.i
20 .
1.806lil
2.191123
2.653298
3.207136
3.869685
4.660957
" i '
21
1.KG0295
2.278768
2.78596:>
3.399564
4.140562
6.033834
i :; :
22
1.916103
2.369919
2.925261
3.603537
4.430402
5.436540
[■•. ' •
23
1.973587
2.464716
3.071524
3.819750
4.740530
5.871464
1|-
24
2.0o2794
2.563304
3.225100
4.048935
5.072367
6.341181
^^^^^H ^ *
25
2.093778
2.665836
3.386365
4.291871
5.42743!J
6.848475
26
2.156591
2.772470
3.555673
4.549383
5.807353
7.396353
{ ; 1
27
2.221289
2.883369
3.733456
4.822346
6.213868
7.988062
i" ! r
28
2.28792S
2.998703
3.920129
5.111687
6.648838
8.627106
' i
j '
29
2.356566
3.118651
4.116136
6.418388
7.114257
9.317275
i ; 1
5 1
30
2.427262
3.243398
4.321942
5.743491
7.612255
10.062G57
^H^^^l.
1
I'
31
32
2.500080
2.575083
3.373133
3.508059
4.538040
4.764942
6.088101
6.453387
8.145113
8.715271
10.867669
11.737083
HHI
i' ' 1
^1 1
i
33
2.652.^35
3.648381
5.003189
6.840590
9.325340
12.676050
■'
•
34
2.731906
3.794316
6.253348 7.251025
9.978114
13.690134
- '
Hj
L\
ll
itk*«b
•Mtokto.
iHtm.
•t f J? ^^^^ '" '^^ compound intewetof |9() for 7 years and
6 mon
OPIRATIOir.
Amt. of$l for Tyr., |l
Principal,
Amt. $[){} f^r 7vr.,
Interest of $1 for 6 mo.,
,605782
90
Int. of amt. for Gnio.,
Amt. added,
Amt. for "yr. 6mo-,
l^rincipal euttracted,
l'14.52"0:}so
4.;«50TU
.7226019
Analtsib, — We find tht
•mount of $1 for 7 yearg in the
table, and multiplyiiiofit by the
giTen |irincipal. olirain the »-
mount of the .j;'.i() for 7 year*.
Wo then (inJ vu thi,» auiount
tho intorest for tho « months,
and add it to its prinoifial.
From the hist nmouut snbtriicf.-
int; the orij,'inal principal, we
have left the compound inter-
est required. Ueuoe ttia
6.0582 1 :i'l
144.5 20:^.80
149.57859^.^
Comp. int. forgiv. time, $59.57 + , Ant.
»19. RvLE.-MnlfipI^ fhr amount of $1 for the. given mh
cnuitcme, as found m the table, by the given prind.pal, an,] the
product xodlle the amount. Subtr, J the principal frmn tht
aowunt, and the remainder will be the compound interest.
EXAMPLES FOR PRACTICE,
at 7^^^*^ '" *^^ •''^'"Pound 'ntere.st of $60 for 8 years .and 6 months,
3. What IS thecomp(.und int. of $3000 for 2yr. 6mo. ISda., at 6^?
6. To what mm will $7.5, deposited in a f^aving.s bank amo.mf at
jampouud mt«re8^ for 17 year«^ at «%, payable feud annual];?^
PROMTSSORY NOTES.
»20. A Promissory Note is a written or printed en-aee-
ment to pay^ a certain sum either on demand or at a specified Time
«i.?fj?' 7f,^akerorDrawerofa note is the person who
signs It and thus becomes responsible for its pay.uent when due.
33t2. The Pavfifi of » note ^h *1i'> n-rsu-- i-.-^'-, . ^ \
order it is made" payable." ^ "'^""' ""' *°^^'^^
»23. Thelndorserofa note is the person who si-ns his
Dame on the back of it, and by so doing guarantees its puyLnt
m«le« he wnta. " WiUiout fiiwurae "%ver his name at the Z«'
194
PROHI880RT NOTBS.
l! I 1
fa'l • 11
! ' »
S24. A Xegroilable Note is a promissory note which is
made p.-iyable to Ijourer or the ordor of some person (ifee Notes
ForviH, 2, 3, 4). r \ ,
in.lSSm!" ^^ " ""^* '■ '""^*''* *° *'"' ***'"'^''' '* """^ ^ neifocintcd without
H i^'-n^."°So!:[d'!J w,"!';:;: i;^ r^t;;.:^""" "''^"^■"' "• •^"'^ ^'''' «"■» ^^ '"^'^^
.•?25. A note nmy U, miide i);iyiihle on demand, as in jPrrrm
ivo. 1, or at the expiiMtion of a certain timn iirt,>i' its dale us
in Forms No. 2, 3, and 4. A note may he made i)ayal,le to a
particular person, as in Form No. 1 ; or to any person who is
the hearer or holder of it, as in Form. No. 2; or to the order
01 a person named in it, as in Fonn No. 3 ; and may be made
payable at a particular place, as in Fonn No. 4.
The Not", For7n No. 1, is due when the payee demands its
l)ayment from the maker of it.
llKMARK.-lf no time is fixed, in a note, it is payable on dornnnd.
The Note, Fonn No. 2, is payable to the holder of it at the
expiration of six eal.-ndar months from its date.
The Note. Fonn No. 3, is due at the time specified in it, to the
•jayee .vl,,. uhi.,r>t.s ,t. Jos. A. VViilter nuiv iiMur-,. ,1,,. „n,ein Ma„k
}„IU,u-H'*^r'^''"*!^''"^'»«'a"dthus make any person law'
thlVX; X '' "*• '''/^' P'^y'"' °''' ^' '"^y indorse it payableTo
Inntt * particular person, i^ which case such person can make
ftoother person the payee, w Jo«. A. Walter could, by indorsinHhe
note m blank or otherwise. ^ u<jrNi"s me
Th* Note, Form Mo. 4, is payable only at the Dank named in it/
820. The Pace of a note is the sum named in it.
l.?*f'^:^ ^^^^ Of Grace are the three days usually allowed by
/aw for the payment of a note after the expiration of the time
specified in the note.
SaS. The Maturity ofa note is the expiration ofthedayr
of grace ; a note is due at maturity. ^
be^Z'^tZ\l^a^tLTf ^""^'''^ '°*""'''' " ^"'•'^ ^' 2' «"d3. the interest
Deg ns at the date of the note, and continues until the note is paid. If the time
exp..s.ed ma note fur us maturity bo stated in months, calendar .nonthe a«
understood ; and if a note promises interest without stating the rate /itVZ
the iegal interest of the country in whioh it is d.t^d • T„ "'^ /^^'V- .! . *"
from the time it matures until paid. * in««weit
J:"i::;i!:'X^i^!!' -*j- -t" •* "'^*"''^ •* -'^ «- ^ "-« «»-
thoy a™ aronee'notifrd'Se;;:^: "''"•" "'' ** "'»'^"^ ^^ P*^ *' ^
^J^ a note matur« o. 0«»ia, or • legal MU^y, k .wt k. »»M « ifc, 4^
ote which is
>n {■■fee Notes,
Ifocintcd without
10 eum for which
, as in Form
: its (hx\('., (18
l)ayiil)le to a
eison wlio is
to the ovdor
uay be made
demands its
id.
L" of it at the
I in it, to the
iiHic ill Miihk,
person law-
t payable to
ion can make
ndorfiing the
nanaed in it.'
' allowed by
)f the time
of the dayr
3, the interect
If the timn
r tnonthe an
%, it bears
vhioh does not
^ of InWireit
tha same day
to pay It if
«i«atb*4af
Poun 9W
IM
»id?r?t*n ?"'^"f "« ?0t« ^ • note giren for a valuable con-
W«e or to an.'? k'" '^' '";''^*^ ''^^'^ ^^' *^« »»<»""* to the
P»jee, or to any subHequcnt bou„JiJe holder.
payee but Sll ; r u '" ""^ '''"^^'" ^^" '''^^'' ""ble to the
.oX"o„-ti::Sr\'i?r^^^^^^^^^^ r if - ^ «''»^'- *•" p-^- ^ ^^
A?.?eraCte^±^jl 7 ''' P"^'"^"*' ^ "^'^^""^ «-^ ^'--^a
to f fpToifi'td^" ouSf. ^''' " ' """^'^ P"'"^«« ^« ^«'^-^ ^^
«.o?^;rttferuivl?^ ^^ ^ ^«^^ ^- i-
to f!fut fh.^n?^ '' f 7'""" Obligation, authenticated by a seal.
aXer^:nSrrti\r;''"°"^^^ p-^~- -
proSc,fve??ol^'''^^';[^^'*^^8^^^«^^^^ ^ conveyance of
dition twlJ '"'"' *^' P"y"^"°* ^f ^ bond or debt, on con-
^Z^az^' ^'''' ''' '''''"''''' '' '-'' -•*
FORMS OP NO i ^S.
Far7n No. 1.— Demand Noti.
$ 64 r%%
-^^ee, ^nuat.u. /5t/i. , /<9'/0.
^a^ Msce^^^U
OtAMP.)
^£cu^
u
IM rOEMB OF KOTJB8.
I
Form No. 2. — Notk Payable to Beaker (Neqotiable.)
Forrn No. 3. — Note Payable to Order (Neootiable),
C/ne yeca oAei f/a^e, Q/ ^iornt^ ^o Aaii. lo ^e
(•TAMF.) S S^. :^^^.
Form No. 4., — Note Payable at a Bank (Neqotiabi-e.)
G^oUy e^z^ aJI(gl (/a^, Q/ /iio?^nt^e lo /lo/u tc
..^unA, &igfovU'iic'Vc7i diici, j^A ooiiuM. '^o'cicue iec^f/ifect.
^afovu
ijnAiaf.)
lon^ ^i)oua^
itr
lOTIABLE.)
(9'/0.
dtiable).
)TIAB1-E.)
'•<»'» AMD LOM.
Form of Produce Note.
Form of Dm Bm.
$103.
(nAMp.)
fUU
PROFIT AND LOSS.
336. Profit and Loss are coinmeroial t«nii« x,^a f^
the gam or lo« in business transaotions ^^^ ** "^^^
PrKd^Lt" ":. t"^ ^""^ ^' ^^-«*i- *• »- oooridered i.
2^d The ^^5' '<i °'>'""^ "T^^""' ^^^•^ » the Base.
^ Thf /? ^ •4^'^*" °'' '^**' ^hi«h i« the Rate 4
4th. The S^Uns Price, which is the Amount' I)iffere«>a
Tie questions follow the same rules as in Percental.
Own = Stmng Frice - Co*t.
"I, r
Its
PBOVR AMS U>^^
' I
EXAMPLES FOR PRAOTIOK.
1. I bought cloth, at $2,.'»0 per yard, and sold it eo as to gain 26 %i
tor how much did I ficli it a yd. ? Ans. $HA2^.
To folre this Example, «ee Case I., 282, KuLl.
2. A farm was bought for $4500, and sold eo as to gain $900 1
how much was the gain % V Ans. 20 %.
!• Mlve this Example, m« Caa* II., 384. Ritli.
3. By sellinr a building lot, a man gained $175, which was 12 %
of the coBt ; what was the cost? Ans. $1458.3;il.
T»Mlve this Example, tee Case III., 2M, KvLi.
A. A genileman sold a horse for $180, and thereby gained 20%;
what was the cost of the horHe ? Ans. $150.
V» aolTa this BzMBple, «m Case IV., 288, Rulb.
f. A merchant lost 15 % oi» his old stock of goods ; how nuich did
Im lose on those that cost 12^ ota., $6§, .SBJ cts., 334 ctfl-, and ilSf^l
Ans. 15 cts. : $1 ; 5| cts. ; etc.
%. Bought Bugar, at 12 c4ii. a pound, and sold it so as to gain 1^
•to. a pound ; required the gain %.
7. Sold butter at | of a dollai a pound, which was at a gain of
K % ; required the cost per pound. .4ns. ()6| cts.
8. A market woman sold oranges so as to gain | of a cent un each
orange, which wa« at a gain of 33^ % ; what was the cost of an
orange ? Ans. 2 cents.
9. SuJd a horae at 33J % gain, and with t]>e money bought another
horse, which I sold for 15: . 20, and lost 25 %. Did 1 gain or lose by
my trading ? and how much ?
10. If I make a profit of 15^ St by selling papor for '0.85 above
the cost per ream, how nmch m«at be added to the selling price to
realize a profit of 32^ % ? Ant. '^^ cts.
11. What ^llould I sell a barrel of flour for, thatcust me £1 2 6,
to gain \^%'t ' Ans. £1 6 3.
12. A neighbor offers his house, which cost him $6900, for 20 %
less than cost ; what is his price ? Ana. $6520.
13. A merchant eellfl cloth for $6 a yard, which cost him $3.76 a
jard ; what is his gain per cent. ? Ana. 33^ %.
14. I bought 640 yards calico at 15ots. per yd., and sold it at a
leduoed prioeof 2i5|J; what did I lose? Ana. $2.40.
. 15. A grocer selU coffee at 7Jd. a lb. which cost hiTii 'JJ. ; what
is his loss per cent, f Ans. 1 7Z %.
16. A merchant buys at auction $»562,60 worth of goods;" it he
sell them at an adranoe of 20 % on the cost, what will be his net
profits; deducting $600 for expenses? Ana. $1312.50.
17. How much ehooU I sell dilereat qualities of sugar which cost
Me MX 16^ £2 1 3, aad £2-12 C the owt., to gain n\%'i
KiOFTP ASi
IN
freight .nd other wpeasea $5 33 Vhlt In ^"''"^ *^*t ^ P»S St
i>^-Buught ahorse for $130 Da;,r*«f u- ^n«' $28.2175
5 wecka, and then sold hi« fc^ IJil ?t£f,^'> noorishmeat da in;
tae whole cost ? '^'^ **20 j what^ ^^ jo^, p.^ ^JJ'^J
-su. i5oij^.|,t codfish at $4 2'i fi.^ ^ . . ^*^' fO.ll 11
''»«"':^ gain por cent, y^^-'^'^^^^^^^^d sold it at $4 93; what
whioL coft?/;. «,:;iV^? ."'S'^fa -? •> lid. for 3«. 9d JrTb !?•
wa. h,sg,i f,,/-Jt^fcT;tfeV-i^' 6 for ^TsV; X
mj at 12 ^ advance : what waJ f f, » - * m selling a certain onan
^ 24. A merchant bonJl.t « K . ^'"^"'•* «old ? ^n* Tl qn?
^7. % selling cloth at .|4 the vaff T 1. on ^ ^«*- -^^^i 56-
*1- Fm, sold at 26 « loa« i. (h ^!« iT *" "* ••W oo>t f
or lo™ per cot in selfng^^Vu « "liV ''»""'"« b, .he g.i.
q« A . -<4fM. Iflt hnw... ^^ /^ ^.x'" 2 ^"**'' u"i each
38. A speculator sold the «,«?« nf^^!^^ ^'^^ ' ^'»'^- i^or«e £52
Is '.S'M'
ifif''!
Il
MISf
)KBRA4M.
. fif^^J.t*iP"r ^^J^""' r"" '^ **-^^ P«'yd., by which I mak«
aprofit of 3.^i ^ I sdl lOO^d. b) wholeaale at 30 ^ reduction on the
retail price. Wlmt w my gain or lose per cent., aud how much do I
receir.ayard? ^«.. 6i ^ lose; $8.32^ a yd.
40 A merchant shells linen 2^ cts. more than the cost and realizes
* P , A °* '^ ^ ' '''^^'^ >« t^« coHt of a yard ? .4ns. :: I i cts.
41. A grocer deuianded for a certain quantity of prunes a price 22 %
above the co8t; but being a Httle musty, he sold them at 10* less
than his first demand, and thus gained $98 by the sale : what was
hid hrst demand? j^ $1220
42. At what price should I sell codfish t/hich costs 168." r>*d. mr
Gwt. to realize a profit of 12^^ on the cost, after deducting 1 2 A ^ of
ttie price/ Ans. £[ I 2U.
4.^. J^ught a quantity of cheese at 12 cts. apound. Supposing the
weiglit to be 0^ less than that calculated, and 10 % of the sales to be
m bad debits lor how mueh must it be sold a pound to make a net
proht ui ] 4 % on the cost ? Ans. 1 6 cent, a pound.
*u J— Y'^'ian &Co. bought dry goods for the amount of $6840;
ifc""^ I *' ^? * P'^^^' * *' ^^i %. i at 20 %, and the remainder at
J^i % prohi ; what was their total profit ? Ann. $1482.00.
COMMISSION AND BROKERAGE.
»;$S. Commission and Brolcerage are the percentages paid
an agent, or broker, for the transaction of business, and is esti-
mated at a certain rate per cent, on the amount of the sale pur-
chase, collection, etc., effected. '
?»f ^- ^ Agent, Factor, Broker, Collector, or Com-
mission lueroliant, is a person who transacts business for an-
other.
NoTOS.— I. An agent may be n S])fe[al AgfiU,—i\txASf, authorized to transact
only suchbuBine.s as i88| eoified,-- cr a Geiieral Agenty who, ae suob,oaa trat.g.
act any biJsiness of the pergon who employ! bin.
2. iVieichaudise and Produce sunt to a ]ier?on for Baloor euperiatendenct, art
!&\A. to he comipced. The peit-on sending them is termed » Contignor ; th»
person to whom they are sent, ii lermed a Consignee,
3. A oonsigDfi'; whose bu.-inega oflQje is remote from a consignor, is romettmeB
termed a CorresjioiideHt, and usually aota «• agent of the lirm consigning hira
the goods.
4. Broliers are oktssified aMordinK to the nature >f the sales and oontraots
they effect. Ihiig, a Bill Broker is one who n.gotiates the uiscount on bilif (f
exchange, etc. ; a.Real-Eita(tBrol:fr\s.onQ whonegotiiitesthe saieol' houses and
landn ; luxmuhcr. Bmker, SJnj» Broker. Stock BruLcr, Paivii Bioka; etc.
i). A ooUccior m ly hare the business of settling accounts between indivi-
duals, or he may bean officer of tho gove»nineDt, at a CoUector of Hie Port,
whose business is to eulleot dutiea ; a Collector nf Taxet, eto.
fro
m a
840. The Net Proceeds is the amount received
•ale or collection, less thtf commission and other changes.
Questions on CMnmission and Brakcrage foilow th« same rules
M those in Percentage.
■X.iMPH!8 FOR PRAOTXOK.
201
'• "^^^ ^"^ ■«»»FK -. Cm, I.. 28^ B«*
wiit^rarotts^St*'^'^^*^*^- -»'•»« wood, .t5U;
^••. $1675.
IW «,!.. tfci. B..,^ ^ 0«. UL, M,, ,1^^
» -ol*. Aim Bx«ip»e, «, Om. IV., 288, Hvl,.
■16^? "'" *l«ron $309.10 at 5if*; on $4706.2?
•1.^40.40, at T^Tofffiifl'^^'i'.^'L"'** <^^*^H It U?of
8..Soldi„er;baBd.«. a. follow,. I.t foT'JlfA''.^''^^^^'^ «^-
Mission; 2nd. for £16 1 1 « .» * ^ q_7 . ^*^ ^^ 0, at 4^* com
9. What amount of brokSLl '^^r '"'"• ^ ^»'- ^^ 7 5 +
biMJks, as follows: $590 tTr^Sri-?.^^ ^^' e-changing^g^n.
«*»d-|wluuitffbwkS;i^rr^^ '' >nre8t,ng $11730, ia Ontaria
liow »Mk HMk Zl k. bv? '^*^°* ■'*^'' ^' * * brokerage ,
•10095.36 toKmJtttplr ^ ^ «« "^l^'^^^-- »»d r»«itt.d
-11 ♦u "^^^ owi^r tu, the a«t proceeds; for what nrW ^w i,.
-.. .„. px^pcrv, aad what was iii« oomin.MJon ? " "~ ""'
k* purchase? "««hii««ob, z^^, how manj •<>«• did
15. A nierckant kairiag on kand 470f !^,r^. .#• '^**' ***'
Ti '^ jp "f -cinfi^ n , wttatare the n«t|j>/i>,}e«ds, if soW at Si$ a hkL T
i:l
209
COM MISSION AND BOOKlKAffB.
If I
16. I p«rehM«d 6000 bash«la of wheat ia Bmflklo, at il.ST^
shipped the eame to my agsnt in Kiugstun^ who ftolol it at $1.62L
Uoiw much did I make, after paying $543 forexpeoM* and a eommia-
«ioa of 2^-%? Ant. $723.
17. A broker eharged ia« G^^^for the ezAhaage of £681 4 10 in
^eeiibacks ; what was his brokerage ? Ann. £35 16 34.
18. A comniiseion merchant sulci a consignment ol oats for $12686.
He charged $66 for storage, and 6^91^ commiusion ; what were the
net proceeds? ^n«. *11827.r2i.
19. An architect charges I % tor his plan and Burvey of a building
which cost $24000, and l<i % tor superintending the work ; how much
did he receive? , Asu. $450.
20. I sent to my oorrespondent in Bordeaux £2097 10, with advice
to invest in the purchase of winea, after deducting his oonimiHuon of
'3} % ; what was the sum inveeted and what was his commiMsion ?
Jfur. £2026 U 4|, wines; £70 18 7 J,' commission.
21. An agent having a deiM of $157t to ooUect, compromises for
909(; what was his commission at 5^ ^ ? Ana. $77. 71^.
22. Paid Folger Brothers $5.46 for exchanging $364 in United
States' money ; what was the rate of brokerage? Ans 1^%.
23. A oonsigoee in Olasgow informs his constituent of the purchase
of Dry Goods to the amount of £396 16 6 ; what is hie commission
at 2i^? ^n«. £8 18 1 + .
24. Bought at Halifax a cargo of wheat, 9500 bushels, at $1.20
per bushel, and sent it to my a^^ent in Portland who sold it at $1.50
per bushel ; what did I realize on the whole atler paying $820 for
expenses, and commission at 3i^^? Ana. $2031.25.
25. My correspondent at Bordeaux ehargeti $74.20 lor purchasing
264 ewt. of honey at $10.50 per cwt. ) what was the rate of commis-
sion? AnM.m%.
26. A broker receives £2085 7 6 comprising the sum to be invested
in Raikoad stock at £20 16 a share, and his brokerage at i^%'^
how many shares can he buy, and what is his brokerage?
2T. A certain piece of land was sold for $3925, but the owner r»>
eeived $38S6.12| as the net proceeds; what was the rate of oob-
misflion? Ana. 1^%.
28. I remitted $5500 to my l»x)k«r with adriec to invest in Bank
stock, after deducting his brokerage at } ^ ; what was the investment ?
29. The net proceeds of a sale were £1408 16, and theeommissioa,
.£28 15; what was the rate of commiseioD ? Ana. 2 %.
30. In charging 1^% for the investment of a oertaiu sum, a broker
realised $286 ; what was the amount of the investment? A. $19000.
31. My agent in Cincinnati gives me information of the purchase
of 4000 bushels of Indian meal at 80 cts. per bushel, and desires me
to remit a check on New York which he can sell to a broker aX \%
nrotnintn • arka.t oKniilH t.h* Anmnnt rkf tlia <«li«r>lr \\a Kia no»^>v,;.^ow,,,
beings^? Ans. $3271.464.
32. A ftctor received £6 12 for the sale of grain at I % commis-
sioa ; what was the amount sold ?
n. fteoeiyed from A $700 in specie; paid 3^ %
Ans. £140.
for changing it to
fUB AND MARINE INSURANOB.
203
gold; and, after deducting the commission sA2%, employed the bal-
ance in the purchase of fruit ; what was pai.l for the fruit: and what
wa« the oommi.-sion ? ^.ns. ^iWil.^l), fruit; SKI.-) I commission.
S4 lleniitted to my correfipDudent at Rouen £265, for the pnrchaBe
of calico at 'M. per yard, after deduotirg his commission at 2 96; how
many yardn will I receive ? Am. 6666iyd.
.^5. A speculator rec >e« $4113.60 an the net proceeds of a sale,
allowing 5 % commission ; what was the ralue of the property ?
36. A cciiiiinission merchant who oharges 5 % commission on sales
and inveHtiiients, receives 260 owt. of cheese, at 6d. per lb., and £748
10 6, m cash, with advice to purchase a cargo of cotton for the whole
amount ; what will be his total cou mission ? Ans. £97 1 ' 1 U
37. A Halifax aj^ent buys 34 box28 of chocolate; he pays $7.50 for
freight and cartage, and his commission is l\<j(, un theam'ount of the
purchane. He ^ends me a bill of «740.83| for the whole; what waf
hiH commission; and, allowing 2501b. per box. how much did I pay
per lb. for the chocolate? Ans. $10.83| com. ; fsO.OBi per lb.
icn UL commission merchant receives 125 barrels of flour from A,
150 bbl. from B, 225 bbl. from C ; he finds on inspection that A'a :»
10% better than iJ's, and C'h is 5^% better than A's; he sells the
whole lot at i;57 per barrel, and charges 4 % commission. How much
must be remit toeaeh ? Am$. A, $842.30 ; B, $918.87 j C, $1698.83.
I
INSURANCE.
841. Insurance is a contract of indemnity, by which on«
party engii<res, for a stipulated sum, to insure another against a
risk or loas to which he is exposed.
343. It is of two kinds : insurance on property, and iniiuriiDoe
on life (1).
348. The Insurer or Underwriter is the party taking tbe
risk ; and the Insured or Assured, the party protected.
344. The Policy is the written obligation or contract.
345. Premium is the sum paid for insurance. It is alway<
reckoned ut a certain per cent, on the value of the property iB>
Bured, varying according to the degree or nature of the risk aa-
mmed.
at %%
FIRE AND MARINE INSURANCE.
346. Insurance on property is of two kinds: Fire Inturanmf
and Marine lasuiance.
34T. Fire Insurance is an indemnification of damage and
loss caused hy fire or lightning.
(1) lift iofuruM wiU b* trMto4 of later.
Iji,
i
9N
'IM AMD UArnn INMntAIfOS.
an?b^c,Shwr'''"T®",*" «'*^™»'fi<»*««n of damage
priDdjL: '"''"'*"""' '^" «*'*'"'^*'«»'' are tM««lon the following
TT* Z^^^^^^ ^* P^c^t^ge. (278)
II. The sum insured is the ba*e of prcmin*.
in. The sum coTcred by insuraaoe is rfifertnee,
BXAMPLB8 POB FRAOTIOB.
ftMOBat
2.50.
To solve this Example, me Cue 1., MS, VmUL
To solve this Kxampie, m« Omo II., SM, Ina.
• w^'JiV'L''''"'""*^'f""".«***"''"^ <■«'!<>''*• value, at 13«.
WM$14.,.bO; requ.re.! the valueofthe tWDery. Am,. $11648.
To solTe this XiAMple, m. C«w III., Ml, WmA
4. What must J)e paid for an insuranoe of $6728 at 11*?
7. A hotel ralued at £8760 i« insured for i of its value at ?'*
'heiit^r? *"^^*^ ^^^'^ ^--^"^ - chtrwyir; :L't t
eur«l\j'ri*2?'*'''^.u"*''*^'"'**-^'^"^^«= ''»»•* «um muV'Jia.
9 {fk ?^ ^. *''''^'' ^^'^ P'^'P*"*^ *»^ premium ? An,. $<;500
9. What IS the premium of in«uring£t;s)5 11 8,ati5 13 9«T
a i ;f Iif*^ """T^ ** ' insurance fo? my library,' and this sum is
jCS i« 8^? P«™ujn for an msuranoe of £1486 13 9, at
.ui^ 4 *"S-Zir%X^.tl'i''?;^ ""'"*' oft^f gel! tltmW
$2000 of Me «to«k IrkJfV!!!*!*' '^,'u ' «o°«ag'-ation, he saves but
]o ^ *°« «<f «> w«« re^ lo«a will be sustain ? Ans. $472
«. to .oi^^fh! r." "I"" ' ''"''**'. '*'""*' *^ '^^^^^^ be injured, at lA
*!? M ! *"*"* '"***' '^ **"* '* •" destroyed by Are ? 4. $8400
14. My goods are worth £1563 12. For what sum m.l« T 7
.h.^jp„o„,, i„o«,.f !«.,. both pr^J^'lTp^Zy, r«
li). rh(. premium Ota echool-hou«,iB«ared at li^k islfiVn. V.,
whirt sum was it insured ? » area ai ij % , , ^50 . for
'"""" • iiw. $360.
AMKSSMBirr OF TAXK8.
2«S
of damage
e following
he aaioaBl
$112.50.
lii house f
$11648.
'fffiMl and
2 14 + .
wrecked ;
887.50.
5 what is
J 15 0.
ist be io-
$6500.
[3 9%r
8 eum 10
>uot?
13 9, at
H+.
them in-
iaves but
«472.
red, at 1 A
P8400.
I iu8«rc
^ at £2
ilGOO.
8*50; for
^4000.
of build-
balaoce
$360.
oJl:^^ ''"' "•."" «"'^« ^^*^'^*' *1938 12 « be injured to
cow both ppcinmm and g(,bd8 la case oflo».H, the rate beiuK 6««?
IH. A .rig estimated at $40000 is injured for % of it« value at
H% and Its cargo, worth $H6000, at | ^ ; what is the insurance ?
•Jf^; ^ '^''"'''T'^ P""' «I450 tor premium ofinmirance on a cargo of
cotton com.ng from Uavana, the rate of insurance being 2^%; What
«J™i.. '^ * ^"''*" »n«"«-anoeof$1200: what is the rate of the
pretnium ( a . , ^
ofJlLll^il^i.^f.]^' '^^ 7i 5* commission, and find the insur*,;ce
of tae sum, at 4J % ? ^„^ ^.^7 5 4^ + .
ftnl^"r ,.!*"'' l'f!i"S a cargo of SOObbl. flour, has it insured for
Klce LTte ? '* ^' ^""^ P*'^ *^"^-2^ ^«' P'-^"*'"'" 5 what was
tae price per bbl. ? ^na.$8.26.
R«t 1 r ^"■P-ow"?'' Ji^s two of his vessels insured for $1^0000 in the
rn' !/ill^'"''"1! ?^-' f ^ ^' *"'^ f-^"" *45000 in the Colonial Insurance
9** A*r ' *"*^'8 to^ rate of premium for the whole insurance ?
. i!4. A house estimated at £300 was insured for I .jf its vahie, dur-
«£)!?"' fu ^ P^*" *?'*"'"• Towards tl»e end of the third vear, it
ZZ J\^ ^^ I ^""^ ' '"^^^ '^ ^^^ *<^^"^' Jo«« o*" ^'i^' proprietor without
any allowance of interest? ^ /Ins £106
«.!?<» J *^-5 V"** •* '^. P'^''^-^ ^""^ P'*»«' and g ^ premium ; every
^3 t"»f ^/m' ^ P^'^ J^ P'-«'"''^"'- The house having been de^
hlvS'K n >'^^^ "'•'at was the loss of the insurance, no interest
flaring been allowed? j-,„ 419m- ok
^t.. 1 paid $46.75 for insuring a store for the i of its value, at
I , % } wha IS the store worth ? ^„8 $,;hoo.
a„<V*J ? * P'^u''^ of £3011 6 for the the value of botli property
rj-in/'To""'' what IS the worth of the insured property, Ihe rate
-ib. A shipment of wheat was insured at 2%%, to cover 3 of its val-
^Jk„IPPu""™P^"^.'^*' '^^^•^^5 ^^^ "'J'^a' being worth 80 cts.
per Dushel, how many bushels were shipped ? Ans. 2825 b».
ASSESSMENT OP TAXES.
850. A Tax is a sum of money assessed on the person or
property of an individual, for public purposes.
»51. When a tax is assessed on property, it is apportioned at
a certain per cent, on the estimated value. When assessed oa the
person, it u apportioned equnlly amonir the male citizens HnKl* to
assessment, and is called 9. poll tax.
352. Property -s of two kinds, viz. : reed estate, and personal
property, ^
1 5 K * ^*^* Estate is jkAi or immovabU property, suoh as
,i'iJ
'.mv^'-i
SM
nmr 09 rAxm.
1. :
f
ji. <
^|'
'' " \
L.
»«4. Personal Property ia »»omW<' property, sueh as money
stocks, lurriiture, cattle, etc.
355. An Inventory is a written list of articles of property
with their value. "''
350 A Schedule is a list of taxable property with its owners'
names an 1 its value as estimated by aaHcssors.
SST. Assessors are officers appointed to make out a schedule
of taxable property, and apportion taxes thoreon.
Ex. A tax of $840.76 ia to be raised in a town containing 65 polls •
the taxable property of the town amounts to $48000, and each poll
tax 18 75 ct8. : what will be the tax on a dollar, and how much will
be 9 tax, whose property in valued at $5600, and who oavs for 2
polls? *^^
OPBRATION.
$0.76 X 66 = $48.75, amount asHessed on the polls.
$840.76 — $48.75 = f792, aint. to be assessed on the DfODertv
$792 ^ $48000 = $0.0165, tax on $1. ^ t^ 3
$5600 X $0.0165 = $92.40, C's lax on property.
$0.76 X 2 = $1.60, C's tax on 2 polls.
$92.40 f- $1 .50 = $93.90, amount of C's tax. Hence the
35*i. Rdl^:, — I. Find the amount o/poU tax, if any, and
subtract it from the whole tax to be raised; the remainder will h<
the property tax.
II. Dii^ide the property tax by the whole amount of taxable
property ; the quotient will be the per cent., or the tax on $1.
III. Multiply each man's taxable property by the tax on $1
^nd to the product add his poll tax, if any ; the result will be the
whole amount of his tax.
EXAMPLS8 rOE PRACTICB.
1. The tax assessed on a certain town is $1485; its property both
personal and real, is valued at $42000, and it contains 300 'polls
which are assessed 75ct8. a piece. What per cent, is the tax- that
is, how much is the tax on a dollar ; and how much is A's tax who
pays for 3 polls, and whose property is valued at $2250 ?
. An$. 3 cts. on $1 ; i69.76, A's tax.
2. What 18 the tax of a non-resident, havinir property in the same
town, worth $7900 ? jifu. $
3. How much will B's tax be, in the same Ujwii, who pays for 3
polls, and whose real estate is yalued at $32000, and his personal
property, at $18880 ? Ans. $1628.G5.
4. What aurn must be assessed in order to raise a net amount of
$11128, and pay the commission for collecting at 2^%t
6. The expense for repairs of a public building was $2521.06, which
was defrayed by a tax upon the property of the town. The rate of taxa-
tion was 34 mills on one dollar, and the collector's commission was
3i % : whttt was the yaliutioa of the proptftjr f Aiu. $80384i.<9 +
aeh as money,
of property,
th its owners'
lit a schedule
ling 65 polls:
III each poll
V much will
• pays for 2
property.
the
f any, and
Inder voill In
of taxable
on$l.
tax on $1,
( will be the
)perty, both
> 300 polls,
e tax ; that
'a tax who
I A's tax.
I the 0Ame
t. $
pays for 3
is personal
$1628.()5.
i amount of
1.06, which
'ate of taxa-
niaaioD vas
38ii.C9 +
oiwrmf-HousB bdiinim.
CUSTOM-HOUSE BUSINESS.
Mt
„nn^^?' ?,"^*®^' **' Customs, are taxes levied on imported
fnduSry" ''' '''^^'' of govorn.nent and the proteotl 7home
861. A Custom -House is an office pst'>hli-«]ir>,i 1^,
ment for the transaction of business Snt Sut c. \fr2
cars attached toitarecdUed(7««.c,..^o,.e|^atT^^^
s to »°«Peotthecargoesof allvesselsenteringatanyof hese^^^^^
to inspect the invoice of goods, collect the duties et^. ^'
etc ; thase oLrge« are oaH.dh«"4r dues '^ "'°"' °^ ""'""« '*"» P«'*'
2. To carry on foreign oommeroe secretly, without •.»„,„,. *i, ^ .• •
by law, is tnugglin^. ""'^uy, mtnout paying the duties imposed
868. Ad Valorem Duty is a certain per cent on thTeo«t
ofgoods, as stated in the I'nyoice. ^''^
864. Specific Duty is a tax computed on the wei-ht or
measure of the goods, without regard to their cost Lee alow
anoes are made before computing the duty. '
865. An Invoice is a statement of goods, from the sellf-r tn
the^uyer, or importer, showing the qua'ntity^nTp"f th^
866. In the United States Custom-Houses, certain Wal al
"ra^elSiZS Vca' f^'.^-^^^S^' ?*«•> be/o^re^Tptifi
bc,xes, etc., containing tL goodsf and Velak^^e'y gaTgin^ tt
.pe^rdT^e?aTefarJSj;frSX^a^^^ the oniy articles upon which
867.— To compute ad valorem duties.
Ex, What is the ad valoram dntv ai i » i^ ^. « •
whinh «o«r «^fi« fio » "*^' •* ^ « »' on »n invoice of
ich coat
OPERATIOir.
$a5«.60 X .18 a: $46.17, An$.
men BO
A»ALTSM._. According to Case I,
(MS), we multiply the invoice, $2,^650
which le the ba»« of the duty, bv the
IJTeB ratt, uui <■ in the duty, $46 17.
H?
m
»h
111'
OUWOM-HOOM BuanMo.
th!^^^ls ^l'';^:~f''''^^^' Pfrcenta^e on the invoiced value a/
««/.ir« r^ ^'"'" "'^^ ^/^'^-i^. -*^ '^« »•««/' ^tW be the orf
3«!>
To com}.ute spfci/ic duties.
<«'...,"^::J;*^,i7, .tct.-.tu.^'^ .iTi/"' ■"'■^'"■«
OMRATION.
J 9J •'* = 716.811... tare.
♦40.^. J X .02|=.|I2I.()H«, ,f„ty.
Analtsw.— We first find the
whole weight of the inroice which
u 612()lb. From this amount we
deduct the allowimoe for tare,
716.81b., and ocaijiiite tha duty
on the remainder. Henoe the
folluwing
KXAMPLKS FOB PftACTIOK.
_ 1. What is the ad valorem duty, at 19 * nn is-rsn ik <•
invoiced at 15 cts. per lb ? *' ^^ *> 00 16780 lb. of cordage,
llsVso? " *'' '"^^ ^^ •'•'*' - «* bale of HoUaud linens which cost
6. What is th« dutv at 20 od ^„ • • ^^- ^525.85A.
cc«t in Liver, ulS' 1 th^' 5° ""T^""! ^^ broadcloth which
6. What thetScdu^riOor'"
-oh weighing I20T; tare % J ? '''' P'' ^^'^ ^" ^^ *=^««t« of te'a,
aot%j^ir^1j-^r„?untrtoXt"s^^
was the wine invoic^ ? ^ ' *' ''***^ P"«e Pe»" gal-
Ht',i6urt„"g^;dSvSTt'^^^
Jf4 ^J on goods'i„voicJar$33lo^1h'e\^1iettV:rth. tj^
16%; goods invoiced at «4800. were free ,,f rl„Tv o 1 ?^® *^^
nianxler, the duties were at the Zi^nff,^ ^ J' """^ ^n the re-
amount of the duties? of -^0^; what was the whole
. 10 What is the duty at 18,^ on 60 ke.s af nr..^J:'::'{^r
' l?^" '"^«'cea at if cts. per lb. ; tare m31%? ' ^ ^eighmg
i value if
^ ht the ad
weighing
Sret find the
nToice which
9 amount we
oe for tare,
te the dutj
Hence the
I compute
' cordage,
1449.73.
egs of to-
re?
) hhd. of
diich cost
25.85^.
th which
t$4.86|?
ts of tea,
is 12250,
15%.
', 42 gal.
per gal.
invoiced
the rate
rate of
the re-
3 whole
JO.tO.
eighi
°g
pieces
■y24c,j;
Ben, at
•>'8<XMTNT AJO) Wta.Nx WORTH. 20f
12. S. K. Wilson A Co., of Toronto • ,^«»- «26l.88 + .
4Ppione«oflinenof.32vd ea... ,.^"u' '""P"^' ^^om Amsterdam
^t -'4 ^.« 1 84.32. andorhercWsS'if' '^^ »*'<' f**' »»»« '^S
«^^^ tiie invoice value tterrA S^u ^''* •'"""»* of f61.44. Wha
cli»-rgeH were paid? ^ ^'*-' •"** ^*»» «^» P«' ^d. after d.Uee „d
nrsoouNT and present wortr
paSo?a?e^bifo«^fi^du'^ '' '*'^"°"°" "^»^* «>r «>.
ru^r!L'':if^^^^^^^^^^^ clebt, payable at .
rayabieiaYy;;;^,'^'*'^-^^^'^ -"d discount of $25.44, .t 6^
OPERATION.
$ 1.06, amount Of $1
■^5.44-^ LOG = $24. '
2o.44, given sum.
J±^, present Worth.
^ 1-44, discount
$25.44 will be M mn„. I ii^° P''®'«"' ''O'^h of
worth vrhich. subtr.. oted f?,.m ii" ■ '^ '''" P'"«*«°»
$1.44 diacou'nt. H^c^ S:"!?/;!" ""' *''"
WORTH "^ '^''' '""^ ^^' 9^i*^t will be the present
n. ASMiimci <A(! present worth from. /A^ «
remainder will he the di6oount. ^"^^ '^' ""^ ^*«
I. To determine the present worth :—
100 + (6X1): 100 ;: 25.44 • x - aai- u
lowing formula ; •**•«-- ¥^ ; whenee the fol-
„ ^ ^ ". ^' ""^ ^^' ^'■^^'»^ "''^^^i 0/ this sum.
II. To deteriuine the disooant:—
100 + (6X1):6X1:;26.44:,^«
lollowing formula : ' • * — •!
i
;m
■44; whenee the
I*
IM
DBOOVNT AUD nUMlNT WORfm.
traotin.' the principal from tho amount. "" ^'^"^ ' "'' ""* "''•'^''«' ^y »"»"
of tho .eroral , av nl'Kri »M ' ''''^^•u ^'''"'' ""^ '^"' '»« '^'e P'esoi.t worth
paymenrwrnCoth^toUldl^^^^^^^^^^ .ubtraotaU from the eum o^ the s.^erl
EXAMPLEg FOB PRAOTIOB.
What is the preHent worth of the following Dote«:^i;
. 2. Dated March 4th., a.nouating ,o US 10 6, on 7 nfuntt' cr«it.
discounted Aug. 10th., at4l»? * iiM £58 3 fi 1 ^
r T^"**^^"'^?^'*'"^""''"*? 1«»206.16, on 4* months' credit
dj^counted May i^Oth., at 4A^? ' aL ^^-iu^ra.^ ^
li. D.ted July loth., ai,j,.ia,iii,g to tZljs.ao, „„ 5 months' oredi.
d,,«=o„,ual Oct. 12th .t4Ji«v J«"*5m!20+^
J^,s^!^^^^l'^-"^ - -- '^^^-^..rii^r
iJ.. Uttted Arsv • ... amountin,'. , 3J4.^6.75, on 3 niont" "' ''*'
discounted Junv, 2:iud , ut 5^ Jj?
17. Dated March 14th., amounting to $600
discouRted
Sept. 7th., at 7 ^ ?
00
(1) We letkM Mlj SO dayi to the oMth for aU the Bete«
— credit,
Ans. $433,110 + .
n 7 montlu' crcdit.
Ans. $696,714.
on
ia tnM
ttuoommr amb nmt^T woith. m
18. D»ted F#k. fth.. amountine to £860 18 im n w»^^tk.^ u
•luKJountrd April I3th., at 7^ ? Afu, £H?^ir^^
19. Dutcl Not. lUh., araunntini. u. JllTA ■^n f ^' ''^ ** ^ •
di«c<.u,.ted Mav 4th., uUJ * v""""« ^ *^^*-^«' "''' ^ month.' omiit.
20. IhiUd Aiurcl. 0th., a.MMu.ting to £701 "J « n t '"^ ^ \
Ji»couiit.,J June 9th at 7A *■' «**'"' •> ♦>. on 4 moH.' oml.t,
^^.^.^What ,. .he present worth of .5117.60, puvaM.. i„ ,' year, "at
h.nc;,'lt'?r/'' ^'■""' -'^t^ of a debt of £96 6 OJ, .iueT„.'l'?L.
2;s. What Hhould be the discount on 1373.7.'-, nu.T i I nf "L"/
theterm of maturity, at 6i«? •^'•i-'-'. pui^l ''*>• before
24. What iH the diBcouMt on £200 12 6 at 7' <^ "" n'"-^^ ,■*" *
26. A note of $139.94 m pa^ble in 9 mon hi' ^' 1^'^>'.^'' « '" »r- ?
worth, .liHcount being f,*?'^^ ™onH'^; wimi^istheprewni
26. Discounted a Jote of £76, payable in 4 year""' ! f'T \
8uai shall I receive? ^ " m * years, at o,^; what
i^^, *' ^'^ ""mediate payment ? \i;i. *„ in^
month, is allowed ? ^ ^^' '**''^ Ai^£\'^''Tlt^'
«q?ikL*'''^ M*''*"'^ ''^"^ *^«* '"• *2964.12 readv money *fbr
¥3660.20 payable in lyr. 6mo. : what w.ll h. ...„ ,.„;„ . •_.' ."'•^' '""^
by oiscountinK at 8 at?
90 T 1 1 . ,1 '*.
liat will be my gain, in ready monev
Ana. $.i08.3^.
^
i ^
32. I bought Hilkftbr $43713.60, on 15 months' 1?;iif'®£;f\
payiug before the time due, I will obtain 5 * ,1 scount hTwL ^ ?
should I pay the debt, so an 1. disburse bur^i" illS" ' ' V.^:!^:''
^ 33. A tlour-mill was offered for $2.5000 cash. ,,r for jftM^Tna ^ ?.
« Ji*: ^<^"'« bought goods to the amount of £82 6A on 20 mn« '
credit; at what time did he pay, knowing that he oltk^ned i tTr,'
count per month, and that he disbursed but £75 19 ? jLK^o
.«. A merchant gave out two notes : the tiret of «'M'A« . i
May 6th., 1867, the second, of $178.64, i^yal'elei^^^^^^
what^sum IS required to pay th. two notes^'ct. 1 utf^seeTisl^oum
% ^^\' quantity of produce must be bought at Ss. ner Ih
on 22 months' credit, in order to oar but £50 1 9 ini 4p- jH^f- '
the discount at 7 ^ ,' " ' ^ 5; »»s«?i acduv^iug
.37. On 9 months' credit, I bsaght 120 bales of cotton p^^k v-.i
w^glung 4881b., at 5Ad t\e lb. ^Selling a i^^ZSyVte^'l
oaeh,^I paid my own d-bt, and r.^ved 6% discount ; Lw niuch did
Ant. £390 8.
'^
212
■AifK Dnoouirr.
38 I paid $320 for a sum 1 owed ; what w*8 this sum, knowing
that f>\% discount was allowed ? Arts. $386.80.
3!). Paid £23 15 for 50yd. of cloth ; having received '> 9^ dipcount,
how much did it cost me per yard ? Arts. Oa. ll^V-
40. Ih it more a<lvanta;^eouH to purcliane flour at |(i.25 per bbl.
oi> fi montiia' credit, or at $6.50 on 9 months' credit, discount being
8 ^ ? Ana. Flour at $6.25 is the more advantageous.
|i 1 1
■ y .1
1)
m
BANK DISCOUNT.
374. A Bank is a corporation, legally established for the
purpose of receiving and loaning money, and of furnishing a paper
circulation.
375. Bank Notes, or Bank Bills, are the notes made and
issued by banks to circulate as money. They are payable in
specie at the banks.
Obb.— A bank which iggueB notes to circulate ae money, is called ». bank <>
ia*w»; one which lenda money, a bank of ducount ; and one which takes ohitrge
of money belonging to other parties, a hank of deposit. Some banks perform two
and some all those duties.
376. The Capital of a bank is the money paid in by its
stockholders, as the ba.si8 of business.
377. The affairs of a bank are usually managed by a hoard
of directors chosen by the stockholders, arid tho principal officers
are a president, a cashier, and one or more teller^.
Obb.— The president and oaahler sign the notes issued; the cashier superin-
tends the blink accounts; and the tellers receive and pay out money. A lj>,nk
eheok is an order, payable to bearer and drawn on the cashier for money.
378. Bank Discount is the simple interest of a note, draft,
or bill of exchange, deducted from it in advance, or before it
becomes due. Thus, the ha?ik discount on a note of $106, pay-
able in 1 year, at 6 %, i.s $6.36 ; while the true discount is but &6.
The interest is computed not only for the specified time, but
for three days additional called dai/s 0/ grace.
*^.^'T-L' "^^^ tlifferenoe betweeu bank discount and true diicount ia the same
as the difference between interest and true discount.
2. The legal rate of discount is ordinarily the same as the legal rate of interesU
S7». The Proceeds, Avails, or Cash Value of a note is its
face or amount minus the discount.
880. Case I.-
■The face of a note being given, to find the
ditcount andprotMtU,
1, knowing
*3H6.80.
5l5<IipCount,
8. lly'^d.
^5 per bbl.
3()iint being
itageous.
Jfl for the
ng a paper
made and
payable in
A a bank "
tftkos nhiirge
porform two
in by its
y a hoard
HiJ ojficers
tor superin-
!y. A hunk
)ney.
ote, draft,
before it
106, \my.
is but, $i6.
time, but
is the same
3 of interest,
note is its
BAHS
213
OPBRATIOM.
Sum difloonnttfd, »RAa nn
Int. for 30 dM. «. 1 ^ foOO.OO
B.nkdis^„„t, ^^"•"^•' jIs
Proceede, or present worth,
f497.25
Analysis. —We find the
mtoreft on the gnm dis-
•ounted according to 297,
and this int. ig the bank
duoonat; we then su btraot
the disoount from the sum,
and obtain the present
worth, $497,26. Menco the
«j^_ ""AKu, .jj-itfi.io. uencothe
for fh.Z f'^^'^'—^-C'<'^P"f^ the interest on the face of the not^
or, 1 JJ ; 500 ;; ?oo ite' x*' ^' f '* '^'''°r* '
•■ '"" ('' X ^-,m) X, or the proceeds.
Note.— We take calendar months for the rAAiron;^^ ..*•*•
bank disconnt. and compute inte^Tas if 2 * '"' °° "" "»" °«'«» ^
instead of 365. then the Lult ,s1r.a". ' f " <'«jtai-d only 360 days,
greater accuracy is required thl tnf Tr ?J^^' *"^ "^^ "^ '^^'«'f- Hence, if
rule, must be <Ji^inished hyVofil " or the 1'/^' "''''° "'^^'^"^^'^ '>y '•^«
page 1S3, must be followed^ ^ ' "'' ** "^^hod of computing intertst,
EXAMPLES FOR PRAOTIOB.
•lioo^tS'r^o'da"^^^^^^^ Of a note of
^ 2. WhatistheprlintlrtLfaTo^eo?^^^^^^^^ pro. $989..50.
and discounted at the Quebec Bank ? ' ^^^^ '' '" ^" '^^^^
^. nesirintr to loan £9fin ,^<• a/ . i ^ ^n». JE1979.
I aJd to o„,„plc.„ the „„„„„, l;Ee7 '^''.^""r?'^ """'
5. Find the d»y of mat.iritv M,. ♦• ^ j- ^"*- ■'•''-•^'^- ^ ^"^ + •
of the following note.!- ^' «"»« of discount, and present value
£40 2.
Quebec, Dec. .3rd., I8G8.
Bank of Quebec. ^ ^ *'"^ ^*^ shillings currency, at the
«* ae Juoe s j 6 1869; tern, of disc. 64da. 5 pra, m 13 6^ + .
rr.ji
214
BANK WSOOUNT.
$10(50^^,^
Montreal, A.pril 19th., 1869.
i i
Ninety days afier ilate, we promise to pay C. Simson, one thousand
»ixty-six and ^^{\^ dollars, at the Union Bank, for value received.
Rappe, Wkbueb, & Co.
Discounted May 8th., at 7 %,
Ans. Due July 18 | 21 ; terra of disc, 74da. ; prooeeda, $1061.40 +
6. What is the difference between the true disco'unt and bank dis-
count of .1950, for '^mo., at 7 ^ ?
7. What is the ditierence between the true discount and the bank
discount of £2000 9, for 6 months, at ;^ %?
tiH*2. Case ll.~ The proceeds of a vote being given, to find
the face.
A'.r. What i5< the amount of a bill, payable in 60 days, which dis-
counted at a bank, at 6^, gives $989..0O for the proceeds?
OPBRATION. Analysis.— Sinoe $0.9896 is tJio pro-
$1.0000 oe«d8Ci'.i>l, the noteof which $989.60 is
Int of $1 for 6^ davn 01 nr. ^^^ proceeds, mu.st be as many dollars as
ini. oi J|>1 lor b.i days .0105 $o.9895 i« contained in $989.60. Honoe
Proceeds of $1 $0.9895 the
989.50 -=- 0.9895 .- $1000, Ana.
. 3^3. Rule. — Divide the proceeds of the note, by the proceeds
of $1, for the time and at the rate mentioned; the quotient will
b4 the face of the note.
By proportion.
IW - (6 X ;ft^) : 989.50 :; 100 : *= theface.
EXAMPLES FOB PRACTICE.
1. What sum, payable in 90 days, and discounted at 7 * at a
bank, will give £170? j^ns. £173 2 7i.
2. A merchant desires to draw $5000 from a bank, and for this
Eurpoee discounts his bill, payable in 90 days, at G%; what should
e the amount of it? ^ns. $5078.72 + .
3. The proceeds of a note, due in 4 months, and discounted at the
bank, at (i %. are £407 18 ; what is the face of the note?
4. Bought goods at Toronto for the sum of $1486.90, and gave ia
payment my note at 4 months, at 749J discount: what should V-
the amount of the note? 4>M. $1526 + .
5. A merchant wishes to borrow $750 in a bank ; what should be
the face of his note, payable in .SOda., allowing 1 % .lisoount per mo T
6. I gave my note at 60 days for a debt of £16* 1«; tf dtMount i*
UK aMtUj, wkat waa tka fiMt •f Ik* »otoT
T>
iud the bank
216
disoounte^Cey^?" '"'^ of interest of a ooie payable in 90 dajH and
^r he given time and rate yields
M Its proceeds $0.9845. Then, if
OFKKATION.
W-«« ^ 0.9845 = 0.06^, ^„.. _.
intere«t*f* J? '.'"pooeeds $0.9845. Then.it
« manl*' • S!'^"'; ^''•^S^^ in the same tiu. wi 1 viSiru ""'' ^''^ » "^^^
ny per eent. « the given rate, .06, oontaln. 984T ' '^"" '"'•"'*' '^
^Jf proportion.
VXAMrLlS roB FBAOTIOl.
^TWlf%-
I- What rate of int«reMt in imu,^ -.u
Ascounted at 6 5^ ? "* '* **•** ^*'«'» * note payable in 30 days is
2. A note payable in 2 moBtba .^ j- . , ^»*- 6,?*, ^
7^f T ""^ *^« interest f^" '^ 7*^.?^ ^. ^'^o7ik ,
3 A note, payable in 1 year, wasdigconnfj?"*^^^ annually.
^. 5. Whm was the rate oer amnt L-. . ^"*- ^^Ui- <£,
0. tvijat 18 the rate of interest Lm^JH j?^8V%, 12f«f jg. etc.
«.-„., on . bill .„ i„ .oto.'IC^CX'ofl.l'^ '». '2«
•MBATIOlf. A„.. '^-^
»0 day. + a d^. = „ d.y^
Int. for 93 days,
<t «
Amt
t«.20 -T- 0.27.S77D
6.20
$106.20
for the prooeeds of » nof« tL*A"'
W«h *^^r of the note $106 20
S.» ?• ' ^o 'nt-erest, $8.20. and
«• ">• P»»oe*af <MM. II«M« tht
ISJV
J«***ai»ikSS!-»
216
>»OmiOOOU8 MXAMPLiCti IN DISCOUNT.
'li
«i^7* KuLE.— I. Find the interest and the amou7it of $1 or
^mjorthe time the note has to run.
il. Dii>ide the intereet by the interest of the a':nount at 1 % for
»M $ame time.
tip proportion.
10# + (J4 X ^) : 100 :: 24 : * - 22^1*, Am.
EXAMPLBS FOB PELA.OTIOE.
1. At what rate of bank diacouut must « not«, payable in 60 days,
b« diBOounted to obtaiu (i % interest? Am 5UW«
t.5„ « i '^l'*^ -^o* '""'^ * "*'**' ^"^ ^» 30 days, be di80ounted to ob-
rWSn « r ''^ i""^* * °*'^' P^y*^'« •" 120 day.., be digested t„
obtain 8 ^1 mterent T Am 7 »<^»SJX<A
«..*• ''^^.'^'■*?V^,''.*IL'' discount, of nate8 payable in 30 7^ ^r-
respond to 6, 6, 7, 1 ^ interest ? Am. 4|m? % 5 \U^ «/ ete
6 What will be the rate of bank discouut,'o^f;7;otTVavle^;^
and 4mo. hence, without grace, corresponding to 5 % interest ? "
pay a broker 1, 1 4, 2, 2^ ^Ij per month ? Am. U.^^%, etc.
PROMISCUOUS EXAMPLES IN DISCOUNT.
What was the present worth, at true discount, of th« followitur nolM.
when discounted: — . ^ ^^
1. Dated Feb. 3rd., discounted June 6th., amounting to $813 80
payable in o months, at 5 ^ ? ^„, ^3,2 62 +'
•2. Hated March 4th.. discounted Aug. 10th., an,r.'"to'£175 ll's
payable in 7 n.o., at 4 ^ ? " '^„., I174 , „ ;^ !^^ ''
■I Dated April 2nd., .liscounted May 30th., an..M,ntii»r to .*618.45
payable in 4 mo., at 4^ %? 4„^ £^^y^ 55 +
4. Dated May 15th., discounted Nov. 16th., a.nt'g' to £406 7*0
0. uated Aug. 7th., discounted Dec. .Oth., amounting to $K000 00
payable in 6 mo., at 5 51^? ^ns \vmSrC
6. Dat«}d Jan. 3rd., discounted Sept. 20th., amt'^r to £270 lo"«
payable .n 9 mo., at 7 515? Ans. £269 16 101 + '
Darable*^3^;;n* ^,*,^^-' 1;««''«'"«d Aug. 2nd., amounting to$4682.70,
„„:.■ iV*-^d.rP*- ^^h-' d'poounted Feb. 12tb„ amounting; to 12385.30.
^T'iir'ii'"'''^^'i''V ... /In*. $2337.89 f, '
y. Dated Noy. 25th., discounted May 11 tb., auit'g to £2626 6 3
'"'ff n'? I r-' fu^ V •^»*- ^^««7 2 lOi -I '
«.!.u • , , ^' 6'J»v isoountedSept. 18th., amounting to $18 9 i. 60,
payable m 1 1 mo., a( 6 jK r Am. $1878.97 + . '
AMPLBS IS DHOOUNT. 217
M. Dated Oct. 9ili., ,li
payable .n !)" mo" atl^ '57""^''' ^""^ ^th., a,nountin.nr to £287 5 0,
iSi,,!,'"!'"! ""-'■ 'J*.- '.li -'counted J„„e 22„d!
payaW, ,„ r. ,;Z at 54'«'i'""""'™ """" ""•>■• •'"'^'x to $1310.25,
P.41.:'r„1,jrt if ••'^"--ed Sept. T.h.,'^aro*:,l^„:-t1l-^eio,
p4a■.??r^,S^f^ ^-"-^ Ap., ,,,., a„,,, ,f/,,»^'JJ-,
pailFr^^al'c?'^-""-— ~?^lo&;»0,
pa^:L,fr^*!ri;t^;?4f-'''"-^""--.-?;.--5«Ve,
21. OnMnroU ]9th ,' . , . ^n«. A2091 5 51 + .
payable nL'V.M;hr^^^^^
•^•.> .7.' ,,-"*•' what .«uiii , lid I receive? /Itj,.? .*«92 54.fi 4-
23. The contr ct Z ^ tnlvr. \^ ' /''''* ^^'^ ^^* ^lut. of ihe bill ?
ordered to do ext work for «I52J' if '"^ ^f '"f ^"'^'^^'^' ^^^ ^^s
-a.^0 that e.e co^^^r^l^^.^^^^^ -— ^l!:
diec'ount being oi^TaVr;? '^' "'"^ '^.l'/ 1^^,« ^'''H -^«'
25. I owe the sum of If -> 1 4. 22 as follows •«';n^^9 . 1 • f ."*" "
^'. vvjiat IS the present worth nf -kTkq «n j. ^u "^*^- 10 -'5.
hence, at 6 ^ ? ^ #769.60, due .^ vfara and 5 months
14
« ':li
; ' ''M
I' I
lit
only £98 • dhi T .-Thtlf ?■ . ^^' **^® discount amounted to
After 16 montKl^lSfeO a^^^^ %^rr"' '^f »*•
remainder, knowi„g^hH^l'dl!ied\S^08:5l<i'' ''^ "*'^ *^^
34. What «um discounted for^mf'Sd;. ' at'V?'^'' '^' P"'''^"'*"
produce a diornnnf wifj. „i • u ; "'•' *^ ^«^ P^r annum, oan
£>vered benSr, Jn. iT 1'*? '"^^^ purobased the makincrs of 8
V^ n^-t' f ^ ^*yd. lor each, at $1.80 per yd.? A #(i6'\7< -u
STOCKS.
8S<S. Stocks is a general name given to ffovprnm^n* k«-j-
and to money capital invested in corpomtTon^ ^o^^rnment bondi^
'u^^^\ ^ Corporation is a body formed and authorised b,
*aw to act as a single person. "umoriaea by
390. The legal act of incorporation which detinen *K« rJ„i.t-
and powers .f the corporation is called a Chartef ^
triS'o'^^ ^7'^^^ ^*°^^ of a corporation is the money con-
tributed and employed to carry on the business of the coinjany
for these .o^n/ontit;:'tro"h2.5jtoT?IXro°L^^^
6 ^ aunually are called 6 per cent. Btook, or H'b] Ao. ' drawing
binVI°i^^:J^"^^"°»."'^^»•<*^hat are called co«»„,^.ei.r,h of »^ ,. . ...
«-e«e..rai.y «.o^.„, P-eSt^^^/ifrthi/K^od::''"'^ °°"^''"'
STOCKS.
21^
UIVJ
us. $2000.
; if he pays
uch will h«
206 4^.
ied£120dM-
imounted to
y purohasea,
Jars' credit,
ant of 1 5U.
e settle the
purchase,
innum, can
ikings of 8
.. f (562.7!) +
and having
liscouiit, at
It). .'{(In. af(.
floor being
is 701b. per
lank, iBt
be obtained
ath.
orized by
be righto
oney con-
smpany.
y tt9 raised,
oiidsitHued
da drawing
hi-- j-
•• 'n a uuc
be amount
'h eoupons
wnuitMg."
t difforent
thJ/iiu^dTS i-slKi^i'^'r*'"'?* "^°«' """"olidated the stock or bonda
Mmi.annuall7MdSeLht^1''T"^ '°'°«'^^ "^'^^ I'«^ annua,. payablS
practically ;l^;^,Xt™^'« wfth h^ "P''°^ '^'\' g^''«™"^«"^ b^oou^inj
deemed. TheVuotat onrofThese 3 J t ^ ^'"'l*^' "'^'^'.^ "'^ "''^ ^''^'^ ''»« ""
siocK IB Jivided. The Talue of a share in the original oontribntiMi
of capital var.08 m different oompanie. ; in ban^ ^TmT^
railroad compamea of recent orgrni.,ti™, it i, nsudfyilol'
».l«e ■" "' ** ^" "^•^ *»y "» ««• '!■«!■• original
for^fet^nTeif :J;^1! E™°" °' •^"°-' "-^ '''"^ --
th^ltlt^i^tL!' ^' " *""■"■ ""^ *^^ -" f- '-
^^'^'i f "^ Installment is a portion of the canital sto^k ta.
qu.ed of the stockholder., as a p^yo^ent on th:i;SLf ?il
meft^fe loJes or'fhpT'^* '' " """^ ^'^"^^^^ «^ stockholders, to
meet the losses or the business expenses of the company
400. A person who buys and selb stocks, cither for him^slf
jiiC "^ ° '°°*''' " "^ • Stock'Broker or siock^'
KXAMPLES FOR PRAOTIOB.
.^Vi Jpti^i'„tr°'" """' °'«-^ Tr„„k Railroad
OPERATION.
$2700 X .045 = $121.50, premium.
$2700 + $121.50 = $282l!50, Am.
Or, $2700 X $1,045 = $2821.50, Am.
»1.«46. $2700 will coat $2700 X $1-046 - $282170' An J^'"'"'^'' ^""^^"^
ANALTBI8. — We calculate
nrstly the premium on the par
▼alue, which we find to be
*12l.60; wo add this to ,<i27oo
and obiam $2821.50 which is the
!"!•:•_ «!'■• sjno* ifl of the stock
or
t ! _
By proportion. lOQ : 1«0 4. 4J
ST X IM
.,j,i„,„^0ig;i^,^jj,i„„^y^
If
I I i
is' I
SIO
£m. a. A broktr sold for me G4 sharos of thf Ocean Swamert
J-o. stock, at Jij^diacuunt, for wbicli he char-jed I % brokerage:
how 111 ucb did I receive? o « tw * »
$0.15
$1.00
OPKRATION.
■h .0026 = 0.1525.
-$0.1526 = $0.8475 pr(H)»eda
of$l of stock.
•400 X $0.8476 = $5424, An$.
Analtsis.— Adding the r»t«
of brokerage to the rate of dii-
oount, we have .1626 j hence |1
will bring .fl ~ $0.1525 :.
$0.8475, and 64 sharaior $H4««
will bring 6400 v .8476 «
9M24.
By proportion. 100 : 100 - (16 + 0.26)
84 X 100
S;^£=SS-H2"H-S«
OPBBATIOir.
fj'22~f J'I5r^2-^^' '""''•* ^ai« of$i.
JO 88 (- $0.00i -. $0,885, cost of $1.
$17700-f-$0.885 = $20000=200 shares, Ans
Analtsu — Sinee the
Btook is 12 f^ below par,
the market value of $1
will be $0.88; adding the
rat* of brokerage, we find
^took win eoBt $0,885. Henoe fwSiirrnf) tu. k i. **"** ^^^'^ ^°"*'" "^ **»"
.885-$20000or200gh8re, '*'*''• »»~k«' o*" purchase jmo^ ^
By proportion. 100 - (12 + .6) : lo© ;: 17700 : » ^ m,
i5f' n r'^^® ttichelieu Company declares a dividend of ISA^.
what will I receive for 24 shares ? 'vmena ot IQ\%;
OPBBATIOir. ANALYsrs—Aocording to 282, we maltlDly the
$2400 X .16i = $372. feend $372! *'* '"*"• -^^i- *°d"b3?2:
By proportion. 100 : 16^ :: 24 x 100 : *.
Prf *■ \ Tl^*' 'J'®^™® *^*" "^^ °''^^^'» ^3^ investing $10260 in Quebec
Province 6 % bonds, purchased at 95 5^ ? Vfueoeo
OPBRATION. ANALTBI8.-We divide the
$10260 -r .95 r= $10800, stock purchased. *°^f»t°?ent, $10260. by the
$10800 X .06 = $648, annual iticome. rS'*^wtiS'tirst:
n^"irome'' '''"'' '•'^"'^^ interest, we have $l08?o'x Toe' r^^S^hf ^1
By proportion. 96 t 104 u lOMO 1
M*00K8.
iU
capital" „aetfeTresUn?i*h "r 'I *'^" *""»•' '«-««««! what
ne inrest ,n o % bondn, when stock is purchased at 80 %'}
OPBBATION.
f»000 X .80 = $7200, co.t, or investment.
Analysis. — siaoe $( of
the stook V7ill seoure $0.06
income, to obtain $450 will
req uire $450 _j_.06 = $9000,
▼iilueof the stock b the market t.rina^f«i u (^^•*)- '^Multiplying the par
ooet of the required^tSror tt^'^uTt^'bt i'n::«Lr ■^'""" ^ '^' ^^^'oo. tl..
By proportion. 6 : 100 :; 450 : , x .80.
OPERATION.
.07 -^ 1.05 = 6J^.
and »a!7?l7TK'^'°"° *^ *>' •*«''' ''"' ««"' $1.06
By proportion. 106 : lOO :: 7 : *.
div^:;d';nrwSwt 8"'^'t'™h^^^^°^ -d ---•d a
did he purchase? '^ "" *^'« investment; at what price
$0.0* -h
•PERATION.
$0.08i=$i08, .4n*.
^iu», the purohase prioe.
By proportion. 8i : 100 :; 9
jr.
share, of ^0 eL, a S'Ztl'^MWdS'iSrrr?"' "^ T^r"'
.de^J will he receive a„„„all/? "" '°°'' ^* jtT&r'Vi' i""
IS. If aoo shares of ihe Oitow. Bank sell f™ .^nnilj I *' ■
the pren, um, e«>h share being tlOOf A^ ^1 """" "
_ 14. When the nominal ™loe of .took is ^ei •) iTJ ?.f "'""""•
is $100 per share ? '"'"" "" "'""'"''' "»'»' "f "I'ioh
1«. Bonghlwock at par, and sold i. »i 1 a . ^'" "-^
'Im
3 '«r
3 1 t*^
yh
222
!' "^^ •■«*"'«^o*l bought, at the rate of $188.76, a namber of ekares
in the Pictou coalmine company, the annual income of whicli is $10
per Hhare. With the income he purohases $2(;0 wortli of .'ooWs ; wiiat
was hia mve8tii<ent, the brokerage being \%? Ana. $i:VJHA(il.
18. A merchant retiren from buHinesfl witliasum of 5134520.50 and
buys with thiy capital government 6'8, at the rate of .f 70.4.J ; what
will be his annual income? ^^s. $2940,
19. Ontario 4V« are sold at the rate of £94 17: what inconie vij]
I obUin for £3794 ? ^^^^ £1,^0
20. Sold $16400 worth of North Bank Stock at 13^ pren.ium;
what ehall I receive ? Ana. ^IHo.'Vi.
21. A person, having £2250, invests this sum in Ocean Telegraph
Company Stock which sells at 17 ^H discount; what amount of capital
doeH he purchase? Ans. £2710 16 101 + .
22. Bought 36 shares of the Western Copper Mine Company, the
par value of each beina $600, at 2 ^J premium, and sold it at 28 %
discount; what is my loss? Ana. $5400.
23. I have an investment of $16000
ID
as
of
Ana. $5400
in a transatlantic steamship
company; how many sharen shall I own after a div'lend of 8 * is
declared and payable in capital stock ? Ana. 162 shares of $100 each.
24. What should be the rent of a farm, which cost $16992.10
order that the purchase capital ma/ produce the name revenue
would be pro<luce<l by the same sunt, employed in the purchase
6i5UbondH, at91|5H? Ana. $U(iH. 80.
25. A farmer mvests £36, the price of three oxen, m die pur-
chase of 6 ^ bonds sold at the rate of £78 10 ; at what real rate was
his money placed ? Ana. 6^JL %
26. An exchange agent having $45000 invested in bonds of the
Canadian Transatlantic Steamship Company, exchanged them at 88 %
for capital stock in the same company valued at 62^°^. The bonds
brought 7 % annually, while the shareholders received two dividends
during the year, the first of 3 %, and the second of 3i « ; how much
did the agent gain annually by the exchange ? Ana. $968.40
27. An agent receives $25000, with instructions to deduct his bro-
kerage at 1 1 96, and then purchase bank stock for the balance • if the
stock is selling aXZ% discount, what will be the amount of his capital
«*<^^ . J- .J 1 . . il»i«. $26329.92 +
28. An individual desires to invest $11168 '\n b% bonds. The
market value being but .*67.35, he waits a few days, when it rises to
$69.10. Find, now, what income did he lose, and what income he
would have gained had the market value lowered to $66.25, brokerage
being f %? Ans. Lost $20.90+ income, wotild have gained SI 3.734-
29. I have $60500 to invest in bonds. I can purchase 4a4 bonds
at the rate of $95.30, and :! % bonds at the rate of $69.25 ; which would
be the more profitable of the two? Ans. The 4^^^ bonds,
30. How much more advantageous is it to invest $1128 in ^i(jL
bonds, at 91 1 9^, than $1 1 28 in 3 «6 bonds, at fiSA ^ »tft>Vprfl ,« K
^\%
Ana. $6,923 -f
;e oeisg
ai. A banker owba 150 shares in the Quebec Insurance Company
nkWPNUlflHTP.
2]f
Charge rne ' «i I ?i,^ "*?,*"" *^» "»«, >cnewiHK th*t the a.-.-nt w,.,
32 % fl " * ^''"."^^'^g^ / .In,-*. «1 5966.26.
he buv. fc' 4Vi1 °*'? ''"[ ^'l" ""'^""^ «''*'*^ •*'•'*'>• ^'^1' ihiH «un,
m*" an! ..!« -^2 . / '''"*^' produce an an.nial incuiiKM.f $18, at
♦kJ*' *?•' •"« -^^ hoiKls, pruduch.K annually -^20 at 64 J « With
what av*rR«« J-»^ I. ?V ^^ *''^''' ''® ^".^^ '^ ^ '«»"'» at 68i % ■ at
33 Tm h..l^ ^ '^! *.^* "*'"* quantity of rerenue ? Ana. $98.43 +
110425 a? S^oTrlt'" **^*. ^^r^-^' ^«'"P^"^ <*"' the value tf
• ferm'er se^ur/ 1 ' '*"'* Producing $H6 for interest and lividend,
oflheik^r 1 • "''?"• "'Z*'^'*^- ^»»'-«"^ the market valu«
or me stock per share, and at what rate he let out hi. money ?
34 In J.n iQ..a ^ ^n§. lst.$6\}5; 2nil$5.?i'.//j.
£37801 9fl'ifi™?'^» 1848, the total amount of British con ho Is was
annually? ' ^'•*^ ''«« t^e amount of interest paid on the,,. He,„i.
belt tt''9Tr*:'t''" ^"" V''' '' ^-^-*' 7^Tih1 mISt Miue
95uV whlt^r.i» TJ^u • ^T '^*-^'' '°"«^' ^h^n stock risea to
teinerl i:.Jm * i^ *^"^.^* r*»'*«*^ ^^at los. would he have nua-
36 A mi'o?h „-w Q«- ^ ^r- *22.75 gain, and $17.60 loss.
deHires to in3 M ^'^ '^'■^^- ''^ * ^*" ^^ «21.80 per 8q. yd. He
interest aJddivid^'n J '^^ •"*' *^^^^ '^^^ ? ^^"-'^ P'^^^c^ *200 as
Kdence Pn th \*"'^ *'" "/r^'*'*^ "^ *« * pren.ium. In the
Sar?dd,V?l.,H '*'T'^'"'^^^^^**<^^' they produce $50 as in-
tt7nK?s adlaS ^"^ *"■! "^gotiated at 45 ^Dremium. Which are
he Drclm.l?n at "'iu*"^ ^y ^^'^^ '""^l* ^ i* How ,„any shares can
he s^ c« e r ^« tT **Jf T'' advanUgeous, and what revetiue could
3 aEs^'andlSo'^rrevTnuT ''' """ -^vantageous by 1.478^j
il
PARTNERSHIP.
401. A Partnership is an association of two, or more ner
ions ,n busmess, each of when is called a Partnrr Suda an^
vocation IS called a Oompan,,, Firm, or HoZe! **
402. Cask I.-T^o/.^.a./^ ;.,h.V,. .,Wa o/ the profit or
A>
O'fl
Whole
8took, $276
" 475
" __ r>oo
OPIRATIOV.
f2T5 X 0.12 - I 33, A's profit.
476 X 0.12 ^- .07, IJ'm profit.
.OOO ^ 0.12 - _60, C'h profit.
Pr-.of !«!ir)0. ACliole profit.
1250 - $0.12. pmlii, ,)n$l.
Akaltsib.— Since I ho whole atook i.i'flJSK, dti.l ilm wholo i,rofit. $151), the
pro It on every $1 of«t„ck vTillbo as many .ioll us ii.s 150 contain-, tiinon 1250, or
*U.I^ on every $1 of stock. Then, each merchant's stock niulti|>liod by .lli jfives
oi8 part of the whole prolit. The s-ame result ul.so may be obtained, as follows :—
By proportion.
276 i
+ 475 J =: 1250
+ 500^
160
;'.i75i (!?:«, A'spr
475^ : .r = Ans. < 57, H'n. pr
500) ( (iO, (."^ pr
8 profit.
.tit.
■ofll.
Proof, $150, whole profit-
40J$. Rule. — The whole profit or loss, divided by the number
denoting (he whole stock, will give the profit or loss on each dollar
of stock; and each partner a stock, multi plied by the number de-
noting the profit on 81, will give his share of the whole profit or
lots.
Or,
As the whole stock is to each partner's stocky »o it the whole
frofit or loss to each partner's profit or loss.
II I
EXAMPLES FOR PBAOTIOB.
1. With £200, two men gainai £50 ; the flret man contrlbuaa
£125, the second, £75: what part of the gain is each entitled to?
Ans. The first, £31 b; the second, £18 15.
2. Four merchants ap.suciated and rallied a capital of .^145000, to
which each man contributed equally. At the expiration of the part-
nership, the capital was found to be augmented by $20877. What
•ball be the part of ea^'h man, knowing that the Ist. ought to have 13
parts; the 2nd., li ; the .3rd., 8; and the 4th., 7?
Ans. Ist., $23959; 2tid., $20273; 3rd., $14744; 4th., $12901.
3. Three men associating together, gained £287 10; the let., put
in 400 yd. of velvet at £1 per yard ; the 2nd., 350 yd. of cloth at £2 ;
the 3rd.. 450 yd. of cassimere at ISs. ; what part of the gain should
each have? ^ -4fl«. £80, £140, and £67 10.
4. Four persons having joined in partnership airree that the ! wt.
put in £1250 ; the 2nd., \ more than the first; the 3rd., as much as
the two others togetiier ; and the 4th., his industry during the vcar,
which' was estinoated at £2000 ; what share of the profits, £1625, hliali
tMk reo«ve? Ana. £260, £312^, £6«24, and £400.
PAftTNRMHlP.
826
eachn-ceive? ' j„ i! '' IL^-' ^- H"w much will
. 6- The firnt of five ,„en a^.^" l""' ^•^'•''*' '['^''i' '">'' *■•'»<'•
oiiii; am ho on witli iJ.n ', ""^•' ^'^^' """'i' than tlu- «i,c
7. Three «pt.culaU;rH hav« t^«rl?t'" *''^*^'^' *-^^'*' **^''"' *■<'"'' *»-'^-'-
fc'am, tAe 2n.|., $206 and the 3rd ftLt. w.'' *"' ''"*''^' "'' ""^
voyage 6:>(.\o,.sw.rrtl XoveXaH °*''" ''' ^'"'^'^- ^^'"-'"y ^'"^
arofle. If 250 ton. were Zi led 1. *^" accm'"' of a storn, which
J. -i^nree ta?inerM h^nvlif i^u ^i «. ^nw. oi,} auii .i7;> tons.
each receive ol' the profits? iJ«/!oi'^'''' ' '"'^^ '>'"«•' ^'i^l
the second" £527 6 104 the thir I , '-"*" «"»tr.buted £400 lA 7*;
received, however, £98 I's il: hi T"^ P?'"! >-^ "^t known, but he
contribution of th; third nerclt^ru t^^'? fl '''! T ''^^^^ '^'^'" "'^ 'he
the price of the -'aplingspr hundred ? ^ A *^%1"^' "'^''"'' «'«
share £494 I 3. Tl,: pK of l!. ^c-, » ^f'-Jhird .Merchant's
£\IS 9 per hundred!^ '" ^^^ ^ ^i' 2nd., £105 9 4^;
and' JvTr Bkt:;;' £U2'?S'LVirn;^ ''' ^^^-'^^ fox
£ 18 10 more than the second ^L T fi^ '' "i^ ^''' ^^'^'" *J^a"ced
ISfton the buying pr!<^^^^^^^ a profit of
gave, and the third fJ^„i«hed*o?^lltrf ? ''^^''"' ^''^ ^-"^^
wha^^w^thecontributio„7eL^'''r$^^
that the 1st. fuihed ^^^Sit"" : 'tS In'd' T^-^rh ^"'^-"S
not meniioned, and that the ?rH ?,?, u , ".' f"f'"-^he<l a quantity
tity equalled the deli™ of t fe' iTT' 5?u ^"";^'^-' ^''"'^'^ ^-'an
bandies? ^*'^ ""^ %i^ io*."!'*!^-' '^^''^ furnished 240
the average price of $7 37?. Tn tL ^"'■:='»?«*' ^*^ ^^"^ clock works at
Jobs of thIlS. «urpa!:;^'Lt"fterd'^'?r&t^ 'l' f'''' \^^
loM and investment of each? Aiu !«♦ t^ •=1«'o'^^** ^^""^ the
I0»
h't '
r ,. ';
'■■} J -1M
836
PARTNBBSHIP.
16. Several pernonB agreed to conduct, during one year, a p«'P<v
manufactory. 'J'lie fiPHt put in | of the stock ; the second, $4000 lese
than the firnt ; tlie third, $4000 less than the second, and so on until
the last. If the iiivesinients had been in sums equal to the highest,
the capital stock would be au<,Miiented by i- The merchandise sold
produced a sum equal to the 4 of what wa^ put in, which was em-
ployed in buyin;^ rags. In admitting that the || of the sum proceed-
•ng from sales serve to cover the expenses of fabrication and infest-
ment, it is required to ascertain how many persons there were, how
much each one put in, and what part of the gain each is entitled to?
404. Case II.— To Jind each partner's ahare of the profit or
loss, when the stock is employed for different periods of time.
Ex. A and B entered into partnership ; A furnished $240 for 8
months, and B $560 for 6 months. They lost $118 ; what was each
man's share of the loss ?
. f?
$240
560
8 = $1920.
6 = 2800.
OPERATION.
$1920 X 0.025 x= $48, A'b loss.
2800 X 0.025 = 70, B's loss.
Proof, $118, entire loss.
$4720.
$118.00 -r 4720 = $0,026, lose on $1.
AMALTBfB.— It is evident that $240 for 8 mo. i? thebame as $240 X » = $'^20
for I mo., Binco $1920 would lose aa much in 1 mo. as $240 in 8 mo. ; and $560
for 6 mo. ia the •ama as $560 X 5 == $2-00 for 1 month. The question then is
the same as if A had furnished $1020, and 15 $28(10. for equal times. Then, if
$1620 4- $280(1 = $4720 lose $118, $1 will lose \j^ of $118 = $0,025. and
$1920 X .025 « $t8, A'8 loss; $2800 X ••)25 = $70, B's loss. The «»me re-
sulU may be obtained as follows :—
By proportion.
$240
5ti0
X 8 = 1920
X 5 = 2800
1 =
4720
< 1920
\ 2800
118
. ( $48, A's loss.
x=AiM. ^ yo^ B,g J^gg
Proof, $118.
405. ^y^hV,.— Multiply each partner's stock by fh" time it was
in tradr, and divide the whole profit or loss by the sum of the
several products ; by the quotient, multiply the product of each
partner's stock and time, and the result wdl be his share of the
profit or los^.
Or
Multiply each partner
as tlu sum of these products
pn^ or loss to each partner's profit or loss
stock by the time it was in trade ; then,
is to each product, to is the whole
»7
■il
IXAMPLSS F«S PSACTIOa.
1. Two persons contribute unequal sums towards a capital: the
m-at puts in !^2300 for 2 years; the second, $1500 for 18 months.
What part oJ the gain, $1400, should each person receive?
., TV, •^••11 .. . , ^"^- =^940-15, $469.85.
^A'J, individuals raised a capital sum with which they eained
£1137 10: the first contributed £200 for 2^ years; the second; £125
for 26 months; and the third, £248 16 for 35 months. What part
of the gain should each have? ^
Am. Ist. £382 16 1^; 2nd. £199 7 Of; 3rd. £555 7 104.
d. A porter associated with a pedler and raised acapital of $16000
tributed $9000, received ^1800 ; what did his companion receive,
knowing that the latter left his share in the business but during 20
^ojithal ji^ $1166.662.
4. i?our persons agree to form a partnership for 3 years. The first
puts in at the beginning $360, and 6 months after $2400 more- the
second puts in $8000 at firH^ and at the end of 20 months withc/raws
the halt of his share, and 6 months after withdraws $2400 more-
the third puts in $1600 in the beginning, and $5000 at the end of i
years ; the fourth puts in at first $600, and every six months aue-
ments his portion by a like amount ; the gain being $80000 what
part did each receive? » «•*
Ans. $14677.36 + , $33336.16-, $19232.39 + , $12754.11 +
6. Three merchants joined in business. The first put in £1001 12
for 10 months; the second, £1761 12 6 for 164 months: and the
third, £2000 3 9 for 17 mo. and 20 davs. Required each meJchant'!
share of the profits which amount to £360 3?
6. Two clothiers associate together; one of them contributed a sum
with which could be bought 90 yd. of Broadcloth at $6 per yard the
other put in a sum with which 60 yd. could be purchased at the same
rate. In supposing the Ist. to have had $6 of the profits more than
the 2nd., to how much did the profits amount? Am $30
7. Four farmers rent a pasture for $976. The first put 6 beeves on
It during 54 aays; the second, 7 cows during 63 days: the third. 8
heifers during 75 days; and the fourth, 6 horses during 50 days It
was calculated that 1 beef consumed 1^ times as much as a cow or
twice as much as a heifer, or H times as much as a horse ; how much
must each farmer pay ? '
Ana. $238.45 + ; $259.66-; $264.94 + ; $211 96-
J{.h *^^r?J?S "1* ""."_^,^""'lg l.yff^' /hree partners g;^
x^^iUA}. xhc ui.^t i;drt..er null put in ^i34oY lu in the beginnina
but after 2i years, hi withdrew £.{275. The second put in his share ■
which was £41000, only l^ years after the commencement of thi
work, tinally^ the third maile his contribution of £63760 but 3
years after the mstalliuent of the first. What part of the profit^ shouU
Moh r«)«v«? Am. £3i«« 1« 0} + ; iS»8«7 « 4?-; £8816 17 7 + .
ll
i.
!
228
^
BXCHANGR.
40f>. Exchange is the process of remitting; money from one
place to another by Drafts and Bills of ExchariL'e.
NoTR. — For a full treatment of this and of the following anbjecu, •«« the Com-
meroial Arithmetic.
F<ynn of a Ih'afL
%^, [STAMP.] M^^^ec, ^. M, (^€7^ /. /ay/.
Q/dii^ c^^ aj^/el HyM, /My^ ^ (^Jceni'U &rim7n&,
^99^e t» m/^ accvun/.
407. The Drawer, or Maker, is the person who signs the
draft.
408. The Drawee is the person on whom the draft is made.
409. The Payee is the person to whom the draft is made
payable.
410. An Acceptance is the promise of the Drawee, to pay
the draft at maturity, and is usually acknowledged by writing the
word " Accepted " with his signature, across the face of the draft.
411. An Indorsement of a draft, by the payee, is made in
the same manner as the indorsement of a note.
413. A Sight Draft is an order to pay at sight.
41J5. A Time Draft is an order requiring payment at a
specified time.
414. A Draft or Bill of Exchange is at a Premium, when the
price paid is greater than its face; and at a Discount, when the
price paid is leas than its face.
415. Domestic, or Inland Exchange, is when both the
drawer and drawM reside ia the aamc oauntry.
• ft:
416. Cas« l.~Oiven the face of a draft, the rate per cent,
0/ exchange, and the time, to find its cost.
1640
OPERATION.
X 1.016 = 1649.60, Ans.
ANALT3 3.--Th« oostof exchango of
|1 18 $1 + 10.015 = $1.(115. „d J
$640, 640 X $1,016, ? ■^^' «'* "^
$649.60.
n^f' 2- What must be paid in Montreal for
Ualifaz, at 33 daya, exchange 2^ JjJ premium.
a draft of f 3500 on
OPBRATION.
$1,000
•006 = disot. for 3«cla. sA9%.
$ .994 = cost at par of $1.
'022 = rate of exchange.
11.016 = cost of $ I of the draft
$3500 X 1.016 =$3556, Jng.
Analysis.— The disooant of $1 at 6 *
tor 36 days is $0.0t)6, whi.^h being sub-
^ed from $1 leaves $0,994, the coat
of $1 of the dratt, if tho (ixohsinge was at
C/wJ*" '■Y'' I'*'* ^^^ premium of $i,
$0,022 and wo have $I,0I6, the cost of
♦V i '^"^ '?'*''i'' ^®"°« t'le cost of 13500.
to« draft, u $3500 X 1.016 « $3536.
Jw^r 1 ; :r^' ^""^ V^^^ draftB.^MHl(iply the face of the
draft hy Iph, the rate when exchange ts at f Lmium and t
1 rn^nns the rate when exchange is at a discounf ' "^ ^^
11. J< or drafts payable after aisht— Find th^ mat n/ «i ^ j. »
leii both the
BXAlfPLM FOE PBAOTIOB.
1. A merchant in Toronto wiehee to pay in Montreal f rqqn ..j
^change ih a % premium ; what will be the coafof thTdraft ? ' ^^
„i.!^''"'i,"'" ,'Ti,'" """i "f • •'"* "'Was., Ibr M Xvf It 6«
roKcion FiXOKAMn.
I
!* f^S;i
■fn
6. A merchant in Quebec retieires from his agent 1200 bushels red
wheat, purchased in Toronto at 65 cts. per bushel ; in payment for
which he remits a draft on Toronto, at f % discount. The transpor-
tation of hia wheat cost $98. What must he sell it for per bushel to
gain $225? ^n«. 10.91 1.
4lJ!ii. Case II. — Given the cost of a draft, the rate per cent,
of exchange, and the time, tojind its face.
E.T. A merchant in Three Rivers paid $6856.10 for a 60 days'
draft on Toronto, exchange being IJ % premium, and interest 69^;
required the face of the draft
OPERATION.
91.0000
.0105 = the disflount fo
! 63 dayt.
ANALTsn.— By 416, Caee I.,
JPae. 2, we find the cost of $1 of
the draft to be $1.00825. Henoe,
$6856.10 -^$1.00826 » $6800,
if the fa«e of the draft.
$ .9895 = the cost of $1 at par.
.01875 = the rate of exchange.
$1.00825 = the oost of $1 of the draft.
$6366.10 -7- $1.00825 - $6800, Jfw.
41 tl. Rule. — Divide the given cost 6y the cost of a draft for
91, at the given rate of exchange ; the quotient will be thefac« of
the requir&d draft,
SXAMPLK8 rOB PBAOTIOa.
I i^;;
'Mi ■
1
!■* i
i
1 ,ii
1
'If
.
J 1
^1
1
1^
1. What draft may be purchased for $16416.10, exchange being at
3) % premium ? Ans. $15860.
2. Required the face of a draft for $158.40, exchaoge i^nvi. at I %
discount? 4n«T$i60.
3. An dgent in Kingston is directed to make the remittance by
draft, of $565.32, to his employer in Quebec, drawn at60day8. What
will be the face of the draft, exchange being at 1| ^ premium?
4. V*hat will be the face of a draft for $962.85, exchange being at
I % distjount ?
5. A man in Halifax, has $4800 due him in Montreal; how much
mort will he realize by making a draft for this sum on Montreal and
selling it at i% discount, than by having a draft on Halifax remitted
to him, purchased in Montreal for this sum, at | ^ premium ?
ilfM. $11.73 + .
FOREIGN EXCHANGE.
420. A Foreign Bill of Exchacse is a draft in wbioh the
drawer and drawM Uve in di&rent wvnkriMk
n whioh the
Form of a Foreign Bill of ExcJmng.
•e.
ferent times; "n tl, payment of ^om th'SL^^™"' oonreyancM, or at dif-
must hare a stamp attMhed ' *•>* ot»»er two are worthlew. Eaoli draft
the old pnr of o..ha„.e. inS „f "'thLew pt'" ■*' ""'^ °°
was fixed at f4.866. NoW tho ,«,« « ° **'.'.*''® ^*'"« "^ **>» PO"nd sterling
old par, thatl;.*4 ^44 I 9 ,v XflU' "H^t'-*" '^^ "''^P^'' P''" »* ^^ of thi
fJreat J^ritai,}. must reach the nom Lrf^Liam or Si T^T\f- °'^°'^» ""^
cording to the new standard. ?««»>"«, or 9^ % before it u at par, ao-
for the bill of eX,^L? * premmm. How mnoh must h. pay
OPERATIOir.
$V X 1.11 =$4,931:
£.j60 3 6 = £o()0.176;
£560.175 X 4.93i = $2763.63, J^n»,
ANAtTBig.— .Slnoe th* old par
•f £.\ Rterlins >= $4,444 or
$^, we multiply $^0 by 11^,
•r$1.11, the giTonrate, deci-
mally erprewed, and we obtain
rate ; multiplying the faoe of the bilL :£fi«0 1 A }^^\ *' °*** "^ ^^ *' ''"'^
rORHON IZOHAiraB.
<,ll I
Ex. 2. What will be the fao« of a bill of exohMiff* on Lirerpool,
purcbMed in Montreal for 95537.40, «x«b«ng« being at 1 ^ premium t
OPBBITIOH.
$5537.40 *:- 4.88| ^ £1133 IS t.
AxuLYvn. — We find, as in the
preoedin;; example, tbe oost of £\,
»ttbe ^Ton rate of exchange ; then
we diride $55S7.4I, th» {pren cost,
bT the oo8t of exohange for jQ, and
oMafa £1132 IS 0, the faee.
^x. 3. What i« th« oost in ToroDto of • WU oa Paria, lot 1780
(htaoa, tJMkange being at 2) ^ dinooantr
OPEBATIOV.
CSonnMrcia) value of the fraoo, => ••.IN
IMnot 2^ % diflooant, e.004M
Valuf of 1 fhuM, ....... $0.1818*
$0.1H135 X 1780 s $321,803, itiM.
43S. From these illustrations we derive the following
Rule.— I. To find the oost of a bill, the faoe being giren.—
Mwltiphf thtface by the cost of a unit of the currmcy in which
the bill is expressed.
II. To find the faoe of a bill, the oost being given. — Divide the
pnen cott by the eo$t of a unit of the cwrren^ in which the bill i$
Co be expretned.
RsDUCTioN or THE Stbrlino Monbt to thk Old as to
TH« New Oanadian Ourrbnot, niw par.
'. fiodttoe £500 3 4 nterliug, to Old Canadian CurroiMy.
Amaitsib. — The pound
■torling m, $i.8«§, and the
Old ourreBO|- peand ib $4;
diff., p.8«}. Then £1 stcr.
ourreney. JS«w, ^ of a num-
ber =^ plu£ ^ ef J of that
BBmbsr. Hesss the
•PiaATlOK.
£560 3 4
4- 4 of £560 3 4 3: US 8
+ J^ol 112 8 - 9 6 8|
£081 10 81, Amt.
Aad in Decimal Currency,
£081 10 81 (233) = $2726.131-
4SS4. RuLB. — To reduce tteriing money to Old Canadian
Curroney, new par, — Add to the fivm $um iti fifth pitu one
tmlfikofihefifik.
I Uyerpool,
i premium ?
od, as in ^he
the ooBt of £1,
cohange; then
th» girtn cost,
Iff* for £1, Mid
the fa««.
M. for 1780
■QUATION OF PATMBIfTt.
BXAMPLEiS FOR PRAOTIOB.
S38
ring
»g given.—
/ in which
—Divide the
h the bill is
LD om TO
A.
— TIm pound
.8«i, and the
p«and _ $4;
Then jEI stcr.
- Xl^ oJd
«^of anum-
>^ «r ^ of that
ss tks
i Oauadian
'h pltu ont
« t/pi:S ^ ''' «°"' '" «-"*' "f « k^°» B°^ "., for ,2000,
35 Ota. ? '•*'''* a^ve par, the mai-c banco being equal to
on Lyons amounting to 49S36 fr 20 Inf """ i""^«oy» ^r a bi"
txohange below par"? ^^ centime. ; what waa the irate of
10. Received from L. Nelflon * r« t j i .'^*'** *0-053 + .
£381 5 0, o« J. Chllter.'&'Sot Qu^l^^'^iLf i«1Ll:i"'""^^ ''"^
mal oonrencj of Canada, at 9 5« preTnS ^'CimoS + !''
BQUATION OF PAYMENTS
be^™*d«^ ^""' ""■••""* '' "■' •^"» <» "•[««= before . deb.
onoe ,rith»at lj.s to debtor or ereditor! ' ^ ** ''"'' "
de?tf*./b^^frrb7XV-r """°'' '^^ ""-"
i %
i I
I
1
^
' s
*
i 11 '
1 "
1
f ■
1 ,
vf
ll
TP '.
i '.' '»
; a
!
i i
'f, I.
'! >
23*
laco
300
■QUATIOM OF PATMVIfTS.
•ra&ATioM.
X 30 = 7500
X 60 = 12000
X 90 = 27000
46r)00
9750
41600 -*. 750 = 62da., ayerage term
of credit.
March I + 62da. = May 2, Ans.
the interest of $1 for 7500da. -\- r^uOOda. -f 27000da. — ,,,«„ «„
Jl nquire 46500 days to gain a certain sum, $260 -\- $200 + $300
AwALTsn. — The interett ef
9SM for 30 days is the same u
tlM interest of $1 for 7500 days ;
ud of .^200 for 60 days, the saue
M of $1 for 12000 days; and of
9390 for 90 day., the same fts of
$1 for 27000 days. Hence, the
interest of all the suns to the
time of payment is the same aa
'" ""^ 4(i000 days. Now, if
- ,- „ ^- , ,— , $750 will
require ^ of 46600 days; 46 JOOda. -;- 750 « 62 days, the averag* term of
eredit; ana, Maroh I, the date at which the orodits begin, -f- 62da. ■» May 2.
the equated time of payment.
E:c. 2. Bought of D. I. Lyons several bills of goods, at different
times, and on ▼arioua terms of credit, aa by the following statement
What ifl the equated time for the payment of the whole ?
Jan. 1, a bill ainountiug to $1^00, on 4 months.
Feb. 7, " " " " 185, on 6 months.
March 16, " " " " 280, on 4 montha.
April 20, « « << <• 210, on 6 months.
Due M*7 1,
July 7,
July 16,
Oct M,
M
OPBRATIO*.
$300
X 6T
X 75
X 172
12396
21000
.36120
69515 days.
«»516 -i- 915 = 71^ days.
May 1 + 71 days = July 11, Ans.
Amaltsis.— We first find the tim* when each of the billi will beoome dtw.
Then, since it will shorten the operation and not change the result, we take the
flr»t time when <my bill bcoomea due, instead of its date, or the point frota which
to compute the average time. Now, since May 1 is the perioci from which the
average time is computed, no time will be reckoned on the first bill, but the time
for the payment of the second bill extends 67 days beyond May 1, and we multi>
ply its amount by 67. Proceeding in the same manner with the remaining bills,
we find the average term of credit to be 71 days, and July 11, the equated time
of payment.
4t30. KuLG. — Multiply eadi payment by its own time of
credit, and divide the aum of the producta by the eum of the pay-
ments.
NoTB. — If the date of the average tia« of payment U requited, at in Ex. 2,
find the time when each of th» »tim»oe«ome» dme. Uu/tiply eaeh ntm ky the numbm'
mf day* intervening between the (UUe o/ite beooming dine and the earlieet date <m
whieh any nmn beeomei due. Then proceed at in the ruie, and the quotient vUl b«
the' average time rehired, Mt daye forvnwd frtm the date ef ike emriieH «wm k*-
RXAMPLKH rOR JPRAPTIOK.
M
wim. will be ihearuounu; each p^yLe t? '"''^^^ f ^"1 '^'^''
^- A man owea $15%!) navabllY^ S . • ^"•- ^^50.
and the remainder ia 1 yeir :^rea„^l? = ' '" ^«^ ? i" 6 mo.,
6'no.,andtheotLriiii0mo^*4'°J*^!°«'^^^^^ viz.: ^ in
a« to n.ake but onepaVnent? ^^"^ t.me «hott d it be paid 8o
4. Bought 25 caskfl'of wirift for tnoR u- . t'**" ^^ ® wontha.
follows: $526 iu 6 ma ZTiU i.^^ .***"^^ ^ ^Rreed to paj as
•«.. one pa.™e;'j;cLt'ftr^^irLti;!^f --^^
6. On the 1* if January l«fi« „ . ^'**- '""O- 18d».
first for .^500 payab^ in^o\iav. ! ?J"*'"°^''"^ «*"* '^*'^« »^t«« = the
time of payment f P^yao^f »n »0 days. Required the equated
6. A merchant bouaht. on tli^ IS.K ^ »* '*"'f* ^^^^ 3, 1868.
of merchandise and SdS,i!v/l^th^/^''^^^^ ^000 worth
-gie payment, how io:;rho«iXir;!;;:;«e;? ati!&^^^* »>^ •
-*•». Hmo. 24d».
th, «p,r.t,on „f « ,„i„,l,8, ,h.|| I „,eth'. baling ?^ '" "*""'■ "^
OPKEATION.
30 X 4 = 120
*0 X 2 = 80
^, 70 200
„^, •I80-$70 = $llo.
200-5-110 = lmo.25da.,Un*.
AiTALYSM.- Iha i,tere8t on the 230 f«r
4 month. >. .,„., eo the intewsrofjl Sf
12« months, and the int . of $40 for Imonttl
U .4ual to that of iil for 80 mo„thf- an^
Jaa the .nt on both PHtrnZymlnts^
To equ , ,,,, ereSu otintl"fb"arrf fe
main unpaid, after the 8 „oneh. ^ ,^^0 t'^lr^l^^tt
^ce r.n.nmn, un^ii ; and tHe V^ui^itt: J^!^
RXAMPLES FOR PRAOriOE.
^ equated time of the b«kiM«- '^ for «33 gal. Required
"'*'^ iiMt 12 na 22 d».
fs^
I ,!,
t36
ALUOATTOW.
i;if
(
1(1
• I
2. Bought of C. Lyon«, at 6 mo. £432 worth of goodn ; tX the
end of 1 1110. I p»u\ him £7r^, ami 4 mo. after £200 more. How \oug
after the t-xpiration of the 6 mo. nhoulii I paj the balance?
Ang. 3 mo. 20 da.
3. A grouer bought $2829.75 worth of coffee whicii he desires
to pay in three diiUrent paynitrits : the drst is to the necond aa 4 is
to 6, and tho third is etiuai to iialf the second. The first paynient
should be made in 4 mo. ; the second in 7 mo. ; and the third in 1
year. Hut at the end of « mo. he paid $975, how long can he keep
the balance? 4mji. 7 muo. 18 da.
4. An undertiiker built a house for £f/0.35 payable in 15 mo. ; but
being in want of nome money, the proprietor pays liim £2847 10 eight
monthH before the time. How k)ng, in equity, can tlie proprietor keep
tke balance to compensate the advance he made the undertaker?
Ans. 22 mo. 4 da.
6. Andrew havuiji; tuAd $8400 worth of linen, at 12 mo. credit,
received the ^ of the prio* only 15 mo. after. Wl en did he receive
the I ? Ans. In 10 ino. 15 da.
5. I owed $6U0 al i;^ months; I paid 'i of this sum before it was
due, so that I can ki ep the remainder 2 years without -njuring my
creditor. Required liie time when the | were paiil ? A. '/mo. 15da.
1. A trader owes $3000 payable in 6 mo.; $4500 payable in 8 mo.,
and 19500 payable in 10 mo. At the end of 5 mo. he pays $12000.
How loBg can h» keep the balance? Ant. 17 mo. 24 da.
ALLIGATION.
4S3. Alligation treats of mixing or oompouudinji, articles oi
ingredients of different qualities or values. It is of two kinds —
Alligation Medial^ and Alligation Alternate.
ALLIGATION MEDIAL.
434. Alligation filedial is the process of finding the mean
or averaze rate of a mixture composed of articles of different qua-
lities or values, the quantity and rate of each being given.
439. To find the average value of several articles mixed, thi
quantity and rate of each being given.
Ex. A grocer mixed 2cwt. of sugar worth $9 per cwt. with Icwt.
worth $7 per cwt. and 2cwt. worth $10 per cwt. ; what is Icwt- of
the mixture worth ?
Analysis.— Since 2owt. at $9 per cwt. is worth
«1U !«.i?f ot *7 i%ap «wt- ia worth *7. and 2cwt.
at |10 per cwt. is worth $20 ; 2owU + Icwt.
4- 2cwt. =o 6ewt. IB worth $18 -f $7 -|- $20 -^
$46 ; and Icwt. is wocth M maay dollars a« 46
•rataiiu tinMi 6, or $9.
OPERATION.
9*
X 2 =
$18
7
X 1 =
T
It
% % =
M
1
4)
ia
AXJJOATIOII.
237
How louK
D. 20 da.
he denires
jnd afl 4 is
t payment
third in I
%Q he keep
). 18 da.
n>o. ; but
t7 10 eight
rietor keep
taker ?
no. 4 da.
310. credit,
he receive
0. 15 da.
ore it was
juring my
ID. 16da.
e in 8 mo.,
ya $12000.
0. 24 da.
articles oi
> kinds —
the mean
■erent qua-
on.
nixed, tht
vrith Icwt.
is Icwt- of
owt. is worth
7. and 2cwt.
ffU + Icwt.
57 + $20 ^
loUuB u 46
di^L ^""''"--f ?^ '*« ^«'"* 0/ each of the article,, and
fhTnJ^ ""tf '^'^.^^i^ h 'f^ ^'umhe, denoting the mm of
ihe arttcies. Tht q,u>Umt will be the averagt value of the mixturi
BXAMPLB8 rOB PRACTICE.
1. A farmer mixes together 10 bush, of oata at 40 cts ner bu 15
bu. of corn at 60 cte. per bu., and 26 bu. of rye atrS c.f per bu •
woat .8 the; -alue of a buHhel of the mixture?^ Am 58 cts '
2 If I ,n,x 20 pounds of tea at 70 cts. per pound with "5 ^und^ at
value 01 1 lb. of this mixture? j^„g 4. j<, ,
rXn J;I J • f • " ^'?"; *'"' ^^ «»•• •* *^-10; how much IH a
gallon of the mixture worth? ' i^. «o 7' i
4. A man bought :i| dozen of eggs at 12 cts. a dozen, '4 doze"' at
lOi cts a dozen 4^ dozen at 1 1 cT.. a doz., and 5i doz at 10 en a
h^rec^vVpt dte": ^ " *° '"^'^ ^^ ^ ^» '^« ^'^ ' J^ -,-•" '^
fl ^" A.^'^J'lu'"^"' '^' ^®^ *<^ compound 3 lb. 6 or. of gold 2i clrata
fine with 4 b. 8 oz. 21 carats, .3 j'b. 9 oz. 20 carats, aniTib 2 oz of
alloy; what will be the fineness of the composition? ^n*. 18 cara?;.
ALLIGATION ALTEBNATB.
437. Alligation Alternate is the process of finding the
proportional quantities to be taken of several articles or in-n- diente
rt"o?;ui; ^"^'"^^ ''' '"^^^" '^ ^°- ^ "-^- ^'^^y^
in^^dtnf^L-^^'lj.^^ i>ropo./tona/ quantity to be used 0/ each
ingredient, v>hen the mean price or quality of the.rnixtaro. is given.
»nf Sover I^ed^lorth'J? T h"?'f «'"*'™«t»^^ ««^^ -orili s2 a bn.hel,
wortr$5 a bushd? ''""'' ^"''^ ''' ^'"'"'" ' "'"'"'••^
OPERATION.
mini'--
ANALTSig. — Since on every ingredient
used whose price or quality is lest than
the mean rate thero will be a gain, and
on STery ingredient whose price or quality
be a loM, and eince tho ./nin. .r.w 1 " ^«'"e'' than the menn rate there will
quantities used of each a bfsur^^^ be exactly e,,ual. the relative
one bushel of ti.nothy seed lrth%2 ft%r?h?r!"^ "■^^ "°'' f Vo^""'- ^^ ^»'"S
$1 would require 4 n^f/bu-h°r"hf;Hli^-*''™''^..S^^^ "^f^^-' '^"'1 ^« «•"»
bushel of closer seed wor«i«7'f;,-?rif''"''""fP"'" ^**" ^- -"^ «eiiin- one
-quire i Of a°bua:;K'e';;^i .ij;:^;: ^b?; ''' *' ' "'^ ^ '°^'^ *' -''••^
•••d. V.0 take iTa btShel offllo^; V'^r* ^'^ '**'"' * of a bushel of timothy
:f
'.ail
III
288
ALLIGATION.
|i '
J
2
H
4
5
:\
1
8
4
4
4
^
1
1
7
1
2
2
[ 10
i
3
3
i7;r. 2. Wlmt proportions of ooffeea worth reepeotiyely 3, 4, 7 and
8l.illings u puixud, must be taken to form a mixture worth 6 shil-
Imgs u pound ?
oPKftATloN. Analtbm.— To preserTe the •quality
of gu'DR and Iomos, wo must alwayncotn-
piiio two prioes or .-iinplee ino greater
and ono /««« than the uieanmte. and treat
eaoh pair or oouplof, as a separate ezaiu-
plo. In the given example we form two
couplois, and may compare either S and
10, 4 and V, or ;i and 7, 4 and 10.
We find that J of a lb. at 3i. must be
,- . , , , taken to !,Min 1 ghilling, ami i of a lb. at
108. to lose I shilling; also j of a lb. at 4b. t.. gain 1 «hilling, and 1 lb. at 7u.
to looe I shilling. Thooo proportional niunbc^ra, obtained by comparing the
two couplets, arj placed in column,.? 1 and 2. If, now, wo reduce the numbers
in columns I anil 2 to a common denominator, iind use thoir numerators, we
obtain thu intPgrnl number.- in columns 3 and 4, which, being arranged in oolumu
5, give the propoitionni quantities to bo taken of eacH.
It will bu .^con that in co!ni)aring tho simples of any pair or couplet, one of
which IS gi-oatcr, and the otli^i- loss tli.ui fho mean rate, the proportional number
hnally oljtiimctl for cither term is the diirrronco between the me'in rare and the
other term. Tims, in comparing :', and 10, the proportional number of the former
is 4. whrh is the dilFerenoo between l(» and the nionn rate 6: and the propor-
tional number of the latter is ;{, which is the dinVronce between .s and the moan
rate. The same is true of every other couplet. Hence, when the simples and
the mean rato are integers, the intermediate stops taken to obtain the final pro-
portional numbers as in columns 1, 2, 3, and 4, may bo omitted, and the same
results readily found by taking the difference between each simple and the moan
rate, and placing it opposite the one with which it is compared.
From the foregoing examples and analyses we derive the fol-
lowing
4311. Rule. — I. Write the several prices or qualities in a
column and the mean price or quality nf the mixture at the left.
II. Form couplets hy comparing any price or quality less, with
one that is greater than the mean rate, placing the part which
must he used to gain 1 of /he mean rate opposite the less simple,
and the part that must be used to lose 1 opposite the greater sim-
ple, and do the same for each simple in every couplet,
III. If the proportional numbers are fractional, they may be
reduced to integers, and if two or more stand in the same hoH-
zontal line, they must be added; the final results will he the pro-
portional quantities required.
NOTBB. 1. If the numbers in any couplet or column have a oommoa faotor. it
may be rejeoted.
2, We may also multiply the numbers in any oouplet or column by any mul-
tiplier we choose, without aflFooting the equality ot ifie gains and loises, and thui
obtain an indefinite numbar of resulte, any one of which l>aiDg taken will aire a
eorreet final result.
li 1 ..
' 3, 4, T and
irortb 6 8hil
the equality
t alwayBcotn-
I ina greater
I lite, nnd traat
parato eznui-
we form two
cither S and
QdlO.
; 9(. must be
d i of a lb. at
I 1 lb. at 7,j.
jra paring the
the Dumbortt
nieralors, we
ij;od in oolumu
jplet, one of
:ional number
rare and the
of the former
the propor-
.ud the moan
simples and
bhe fanal pro-
nd the same
and the mean
76 the fol-
ilities in a
! the left.
/ ?ess, with
Kirt which
'ss simple,
'eater sim-
ey may he
\ame hoH-
be the pro-
V}* faotor, it
t)jr any mul-
let, aod thus
I will glTc a
▲LUOAnOM.
BXAMPLEH FOB PRAOTIOS.
1. A grocer ha-s Mu<»ar» worth 10 cents, 11 centn, and 14 centH oer
P'T Ur U v''" ■;''"'"? u'"'*^ he mix them toforn. a >...xt„re worth
-. VVhutpr.)portion«ofwateratno vaUie, ami wine wi-rth $1.20
a gallon, nn.Ht l.e .i.se.l to form a mixture worth 90 centH a gal-
V \ ♦•... . 1 u i^' ' "*'• «»'■ water to i^'al. of wine,
■i A Jarn.er had sheep worth $2, $2^, $.{, and U per hea<l • what
numl^r could he sejl of each, and r'ealize an'avera^e pr c o* V2rpe
4. What relative quantities of alcohol 80, 84, 87, 94, and 96 ner
"'"in^^TI-r'i ^ r^^. '^ ^'•'" ** '"'*»"^« 90 'per cent: strong ? ^
of U)75th ' ^"''" ''^ *^* ^'■'*-' '^ °*'^^« '^^•»- ^"'^ 16
4
4
tV
8
8
A
5
5
10
20)
i4n«.
• '*^,^-/'^/«'^/'*« proportional quantity to he med of each
u>gre<hent, when the quantity of one of the simples is linJed
Ex. A miller has oats worth 30 cents, corn worth 45 cents and
ou cents per bu*- hej, and which shall contain 40 bushels of oom •
how many bushels of oats and barley must he take ? '
OPBBATIOK. Analtsis. By tho same
prooess as in Caso I we find
the proportional quiintitin«
of each to bo 4 bushels v,.
oats, 8 of corn, and 10 of
each of the othTr simple" 07^ v 4 \l k "S"? *^? proportional quantity of
bushels of barley Ke tCfoll?„fnr " ' *"' ' ^ '" = **
/i,^w*',i.^"^*'*~~^*"^' ^''^ P^'^portimal guajitilms as in 438
Ihmleihe gjven quantity by the proporLud^aniitofthe
same mgred.e,a, and multi^uy each hf the other proportu^
quantities by the quotient thus obtained, ^ roporuoual
t
tXAMPLES FOB PBAOTICE.
1. A merchant has teas worth 40 fin 7^ o»^ on
76 cents, to form a mixture at 80 cents ? .P"""u« «Ji "»at worth
Ana. 20 Ibe. each of the first thr-'^ kinH« on j •«« lu
fuurih. Kinae, ana laO lbs. oj the
'v.\
U
•Al
. t
240
ALLIOATIOir.
' • : I
111 'I
3. How inncb alcohol wortli 60 cents a gallon, and how maoli
water, muHt l,e mixe.l «r;th 180 gallons of rum worth $1.30 a -allon,
that the iDixture may be worth 90 cents a gallon ?
A „ ^"«- 60 gallons each of alcohol and water.
.;■ , ."^"^ "'*"y '^c"^-' <•'■ ''i"ti worth .•J;? dollars an acre must be
adtled to a arm of 7.0 acres, worth $50 an acre, that the average
value may be .^40 an acre? Am. 150 acres.
6. A mcrcijatit mixed 80 poundsof sugar woitli 61 cents per pound
witb some worth 8 J cents and 10 cents per pound, so that the mixt
lire was worth 7^ cents per pound; how much of each kind did he
442. Tojind the proportional quantity to he used of each
ingredient, when the quantity of the whole compound is limited.
iJar. A grocer has sugars worth 6 cents, 7 cents, 12 cents, and
i.i cents per pound. He wishes to make a mixture of 120 pounds
worlli 10 cents a pound ; how many pounds of each kind nfust he
OPBRATION. Analysis. By Case 1 we find
^ /■ ct \ .. „ -- the proportional quantities of eaoh
, . ., „ „_ t" bo 3 lbs. at t) Ota., 2 lbs. at 7 cts.,
lOK,., » ^ * 20 3 1b9. at 12cts.,and41b8. atlSota.
By adding the proportional quan-
tities, we find that the mixture
would be but 12 lbs, while the
required mixture is 120, or 10
tobe 10 times a., much as the ,„n» of tho prr,:,r\LaY lUS "tlfcn^he
Jo?thn!rwhST';,n"'''' •""fln^'lu'" "'"^^^^ much L"tts reject ve"pS!
K LJoL ;;^^^^^^ Ibs. ateot?., 20 Ibs. at 7 cts., SOlbi.at
\.i ots., and 40 lbs. iit 13 cts. Hence we deduce the following
44;$. Rule.— i^^mcZ the proportiomd numbers as in 438.
Ihmlc the given quantity by the sum, of the proportional qunn-
titxes, and multiply each of the proportional quantities bu thi
quotient thus obtained. *
f 6
1
3
,S
30
7
k
2
2
20
12
h
3
3
30
Ll3
\
4
4
12
40
120
I
Iq;;
EXAMPLES FOR PRACTICE.
1. A farmer sold 170 sheep at an average pwce of 14 shillings a
head; for some he received 98., for some I2s., for some 188., and
for others 208. : how many of each did he sell ?
AuB. 60 at 98., 40 at I2e., 20 at ISs., and 50 at 208.
2. A jeweler melted together gold 16, 18, 21, and 24 carats fine.
«o as to make a compound of 51 ounces 22 earats fine; how much of
each sort did he take ? An». 6 ounces each of the first three,
and 66 ounces of the last. '
3. A inan bought 210 bushels of oats, ouni, and wheal, atuj paid
for he whole .5 78.50 ; (or the oats he paid .f i, for Hie corn, .1^, and
for the wheat *li per bushel; how many bushels of each kind did he
•»uy I Am, 78 bn. each of oats and goro, and 64 bu. of wheat.
■VOLOTIOJI.
X41
5. Uae raau and 3 bovb received •SfSJ. fhr -.r ) .it
received .$3 per day, audtlie boys .U i '^;^;^!^ '^,^>-^ ^^bor; the ,„an
n.a.y days d,d eacTh lab.r ? ^ AnsVhl.nl ' ''rHpectively ; how
boys 24, 4, and 12 daya respectively " ^^ ^^•>'''' ^'"^ the
INVOLUTION,
many times it is used to produce the powe?-^ ' ^'''' ^'^^
Thus, \ 3» ^
= the first power of 3, or the root.
" 3 X ? ^ ?' ^'*?,f««nd power, or square of 3.
.(I) - i X i X j X i X j = ,«^, thefitih power of|.
Menw, from th.M iereral powers of 3. we derive the following
447. RvLJi.— Mult iplu the qiven nwmher h,, it^^lf ^-
1* Square 25.
2. Square 79.
3. Cul)e4r.
4. Cul)e 39.
6. 24* = ?
6. (1.2)6 = ?
KXAMPLE8 FOE PRACTICE,
Ans. 225.
Am. 6241.
^ns. 103823.
Ans. 59319.
4n«. 331776.
i4«*. 2.48832.
7. (1.06)* = ?
8. (i)» = ?
9. (5)3 = f
10. (2'^)* = 7
11. (lf)« = ?
12. (2J)» = ?
Ans. 1.263476
Ana, A
/"»• m
Am. Soif,
Am. 167*^*
44S. Evolution is the prooeas of ertrfl«.t;no. ♦!,- * «
° «»" The s;tr„;.r 7 ^« '-'--■-ftv„r«r •
M2
SQUARS ROOT.
451. The Second Root, or Square Root, of a number, u
one of its two equal factors. Thus, 4 is the square root of 16 =
4X4.
453. The Third Root, or Oulie Root, of a number, is one
of its three equal factors. Thus, 4 is the cube root of 64 = 4 X
4X4.
453. The Radical Sign is the character, V, which, placed
before a number, indicates that its root is to be extracted.
454. The Index of the root is the figure placed above the
radical sign, to denote what root is to be taken. When no index
is written, the index, 2, is always understood.
455. The names of roots are derived from the corresponding
powers, and are denoted by the indices of the radical sign. Thus,
V 36 denotes the square root of 36 ; ^/ 36 denotes the cuhe root of*
36 ; V 36 denotes the fourth root of 36 ; etc.
450. A Rational Root is a root which can be exactly
obtained.
457. A Surd is one which cannot be exactly obtained*
M,,
SQUARE ROOT.
The roots of the first ten integers and their squares are i
1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
1, 4, 9, 16, 26, 36, 49, 64, 81, 100.
KoTM. — 1. It will bo obgerved that the second power or square ofeaohoftht
■nmbers ouatains twice a* many figures as the root, or twice as many wanting
sne. IJence, to ascertoin the number of figures in the square root of a given
%nmheT,—Btginning at the right, point it off into ng mnny perioiU ii$ poBtible, of
Iwo figures eneli ; and thare will be as manyfigweB in the root at there are jperiodt,
2. When the given number contains an odd number of figures, the period ai
Ifc* left can contain but one figure.
Ex. What ia the square root of 40M T
oraaATiov.
4M«I 64, Am.
1S4
y.
Analtbu.— Beginning at the right, w* 8«f •rala
th« number into periods of two figures aaoh, by plac«
Ing a point (.) over the right-hand figure of each
period. Now, the greatest square of 40, the left-hand
eriod, is 36, th« root of which is 0. Placing the fl oi
I right c^ th« aomber, we subtract its square froa
the period 40, and to the right of the rennainder bring
4own the next period. We then double the 6, the
aert of ths rod aire^* found: ftsd^ pl^u^inir i| on the
left ef the dividend for a partial divisor, we pereeif*
tt is iTtrieiMJ la the dlvUlend, (oautting its right-hand figure), 4 times. Plaeing
the 4 ea tke right df tba Not, ako eo the rigtit of the pnrtiRl diviaor, we multipiv
(he diviaer thM ooaiploted 1^ 4, aad ■uMrMt the piodaet fron the iivideaC
fhe reel or eaevethiMt
49«
4M
ms
lumber, is
tofl6 =
ber, is one
4 = 4X
jh, placed
jd.
above the
I no index
esponding
n. Thus,
he root c^
)Q exactly
led*
ire:
0.
0.
f eaoh of th«
tiny wanting
it of a given
• poBiible, of
are jieriodt.
le period t4
IT* ssfiaral*
toh, by plM«
ure of each
,he left-hand
oingthe 601
equart from
ainder bring
I the 6, the
ificr 11 on IMc
wfl pareaif*
lei. PIa«iDg
«• multiply
le divideiM.
fefeps^^ia&
243
figu^rs each counting from units' place tou>ard the. Inland right.
wrtte Its root on the right for the first figure in the mot.
veriod n.J7''!i *^"'"T ''^^^' root figure from the left-hand
JV' n 7>7 r ''^«»"^^^ '"'"«»: ff^e next period for a dividend.
and\:.r ^""^^ "-^ '*' "'"^ "'^'^^V /««"^ f'>' ^ (rial divisor,
TftCri2rjJ''^'' *' *f ^•""'^"■"'''^ '^ «^' dividend, exclusive
of tZ Z^M-hand figure, and write the quotient as the next divisor
0/ the root and also at the right of the trial dimmyr.
vTJ' T^ '^^'"'"■'^ ^^' product from the dividend. ^
continue in /At« manner until all the periods are used.
<H,n^S'h7LS'"a^a'''l^""?'^"i"«'7.^ right-hand figure, doe, not
the divisor ; hen : ' ' rinifnl\ ^ '''u°''* '° ^° '«'*' *"'! »'''° ''^ t»»e right of
used as the divfso' ' ' new7vl!S. "'** ^ '^' '^^ '"' '^'^^^ """ »*
peri'odlifVnfc ,. ' . ''•«'«>• after all the periods hare been brought down.
be decimals? ^ ^ *°""'^' '^"'^ ^''^ fig'"-"' "^ »»>« '^ot thus obtained riH
root^■!«'lrS°i^t{^o^'Ii'"'*''™^^^ * *^°'« °"'°»>" «°d a decimal, v*,.
> point over every^cond hVurl ^^"^Tv,""" ^,!'^'^" ^^^°'« °"'°»«^' ^ P»'«^
««} period, if IncL'plS with" '^rphS *'' "^''' '"" ''' ^''P"'*'"*' ^'""« '''•
.qLe r^JtfonhrnulraToTnT [^ """ T' '^ "'''"^«" ''^ "'^"^"^^^ »»>•
KXAMPLES FOR PRACTIOB.
I. What ia the sqaare root of 133226 ? of 62.8 T
% X %
3x2
66 X 6
36 X 2
726 X 6
X 6 =r
OPKRATION.
133226 ( 365, Ans.
±_ 7x
6 6 ) 432 7 X
J96_ 14.9 X
72 6) 3626 7.9 x .2^15.82)
3626 15.82 x M =, '
r =
2 -=14.9)13:80
.9- LS.41
OPCRATIOV.
62.80(7.92 + ,4.
49
.3900
.0104
T0736"
.T^,i'«ii%'s;i?',oTL'';,'fr_.".';,,"" •"■. '^^r „, ,4«, ,
Of 3249? o<-40»6? of 6329 7 of 6724?
or 9801 ? ononis ?
13, 24. 35, 49. 67. U,
4 I
^'•^^u^iimi^^js:ti^^Ajimmmm.-'.->>^»
tM
SQtTABS BOOV.
h '
1i
i
1.*
ill
1
i
I ;'
J I II
.1. • K t
3. What i3 the nquare root of U1009? of 454276 7 of 605621 ? of
637821? of648132V of 738417? of80»aij? m 927748? of 977137?
of 9999[)9? Ans. 247, 674, 711, 798, 805, 859, 899, etc.
4. What is tl square root of 234.09? of 5.4756? of 17.3056 ? of
256.6401? of 0. J24 ? of 0.120409? of O.O0008836? of 609151. 761 GO?
Aru. 15.3, 2.34, 4.16, 16.02, 0.32, 0.347, 0.0094, 780.481.
5. What is the square root of f? of fiw^r? of ^AA, ? of 60J»? of
^? off? of28||? ofjf? ofWJf? ofSsVir?
Atu. 0.86602 + , 2^. ^, 7|, \, 0.7746 + , 6|. 0.868 + , 1|» 'I-
APFLICATIONS OF THE 8QCA.RE ROOT.
1. Whnt ip the lenjjth of one side of • square (ami •ontaining 98
•cres? At%8. 120 rods.
2. A certain general has an army of 141376 men ; liow many must
he place in rank and file to form them into a square ? Ans. 376.
3. A company of persons spent $75. «9; each Hpeiuhng as many
cents as there were personp in the company. How nuich did each
exiiend? AnM. $0.87.
4. Bought 200 yard>< of carpeting 1 i yards* wide ; what is the length
of one side of the square room which this carpet will cover? A. 45ft.
6. A man owns three piecew of land ; the first is 125 rods long, and
63 wide; the second is t;2^ nxls long, and 34 wide; and the third
contains 37 acres : wiiat will be the length of the side of a square field
whose area will be equal to the three pieces f Ans. 121.11 + rods.
6. Purchased 2 house-lots ; the first is 242 feet square, and the
second contains 9 times the area of the firat; how many feet square
iu the second ? Aiu. 726 feet.
7. Required the sides of a ri'>cungnlar court-yard haviag an area
of 432 reds, and whose breadth is only the | of the length ?
8. A certain field contains 48020 square rods ; the length exceeds
the breadth by 49 rods : what are the sides ?
Ans. 246 rodr long; 196 rods wide.
9. A dchool-nia«ter says that the number of his pupils multiplied
by I of itself is 2523 ; how many pupils has he? Ans. 8".
10. How much will it cost to roughcast the walls of a garden,
having a surface of 8100 yards, at Bit, cts. per yard, the walla beiiyi
2^ yd. high? ^n». $1449.
11. Tiie greater of two numbers is 40, and Ih* sum of their squarM
1625; what is the smaller number? Ans. 5.
12. A clock-maker sold three watches whoie prioes are as 5 is to 6,
and as 6 is to 9; the sum of the squares of the prices is $3550. What
is the price of each watch ? Ans. $25, $30, $45.
13. What is the price of a raking machine, knowine that the price
added to its square giyea $186 tor result 7 . Atu. $13. 13 A.
4 of the number it«elf 1 obtaia $96 for result. How many barrels of
codfish, at $4 per burel, oaa I buy witk the inoBey I poaeese 7
fibanek
*vn Kooc
S45
CUBE ROOT.
The root, of the first ten integers and their cubes are:-
> '> 3, 4 5 A n o
1» 8. 27. 64,' 125,' 216.' 343,' 512,' 729,' 1000."
^-^''^^n.'airS.^^^^^ of the „u«.
P«2'.rf*».po^Afeo/«AreeA^«,.«^'''^«'2^^ i< o/ tnfo a. many
•^ « the^ear^pe^. ^ '^ *^' "^ ther^ **Ul U a, ma*y figure, in t£
Ej-. What le the cube root of 157464 ?
S4
X 4= ,
p«oor.
54 X 54 = 157464
167464 ( 54
125
32464
J2464
~0
°"'^"«"- .AxALTs,8.-Begin-
■ing at tho right, we
•eparate the given
number into periods,
by placing a point
over the unita' figure,
then over thousands.
Since the number of
periods is two. the root
will consist of two fig.
ures, tens and unita.
Then 157464 =. the
oubeoftens,plusthree
times the square of
piM thrw timed the tens into the Miiar* nf*K- . •. . ^'>« tens into the units,
Jhe cube 01- ten. .. thousand^. andStheref"-'^' f""'^- ° u**" °^ "^° "°'^
the number. The greatest nunTSerSnlwh/l ^,°'* '" **»^ thousands of
sands is 6, which we write « thel^M fh^^J f ' ! ^"^.'^oef. not exceed 167 thou-
125 thousands, the cube of 5«st?rfcu"/S? 5,^^^ ^^° then "ubtract th.
82 thousands; and, »nne«ing th. nwt no^iS i k ''"''*°i'' *"'* *''"« '«°>ain
S24<i4, equal three times the squU of Sil Mn.T »''?u'' "" ''^ •°"^° remainder,
the tons into the square of the 1,*!! .,lS .h ° k'° J^.! ""'''' P'"« '»>'«« times
three times tho square ot^e tens nhf, rhri r^*" **£ ^^^ ""*'«• ^'^ '^^ Pr«d"Ot of
the square of tho\nits, mul iJ^Ted tX^'ZT'lflwT 'T.-'''' «"'^^' ?'"»
three times the square of the tens >f f !,« ,1? J dmdmg this reiaainder by
«omewhatt«,oIarle. Although it may irti,Ta*r«'r ''" ""J^' °' * ""'»»«"
the remainder 32464 cont.uns no onl? thre^iirJ^hl?*""''* bo too small, since
anit«, but three times t he tens into SeVauL^T*., "l"*"^. "^ '•"« '«"» *"'» 'be
units. We therefore make three times t?.erul.«„f^K'^; '''"' ^^''^ ""''« "^ th«
hundreds, a trial diyisor. with whiTw„ r *5 .^° ~^/^® ^^"^ "t-'he root, o= 76
der, disregarding the 64 uTiS Sc. th«™ ^ ^^ ''^^ ''""'^''^^^ "^ 'be remain-
the squarf of the%ons by .^e iS ThL^H^nffi™ ""^Kr!"* f ^'^^ P^"<'"<""f
units fig,:re of the root, or a number somewha l^rJ' '« ^"'•^' ^' •"""* '"^ ""•
oon^ lete the diyisor on the supj Jtirh;:;'^^^^.-^:^.""..:?.^-^]^?-^ '»
root, wo add to tho 75 hun-ired^^Vhefr^^i^ ^f^*' 'J"'"''"' "^ ""''« *" '^e
root into the 4 uuits, plus che squii^S? J ^^i""'". '-^^ ^ '"» «f '»>•
divisor 81 n«, thus fiUc^ by \rLDitaaL^L?J* ■"'"P'yi"? the tru.
from the ni«rtnd«,th«»i;it,SL"££' Slr^fi?£? ""> ET^"*". 32464.
M *teMMb» VMt -««iiHi •«». MMo% 1674C4 is a pmrfeot eobo, And
!1
'^ ill
»h» ill
I > i
If ^
'A'
S4«
4IS9. Rule. — I. Point off the givm number into periotk ^
three Jigures each, counting from wUts place toward the left and
right.
II. Find the greatest cube that does not exceed the left-hand
period^ and write it$ root for the first figure in the required root ;
iubtracf the cube from the left-hand period^ and to the remainder
bring down the next period for a dividend.
TIL At the left of the dividend write three times the square of
the first Jig i( re of the root, and annex two ciphers, for a tried div-
isor ; divide the dividend by the trial divisor, and write the quo-
tient for a trial figure in the root. •
IV. Add to the trial divisor three times the product of the tens
figure of the root by the units figure with a cipher annexed, and
the square of the last figure, for a true divisor.
V. Multiply the complete divisor by the trial figure ; subtract
the product from the dividend, and to the remainder bring down
the next period for a neu^ dividend.
VI. Multiply the square of the root figures already found, by
3, and to the product annex two ciphers for a new trial divisor ;
and proceed as before until all the periods are brought down.
KoTB.— The observationa made in Notee 1, 2, 3, 4, and b. and«T .he rule for
ti»e extraction of the stjuaro root (458), are equally applicable to the extraction
of the cube root, except that two ciphers must be placed at the right of a true
dirisor when it ia nut oontiiinod in its oorreaponding dividend; and, ia pointing
off'deoimab, each period must contain three figurM.
Hi f
EXAMPLES FOR PRACTIOB.
1. What is the cube root of 12326391 ?
OPKRATIOX.
4
,x,> ,M
!'ij.
2» -
Trial divisor, 3 x 20» - 1200
3 X 20 X 3 = 180
3« = 9
True divisor, 1389
Trial divisor, 3 x 230* = 158700
3 X 230 X 1 = 690
1« - 1
1 232ISf 1
8
3s
True divisor,
169391 X I =
432fi
4167
SSI
169391
16 939 1
2. What is the cube root of 1331 1 of 3375? ol i21ST? of 32768 7
of 110692? Ans. 11, 16, 23, 32, etc.
3. What is the cube root of 1861MT of 272144? of 456633? of
704969? of 970299? Aim. ^7, 64, 77, 89, eto.
ovmm EOOT.
347
APTLicinoNa IN am goor.
i« height, and X™™ .h "filutl/'T TJ''? "^"'f '« '"«
contents of the box. '* """' "« "'*'>. Required the
6. How much miut he ni.,d fnr . „—■ f*"*" '"' ""b' '".
««l, bought at i5Mnt,nS^lhl°"^."*'° '■"■»'*' of pouiid. or lin-
theiumllrequal^Sgi?!,^-'''""'""**" "" » "^ "« ""b^ of
>».cubee,„.,Aff'jtl':k'Re''^TrJ*^.l4^''"'
7. Required th« value of the artiVl*. -^ * • j • '^***- '^1S3.80.
r^T' " ""^ -c'«.:''.^siStrr.^ cLf a?°a'-5
8. What ia that number, whose 1 I -„-j i i"^***" *156.26.
give 9 for product ? *' ■' •"'^ i multiplied together,
9. Bought $164.64 worth r»f ^-„ . -^na. 6.
"-•-"n"-, each ZSw^g Sf L'T'S' "'' '■■ " -"«"'
there are boxes; »nd each oraui ooS. twio. .. ^^ °""'S™ «
•" boxe,. Bequired the »«mblr on.oxerL"™^""'*' " '""•
!«• In dividing the cube of » ™».i«i„ '''* .''' t"""*' ^'8 oranges.
jrj^.-..e uu„L, w.?b;:Sn%TaTo^e;?f K ?f ^1.3
11. A rwerroir, whost lenirth i. t^ ;.. k-„^.u _ ... ^n«- 9-
aeptn «a 13 is to 8. contains QOsin 7 i7 "''"•^lu sts i3 la to 6, »nd
dimewions of the CJvdr ? ** '"*''*' *** ^^^^^'J ^^at ar'e *he
12. Some merohaolT forS V "/rt^"' ^k**^^'^^ ''^ '''' '^^P^'^ ^4 ft.
-MMv wwMB M ti»ere wdn wsooiateB. Hari^t^adc
.11: I
S4t
A»ITHlfBTIOAL PROORUMOH.
It . '
' rf!.''^*^,f *' ^^'y ^""^ >*^«t tW have gained the half a. mi.«h
the com anv ? "^ "' '^"''*"**'"'' ^"^ ™»'^J^ partnew were there ia
•HI ^A ^^ lu'*^^"", ^^"?^^* certain quantity of pearl-shella ; by^^jing
rh;\\ff!"J;;-T^™"'''p'-^T*^^ «»»" heiaiiSutb?
the f of Itself, It gives a product of 59049. Required the number of
108. he bought ? j^„ oc r. m
ij TT,* , , , iln.f. 35A. 'b.
a^rtlin n?,^" ..u'f* V"^'"''.**^"' P*^' ** ^S °e"t8 per lb!/ for a
^,li Tu^f ""u ^*'*' ^^ «'^"'' «»«*^ ^*'*' containing Uo lb., che
number ^ba eg bemg such that in multiplying together its J, i, and
I, the product will be 8640 ? r j s, & ^^ $3828.
PROGRESSIONS.
ARITHMETIOAL PROaRBSSIOM.
4«0. An Arithmetical Progression is a series of num.
bers n.cieasino; or decreasing by a constant difforenoe.
formed Terms of a series are the numbers of which it is
m*i mf"® Extremes are the first and last terms,
tJ? i ■ m ^®a^S are the intermediate terms.
4«»4. The Common Difference is the number added or sub-
tracted, m order to form each sucocHsive term.
4«5. An Ascending Series is produced by adding the
common difference to each term successively ; as 13 5 7 Q
11, 13, 15, and 17. J »'.♦'.«',*, »,
*®*' ^J^escending Series is produced by subtracting the
common difterence from each term successively ; as, 17 is' 13
11, 9, 7, 5, 3, and 1. ' ' >
467. Thesumoftheextreii . is equal to the sum of any
two terms equally distant from tium, or to double the middle
term. Thus,
13 5 7 9
U 1_5 IJ 1 1 9
18 18 18 FS r'8
.^*?^' J.'^'^ following are the Jive quantities considered, three
ef which being given, the other two may be found :—
1. The first term, denoted by
2. The last term, *< **
3. The common'differenoe, « «
4. The number of terms, " «
6. The sum of all the terms, " «
Nort.--Hftlf the imi of mj two auubtn it MU«d their AriiAuutiwl Mtmt.
a.
I.
c.
n.
§.
MUKtAJti*
er« th«rt ia
Ana. 8.
; bypajiog
laid out bj
Dumber of
r lb., for a
40 lb., che
i aad
iS
9'
«. $3828.
18 of nam*
hitih it is
led or sub-
dding the
5, 7, 9,
icting the
, 15, 13,
n of any
le middle
red, three
a.
1.
c.
n.
8.
alMtmm.
ABITHJirBTioAL FIlO«RMg,o„.
4«». Case l-— Given the /ir,t ferm ,j.
18 ^ 19 _ 1 J- ns iy , ^i,at in the last term ?
18 =1: 19 -_ I
68, the last term.
iMt term ^4 T?8 ifl T°^' "*"• Therefore the
Hence the Formiia « T**/'^ ° '*,"'"°" difFerenoe.
'"■^ '*■ — 1) C =- 1, or the
■XAMPLBS FOR PRAOTIOE.
width ofthe wide end? ^ '^^'^ '" '^"gth. What is tS
I t.l\^u^ a"t term of an aacendine eerie- be i th- « ^""'- ^ ^^ '"•
I, aud the number of tenne 20, whaYfeX'Taft^i'r^T'li^ii^^ll^^
471. Ca8« IL--(»^ ,a, ^,,^, ■
></ ^A* «^;„^ difference ""^ "^^ *»
l-«
^ALTMi,
•'♦"(■-i)c-i,e«
n-i
Henof/, th«
u — I —
473. RcLK.— ZX,^ ,4, A*jr«v«^ /■ .X
»wm6«- o/ferm« fcw one. "V*''*^ of the extremes hy the
■XAMPL18 roB PBACTIOB.
« T-j }^^^^itrJ^L^^^ ^ ''' -cl the number of terma
i. Ule common 3iffe?enc: ?'" ''' *°^ ^^* »»«>'>•'• of tenna i;^?;-^.^
3. A man has 1 eons : the Tounaeet in ft . ^ »u . . ^'»»- 3.
oW; their ages inoreaae o aritwS^ ' '"'^ ^^ «''^««* 44 rears
Aftrenoeofthairafear •"'^'"^**«^ ProgreseioB. Required thll
|1» ^••' *7««w.
J.
81
L'
I'
!!■
1 (
" 'i
1
11 PI ll
I 1 I "5"
^B«?S'i/.
859 AlWTHlOmOAL F»0<111W8T0W.
4.gif the extremes ar^ and 2^, and the number of termn is 18,
wliat is the common difference ? ^»t*- A'
473. Case III.— Given the extremes, and the common dif-
ference, to find the number of terms.
Ahaltsib. — Since, a + (M — 1) C « 1» H
1-a
-f. 1. HoDoe, the
474. Rule. — Divide the difference of the extremes by the
oommon difference, and increase the ^juotient by 1.
EXAMPLES.
1. The first term is 8, the last term 203, and the oommon difference
6; what ia the number of terms? -^n*- ^O.
2. A man going a journey travelled the first day 7 miles, the last
day 51 miles, and each day increased his journey by 4 miles ; how
many days did he travel^ '****»• 12.
3. The extremes are 2^ and 40, and the common difference is 7i ;
what is the number of terms? ^»w. 6.
4. In what time can a debt be discharged, supposing the hrstweek 8
payment to be $1, and the payment of every succeeding week to in-
crease by $2, till the last payment shall be $103 ? ^— ""* "—^'^
Ann. 52 weeks.
475. Case IV.— Given the extremes, and thenumber of terms,
tn find the sum of all the terms.
Analysis— Sinoe, the sum of the extremes of an arithmetieal progression ta
equal to the mm of auy two terms equally distant from them, it follows that the
tornifl must average half the sum of the extremes. Henoe, § « J (a + 1) H.
476. RWL^.—Midtiply kalf of ilu sum of the extremes by
the number of terms,
BXAMPL18.
1. The extremes of an arithmetical series are S and 19, and the
number of terms 9 ; what is th: sum of the series ? Am. 99.
2. A man bought 16 acres of land, giving $1 for the first acre, and
1121 for the lastlvere; the prices of the successive acres form an ar-
ithmetical progression. How much did the 16 acres cost? Ans. $976.
3. A «^entlenian wishes to disoharse a debt in 1 1 annual payraenta
such that tlie last payment shall be $220, and each payment greater
than the preceding by $17 ; what is the amount of the debt, and the
first payment ? Ans. 1 st. payment, $50.
4. A merchant bought 20 pieces of cloth, giving for the first, $2,
and for the last $40 ; the prices of the pieces form an arithmetical
series ; how much did the cloth cost ? Ana. $420.
5. If 100 oranges are placed in a line, exactly 2 yards from each
other, and the first 2 yards from a basket ; what distance must a boy
travel, starting from the basket, to gather them up singly, and return
with each to the ba»ketT
an is 18,
rion dif-
Henoe, the
\s by the
differenoe
ln«. 40.
!, the last
ilea; how
[ru. 12.
ce 18 7i;
Ans. 6.
rst week's
jek t(j in-
I weeks.
of ternu,
agression ii
)W8 that the
fc + 1) n.
iremes by
\ and the
Am. 99.
acre, and
)rm an ar-
is. $976.
payraenta
mt greater
t, and the
ent, $50.
; first, $2,
rithmetical
19. $420.
from each
must a boy
and return
OIOMITRIOAL PROORISSION. 26t
GEOMKTRICAL PROGRESSFON.
SnnlT"^" '^ ^®0™elrical Progression is a aeries of numbers
inoreas.nn: or decrea.in^^ by a constant ratio. ^^"^
Sfi' Z'^® "^"0 IS the constant multiplier or divisor.
thafl'^.f2.t8'"G".^'li*t^P^°'"°«'^^^-^-*-«-ter
lesf th,?n l^ ?sT *" i ? f 'K^r'""' "'^° ^'« ^""^ •«
^twi rp'. 7. t; 2'. t. t- tV» a. A» etc.
wKr„?k' . ■^'^^**^'''^^|"f? i^re the>e qnanHde, considered <*rMof
which being given, the other tioo may be '. md ,_ ^' '*^'*°*
1. The first terra, denoted by a.
^. Ihe last term, « i« «
3. The ratio, «• «« *'
4. The number of terms, « « n'
5. The «nin of all the terms, " " „*
IkSTTriTJi" ^'•'^••^^ ^-« between two a«nb«. ta the ,,„.„ ^^
4«a. Ca8I I.^GStW ^^,/..,, ,erm, the ratio, und the num.
ber 0/ terms, to Jind the last term. " ''*"**^
^^iJ^:^'^:^^'^^^'^^^^^^^^^ and the ratio is 3 ,
A...vsis.-The «rsuerm ^^ . 4, and from the nature of the series,
The third term = 4 x '^a «„,,
The fourth «„„ , \ I l. , , ^."^-^^^ ^^
•na 80 on. Hence, the last term, 1 =- a X r""^'
../**?■ "^^.^^--^^Mplif the first term by that power of the
ratio denoted by the nnmher of terms, less one ^
^^'"^'^'l^:i^TZ':^tX'^^^^^ «d the
EXAMPLKS.
^rZ^r^:^-\^:^^T^^ --^r of teru.^-..,
1 ™illt 7"?!*" ^"^?* ^ ^Sg«' ^^^^''g t*^ W 1 mill for the fejt tg
a mills fur the second, and so on , what did the last e^ oost her ?^'
Am. $0,266.
- I
'J
If r
tM
aOMKTBIOAL PK0«UU1I0M.
I.;
I
>.J,.
liii&J.i.
^^^^B
1
^B^^^B
Iji^ii,; V ..-J- r
!
i.
4. If the first term of a eeriM k M, the ratio l.tf, and ttie nanbw
•f terms 6; what is the last term? An*. 40.146787328.
5. A person traveling goee 2 luileH the first, 4 mileH tke Hfcood,
B miles the third day, and no on, increasing in geometrical progression
Jor 10 days. How tar did he travel the last day ? Ant. 10';.4 miles
$. Bought a lot of land ooniaining 15 acres, agreeing to pay for the
whole what the last acre would come to, reokoning 5 cts. fur "the flrnt
aore, 16 cts. for the second, and so on, in a threefold ratio. What did
tlM lot ooet lue ?
Ans. .i;L»;^9 148.46.
4S4. Case IL— Given the txtremet and ratio, to find the
turn of all the termt.
B». The first term ie 2, the last term is 128, and the ratio 4 1 1*^
quirvd the euui of ail the terms.
8 -». 3a + 128 -♦■ 612 = 4
1 + 8 + 32 + ris
OPiaATIOll.
X snm of the series.
= I X sum of the seriea.
612 — 2 = 3 X sum of the i^eriaa.
Hence »",- » = 170, the sum of the series.
AWALT8IS.— Since 512 = Ir, 2 = a, and 3 =■ r — I a = ^'' ~ •
Hen«e, the ' |. _ 1 •
485. B.VLE.~~Midt:ply the latt term by the ratio, mhtrnei
thefirsttermfrom the product, and divide the remainder by the
ratio lett one.
NotM.-l. If the ratio it leas thM 1. the product of th« last term. maltipHed
by the ratio, must be subtracted from the fint term} and, to obtain the divW
the ratio must be aubtraoted from the unity, or 1.
2. When a doBoending Heriea if oontinuei to infinity, it becomes what is oalUd
an Isnuvn aniKS, whose last tern ranst be regarded as 0, and iu ratio as •
traeiion.
A ^? ^^1*^" ' T *'^- *° a"*'"''^ Seriei,-i>Hri«<« tkeJtrH fn» 6y a mmU dimimMMd
6y th»fram*«n demitmg the ruHo.
BXAMPLE8.
1. Tha ilTHt term of a series is 4, the la.it term is 62500, and the
ratio 6; what is the sum of all the terms ? Ans. 78124.
2. If the first term of a series is 12, the ratio 3, and the number of
terms 8 ; what i>^ the sum of the series ? Ant. 39.S60.
3. The first term of a decreasing serie8 is 102, the last term 4 and
the ratio ^ ; what is the sum of the .series? Ans. 151.
— " — -^^-^ , " "^~-= i~ ", tiie ratiu |, Skud tne number of
terms 6 ; required the sum of the Hcriet^. ^n^. 1 31A&.
6. The first term of a decreasing series is 106, the last term t Oand
Ike raiM i ; r<N|uiied tke sum of the terma. Ant. 130
Ih« naiab«r
6767328.
tbe Hfcood,
progresdion
hi raile«
pay i'oT the
for the first
What did
9148.46.
find the
alio 4) r»>
8.
«.
8.
. lr-«
" r- 1 •
, subtract
I, mnltiplted
the (iiTu«r,
bat is oalUd
ratio aa •
and the
, 78 124.
number of
H9360.
rin 4, and
IS. 151.
umber of
m • 0, and
iM. 13U.
Irllfi-i-fWHlB-li' -^'^
MIAHURBMINT Of LUMBH. 2(|S
memJ?nteunfit"rL7nrn "'""''" *'''''>' di-chargad bj monthly pay
first n.orith h? il »^"*''-^ '"^* "^ * "^''^ f^r 6 "'onthn. For th«
were lo '^re.H d 1,^'?. ' '' ""'' T*' ;^"°««^*'i°K -onth'^ wa^t!
thelein/ttgreed to 3 1 *i f 7 ''^; '^^ '"" '"^^ * price ; he, never-
for the'thfrd. aud Ton ."«*"" V'f, '''■"' "'K"^^ ^ *'"• ^»'' "•^^"J' !«
cost hiw ? ' ' '° ' ^''"'^^'^ '■•^<> 5 bow much did that ground
Am. $34S>5.25.
MPUSUREMENT OV lu.V BER.
J™";'",:,!;!'" ■' "°"'"'"«" ""•"""'' •^ "« ">°. -"i ~".«im™ bj
4»^i. To find the contents of a board
thSthT'' ''' ''"'*'' " "*''«"°=' "''^^ ^-^f "tf -- of the width of its endB fo,
,if?- '• ^'>^^-«^J- contents of a board .36 feet long, and l^feet
J. What are the conteota of a board 24 feet lonf 'and' Jl S.
3. What are the contents of a taperiu.. board 2^1^^^} '"'^' ^'u'
ends are, the one 24 i„(^e«, and the other 13 [n^hes wfde ? "=' ''^''*
489. To find the contents of planks, beams, joists, eto.
in S^f^'&,:J;,,:ff ;f ^ ^« -cAe., t, the tkickness,
w/tnf7hi^*SdstS;o''wS*^^^^ '" r'*^ *'»''« ^'^^- «"•« of the
thicknes..th« common ru^ZbtaSnf/fh^^^^ "'^^^ '^nd the
^tk. ««H of tk. ar^ o/^L CSiifirS? »« «"bio feet i«, to ««/ay^
In
I
hi
354
I ' '
( I
I f
VnOILLANBOITS BXAMPL18.
•nf f inoheTJhtk? *^' *""*•"*" "'' P'*"*^ ^^ '^^J^^^g' 2 feet wide,
4?:s:3 ti^r sr ^^^-' -- -^ S^
4»0. To find the contents of round timber.
fomanfThf'^^'^^^ fA« ?«n,9#^, taken in/eef, by the square of one
2dhv{A "^T ^*"1' '"*''* *« *"''^^^'' ^nd,thi4roduct,div
xded by 144, ?<,i?^ ^rftre the coni^ts in cuhic/eet.
i II ,1
MISCELLANEOUS EXAMPLES.
doJ; ht SeeV? "^ ^* ^"" '''"* '•^' ""'^^ P*' *^°S ^' ^'« «-•
.«™ ^11 be fi!"?'^' '■' ^''* ^ ^^«^' '^^^ ^^'^ * of ATit'efn^th.
3. A gentleman boughi 95 yard^ of cloth, ? of ayard widtX'Ahn
•nd gav. the .ame and $2f for cloth of the'sLaqSri i^S li3J'
How many yards did he buy 7 ^ Zl on i ^
4. A father devined ^ of bis estate to one of his ,om' an^ 2* «/
the residue to the other, and the remainder to his wife ' The ^C
ence of h.s sons' U.^acies was found to be £257 3 4 What mf «v
did he leave for h.s widow? Ans £635 Tim ^
6 How many bncks S.inches long, 4 inches wide, and V?&„,
feet^hirkV"''"^'^"""'^"*" '' '''' '•^"g' f f-t hig,- -di
6. Ifan.aneanpaini4 ..uare yards in one h^ur^'ln^filTK
<^.^40 .ec. .. painting two aides'of a wall 7 feat high X 4 1
Jitt^
WTOBLLAWBOUS BXAMPLM.
7 B • ***
titj p«rdS^ bmff fVofl k for* RH^"!?'''i«r°,^3« °° ^^•q-"-
on the 8a,.,e quantity . How Tnanv hnlJ' * ^"^^^''' ^ «f'*" g»'" ^42
^. A groce? bought a hoXa/nf l^ f '^!'fo^"Sht? Ans. 240.
must be added to reduce th^£uo 35 .'t^*^^-'Ti.^^''^">"<^^ ^*ter
9- A father, dying, left his snn I i * " P^"" «*'• ^ ^"»' 18 gal
months: 1 of the'WnfirL'J^^^^^^ «P«"t^o 8
which he had only «410 left Wi!!! ^ ^^ month8 Jonger, after
hitn? ^♦410 left. What amouut did his father be<iueath
10. A man had I of a va«l «rk- j • . ^*^' 1956 '6i.
rate of $8i per yarS^he £^.1 it VrScloth a'7«'n'°' ''' P«'^ ^^^^^
of cassimere. What di.} fL Z ■ ''^^'^^cloth and 50 cents for J I vard-
States currency?^ * ^«"*i» currency, are equal to $160 United
. 13. If the lonfitude rBo^t^nls 7o'o' 1 of w.ne and 5 of brandy
m that place when it is 3 h?t Jn A M^'f "'^^ ^" ^ *»'« «"»«
Anji 1 n K K/« • ! ." ^- "* i'ondon f
had I at first 1 *" *" * "^^ ^nat I had left ; what sum
, 16. If I3i bushels of wheat make "^ hRrr«l- r « "*/*•' ^8248.80.
18. By selhnga lotof book«ftw.«iaQ l , ,. ■^««, Ti^t.
much should the books have ?i^ Sor ^^"^"^^'^^ 10%; how
of Itfead, when flour k $12 i^r bbl ? hoarders eat $60 worth
^^; B hired a house for one vear fi>r «Qnft . ., "*"*• '^2^ mo.
he takes in C as a partner, and auireSoVR** '^?.'"? ^f l^monthe
_. -.1,, .n*. o, t«f year, wimt rent must each pay ? •■''° ^•
23 A person mixed 12 cwt. of slTar^lf «ij' witf ? ' ^ *'^*-
•-d 8 owt. at m , how much was fowt^of Ih"; mSure";^^ *'*'
I'li
256
MISOXLLANBOTTS BXAMPLM.
24. A shipment of wheat was insured at 2^%, to cover | of its
value ; the premium paid was $44.07 ; the wheat being worth 80 cts.
per bushel, how many bushels were shipped? Ana. 2825 bush.
25. A stack of hay will keep 24 cow8 or 18 horses one week. How
many days will it keep 5 cows an(i o horses? Jni^. 14f da.
26. C. of Montreal, remits to D. of Quebec, a bill of exchange on
Liverpool, the avails of which he wishes to be invested in goods on his
account. D, having disposed of the bill at 11^% advance, received
$9675 ; and, having reserved for himself J % on the sale of the bill,
and 2 % for commission, he invests the remainder. What is the amount
invested, and for how much was the bit! drawn ?
Ana. Investment, $9461.58^; the bill was £2025.
27. What per cent, is gained by buying oil at 80 cents a gallon,
and selling it at 12 cents a pint? Ang. 20 %.
28. A merchant pays $10050 for a stock of goods ; he sells them
ftt an advance of SiiJ % ; the Expenses connected with the business are
$1760. How much does he gain? Ans. $lfiOt).
29. What o'clock is it iwh«»n the time from noon is ^^ of the time
to midnight? Ans. 6 o'cl. 24 min. P. M.
30. A merchant receives on commission three kinds of flour ; from
C he receives 20 bbl., from D 25 bbl., and from E 40 bbl. He finds
that C's flour is 10 % better than D's, and that D's is 20 % better than
E's. He sells the whole at $6 per bbl. What in justice sliould each
man receive? An$. receives SslSym; D, $158^; E. $211^f?-.
31. For what sum must a note be drawn at 4 mo., that the proceeds
of it, when discounted at bank, at 7 %, shall be $875. 'ii ?
32. If 2^ yards of merino If yards wide cost $3.37|. what will be
the cost of 36^ yards 1 ^ yards wide? Ans. #52.779.
33. What must be the face of a note at 60 days, the proceeds of
which, when discounted at Bank, at 6 %, are$100 ? Ana. $101.06 +
34. A merchant sold a piece of clotii for $24, and thereby lost 26^6 ;
what would he have gained had he sold it for $34 ? Ana. &\ %.
36. A bankrupt compromises with bis creditors for 37 ^^(i how
much will he pay on a claim of $3656 ? Ans. $1371.
36. A man, dying, left $3565 to be placed at interest for bis son
who was 16 vr. 5 njo. 15 da. old ; how much will he receive when he
ia 21 years old, allowing 7 % interest? Ana. $4698.37 + .
37. A garrison, consisting of 360 men, was provisioned for 6
months; but at the ei. of 6 months they dismissed so many of the
men that the remaining provision lasted 6 months longer ; how many
men were sent away ? Ans. 288.
38. What sum must I invest in the New Brunswick 6 % stock, selling
at 2i % premium, to secure an annual income of $840 1 Ans. $14350.
39. A grocer divided a barrel of flour into two parts, so that the
smaller contained \ as much as the other; how many pounds were
there in- each? ^n«. 78f lb., U7f lb.
40. A sportsman spends i of his time in smoking, | in cunning,
2 ho. per oay in loafing, and 6 ho. in eating, drinking, and sleeping ;
how much remains for useful purposes ? Aiu. 2 ho.
ii. Exchanged 250 whares uf 6 ^j^ stock, at 1^%, for stock bearing
8 96, ai 120 9( ; what x* th« di£ter«n«e is nj income ? Ana. $333. 33^.
ver I of ita
orth 80 ctH.
?25 buflh.
week. How
'. 142 da.
^change on
;ood8 on hie
!e, received
of the bill,
the amount
,8 £202i.
8 a gallon,
w. 20 %.
sells them
»u8ines9 are
9. $1600.
)f the time
M.
from
Hnda
in. P.
iiur ;
He
better than
hould each
he proceeds
lat will be
$52,779.
proceeds of
;I01.06 +
/lo8t 265g;
n». 6i %.
;7i%; how
s. $1371.
for hie aon
I e when he
198.37 + .
oned for 6
any of the
; how many
ins. 288.
lock, (telling
[.$14350.
BO that the
ounds were
, 117f lb.
in gunning,
d flleeping;
ins. 2 ho.
Mik bearing
1333. 33^.
M180BLLANBOU8 EXAMPLBS. 257
42. Purchased 100 barrels liprrin(r<j «f«Kv.«.. uvi j-
sold them on a credit of 8U , o„thf ' ^^f P^f ^^l-.^n-t^n'^ediately
pay, I got discounted at U.e Un n' Rank "an^''^'"'^ ^ '''''''^ *'^'
money, I found that I had gained 20 inn. ' T" ^-^^'22!"'"? "^7
receivjper bbl. for the herSlg":' '' ^ " "^^ P"^«'^^r„- .^V« '"' ^
8 in in l7nXT5^t?1' ''' '^"'T^ '^ ^^"^' ^ ^''« ^-^^t "a h o .i ' .^0 ft
at etatTofrfor"^"c?^P^\^ ^' '''' '^'^ ^'' ' ''^ '^ct'fa ''^ t'em
^profit of $4 20? ' ^''' '"""^ "'"^^ «^^ b»3^ «"J «^" to uTe
.any balel^S^S'ltr^"^ '^^'"""-'^^ ^^^/l20?^^
46. »-JnrrAwpi1 nf A ■51 /i;n »\_ • . /IKS. i^iDO.
$100; howlonishailtiLn-.y "'°"'^"' aOerwards I lent him
sum he lent meV ' '''^ '' '"^ compensate bin. for tho use of the
became worthless • T fli«r.n«n , f f ^^^f^j *iO each, and one of .'$50
»o„i. .1 L per' .. Rei.;:? ^ ';tc?;'r ;tt, z r i-, ™
a.,d hereby I ,ataed ,.500. iiirrhSr^^ tii'S'd:^
cWof 6 moi„Caa/7 *!>at1o,;T roS;'*''','^ "" ^
lie mav make a clear gaia of 24 « L i ,. Sf,''' "^f l;'»,"'P™»e«,
money beiog worth Oj? '* '"' ^"' T' >" "« gooJs,
plaid^'o' a\'5*Xne''.Zt o"""'" °f ■'"'' °" ''^^
,ii^i;crtrd."::driiT:,rat^3i!f.-T^,;r-'^^^^^^^^^^
m
»t
what did be give
An$. $600.
i I
I
I
ri)
If
If
I
MIWILLANIOUS KXAMFLW.
to tL!!!fl ^''^•'»'.>»boring 7 hours a day for 16 days, were able
.'Jn. k^ ■ u-^nl "* *'°'' "'^"-^ '^^^' c»o they complete the res-
aumber r'^'' ** "'" * •^*^' '*" * workmen be a.Med to their
fn/v ^*^*^*»««? 50 Ontario boads of $1000 each, at"^*i^piSm,
he SL'r vT? ^"^' f ^^'^^ **«^' «* ^ * P'^'"''^"^- How many ot
me latter did I receive ? ^„, 3jq
i.fwr'i '''"^ * friend $700, which he kept 20 .nonths. Some yekra
ih^favor r'"" " *^°® ' how long^ehould I keep it to balance
ea u ' L. . ,. Ans. 46 J months.
on^ft -?''"* A ™«^°h«»ndiee as follows: July 3, if 85. 26; July 4, $48.65,
Z^n, ?f •;' A"^- ^^' ^^-^^ 5 ^^P^- 12, «60. What is' due on the ac^
count Oct. 12, interest at 9 5l5 ? Ans. $142.60.
7 „,« *;«"'* certain «"« of money to A, and at the ev.d of Syr.
T mo, 20 da.. I received for interest and principal $1000: what sum
«1 rnV «.,.„, An.. $820.79 + .
«f „J ""'' "•'?' '"^''f 25 yd. of cloth, liwide, how many poundi
of wool are required to make 116 yd. of cloth 1 yd.' wide? Ans^ZA.
and th« r!^ • ^^"^^ ^o' *^^"?' * Pt?^*^^« '•» 3 ™<^"*'^«' * '" 6 months,
and the remainder in 9 months. How much ready cash ought r to
Purchased a quantity of oats, April 1; May I its value ha(^
ncreased 2.^ ; June I it. value wa. 30 % more than May 1 , July 1
1 sold t for .u^ less than its value June 1, receiving in payment a
luSi ?°^*A^^'«^ I ««' discounted at a bank, a* ^ %: receiving
«? r^o.V How much was my profit on the oats? i4»<. $3238.52.
.ff:, fi? i " • ^"^ u ""^'^^ °/ •***^ ''^'S^ 1^ 'b-' '•^quired the i^imber
of feet of lead pipe that can be made ^m 80 lb. of lead, the caliber
of the pipe M) be 1 inch, and the thiokiieRs of it i of an inch.
cfi t\ .u J .. iiiM. 10.35 + feet.
b6. Une-third of a quantity of goods was sold to gain a certain «.
.one-fourth to gan, 4 times as much %, and the remainder to gain 2*
thlwhouT'' ^,. I}'""' 'I '^' «^" * "» «^^ Par^ the gaif upon
the whole being 21 %V ^n#. Ut.. 12sSj 2nd., 18%; Srd'VsO^T
. *J' ^ '"erchant in Kingston has 6000 francs due him on account
bni a.'T.i3 .r *"*° r''^'" ''" ^?^ ^'"' ^^'^ ''"'^'"'^ »»d negotiate the
u^ Llit I f ^' P®"" fra»V o^ he can advise his correspondent in Pari»
to wmit adraft on Canada, purchased with the sum due him, exchange
on Canada being at the rate of 5 fr. 20 centimes per dollar Wh|t
sum will the merchant receive by each method?
Aru. By drafi on Paris, $970 , yy remittance from Paris, $961.5:^
67. A mil m IS required to grind 160 bushels of provender, worth
$1 a bushel, from oat« worth $.40, corn worth $.80, barley -., i;
$.90, and rye worth $1.10. and wheat worth $1.30 pei^ bushel, now
voAnj bushels of each Kind may he take?
««. H.- ^„^ ..fl., .JrJ?':^P.* 20, 60, and 40, respectively,
of siVupTat $;7T;S^W ^•'"' • ■"" """ ^ ^''"' 'iJ'2T[,'b^'
69. A servant draw« off a gallon on each day, for 20 days, from a
Jilriwv"*^^'^ ^'''Ir ^'■'^°*' •aohtimesupplying the deficiency
hjr ih« addition of a galk>o of w«ter j and thea. tS !»ia^ de.eoUon. b^
MIMHLLAN10U8 BXAM»L„.
'4. Jij working 9 bourg a Hov <'^> is. j ^ns. $386 67
Wuetl ^?f ^ ^-" A Sinti;^^^^^ "^'^ wL able to
■due be finished in 15 daye more if^h^ ^kJ'*^*^"*'^°' ^"^ t^^e rP«.
r hours adaj? ^ '"°'*' '^ '!»« laborers are employed only
'o. At a certain time bptwpon 9 „ j r. . ■^ns. 4 men
was between 3 and 4. WirhTn L^J^ ^ "1*^^^^' »l»e .uinuSnd
mmute-hand had exactly cWed^^^^^^^ the hour-hand aad *
the prece t,.e when th'e hanlst^ir S VS^^^ ^'" ^^^
76. D and E traded together • n '^"^* ^«^^- ^^ '"'n- 56t«A 8«j
'7. If stock bought at 8^ dispni.»» n "4«». •t.)20
.t what rate shoulJ it be L^h ri^'te? ^ * - the inve.t,fen^
aJ^K iL"f P^'^' ^^^^•i clotli to a wffieiai? I . ^"'- '^^'^ * '^'«ct-
i^ Jm'^^^ ^**^«' ««^*1 it to a cloThier 2 ! ^i^"" f ' ' ^ * ^•^^ance :
"* "^'d It at a farther advance of 25 ^ 1 !?^ * ^^^^nc^ ; the cloth'
much d,d.t cost the importer^ ^^^ *°^ '«<^"'«d |I452. How
•7an /^ , '^ tl*« difference between »h- • ^^' ^^'^ «6S.
$730, for 5 yr. 9 mo., at 8 jT? « * •°**'**^ *"<i discount of
80. A merchant sold I of hi? gooda «f o ^ ^''*- ^' 0'-«0.
them at a loss of 8 « • X of fhl^^ " *° advance of 25 f^ ■ " «/
at a discount of 20 |; ^or whatVof*.r^* o*" '^0 5», and f of [ifem
«>ld m order to losers % Z tt'tifof .^'^ °°^ '""'^^ the renfai„der S
invest tr.::ll":?*d'-^->'^ -,Montrealcitvr.-,.tl%'^'f-^- ,
8Ta'?*/^1^^' whatwastheamountoflfr ^F ^o^'t leaving in-
«-«. A tailor bought 40 vanl^ of T. J^ . i>^ divxlend ? 4. $1000
"""3f.«'''''«^'-'''i°Ctil^^^^^^^^ 2ivd. wide* but on
I width. on« nail ^^A - T.-iP ">^*" every 4 yd. i'lilfn quarter a d
^this cloth,
'" the whoJ«
82. A tailor bought 40 vards of L J" i™? ^'"''^^"^ ? 4- $
sponging i^ it shrunk in Ct^L^*"*^'^^*^' ^i yd. wide*
m width o'ne nail aad L haff^reVVr^'fi V^' ^"' ^ <^"-«,
I».bou^tfUn„.U,uarterswi5:,\^Jfe^UiCwerJ;u^^
I tm
^
II
fll
SM
MUOILLANBOTTB BZAMn,!!.
i M
■
■mi
i.
■ir
^^H'
si . .- :
■l
1' ' •. |.
^1 \i $' I
^^Hi^
iii V i
■iPfiiii
^■1
■Jiniy
width on eyery 20 yards in I«i,^h, and in width it shruni half a
nail. Required the number of rards of flannel used in lit.; jg ihf
83. Stock purchased at 5 % pivniium paya 65^ on 'die inv« (..nent,
what % will it pay if purchased tu 15 % discount ? .ins. 7,1 %.
84. A riKTcliant failing' in business can pay 70 eta. on li dollar, ile
oflfers, to pay his whole indebtedneBS without ix', rest in 5 ycar.s if his
creditors v/iU allow him to go on w.th his b>; In ■•js; his otl'er beir>g
Jiccepted, how much will his crediiore lose in ii\e 6 years, money
being worth 7 %1 Ana. 5'^.02e on a dollar.
80. Purchased a quantity of wine for $675. 32^, a^, 85 cento i>fT
gaLon; but a part having ieaked out, the remainder wr.' sold'iM
40 ^advance, s/k! the oii(,;inaI cost was realized. Wha; quantii,^
leaked out? ^ns. 2;i7gai.
86. A owes B ^i'm .'ae in 4 months, and $840 due in 6 months:
B owes A $1600 duo ij» 7 months, ff A should make present payment
of hia debts, wiieaoi;, au!! in jviBtice to pay A? Ana. In 2in-- lO^da.
87. How muny T ii.'ds of sugar at 8, 13, and 14 cts. p x- pound,
may be mixed with 31b. at n cts., 2 1b. at 8^ cts., and 4 1b. at
14 cts. alb., 80 aa so gain 16% by selling the mixture at 14* cts.
per lb. ? Ana. 1 lb. at 8 ; 8^ lb. at 13 ; 8 lb, at 14.
88. What IS the dift'orence between the true and bank discount ol
$3000, p^iyable in 120 days, at 8^ ^ ? Ana. $4,467 - .
89. A general, forming his army into a square, had 284 men re-
maining; but increasing each side by one man, he wanted 25 men to
complete the .square. How many men had he ? Ana. 24000.
90. C bought a house of i), and gave him his bond for $6000, dated
April 1, 1866, payable in 5 equal annual installments of $1200, the
ti-i St to be paid April 1, 1867; C took up his bond April 1, 1869,
eenM-annual discount at the rate of 7 % per annum on the payments
due afttr April 1, 1869, being deducted. What sum cancelled th»
bond Y Ana. $3365.94 +
91. I have a plank 42i feet in length, 24 inches wide, and 3 inches
thick; required the side of a cubical box that can be made from
'*!.o T-^ * 4n#. 48 inches.
92. IfB owes $500 due in 6 months, $400 due in 4 months, and
$300 due in ? months, and pays | of the whole in 3 months, when
ought the remainder to be paid? Ana. In 10| mo.
93. A wholesale merchant seni a quantity of goods into the country
to be sold at uuctiun, on a commission of 4^ %. What amount of
goods must be soil, that his agent niay buy produce with the avails
to the amount of $1910, after retaining a commission of 2^?
Ans.
94. If the annual rent of 23 A. 1 B. 27 per. of land be $18'
much will be the rent of 71 A. 20 per. ? An
95. A Halifax merch; ■, . hipped 1000 barrels of saiu.jn v.
in New Orleans, diivctii) m to fcell it, and invest t
cotton; his agent sold the salmon at $14 per bbl., paiu v !■• uumges,
and bought cotton at $.65 per lb., charging '6% comraisficK morselling
the salmri and 5 % for buying the cotton. How ma 7 rvu.-isof
wtton did he buy ? An$. 1M85. .b.
'0.
lOW
56t).
' ' H aofpnt
.■•■;i'eds in
■?'< charges,
3nSffln.LAlflODS MXAMKJm.
he finds that tm^'JTL^^Z'h ^'^'^l!"* ^«'"g »"«^«<^ ^t s'j?
owe ? * " "^^^^ ™°°«y ^'JJ pay the debt ; how much did he
-ne,,p,u«,,,lr-,^-^Dj^B^^^^^^^^^^^ to E.
quired C's stJck aK°s an!l B 's'sain"! ^"^ ^ ' '^^'^ "'^^ *''*«• ^
100 A ^'»*: C'e stock, $10000'; A'Bgain «3'-}6 • R'« SRsn^
iUU. A man havinw Inst « ^V k;„ ' " g»iu, ipaao , tj s 5>504.
only ,672; ho/mich td-hfattsT^^' '^""'^ '^^ '^s'^S'^'
aelling tLTstt^' a^el-i^T^^^ - railro^J-st^ocHV
b7 investing tl e remaiader he'^ ^L'*^ f'^T,^' ^^f ' ^ ^^ ^""^ iavest.nent^
money he had remS" wJich Li hi ' ""^^ ^*^'7"'''^ '"^^ '^' «*" '^^
much did he invest ?^' ^'"^ possessed of $480 ; how
102. Bought a certain number of horses for 3;2fiOft 1"*! f u ^'^V
gain ? * '^^^ P"*'- What per cent, profit was his
The oonsigoM pays $1 20 40 for tS , - *' °" !"<"=«'* '>y =>'■>»•
«8.40 per bbl./oi;i»» 2' « ^™^ ^ """ «{«"»=«. sella the flour at
•vey 2 ho,«,, 1 acre olpMurt?""'' ' "^^ '"'''T' tj' ""' ''""
gain on the whole? * *'''• ' '""'" "'"ch did I
1 09. I paid *93 16 0, at tij- rate of 9 . ci f ■ '''"'■ **"•
^'?7vV''"™-°'»aetheHL^'*;etV°'""°°'°° " *«
' 4 i*. What WM my aain ? *^ ^ '^ * premium, brokerage
' * iliifc £26.
Ml
'I
B**!*-
( i ^
^"ir
15
! i /
(
i i
VTSOHLLAinOUS BXAMPLli.
112. The londtudeof Paris is 2" 20' 22" E., and of Constanti-
nople, 8° 59' E. When it is I A. M. at the latter place, what time
is it at the former? .4ns. 33 niin. 25 j^ sec. past midnight.
113. Having placed a bill of $775 in the hands of a collector, who
succeeded in obtaining 75 % of it, and charged 8 % commission, how
much did I receive ? i t> o #
114. Suppose that the earnings of the Grand Trunk R. B. for
December 1870 were $472240, wliich was an increase of 11J% oyer
the earnings for the same month in 1869. How much was the in-
crease? ^ ^na. $47224.
115. In a cask containing brandy and water, | of the whole +3
gal. 18 brandy, and ^ of the whole + 2 gal. is water ; required the
number of gal. of each. Ans. 43 gal. brandy, 17 gal. water.
116. Hamel, Perry, Lane, and Garneau are partners; Hainel takes
\ of the gains or losses; Perry \, Lane ^, and Crarneautherenminder.
At ihe close of the year, the resources of the firm are : Cash $10312.50,
Merchandise $13447.50i Bonds and Mortgages $1147", Bank Stuck
$4500; Hamel has drawn from the business $900, Perry $o25, and
Lane $285; the liabilities are : Notes outstanding $5460 ; Balance in
favor of Ross & Co., $1120 j Balance in favor of J. L. Murphy,
$3'J67.50; Hamelinvested $9547.50, Perry $7905, Lane $6270, and
Garneau $.'^480. What is eaclx partner's interest in the business at
the close of the year? Ans. Hamel, $9877.50 ; Perry, $8302.50 ;
Lane, $6723; Garneau, $4279.50.
117. What is the difference in cost between a draft on Toronto o!
$17302.80, at li^ premium, and one on St John, N. B., for the
same amount, at ^ ^ discount ? Ana. $302.80.
118. A mechanic received $3.75 a day for his labor, and paid $1.26
a day for his board; at the expiration of 100 days h'- ^-^ ' • ved$200 j
how many days did he work? ^l"*- ^^ ^^'J^-
119. For two successive years, a merchant annually contributed
$100 for charitable purposes, and added yearly to that part of his cap^
ital not thus expended, a sum equal to its half; at the end of the sec-
ond year his capital was dq^bled. Required his capital. Ana. $1600.
120. A merchant in Halifax purchased 350 bales of cotton, each
containing 450 pounds, at $.80 a lb., and shipped them to Liverpool at
a cost of 16 % for freight and duties. How much in Canada currency
did he gain by selling them at 28. lOd. sterling per lb., rate of exchange
171^? ^***- ^23416.
121. A piece of merino cost $.80 per yard ; at what price shall it be
marked, that the merchant may sell it at 10 % less than the marked
price, and still make 20^ protit? Ana. $1.06iJ.
122. A merchant in Quebec gave $2000 for a bill of exchange of
£400 to remit to London ; what was the rate in favor of England f
123. What yearly debt can be discharged by monthly payments,
the SrHt being «2, llie second $6, and the thii-d $18, and so on. id
geometrical progression ? Ana. $631440.
124. A farmer sold one hog, weighing 250 lb., at 4 cts. per lb. } •
e'eoond, weighing 300 lb., at 4^ cts.; and a third, weighing 369 lb., at
ots. ; what was the average price per lb. for the whole 7 A. 4f^ ots.
' tii^'iaiiMkil
Cet'Htanti-
;vhat tim«
idnight.
•ctor, who
sion, how
R. R. for
llj^oyer
an the in-
$47224.
whole + 3
quired the
I. water,
aiiiel takes
renminder.
810312.50,
a.nk Stock
$525, and
Balance in
. Murphy,
S6270, and
3usines8 at
^302.50;
Toronto o!
B., for the
$302.80.
paid! 1.26
■ ved$200;
)J dajrR,
contributed
t of Ilia cap-
l of the eeo-
8. $1500.
)ttoD, each
Liverpool at
la currency
)f exchange
$23416.
e shall it be
he marked
(. $1.06"j.
xchange of
England f
payments,
I so on. in
$631440.
per lb.; •
/369 lb., at
4tHot^
1IIB01LLANB0TJ8 BXAMPLRg. 3^
goods. * *^' Required the cost of the
exchange ? ^ ' '^^'"^ *2o70.89. What was the course of
129 A man gave \ of his estate to his wife 1 ot^Z ri^JH"^' .
his oldest eon. I of the rAfliWno t 1 • 1 1 ' * , ^"® remainder to
what then renminedwWclwaifKon'' '''M ^^"-'>*^'' '^"^ ^ of
Mc«i^iSr^;=
waL't^ie teTh^isT^iS/r ^^"^^^'"^ ^ '^'^ «^ *i^«« ' ^hat
price supposing he should make &%. Did he 1^^0710^ ? '^"^
abIe'i;2%rrrTi:'at;Trh/Lf'«'' '''> ^^^^^^^^.y.
S^elrSp-bi^h^e.^^^^^^^ ^-^^'^-^-'^^^^^^^^^
6, i'p;o±o'r;t^f?;r;^^ - Pa1^n;nt!-i'pril
counted at theCk, IpT'lt^ll J^S-'^^f '"^'^T^ «"d had dis-
ceive? •'^ ' ^^ 7%; how much cash did I re-
136. Suppose bank stock is purchased at ... ^ ^"••.«344.93 f .
bank declar^a dividend of 9 /per Z^^ ^^"'^ *•»«
price of the stock ? ^ » Per snare, what % la that on the cost
137. A person, wishing to buy wheat with fh» «.^^^^* y*^*
sends to his agent 32 bales, each weigh n^ 380 Ih ^ T^^^' of cotton,
the cotton at 26 cts. per lb for wS l.I^.i? "'"o. ^S"^ ^8^"' «ell8
pay. for freight and ch .- a *-Ti fif ! f^'^^^ ?** commission;
re8shiscon.mis«in.«f'r:-T,f;/4Y^^^^ .«*Pends the remainder!
bushel, for whichhe ch ir.e f »"i rn7^"^'- '° ^u*'"'*^ '^^ «^ ct«- Per
obtained through this Sr ? ^^ ^ ^«"''»'««'««; how much wheat is
138. A pole 63 feet lone in falUn^r »aa u i. • ^^^^ + bu.
^«. le and 46 ft.
k:j
164
imOBLLAItmtVft IZAMFLia.
I !
139. A farmer heA Hfln rv
4'\
'SOWS, each fbrnishing 18 qt. of
milk a day, from whi.;h he rstAiC 40 tubs of butter of 60 lb. each in
30 (lays. Ho made a cc'Utract to deliver 100 tubs of 96 pounds each
•n 80 day^^. How mm.y cows mu8t he add t<i hia dairy provided each
additional cow furnish t gallonn of milk daily ? Ans. 27.
140. In wiiut time will $3045.20 gain $l90.:}2i if the gain of
$2494.75 for 1 yr. 13 da., is $258.43, and wh«t J= the rate per an-
oum? An 7 ii.c. iiUa. ; r»te lO^g.
141. And"ewfl, Baker, and Childs entered into partnership. Andrews
put in £3000, liaker £2000, and ChiMs £17?0. At the end of the
arst year AmlrewM drew out £500, Baker JE250, and Cliilds put in
£750. At the close of the second year, Andrews and Baker each
drew out />i 50, and Cliilda put in £500 more. At the end of the
third year they dissolved partnerflhip, and found that their joint prop-
erty was £7125. What was each partner's share? Atu. Andrews',
£2393 .0 4^ ; Baker's, £1597 4 5^ ; Childs', £3134 5 2J.
142. If T buy 50 sharefi Grand Trunk railroal stock at 141 %, and
60 shaies Canada Central railroad stock at 139 %, the former paying
% semi-annual divi(Jend of 4^ijj %. the latter of 5 ^ ; what rate of in-
terest shall I realize on my mvestment? Ana. Q^%.
143. What is the cost of a bill on Lone* m for £800 17 6 sterling,
when the rate of excliange is 9 J % premium?
144. J. Sheridan bought of L. H. Miles & Co., the folic -wing bills
of goods; Not. I, 1870, a bill of $760, on 6 mo. credit ; Dec. 16,
1870, a. bill of $300,on 5 ino.; Jan. 1, 1871, al)ill of|425, on 4rao.;
Feb. 6, 1871, a bill ot ?275, on 2 mo. What sum would settle the
account, May 29, 1871, interest at 7 ^? Ans. $1760.10.
145. When exchange on England is at 10 ijlj premium, itnd freight
at Is. 3d. sterling per Winchester bushel, how much can be paid in
Montreal for wheat per bushel, in an«w<;nn<; an ordir from Lon ion
limited to £3 10 per Imperial quarter?
146. The duty on an -oiceof ,{00 do? « London porter, at 30^
was $190,512; break a^ , 2%. Required the invoiced price per
dozen. Ans. $2.1().
147. Three merchants ha''e *n interest in a steam vessel ; A puts
in $9fii) for 6 montiij; B, j.sua unknown, f"T 12 monti^; C, $640
for a time not known when the accounts \ -re settled ; A received
$1200 for his share, stock and profit : B, $24u0 'or his, and C, i,ii040
for his. What was B'a stock, and C's time ^
Ans. B's sto-\ $lv.OO; C's time, 15 mo.
148. Merrill, Wells and Roche we' rtp s inthe gi'ain b" inesa ;
Merrill had invested \, Wells ^, and ne of the capital. They
were to sbar.' equally the gains or It 's. , he business not being
»n<^cessful, the partnership was dissol.ed at tiie close of tlif' "ear,
when the resources of the firm were found to be: Cash, $l78a , bar
•ey ou hand. !*i'2n00: corn, *1 722; rye, $.350; oats, $1650: wheal.
$5000. Tiie liabilities were: Notes outstanding, $1562; they owed
P Myler, $1200, and P. Riley, $1875. The net losses were $730.
What was the net capital of the firm at conamenciog, and what was
lach partner's net capital 7
^■Wt-m^jk,,
A00OUNT8 Of HT0RAO«.
ACCOUNTS OP STORAGE.
26fi
oJil? '% n"* """''""''" '"^^^^^ °f computing stora-e The
andratP«7^r'"''"' 'I '^' '^''^'''^^' cities, -Hlopt such ruleJ
and rates for storage as they dee.n equitable. Th. ch rJs fo,
•itie. an fractional ,.art« of r.^th^a.^' ^ISored fUlfrnonth;"""''' *" *«"•
bu.intsBXTr?ieTvt?a"dTii::lra th'e'.r "rr^- --'"-oa.a,i.«ion
« k. pt. .bowing the date and number cfbS^ ' J'' °' "'• ^^ '"''snor. an aooount
number sold or delivered. In cZn, ti^nrth^^^ roc,i,ed, and tbe aate and
customary to avcnM-e the time nnThlrS *'"''''^* "" '"'^*' »" account it la
It- there i/a fraction"a. par of ^ ba^ef et^o i^„ 't^""' '" '" f'?'". """"'^ "* ^" ^^J^"'
oat J of parta of months above. ' ' ° ""^ "''^'^'^S^' 't >^ treated 8^ in the
OP' RATION.
da.
X 15
1871.
May 1, Rec. luu
" 16, Deliv. 600
Eal. "500 X 10
" 26, Hec. 2000
Bal. 2500 X 6
June 1, Deliv. 1000
Bal. 1500 X 11
" 12, Deliv. nOO
Bal. 400 :< 20 »
prod.
. 16000
5000
12500
16600
8000
Analysis. — The srora'o o*
1000bbl.forl5da., + .50UbW:
for 0d,)., + 2500bbl.for5da..
+ loOObbl. for II da., + 400
bbl. for 20 da., is the f-ame as
the stora ire of 57000 bbl. fnrl da
orl'JOO bbl. for a month ofao
days. Ai.d the storage of IDufl
bbU at 6 ots. each « ^114, Jm,,
July 2, Deliv. 400 3|0 ) sTooJO
-.» s,ore,/,om eaa, dale to Ih, mu next Hlowhl^it hZL T T
/«• wM^i Zm ^Z ,T ''"'"fl"'l h "" rale o/,lcr„a.
If
I .i;
?1I
tet
OINIRAL AYBRAOB.
r !
t
■XAMPI.RS Fori PRAOTIOB.
1. What will be the cost o{ storini: salt at 2 etc. per barrel, reoeived
and deli veretl a« fol lows: J ine 6, 1H71, lanbhl. ; June IH, 14<>bhl. ;
Jnnc'ifi, GOO bill.; July."), HOO bbl. ; July 16, IHu bbl. ; Jnlv 20,
ifiO 1.1)1. All delivered Au'^. 1. /Ins. $21.44.
2. What will be the ntoraj^e of flour at .'» oenta per bbl. per month,
received and delivered as follows?
li«ceived Jnlv I, 1871, 400 bbl.; Julv 15, M^O bbl.; July 26, 4.50
bbl. Deliverc 1, July 12, 200 bbl.; Julv 20, 400 bbl. ; Aug. I, 200
bbl.; and Aug. H, 40) bbl. ' Ans. $2.5.10.
'^. Received, and delivered, on account ot JameH O'Neil, sundry
bales of cotton, aw follows: Received, May 1. 1871, 1848 bales; May
Ki, OtibaIc«: June 1, 210 1 alea. Delivered, June 12, 800 bales;
July 1, 480 bales: Aug. H. H2(i bales; Aui?. 10, 2:)0 bales. Required
the number of bales remaining in store on September 1, and the coat
of storage up to that date, at the rate of 5 cents a bale per month.
Ans. In store, 334 ; cost, $240.75.
4. Received. July .3, 1871, 256 ca«ks of wine, on storage, and on
JnJy 1.5, 381 more were ad.iedj July IS', delivered 261, and July 26,
312aisk8; July 30, received 321 casks, and Aug. 8, 163 casks:
delivered, Aug. 16, 208 casks, Aug. IS, 103 casks, and Aug. li), 116
casks; received, Sept. 1, 320 casks, Sept. 2, 106 casks, Sept. 7, 342
casks; delivered, Sept. 12, 250 casks, Sept. 18, 321 cask.s, Sipt. 21,
133 casks, and the balance, Sept. 27. What was the cost for the stor-
age of the above, the charge being 6 cent.^ per cask monthly?
i
If I r
GENERAL AVERAGK.
49JI. General Average is the process of computing the loss
to be sustained by the owners of the ship, cargo, and freijrhl,
respectively,— when, owing to common peril at sea, any portioo
of the property has been dani:iged or destroyed for the common
safety.
404. JetSOn is the portion of th« cargo or of the equipment
of the vessel thrown overboard.
4»5. The Contributory Interests are the three kinds of
property whicli are taxed to cover the loss. These are, 1st. the
vessel, at its vdue before the loss; 2nd. the cargo, inoluding the
part Bacrificed ; 3rd. the freight, le.sa j^ as an allowance for
seamen's wages.
406. The loss which is subject to general average includes,
1st. Jetson ; 2ud. Repairs to the vessel ; 3rd. Eipeuae of de-
tention to which the vessel is subject in port.
N«TK8.--1. The goods, whether saved, injured, w deitroj) d, are estimated at
uieir valne at *he port of degtiuation, except when the adjuatment of the eeneral
aTerageiHiui - at the povt of lading.
MNR«AL AVBRAOE. 267
.^■J?. The Hhip « ArMie,|« '> ^„ „ *•
w.tl, a car^fo of silk, tea e o ' v "i T^""-^^' ^''''"' '^''^'^"••'^ '-^ Q'^^bec
gaie. and the captain v. i co,;;;.?, l!,"' ^^ '''' r""^' '^ '-'< '" ^
her cur^.o value.! at .?<i:i7.-. t^ w L L .'''' overl.uani a portion of
cargo. The vessel was va e at ^7- um'' ?'' !.''*' re-nain.ier of the
'"g $2l,'-.55 t., Murphy & F eM Of / J n * ^""""^' *"^^ ^''^ "-^-''^in-
belonged to P. N. GuVneaVir.iW, ..']'"'' """^'" overboanl $2150
•n- Ti,nM.s, a„,| $177 'to Mn , y u.rri 'lT'"\'^ ^"' ^''^ '« ^•«-^»
ol tlie vesflei were n.a.le af c! l\u '''• ^ ''^ ii«'ce.-t^ary reDaire
of the detention ^tZli ^InV^Zh^t^'l/''' \ ^'iV'^ ^P-^-
<i-nhuted a.nong the oLer. ^Vthi^^;^, SlZ^^^^ltJZ^
OPERATIOK.
LOSSE8.
<co-t of repairs , goO.OO
Coat of detention 155 wg
CONTlilBClOKT IKTKiieSTS.
J;"'^^' ■•..$ 7r,ooo.oo
ri'>^",- 692ir,.00
^'^^^'^'^t ... C400.00
.,„ ^^'^^^ n(m75 , j-,,,^,
$7030.75 -f- $14061) - P'i . .
S/r.nnn y^"'''-' - -05, rate per cent, of loss.
9><o()00 X .05 a f<'^7-,(\ nn
6!^2I5 < .05 = vJoo 75' ^''"iT ^'^^'^'''^ ''-^ ve.s.el.
' ' * " cargo
Total .....f 140615.00
6400
•05 = rJiO.OO,
It
" freight.
Total coniiihntion $!70.30 75 fn l,« .j; * -i . ,
6400 X .0.5 z * • 2iM 0' ''•"";:"' ^"^'^^'^ ^'y ^^'-^^^i.
175G0 X .05 « 87S 00 ' » T ''■'''-''^•
11600 X .05 „ 58000 - ^- ^"^^ ^'«rneau.
8500 X. 05 « SoS; ;; ;; ;;f;i^--n&co.
215.05 X .05 =. 1077.75 u ,, ||'-s & Tinin.s.
From tlje amount r,.M.>i 1' i ^ -Murphy. & Field.
1155.75 =V;;SKtS%^:--'-''n^'^^ $500 ^
the general Iosm i.s .^•.^750 - §'g:,,-, 75 -- .-?^„ ,■■;':' '""^t conirilaue to
other owner, of coniributory interests TutX;. •'^"/'"'='' "'" ^''«
f;°»^\^''« amount of hi, pa/,,;;;r'jj^^^^ '" ^'^'^ •''*''"'^'«'^
^'Sio:'''^^^^^*^'^;'''^^;--'-
« . freight.
" <i i<^i'. A. Garneau.
i- ^•;"'"" * Co.
" Murph;' & Field.
$3750 - $655.75
.320
2150 — 878.00 «
iooO — 580. 0« »
895 — 425.»0 -
1770 — 1077.75 .
^20.00,
l272,t)0
980.00,'
i70.00,
692.26,
From the analysw- of this oxampio we deduce the
ii
SVB
AVERAOINO Of ACOOUNTS.
40T. Rule. — I. Divide the entire loti by the mm of the
contiibiUory interests ; the quotient will be the loss per cent.
II. Multiply each contributory interest hy ihe loss per cent. ;
the product will be ',he amount of its contribution to the general
loss.
III. The difference between the loss of each eontribntory inleresi
and the aviounl of its contribution will be the balance to he paid
hy it if its contribution exceeds its loss, and the amount to he re-
ceived hy it if its loss exceeds its contribution.
FXAMPLES FOR PRAOTICK.
1. The ship Nestor, in her passage from Antwerp to Quebec, was
eripplcd in a Htorm, in consequence of which the captain had 14800
worth of the cargo thrown overboard, and put into port for the neces-
sary repairs, which cost $1260. The charges for board of seamen,
pilotage, and dockage, amounted to $170.40. The contributory inte-
rests were: vessel, $37800; grops amount of freight $4992; cargo
shipped by S. Keller & Co., $2574; by Shiller & Morse, $1752; by
Krauss & Heir, $1152; by Lebrun & Co., $804 j and by Ross &
Daller, $1200. In adjusting the general average m Quebec, the de-
duction made from the gross amount of freight on account of seamen's
wages was one third. Required the several shares of the general loss.
2. A vessel valued at $.H5000, having been disabled m a storm, en-
tered port, and was refitted at an expense of $337.50 for repairs, and
$150 for board of seamen, pilotage, and dockage. Of the cargo, va-
lued at .10250, $3000 belonged to A, .$2312.50 to B, and $937.50 to C;
and the amount sacrificed for the sliip's safety was $1750 of A's pro-
perty, and $212.50 of B's; the gross charges for freight were flHli
Required the balance, payable or receivable, by each of the parti as,
the loss being apportioned by general average.
j_„ < $1618.75 payable by ship owners; $1585, receivable by A:
-*"*• j $5I.56i " " C; $85,311 « " B.
AVERAttlNa OF ACCOUNTS.
498, Averaging of Accounts (also called " Equatjon of
Accounts, " and " Compound Equation af Payments ") is the pro-
cess of finding the equated time for the payment of the balance of
an account that contains both debits and credits.
The debit and credit sides of an account being respectively
equivalent to the sum of their several items, due at the equated
time, the Jirsf step in equating accounts is to find the time wheo
each side of the account becomes due.
This may be found by equating each side of the account, with-
ouf. any reference to the other, commencing either at tha first or
the last date of each, or by using ih^firtt or last date of the tmy
eount as a common atarting-point for both side*.
AVBRAOINO OF ACCOUNTS. 269
fl=-";l^££2^-I'L!^'liZ';i^. Thompson. Or.
April 3
May 1
" lo
June 24
July 1
To Mdse.
TiDie ofcrcflit,
•?220| 3,nonths.
125
20f)
140
190
6
6
8
9
1.^71
July 1
Oct. 3
Dec. 20
By Ca-h
$200 00
150 00
300
PIR-T METII')r.
Debitt.
Due,
1871
July '^, $220 X 00 =
2«. 1, 125 X 90- 11250
.1-7.;'' ^°'^ ^ ^^5 « 27000
Feb. 24, 140 x 236 = 33040
Apnl 1, 190 X 272 = 5i6so
00
Credits
Due,
1^-71
July 1, $200 X 00
Oct "
3, 150 X 94
14100
SKJOO
$87.:
) I*22!)70
Dec. 20, 300 x 172
$650 ) 65700
101 da.
Debits are due 141 davlMom T f '"^/'"^^'-^ d',e lOI days from
J«?y 3, which is Nov 21 I ^ ' '''^"''^ '■' ^'^'- ^"•
The above account thus equated will .(and as follows •
JJr.
Due, Nov. 21, 1871, $S75. l n /w ,^'''
0rthu8: ' D.,e, Oct. 10, 1871,
S50.
Due,
1871
J'lly .3, $220 A 2 = 440
Oct. 1, 125 X 92 = 11500
1872 ^'■'"" Dec. 20, 300 x 172 =51600
Due,
1871
July 1, $200 X no =
Oot. 3, 150 X 94 = 14100
Feb 2^, 140 X 23S = 3;«20
April 1, 190 X 274 = .020^0
$875
) 124720
U3
Debits due 143 days from July
1, which 18 Nov. 21. ^
$650
Credits due 101 da
I, which id Oct. 10
yn irom July
^ M-
I 1
i: i
fi 1
I?
1; I
ii
I '
270
AVERAGING OF ACCOUNTS.
The account thus eqtialed stands as before :
Dr. Cr.
Due, Nov. 21, $876. | Due, Oct. 10, $6.50.
Moth.— In the nhwe opemtion, we start from the earliest date upon which
any item of eithe- side of the aooount I'ecome^ due.
The next step is to find when the balance of the account, as thus
equated, becoined due.
Debits, $875
Cre<lits, 650
Balance, $225
Difference in time 42 days.
Or thus, by Discount :
(660 X 42) -^ 225 = 121 days.
$6.50
3.25, dis. for .^0 flays.
1.30, '* '< 12 '<
$4.55 ^ .0375 (dig. of $225 for 1 da.)
= 121 days.
$4.55, " « 42 days.
Tilt balance is due 121 days fi^jm Nov. 21, 1871, which is March
23, 1872. '
isSTLANATioN-.— Assume the account settled Nov. 21, the latest date. The
credit side of the account haa been duo from Oct. 10 to Nov. 21, or 42 days.
Kov. 21, the credit side, is equal to $650, and the interest of the same 42 day.i.
That the debit side of tlie account may be increased by an equal amount of
interci't, it is evident that the balnnoe 'if the account must remain unpaid 121
days, or the 121 days must bo counted /brwnrd from Nov. 21. Or thus:
The above account may be stated as follows : Oct. 10, 1871, L. N. Thompson
paid R. Seeley & Co. $650 ; Nov. 21,1871, H. Seeley k Co. paid h. N. Thompson
*8.i). ^ow, since R.S. &. (^o. had the uso of $«50 for42days L N.T. is onlitled
to the use of $22i ^he balance) until its interest equals the interest of $ii50 for
42 days, which is 121 days. 121 days from Nov. 21, 1871, is March 21, 1872.
PROOF.
Dr.
Due, Nov. 21, $875.00
Int. to March 21, 1872 17.65
Cr.
$81*2.65
Due, Oct. 10 $650.00
Int. to March 21, 1872, 17.65
Balance, 225.00
$8!)2.65
Suppose the debit and credit Hide of the alK.'v<> account when
equated, to stand as follows:
Dr. Cr.
^% Nov, 21, 1871, $660. j D«« Oct 10, 1871, |876«
AVERAGINO OF ACCOUNTS.
271
Creaks* '' $87?""''^ ''""' ^'' the pay.ent of the balance ?
Debits, 650 f;^ ^ ^V -^ 2::r. = U3 dav.s.
— Halance due 1(];5 .lays previous to
Balance, !i!225 '^' ' ^^^^' "'^''"'' ''' J»>ie II, 1871.
Difference in time, 42 days.
toJfrTa'tdTt^^^t&tTom Vr".rif '^^^ ""Z- ''-J^' -«-^'' -^'« »' equal
"de of the account may beTry.reLdiJL .^'' "^ '^^ '^^''^''- Th«t the d'obit
of the account must be re4rTed ' if fiV?"''' "'""•"' "f i.i.rost. tho balance
Or tkm : ™oaraoa as duo 163 days p,-ev!oua to Nov. 2J , or June 11.
Jays. L N. ?^ ,t en^M.J, '^J^ ^e 're^t-of V'^,.'^'';;^'^^';! '^ "^ <'f^^r^^?^
Hence, the balance must he rei^rdec Is l! if -^f ^^° ''■''"''"> ''"• '«•'* ^'-^ys.
simple question is : How lon^^mn,/ t'";- ? ^^ ^'''^' /"-em-.u, t.,. Nov. 21. The
J!875 fo?4L' days. '""^ "'"'' *"^^ ^'^ «« "ifor«'t to equal the interest of
evlT^r/nJt; mus7be*d?ted Juie Tl'^87t'' '^''' ""'^ '"' ^"^^ ''*"""'«' ^^ «
accl!!?;«,v"^^~^''''*'-^'''^ ^'"' '<l'i^ fed time for each d,le of the
"•ccount without any refereiiro tn h„ n rm '-"' ^^"'^r tne
»lde of the account whTf J, !/ ''''^ ^^"' '""^^'>''.'/ ''*«
haiZ'o/ttt:!:^^^^^^^^^^ t?'' f-;>.w^.ri, ,f:
LARa4,:r7«?rfi,Ht. '^""' ""'^ "'^^"^^^^'^ -^^^^ '^^
;j»frf f^^^^J^Ji^^^^^^^^ smalle. «".« of
^'•.-.^ -« . j; i E;?r;t^;/srs;fi?st '"""^"'^ ^'- "■" ^•
ANOTHER METHOD
Due,
1871
July 3, $220 X 2 = 440
Oct. 1, 126 ;; 92 = usoo
Nuv. 15, 200 X 137 = 274i:0
Feb. 24, 140 x 238= .S3320
April i, ii;0 X 274
$876
660
$226
Due,
1871
July 1, $200 X =
Oct. H, i/,o X 04 = 14100
l>ec. 20, 300 X 172 = .01600
II
/' /
272
AVBRAOrNO 0» AOOOUNTS.
ExPLAXATioB.-We assume July 1, 1871 (the earUeat date upon which any
Uombeeomesdue , as the «rne upon which aU the items of the Loount become
due. The interest of tho debit items, from this assumed date of maturity to the
time thoy respectively booome due, equals the interest «( $1 for 124720 days •
the interest of the credit items equals the interest of $1 for 66700 days. Henee'
the b.lanooofinfcrestiB favor of the debit side enuals the interest of $1 fo;
59020 day., or $225 for ,^J^ of o9fi20 days « 262 days. Since the balance ot
.tem« ,s also m favor of the debit side, it is evident it can remain unpaid 262 da
mthout mterest, or will become due 262 days from July 1. 1871, whi h is March
H ,o 9P r, •"''*°°* °^"®'"' ^"^ ^««° °° *»»» credit side, it would have been
due 262 d:)ys previom to July I, 1871.
501. Rule.— I Assume the earliest date vpon which my
Hein of the account becomes due to be the time ofmaturitu for all
the Items. ^ •'
II. Multiply each item by the nnmber »f da i/s in fervenitw be-
tween ths assumed date and the date upon 'lohich it brcomesdue
^'^^J'^y/'yi'"^ of these products on each side of the account.
Ihni divide, the uiFFrRKNCB lefwecn the sums of the debit and
aedit products hj the bahince of the account; the quotient loill be
(ue time for co7isidiO(ftian.
III. Whm the d:ff,'tence of products and the balance of the
account fall on the same side, count FORWARD; when on opposite
SldtS, COWlt BACKWAIin.
Notes.— 1. Tho latest date may be used as a startirg-polnt.
n .™ . 1"'^'"'=' "^ ""3^ «f '^ *LT' '''"'" '^« '^^'^^♦''' 'f ""J"' '"-e less than 5». reject
ti em } whoL more, ad J $1. The work will ha .ufficiertiy accurate.
KXAMPIES FOR PRACTICE.
i. J. Mar|«hy has wim C. Duval an account, which, when each side
fe equaled, eiaitdaaa follows:
Dr. Q^
Dae, Sopt. 5, $1542. | Due, Sept. 24 $12%.
What 18 the equated tiiue of payineit for tlie lal. ? Am May 28.
2. L. N. Carroll has with Simina & Norris au account, the debit
and credit ndes of wtiicli, wlien equated, are as followa :
Dr. cr.
Due, Feh. 8, $650. ) Due. Feb. 12. $2180.
WhAi inu^t be the date of a note for the balance ? Ans. Feb. 14.
3. What is the equated time for the payment ofthe balance of an
accoautj which, wh?n the two n^des are equated, tianu? a« toiiows.
^r. Cr.
' ' Due, June 12, f 540. | Da*, Aug 1. *960.
Ans. Oct. 4.
AVBHAOINO or ACWOCNM.
Dr.
Due, Oct. 20, $2528.
Cr.
I Due, Nov. 25, $1800.
• Wl,at „ the balance of the foH„.i„g .„„„„„, .„, „,^„ ., .^ ^^^
Dy T
JOHlf WOODLKT. fy
June 15( '« Mdge., ifol
II *^^^ I I
J!! f P"J 25 By Cash ||615
yu June 10 " <■< I ion
00 II July 20 1 " Mdse. 540
00
00
Ans. Balance, $615; due June 2M87l7
Z>r.
C. Rtan ,k ^cot. with N. Mi,,kr & Co.
Or.
Feb,
Allrch 20 I u ,; I f8 | 00 || May .. -
" - ' ' ,;^f 50 June 14 " «
106 00
<<
22 To Mdse. $ 44 7n P.. L
24 '< « oo !" ^^^- * By
20 w « ?8 00 May 16 <f
May 4
June 2J
138 50
20 I 00
76 J 60
94 30
15 I 00
^"*-25^ay8backofAprillst. = March7.
' '^"''^' ^^^ ^^^-- ^^ ^'^^ ^olWin, «.oun, and .Wn . i.
A. E, Rot ?» acot. witii t t „, . „
March 14 To Mdsp nn « ■»,. II '^''M ""^ -■■-===
April 20 '' ""r- °? «r-i-??;: l"»e iO By Md«e. on 2 «o Uoo
W.„ ,J ,. ^ . , .-.O Aug. 5 '^ Cash ;S?
I &^' 20| :' Mdee. on 1 mo\ Z
due
Dr.
April 20
?^y 1'' " Cash
'une \[,\ <' u
i^>40
\i
I; ;■
*rM
El i
274 AVEIRAGIiro OF JLCOOXKI'TB.
Dr. S. Thomas & Son in acct. whh R. Hill.
Cr.
1871
1872
May 11
To M(lse.
.•*680
56
Jan. 11
By Cash.
$400
00
June 16
u u
272
60
" 29
« it
352
00
July l.'j
<( (<
144
20
Feb. n
« «
80
00
Aug. 23
(( u
400
00
" 25
U H
784
00
«' 30
« it
272
32
Sept. 9
« «
64
00
Ana. 808 days back of Feb. 7, 1872, or on Nov. 21, 1859.
9. What is tlje balance of the following acct., and when is it due?
Dr. L. Murphy in account with A. Kelly. Cr.
1871
1871
May 1
To Mdse.
$218
00
May 25
By draft, at 60 da.
1200
00
June 12
a li
274
Oil
June 6
" Cash
325
00
Sept. 16
'* Sundries
156
00
Aug. 20
" draft, at 30 ia.
100
00
Nov. 14
<' Mdse.
268
00 1
Oct. 3
" Cash
42
00
Am. Bal., $249, due Sept. 22, 1871.
10. Suppose the following account was settled May 6, 1871, by
draft on time, how many days' credit should be given ?
Dr. P. Robinson in acct. with O'Neil & Co. Cr.
1871
1871 1 1
Feb. 1
To Mdse.
$ 73
44
Feb. rO
By Cash
$197
44
March 1
t< «
96
50
" 21
(t u
51
68
April 17
« <(
144
72
April 23
" Sundries
30
34
May 1
« «
196
96
May 6
" Mdse.
17
92
An8.
19 days
).
11. When shall a draft for the settlement of the following account
be made payable?
Dr. S. T. Mitchell in acot. with R. S. Lee. Cr.
1871
June 1
July 14
Aug 16
Nov. 25
To Mdse. oa 2 mo,
" " on 40 da,
'' Sundries
$108
56
191
52
72
1)0
44
1871
Sept. 1
Oct. 15
Nov. 10
" 20
By Cash
•' draft, at 30 da.
" Cash
$100
60
250
300
Ana. Feb. 10, 1872.
12. When shall a aot« be madf payable to b»lanct! the following
wcount ?
Dr.
$400
00
352
00
80
00
784
00
1869.
is it due ?
Cr.
dk.
1200
00
;J25
00
\.
100
00
42
00
,2, 1871.
1871, by
Cr.
$197
44
51
68
.30
34
17
92
19 days.
>g
acco
unt
when v^i] the baJannlTA"" *"' *^^« "«'"« to
and wishes to diXrAi' ir ^r""' l^> ^"<^ ^15uf, dueNoJ 1«
at an interval of 40 d^,f ,ft^^«»^,^ two equal p^ymen^ n. d^
16. A merchant holds 3 notil ^^ i'^ '"^^ payments be made?
-^ace, !j,1080; maturity Aug. 6.
CASH BALANCE.
''mmmmmf:-
0A8H BALAN(».
OPBRATIOIT
Debits.
88 = 14080
68 = 29920
51 = 5100
43 = 4730
31 = 10230
28 = 10360
11 = 2420
OrtdiU.
100
110
330
370
220
X
X
X
X
X
X
X
Due,
March 7, $ 270
" 28, 200
Ma7 2, 440
20, 720
$1730 6 ) 76840
Sum of debit items,
" " credit items,
$12,807
$1730
1630
it
Daift.
86 =
65 =
30 =
12 =
23220
13000
13200
8640
$1630
6 ) 58060
Interest of debit items,
" " credit "
$9,677
$12,807
9.677
Balance of items, $100 Balance of interes*, $3,130
True balance June 1, $100 + $3.13 = $103.13.
Explanation. Since each item of the debit side of the account was on interest
from its date to the time of settlement, the total interostof the several debit items
equals the interest of $1 (or 7(5840 days, which, at 6%, gives $12,807. (The int.
of .-S I for 6 days is 1 mill; hence, the interest of $1 for 76840 days is found by
dividing 76840 by 6, and pointing off three decimal places.) The total interest
of the several credit items equals the interest of $1 for 68060 days, which is
$y.677. Now, instead of imreaaing each side of the account by its interest, and
then finding the balance, this same result may be obtained by finding separately
the balance of items and the balance of interests. If the two balances fall en the
same side of the account, it is evident the true balance will bo their turn ; if, OD
iifferent sides, their dijerence.
METHOD BY INTEREST.
I
1
1
■
1 JF^
■
Wp
I
Dv», Daye. Int.
March 5, $ 160 for 88 = $2,347
April
(.
May
<«
u
25,
440
" 68 =
4.987
11,
100
" 51 =
.860
19,
110
" 43 =
.788
1,
330
" 31 =
1.705
4,
370
" 28 =
1.727
21,
220
" 11 =
.403
$1730
112.807
Due, Oaye, ht.
March 7, $ 270 for 86 = $3,870
" 28, 200 « 65= 2.167
May 2, 440 " 30 = 2.200
20, 720 " 12= 1.446
«
$1630
$9,677
Balance of items = $1730 — $1630 = $100.
" " interest = $12,807 — $9,677 = $3.13.
True balauu«) ;ipliiO ■^■ «i3.l3 = $l03.io.
NOTK.~Tbe " Method by interest " will generally be found most eonveiuenk
•ither for finding the equated time for the payment of the baienoe of aooouatt, or
(■ iadiag tbe oaw Ma-'^^
•ASH avrAWOl.
f'
6 =
23220
5 =
13000
=
13200
2 =
8640
6)
58060
$9,677
9, $12,807
9.677
$3,130
as on interest
A debit items
7. (The int.
8 is found by
otal interest
l^s. which is
interest, and
ig separately
8s fall en the
: ium ! if, oo
•, Int.
< = $3,870
= 2.167
1= 2.200
= 1.446
$9,677
13.
t eonveiMent
aooouBta, or
277
Mar. 6 ToMdse.
" 25
April 11
* 19
May 1
4
21
June 1 Jjyint.
EnroK excepted,
Quebec, June i, i87i.
AsDREws 4 Son.
ANOTHER METHOD BY INTfiBMT.
*!f-,ilT?i»^'-.«fa"acot.$100
;; l5;;Ca^,paiddraft
-fiO Mdse. on 6 mo.
By Mdseon 6nio..$I60 8#
,, J^«!» 10900
.uX'"^ u.e cash ™.„. of 'i^^i^^r^;::;;;::^;;:;:^^
OPERATION.
Mar. I
" 15|
Sep. 20
^,¥JJ-i5 + .3.l38 10.'J.288
15|180.86~. 4621180.398
.April 1 157
'llJuiie 1 96
'("""15
!oot. 10
324.846
JOJ-00 + 2.617 102.617
120.00 + 1.920 121.920
inl]«n'SJ+ -"^'^ ^0.033
351 80.G0~ .'G7| 79.533
•<Ha.«36 ~ $334,841 .= ,188.J)9, ^„.
I
J I
■""''■'-■•' •-
278
CASH BALANOC.
ImlLI-
«03. Rule.— Multiply each item of the account bu the number
vie time ofscitlemmt. Divuie the. sums nf the debit and credit
products .jeetiveJy by 6 ; the. quotient will he thht^^^Z
two sulcs 0/ the account, at 6^ e^cpres.ed in mills Find he
balance o/Uems and also the b> dan J of interests.
cashbalan^ 'Z'l T^""" ''' ''^^'^*''^ ^^d^ of the account, the
duft\t'r''''i' ''^V'^ 'temfromthe dateon which it becomes
t2^VsonZ\flT^T'^ ,7^5 ;A:^b,..ce between the sumZ}
JKAe« //ie lala, ce of interest falls on thi same side as the
balance of, te,ns the cash balance will be their SVM tolZ ol
"PP0>>,te sides, their mvftMESCt:. Or '
0/ ^hT'add^^'^""' T "'.f '■'• "'^•^"'" ''^^ <^^-'-^^J^onding interval
^(/c^ each cotwiiu of cash values, and the difference of th.
amounts will be the cash balance required. '^'•^*^'^"^" ''f ^f"'
EXAJIPLES FOR PRACTIOE.
1. The following account was settled Nnv ifi ib-ti uru .
Ih^caA balance, i.e.«. being corpSdt"e'ao'h «™V,„?jr«
/J- T TH ^"«- *2 15.54.
^r. John Fbaseb ly acct. with L. R. Barry. Or.
1871
Feb. iITo Merchandise
4 « a
22 " u
19 " Cash
22 «< Merchandise
10 « <.
]^|*' 6a/. new acc't.
April
May
July
<(
Oct.
Abv.
$ 72
187
250
60
300
125
00
00
00
00
00
00
1871 I ^~
Feb. 16 By Cash
March 241 " "
April IG " <•
" 20 " Mdse.
June 27 " «
Sept. s\ " Cash
^ov. 161 '< bal.ofint.
$100|00
160
300
90
360
200
00
00
00
00
00
Errors excepted. Quebec, Nov. 16, 1871. L. R. Bahrt. ^
Detc r,' Ma^rT '"ZTT' '"'f"' "^^ '^^^"^^ * ^^^ ^^ f^'^^^- .-
A-;'9 tn m^L ' Q ' ^ inerchan.ljse, on 3 months, $721.50 •
.48 , July 14, to indse, on 2 months, $470.60. Credi or Mam
71. by cash on acct., «600j May lo', by iM^epUace at 30 day^
II
21
ACCOUNT OF 8ALM. ^
*'^°-"'i"- -^ -"-nfa o'„"i/;i^, -■.. o" .00,., ,;o„
Cred.tor, April ., l^Tl/by cash "mo ''/""." ^' ^^ '"d.^e,So 75'
^n»- »23.52,
ACCOriNT OP 8ALES.
-f K^ ^.-5s^^: ^^S!oi^„:^;^-ent of the ,..n,:e,
ne proceeds, which n cormulXnl^'X^f "" '^'' ^.'^^■^' ''^"'^ »»>«
to his employer or consignor ""^'^^hant or consignee wakes
aft^ ^UhCt ^d& I? jii^V''^ ^:?^'^^^^ '^ «-'^'ed
at the equated ti„,e of the different 'Tes ^''"""^' ^'' ^"« '' «^«1»
^ate. I Purchaser.
1871
Jan. 30
Feb. .s
" ](i
**■ 28
Marcli 20
April 9
May 7
" ;^o
L- N. Maguire
KeiJer & £ee
J'- A. Thibodeau
i>' L. Morris
Vanner & Simins
o. h. Ljnian
A. Hamilton
H. F. iJurton
1*. Sullivan
Description.
Wheat, white
Wheat, Ont.
Corn
Oata
Wheat, white
Corn
it
Wjieat, Mied.
190.00
704.00
880.00
450.00
600.00
S86.00
>03.2«
216.00
687.60
l$53US0
IMAGE EVALUATION
TEST TARGET (MT-S)
1.0
I.I
^1^ 1^
^ i^ 12.2
•yuu
Hi 120
L25 II 1.4
m
1.6
irvr'^
Sciences
CoipoiBtion
23 WEST MAIN STREET
WEBSTER, N.Y. 14580
(716) 872-4503
^
i-C
V
\\
^\
^■a>^- 1^'
£^.
i/i
1 I
2W AOOODNT OF 8ALM.
Charges.
ComnoiseJon on $5316,80, at 2^^
Way 30, Freight on 764 bushels of wheat,
Drayage and sacks.
Advertising in " Mercury ",
$182.92
38.20
40.S0
6.26
218.17
Net proceeds to credit of C. Morgan k Co., $5098.63
Errors excepted.
Quebec, June I, 1871.
JoHK Laird & O'Nbil.
Ex. 2. AoconKT Sat.es of 1300 barrels of flour, sold for E. A.
O'Dow 1, Moitreal, P. Q.
1871
March
«
u
23
27
28
500 I arrels Flour, at $6.00 cash
400 " " 6.00 60 d
" 6.00 60 days $500.00
Ca^h 700.00
200 "
200 "
i<
3 months
CHARnxs.
Storage on 1300 Ibis. 1 mo., at 3 cts.
CoiLiuisijion on $7850, at 2\%,
Net proceeds, due.
K. E.
Quebfc, March 30, 1871,
L. RussfiLi. & Co.
Per Louis Bllodeau.
a
as
fei
•S3
■H
eS
O)
m
h3
■<
O
<
4
ACCOUNT OF iALM.
218.17
$5098.63
t) & O'Neil,
M for B. A.
1250
7850
00
7614
75
c
03
eS
0)
CO
u
00
02
h
O
o
?-^
■o
a
o
u
c
J3
CO
00
4)
9
Z, -•
9>
OJ ■*
s
01
«
.5 2
"t/J
o
a
c8
CO
•*3
CO
■iu
ig
!J3 - 3 -
2 ■» ••
<«
—'■—<•—< i—(
-< csi esi
-H
C^ 00 »— * CVl
"— • c:; »— i ^-'
c^ r<4 ivi ivi
Cs 1— 1 Cs| •* i.-j
O C? O Oi C5
«^ CM e^ e<4 5S,
o
SM
o o
CM 5M
c:
a,
fC —
^
i Bilodeau.
.4
u
fi ;.
•il
»
m
H
i I
lil
i
!
MPTTg^ *C" i!-''nQftig*TJ ' •&
gimjg
282
EXCHANOl — fORBION OOIWi.
BXAMPLES FOR PRACTICE,
Montrea , by L. J. McGreevj A Son. Quebec, viz. : July 2 I87i to
Jo,^ Wlute. 400 bb . Ohio extra, at $8.30, 19 bbl. fine"i $5 : Ju ; 5
oSweeuey&Co 125 bbl. Canada extra, at $7.50. 'charges as fol-
«in J. i ' ^'"'S^** P,"" Steamboat " Quebec ", 544 bbl. It 16 cts.,
in Is f ^'"^?' °'' 'ilfTrV '^^'■^«"' 3 *'*«• P^'" bbl. ; insurance
ai^'fl i f «;»'"'^«'"" «" ^P?,¥^' *^ '-^^ ^ ^'^^"'••^'^ 'be net proceeds
and the date when they shall be accredited to the owner
9 T Rn /i?*^^^*P''«ceeds,.f 4 139.46; due, July 10, 1871.
.f k, ; P^ fa?*"- *?^ ^^'•on'"?' received into their store an Invoice
of Fru.t per Grand Trunk, from the United States, on acct. of T. A
Kane, New Orleans, and sold it as follows: Aug. 3, 1871, 100 boxes
raisins, at ^3, cash, 52 boxes lemons, at $3, cash ; Ad<^. 4 25 boxes
oranges, at |3, and at 60 da., 200 jars olives, at $0.50, and at 60 da.^.
Tn^'T' :^-T^''' f* *''^' ^'^'b: Aug. 9, 25 boxes oranges, at *3, and
at JO da., 20 boxes lemons, at it:3, and at 90 days; AugTlO, 150 boxes
oranges, at $0 cash llO boxes, lemons, at $3.80, Sash 220 jars
T ih^i !^0.50, cash. Sold at auction the three last items amouniino
to .>1278; auctioneer's commission on .>1278, at 3A *. deducted"
Aug. 10, 4000 lb plums, at $0.50, and at 4 Months' \7llttl
were: duties and permit $340; freight and primage, $108; cartage
and labor, !t,12 ; relunded for damages, $55 ; storafe and advertising,
$.2.54 ; commission on $4314.27, at 5 %. Required the net oroceeds
ffid when due? Ana. Net proceeds, $3531.22; due, Oct. 24,*1871
TABLE
OP FOREIGN MONEYS OR CURRENCIES, W..fl THE
PAR VALUK OP THE DNiT, AS FIXED BY OOMMEROIAL USAGE.
Cities and
Countries.
Argentine Rep.
Austria.
A zores.
Baden.
Batavia.
Bavaria.
Belgium.
Denominations and MetaL
I
100 centesimos = I real;
8 reals = 1 dollar (silver)
60 kreutzers = 1 florin '*
120 " = 1 rix-dollur '»
60 batzen = 1 ducat (gold) =s
1000 reas = 1 niilrea (silver) =
60 kreutzers = 1 florin " =
48 stivers = 1 rix-dollar '• =
60 kreutzers = I fl rin (silver) :
crown, "
dacat, (gold
100 oentimM = 1 frano (ulTer) ■
Value.
$1,016
0.485
0.971
2.278
0.830
0.397
0.782
0.395
1.072
2.274
0.186
nand 4 Co.,
2, 1871, to
$5 ; July 5,
larges as fol-
)1. at 16ct8.,
; insurance,
let proceeds,
10, 1871.
e an Invoice
;ct. of T. A.
, 100 boxes
4, 25 boxes
\d at 60 da..
3, at !?3, and
0, 150boxee
b, 220 jars
i amounting
, de.ducted ;
riie charges
08 ; cartage
advertising,
let oroceeds
24,'l871.
rHB
Ali ns^QE.
Value.
$1,016
0.485
0.971
2.278
0.830
0.397
0.782
0.395
1.072
2.274
0.186
«xoiiA:,MK--roREioN concB.
Cities ftnd
Countr'es.
Denominatirns and Metal.
Bolivia.
Brazil.
Bremen.
Bruno wick,
f^hili.
China.
Columbia.
DarmstiJt.
I^enniark.
Egypt.
England.
France
Frankfort.
Genoa and
Piedmont,
} ^ r^M= ^ dollar (silver) -
I doubloon r„\ul ~"
bnnkt'tcT "° ^"''''"' ''''■ «'-ling per milrea in
Spr:firi-?--OP-0 core.
j 100 cents* I dollar " -
i . doubloon Ccrnlfl^
'Oca«h,,candaruif?Jern.)
^ Thr "i"*^®' 10 mace = I tael i C'^'Iver)
for'?n?|;?„^K?,a^r'^°"'' ^^- «d-. -re orl«s.
j ''^ ^.^^'f .-^ 1 doUar (silver) -
i douWoon (sold) .
60kreutzers»Ig„iMer(„,ver) =
n.ark,rri:lrarUltt:i^^^^^^
Frederick "or fcro hh
^ Jxchange on London U 9^n,.bank~' daler for £1
2r.f rer^rK^f t<^-'^) f- f- 2.60 to fr.
r^reaTSerlJ^^'^^'^^'^-'^-.i
i'.xohan<re on r.nnHnr> on
for £1 .teWing ^' ^'^ ?'*«'«•"' "o^e or less.
Exchange on Paris ".ll •> qoa
f l2penc^=rSC"320a.pperl00fr.
I f/l"i;ing8 = i;iet;i.ling.C(.oId)
I .£1 or 1 sovereign = C
I n'New^tr'^"" '^„*^-««5 in Canada,
ill i\ew icork u is usually 7 to \i),- . >
sterling in London is wor'h «4 j//' t'^*" ''"'""^
addiUonal, in New York * ''' '»"'i ^ to 10 %
100 centimes =1 franc (silver) =
^xchange on London, fr. 25 50 fnr J^i =» .•
^ Excha^nge on Na. York f^d^^^a^ 1v.^"& to
ti;^^^;;^:^rS; or tloria (silver) =
£1 8te,lin|. ^*"^ ^^-^^ '"•'^' "Hre or less, for
Bxdiange on Pgd*, 31 y^ ^ ^^ ^O.
28a
lVali»*.
, l.&M
)15.580
0.830
0.788
0.692
1.011
15.660
« 1.480
1.022
15.617
0.397
1.051
3.932
4.866
0.186
* 'II
■■ 'i I
'
II-
;• 11
h ft «
i 1 '' ' I
■ 5
Hi
284
EXCHANOB— FOBKICMI OODII.
4;. ^1
Cities and
Countries.
Greece.
Hamhiirg and
Lubeck.
Denominations and Metal.
VaIm.
Hanover.
Hindot-tan.
Holland.
Italy,
Florence,
IjOghorn,
Lombardy, [
Venice. J
Japan.
Madeira.
.Madras.
Mecklembur2.
Mexico.
Monte Video.
Naples.
Norway.
Persia.
Peru.
Port,u<'ul.
100 lepta = I dragma; 1 dra-^nia (silvar) -
( 12 pfennings = 1 skilling; 16 .^killings > 1
< mark banco (silver) -
( 1 ducal (gold) =
less, tor jbl sterlin'T.
^^^^^^''ange on PfTfis, fr. 1.60 to fr. ].70 per mark
j 80 groshen = 1 florin (silver) »
I ;^0 groschen = I thaler '< >
j 12 pice = 1 anna; KJ anna« = 1 rupee(sil.)-:
( 16 rupees = 1 niohur (gold) =
lof ^"''"r?? "" London, at^ Uoinbay, 28., more or
less, for 1 Comiiany'.s rupee.
j 100 cts. = 20 stivers « 1 guikier or florin
( (Sliver) =»
Exchange on London, 11 g. 80 ots., more »t lots,
tor ±1 sterling. '
guHdeJ""^^ °" ^'"■''' " ^''* ^" "*'•' ™°'^ " '"«' P«'
100 centesinii = 1 lira (silver) =
Fxi'hango on London, 30 lira, more or less, fcr £1
}V ■ '"/«"' '° "nd Milan; 30 lira, more or less, per
±1, ui Horence and Le.,'horn.
Kx(;han,^e on f'nris^, fr. 85, more or less, 100 lira, in
V.nicoandjMilan; 80 to 85 centimes per lira, in
J lorence and Leghorn. ^ '
10 mace = lOO candarines (silver) —
1000 reas = 1 milrea <* »
42 fanams = 1 pagoda (gold) -i
1 florin (silver) -
S S reals == 1 dollar « „
^ 1 doubloon (gold.) ■=
J 100 centesimos = 1 rial; 8 rials =- 1 dollar
( or 4 pesos duro «■
^^Kxchange on London » 52d. aterling for 1 peso
' 10 grani = 1 carlino; 12 carlini = 1 scudo
(silver) =
10 carlini =. 1 ducat; 3 ducat = 1 ounce
(golil) =
1^ xchan.^^! on London, 575 grani per £1 sterling,
hxcha.igo un Paris, 22 a 2a grani per L fr.
V lb skdliiigs = 1 mark; ) , .,
I 6 marks = 1 rix-dullar j ^^''^^^) =
100 n)aravodis= 1 tomaum (gold)
1
8 reals = i dollar
(silver)
'100 reas == 1 cruzado; 1000 reas — 1 mil
rea (silver) •=
1 crowu (gold) «■
0.1 cs
0.3»0
2.25T
0.04)
0.694
0.445
7.109
0.400
0.16S
0.T60
1.000
1.H40
0.641
1.005
15.534
1.000
0.960
2.485
1.051
2.233
1.005
1.120
5.813
Cities and
Countries
■XOHANOR-FORKICN COINS.
Denominations and iMftai.
285
iValue.
Prussia.
Rome.
Russia^
Sl Domingo,
Sardinia.
Saatony.
Sicily.
Smyrna an(i
Ihe Levant.
ISEF?^"^-":s-.
I grosjipn:
;io
Irea.
per
^Tosjien =
Spain.
for^J?t"r; ^°"^°"' « '»>»'-■' 25 ,.., .ore or ,es.,
b.e'^Sr^^'^ "" ^°"^-' ^-'o- ^^^'^^ to 42C1. for , „>„.
roS'sK."" ^^"«' ^-- ^- ^.10 to 4.20 per
100 centime.s =. 1 dollar =
100 ccntesimi = I lira Csilvor'i :.
(iTo^oT'"^- °" "'""'"'^ ^"'^ ^-'« - for Genoa.
ilf'*'^'''"r ^ thaler ^silver) -
ii-xobango on London, thal«. 0^'' " ^
or less, per £1. ' '"'"'" -^ 'iroschen. more
j30/ari=lL';^^^'^^'7~'--li(s^^^
Like Constantinople. " ^^ ~ i
In the Levant are likewise u^o.i f ,
Spanish dorars and Dr.tch H.^n •" ' """^'^ «^'ent,
ducat?. Likewise Ge man r^""''"'^ '""' '''^^'''i'i^"
$0.96 to $, being sul?:7,t:S^ tl.aler =
r 4 reals vellnn — i . f * * par piaster,
I 1 doubloon /• . ,. ^
I 1 pistole ^"''/.'J) =
Exchange on London, 40d sfori;„» ' "^
per peso^duro or Spanish .oiuf^'g.-- ^i-'
du^^Sar''''"^-''-^-^^'^^^- 5 30 per peso
'C4S.kHlu^.e marks. I nx-doilar specie
( 12 n.arks = J j^cat (gold) =
S:o::K°r;^^^if^^'"f-^-on.^,«^..
Kxchanc^o ot Ba«Io on I i'"'"'"^ =
le«8.for£l. '" °" ^^°"don. fr. 17.5, more or
li'xchange on Piu-iH fv i -„,
0.227
1.000
0.7;j4
o.:i«i3
0.186
0.61)4
O.9.S.)
2.4U0
1.059
2.267
(
286
EXCHANGE — FOUaiON OOINB.
I I
Tripoli.
Tuni8.
Turkey.
Tuscan V.
United States.
Wurtenibur'T
120 paras = 1 utchlik (silver) «
16 carobas = 1 piaster '* »
100 aspers = 1 piaster '< =
20 piasters = 1 yorniilik (gold) =
Exchanj,'o on London, 104 piasters, more or lew.
for £1.
Excb. on Parirf, from 400 to 410 piasters for 100 fr.
' 12 soldi = 1 florin (silver) =.
1 crown or corona '* =»
1 ruspone (gold) -=
1 sequin << m
NoTA.— For Exchange on Lonaon and Paris, f«M
Italy.) ^
i 10 mills = 1 cent; 10 cte. — I dime; 10
I dimes = 1 dollar (gold) «=
£ ftO kreutzers = 1 guilder (silver) «=
< 1 crown •< oa
( 1 ducat (gold) =.
Excliango on London and Paria, the same m for
Frankfort.
0.149
0.124
0.026
0.877
0.262
6.92d
2.301
1. 000
f..H95
1.070
2.236
EXAMPLKS FOR PRACTICE ON KXCHANGE (see 406).
. « / '^''^^- "^^ Toronto cost £187 lOs. in Liverpool, exchange being
at 8 ^ prennum tor sterling ; required the face of the draft ?
^ Wiiut IS the cost of a draft on St. Perersbouri,' for 6i)1.5 roubles
50 copecks, exchange being at 74 cts. a rou ble ? Ans. $5 1 1 7.47.
3 Received of J. Walter & Son, Glasgow, a bill on Messrs. S. Ross
t?Z'L f^"^''^^'-^'''i^^'^^ ^^'' W^^^ ^«« •*« value in Canada
currency, the premium being y% in favor of sterling currency ?
A WK * ■ .1. ,• ^"»- $5540.833 + .
4. What 18 the value in francs of a bill for $976.60, allowing a
premium of 3 ^, and ;-i^ fr. to the dollar? Ans. 6359 fr. 29TeQf
o. A merchant in Halifax has 8250 guilders 5 stivers due him in
Amsterdam, and requests the remittance by draft; what sum will he
receive, exchange on Canada being in Amsterdam at 2^ guillera
^ . . , •:, . « ^ AnS' $3666.77+.
6. A broker paid m Ottawa $8030 fbr £1650 draft ou Dublin- at
what percent, of premium did he purchase it ? Ans 91%,
vT^l , ^' is the value in Canada currency, of 2000 florina in the
Welherlands, at 2^ ?« premium ? Arts. *.S20.
». Iwenty days alter the date of a draft drawn at Genoa, Dec. 3
ib. I, at muety day-s, for 1820 bras 15 soldi, C.Jenkine to whose orda
.'t was drawn, requo.sts payment, and proposes for prepayment a
iisoount of 3 %. What id the value of the same in Canada curreacy
alldwing that the «oroDa bears a premium oi5%^ Am$. $1948.11.
ARBITRATION OK EXCHANa*:. ..gy
lor tin. .„,„. .,a the rate of Sd. 'ter n / ni ?L 1''/ '''" P^'-ol^ased
'f'- f- O'lJrieiK.fMontro'il 1>^;. • . ^"*- i^"'Jf"» liras.
;;; :£<-0(), to IVne & ^^^'1i,^^"f "S' , ^ '^'^^^ °^<^ats. val„e,l
>aoetlK^.a..etoU;ra£^;;,l';^^^^-^i^-Krauss, 11301.50, and
Toronto, Sept. 14, 1871 Yours &c.
„^Naple.s, Jan. 3, 1871 ^*'"'" °^^ 'T""''''^
What i.s the value of ihe above ,^rnf> v "^'^ "f'^^« * Omim.
■'^ dwoouut of 2 5^ being a lowed for n^. '^ ^'''^ "^^ '^■^^ ^^'^ ^^te, at
'"andingaprenuumofsiT Prepayment, and the scndi c^,»-
^w«. |208;igJy.
AliBITliATION OF EXCHANGE.
Putl^tct't^e'^b'tl^^^^ - *^« P-eas of co^.
clrawn on one ^r .norr"t^re!l1i;r&" ^' '''^ °'^^°^-^«
?. "Iiat must a neraon in ir!»> °' ""= ^'o »f '2-5 guililen tn f 1?I
Ol'KRATION. *'
Or thus :
' ^ I $40 X 1.096
• * = $4«7.2fiL
-Analtsis.— Since it takes £i in
12.5g,ade„on Amsterdum.it^m
'^'^^ T2T *" ''"y a «>ill for 1200
guUder8;bnta bill on London for :£!
costs m Montreal 1^x1.095(42?).
Moi?l!S! "•"""V"™ ''• draw a rer-
Meal line, ^d pli^f, .qaividento wUk
M
ft
268
ARHITaATlO.N OF RXnHANQK.
I :'■
Squared a?i,Mv^r^r°/'^ °PP^"^ ""*> "*^«'' »>«'^"nl''(f with that oflh.
tennru^,?r ??i ^' * *•• ^1'. '":"!«"!«"<'<' i^ 'l<"n"t«d by «, and so arrange tha
first on^lr St .T"'k?",'''\''''^' '^'^' ''° "f 'ho same denoraination as the
■0 on should there be a Enrcator number of terms.
Eof. 2. A morchant in Toronto wishes to remit 8000 franoa to Pari«
Jy circular o.xcl>an-e throu^'h Lotvlon. If exclnn-e at Toronto on
1 ans 18 at the rate of 5 francs :{0 cc-ntirnos to the dollar, that at
iZu ,r^" '''"' ^^'''^ "^^'^ "'■ ^^'' '''^"^8 20 centimes to tl.o £, and
tlmtHt Toronto on London at 9 % premium, how much le-^.s thin by
airectexclian^^e, will It coat him, kuowing thut he pay.s his a^ent in
Liondon i 91$ commission? °
A\Ai-YSi?.— The cost of the 'lireot
exohanj^o would be an many ilollnrs
as .SOdll contiiitis 5.3 == lo()'.).43.
To (ind tlio cost of the oirculnr ex-
chan'j;o we [iroooed as in A*, l.ex-ept
that in ihis cajie the factor I -(- ^ c^
== 1.005, iiuiift bo in-iluded amoni,' the
ftictorfl on iho right of the virtinal lino
to cover the commission paid to the
agent in London.
OI'EIUTION.
W = *150',u;i + . thecostof
direct exchuncje.
t:t I HdOO fr.'
26.2 fr. I £
9 £ !P40 < i.o<>
' 1.005
$T = IS14S6.6I +.
$1609.48 — *148().f;i = ^522.82.
— difference in favor of indirect
exchange.
50« lltiLE.— 1. Draw a vertical line, and place the equivalevt
sums with the characters denoting thrir rer,pecfive units direetJu
oppns%teeach other on the left and right of this line, representinq
the required sum hy x, and writing it first and on the left, and
arranging the other terms so that the second on the hft shall he of
the same denomination as the first on the right, the third on the
left the same as that of the second on the right, and so on.
II. When a commission is allowed for remitting, put 1 plus the
rate on the right (Ex. 2) if the cost, and on the left if thr proceeds,
0/ the^ exchange is required. When a commission ' ts nUowed for
drawing, put 1 minus the rate on the left if the cost, and on the
right if the proceeds, of the exchange is required.
III. Divide the product of the terms on the right hy the product
of the terms on the left, and the quotient ivill be the answer.
rinI^Z'"Jh-rP°''T'"'"^''i'P''''^«"'''Soon the price the agent who
T^h^UL f^u^t,"/^'"'^''"^^' ""'^ oommission on drawing i. a percentage
on the value of the bill at the place where the agent besides. t-ain.ige
EXAMPLES FOE PRACTICE.
h When exchan-e at Quebec on Liverpool is at 9 % premium, and
at Liverpool on Brusseln 25 francs per £ sterling: what wilUe^he
Ilh that of the
so arranjje tho
aination as tho
the right ; and
inca to Parifl
Toronto on
lar, that at
[) tho .£, atui
le<s th m by
liii) agent in
; nf tho 'lireot
many ilcillnrg
10011.43.
3 circulnr ex-
1 A'iC. l,ex.-e[)t
tor I -\- i'.^
led arnoiiL; the
lu vortical lino
1 paid to the
', equivalent
'ts directly
epreseiitiiiq
^n le/t, and
shall he of
lird on the
on.
1 pins the
I- proceeds.
Mowed for
ind on the
he product
wer.
8 agent who
b percent:ige
nium, and
^ill he the
upsda for
7.64 + .
AllBJTRATION OF EXOH.VNOF,.
28')
[1.0 ™.„ „f 25 rranJ h! Si ::■ t''",' , T'"", ',""'''.'" ""' l'-i» '>'
ami ren.it,, the ,Hiiie to l,h u -,.„ „ p i'"'';'"' "' ' V""»<"» "f » %
i *, '.ow ,„„„,. ,„„, Z:^ e„'l-- ^.n.i .1.; «l,i.l.^- |;;H,r,*,.„,,e
•''• When evohinrfo ;« c. i ™ '^^'«- $33(i,".s7 ;
on H„,i,,„ aTl'^" -: i4"„ :,f ^? ™ J;X'" "."' •■ '^ '"^""""'' »"'l
Toronto i, at parri.ow m ,oh betler i/th ^ " ■, '"■'™ ''"'"''"' ""'I
n.oney, allo"„ing *^ to be eu ,al VTp"?""' ""<""" "' '° «'"'i"S
pound stcrlin-? "•""' •" '^ f""'««; »">! 2l ihinos, to 1
-'Miv^"e"„L?is: rnd'TiS", °" """"I" ^- -'^'-^
(liscount; howmuchwllK-. IT *^""'^''' <^" UamiUon Lsl'^g
af 4 56 Prerni'm allow J'lLfi;;.'^^*^ «» '"" '^gent in Tort.^to
di.scouatrbrokera<.eat i2? ^ "^ '" ''''*'"' ^° Humiltun at 1 ^g
9. A banker in°Quebec romit^ If - .w v, ,. . '^"■'- *' ' -f*-"^ "- -
as follows: first to Lyonrat 6 fra , .,^0^* ^'^""'^"'•g- ^y arbitration,
Hamburg at 181.50 fmScs per iSo ma,lr";l'"'' ^'' ^' '' *^^"°« '^
3o stivers per 2 marks- then J !^ ^f f' *^«nce '<» Amsterdam at
sterling. &ow "^S «le Sg ^^ne^tu h?."' ''' ,^^'r" P" ^
burg, an,, what .vill be ^i.^^:^;:^^^ ^I^tl^^!-,
4«, S Proceeds in Etiimh.,,,. ^..1,^ prem urn I
Ans. \ P'-?ceeds in Edimburg, d^ ""Tu
§ Gain Kv afKW..o#.... ° i , , .-: .*'?'
;" Ottawa, and for that purSbrs a ll^nT^'l'* "'^^''^^ ''^^^'''^^
the rate of 2 francs per mS banco wS i ^-^^i^ange on Paris, at
brokerage ^%. Allowing Sfi tTrofl' L*\ ^^ '"""^ards to Ottawa,
ooet him ? ^"ow»ng *J6 to 100 mark bancoe, what di.i the hill
12. A of Barcdona owfti H «r r. . '^"'' 1^884 francs.
eeionaoww B of Urerpool, £lyoo. BofLirerpooJ
m
sLai
r
290
ABUITRATiON OF MKUCUANDISR.
(-'■'
?wn 4 '''^'""*?'"^*'"' ^ ""^ Amatenlam on I) of Bonfeaux, and
DofnoHeaux on A of BarceJona. Allowing £1 oxohan^.e" f .M2
flor.n«; I9f!onnHfor4()fmnc«. and 100 frHMO« for 1 !> Spun idoN
lar«, how many .loNars will pay the bill ? ^„/ -J«!| -Id
I.^. IwiHUtoreinit fruin Glasgow to Qupboo £127:. I "..s.' VVlmt
w I r.e Its value in Canada ourn^ncy, reinittin-,' tlvrou-l, r'aris at tlie
fo iow.ngrates: £1 eqnal« 26 francs 80 centimes; and 5 francs
ce.tnnefl, equal SI ? ^„,. $fi2l0.25' .
14. A merchant in Halifax wishes to remit to London !?f)2r)0 so as
to receive the largest possible returns for the name. Ff he reinits di-
J 2 ^TM ?V'® ^^«''''">? currency will command a premium of
f M 'Vn "-*' f't*:'^; 'f '""^t ^>P at the rate of", franca 20 centimes
o the dollar, and 2., francs .so ©entimes to tlie pound; but if ti.rou-h
per A4. VVhicli iH tlie moM desirable cour-e ?
ylrj,-*. The course through Hamburg is preferable by £8 1 1 31 to
the direct course, and by £39 23, to that through France.
ARBrTRATION OF MRRCriANDTSE.
50r Arbitration in Merchandise consists in compnrin-
tho wci-hts and measures of different countries; also, in Hnrlini^
rem the value of any particularweightor measure of one countrf
the value of the corresponding weight or measure of another
country.
By tlio operations herein involved, the merchant is enabled to
determine in what way he can most advantageously export or
import any species of merchandise. The operation obviously con-
sists, not only in the comparison of the weights and measures of
different countries, but also ia the exchange of ourreneies.
tablb
op the principal weiohtb and measuee8 of the most
IMPORTANT COMMERCIAL COUNTRIES IN THE WORLD
REDUCED TO THEIR ENGLISH EQUIVALENTS.
AUSTRIA.
(Chief commercial cities, Vienna
and TiiiKnTK.) i
100 commercial lb. = 123.6 Avdp.
i Htaro = 2.34 Winch, bu.
1 polonick = 0.861 " "
1 aimer = 15 wine gal.
1 bMril* s 173 " •<
1 ell, woollen meas. =2C.6 in.
1 ell, silk =2i).2 "
BADEN AND BAVARIA.
(Principal com'.iercial city,
Alusuuiio.)
I pound = oiU) gram. French «
1.25 lb. Avdp.
1 Aug8b«rgmark=3643gr. Troy.
>rtfeaux, and
lanires for I 2
Spanish <lol-
l«. !?{)I2I1.
l>s. Wlrat
Pari.H at the
5 francs MO
210.25 f.
?r)2.')0, Ko a.H
10 rejnitH di-
prcmiiinj of
20 centimoH
t if tlirough
nark ban COS
i 11 ^, to
oe.
comparing
in (in ling
le country,
of anotlier
enabled to
export or
iously con-
leasuifes of
es.
IE MOST
= 2C.6 in.
= 2a.2 <'
ARIA.
al city,
French «
t gr. Troy.
= 11.8 in.
= .33.75 in.
= S-Tf) fiH't.
= 6.i2r)
I foot
1 elJ
1 klafter =r fifrpt
1 flche/fi?! for c<,rn
1 eitner of wine
1 maan
. ."RLOIUM.
{Hrincipnl commercial city,
Antwkkp.)
WWWV WrrORTR AlfD MLARim*,.
im.
= 14.062 .^al
= l-'^TDpint.
WeightH an.l Meanuros the same }
M in France
. , HRAZTL.
(/ nncipal commercial citu
It'o l)K JaNKIIU) )
Weights an.l Mea^nres ti,e san.e
as in Portugal.
(U/ie of the/our Free Cities ef
Germany.)
{ f ""'' = 1.09 a,.
I centner __ hq ^
1 viertelofwine =1.9.-, .^.J'
1 anker = 5 vierteln
1 oxljoft .-- 6 ankers
1 scheffel of grain
1 last = 40 shettel.s
1 s;one llax
CHIXA.
{Principal commisrdal city
CXHTOS.)
}f"^, =i.;{;nb,
* P««"i = l;^3.3;J ib.
211
!&=:i?.^"^,,7,V«^'•
— -4.00 in.
KfiVPT.
(FrtnctpaJ nmmercial city
Al.K'XA>DHIA.)
1 rotolo Ajrforo ~ j ,r, ^^
rotoJo zaiiro
= 3;5..]:j n-A.
y.G.l gal.
= 5^ gui.
= 2 l,u.
= -SO. 70 l.u,
~ -'0 11,9
I covid
= U.62
lU.
CUiU.
{Principal commercial city
Hatana.)
.quintal = 101.75 lb.
1 arroba of wine = 4 1 ^^j
1 feuega of grain -'alu'
^ara ~ 33.34 in'
DENMARK AND NORWAY
{Principal commercial cities'
LoPKNHAGKN and Chujstiana.;
fP'-"-^"'^ =i.iu"ib.
i centner = lOU lb. = lio.2,s|(,
I riertel of wih = 2.04" ./al'
I anker of wine =' lo ^ai
1 rotolo za(lino =r 91 -n-yr ,.„
rotolo ,n urn = 2(1.714 oz.
I 'l"'ntaIcom.oinC!iiro=l(i;j,,;|i,
f^ = ;;.2,{:. II,. Tr.'
-Inigma =,,.,.,,. ^,^^,^^
pik ot corn = 2,i.8 in.
robebe ot corn ~ 3,; „j,,^
^ "^''^'^^ = ;!y gal.
^„ . EN'nr.AND.
{I^nncipftl commercial cities
Lo.vDoN a?)rf LivKiiiMioi,.) '
The EngliHJi Weight. m,d Meas.
urea are tho same us j,; Canada.
FRAN(^E.
{Principal commercial cities,
rAiiis. Lyons, and Maksku.i.ks.)
Weights and 'Aia-\\i\-<,see p. 1 2(;,
FRANKFi)RT .„, the Main.
AND TH!-; 8oL-MI|..(iX I'AKTrf OF
(-ieUMAXY.
1 II'. heavy = iT.G.'j 02. Avdp,
lb. light = 1 -,.0o oz. Tr.
[ '"^"'^ = J25 oz. Tr.
1 cwt. of 100 heavy, or lua li-dit
lb. = Hi Jb. Avdp.
1 carat of jewels = I.32I dwt. Tr.
'•f^^ =11.25 in.
I ^1' , . = 21.555 in.
1 J?rankf. Brabant ell = 27.(;GG in.
I maker of corn = 3.1.5() bu.sji.
1 sinuner " = (i.312 gal.
i uiaasof wine ^ 3.156 pints,
f J?^"" - 31.312 gal.
I tuder - 6 ohtns ^ loT.S?;-; gal.
HAMliCJRG AND LUJf>.CK.
{Commercial cities o/Uki;kany.)
i P^^'iiJ - 1.068 lb.
%
i [■
r.
mh.
B92
rORKfON WEIGHTS AND MRASUIUCS.
' I
100 commercial lb. = lOiJ.838 lb.
} '■"^^t «= 11.289 in.
1 ahrn oJwiiie ^ .S8.2o t^al.
1 ftuler = (j Hlini.s = 22D.5 gal.
I last 01' grain = 8i>.64'bu.
1 stocks l\ laht = l;u.4 bu.
1 Brabant ell = 27.58 in.
lilNDOSTAN.
(Principal commercial cities,
BoAiiJAY, Hkngai,, Cai.cltta, and
Madras.)
I maund «. 74.625 lb. Avdp.
I seer « 29.875 oz. Avilp.
1 Sicca =x 178.666 gr. Tr.
1 cubit, or 1 covid =^18 in.
} g"z = 36 in.
1 C0.S8 == 4000 cubits = 1.125 mi.
1 palhe of corn - 9.5 lb. Avdp.
1 candy = 500 lb. Avdp.
1 gareeofcora « 135 bu.
1 candy of corn = 24.6 bu.
HOLLAND.
{Principal commercial etfiM,
Amstkkoam, Haaklkm, The
HAeiE,itoTTBRDAM, LbJYDEIi, etC.)
|f"?ot -11. 142 in.
\ f " , = 27 083 in.
1 last for corn « 85.25 bu.
1 aam of wine =" 41 gal
1 »at = luu kan - 1 hectol. Fr*
^ 26.42 gal.
1 muddle = luO hop- 1 hectol.
^ 2.84 bu.
1 pound . 1.08 lb.
1 i^r. kdogramme — 2.20 lb.
1 last, marine -: 4410 lb.
LOMBARDY (Italy.)
{Principal commercial cities,
VKNJCi; A; Milan.)
1 libra = 1 kilogramme =» 2 lb.
3J oz. Avdp.
The Mea.Mures are equal to th«
French.
NAPLES (Italy.)
{Print- i I d commercial city,
Naplk.s.)
I rottulo = ],yg ]^,_
I cantaro groeso =» 100 rottolo =
196.50 1b.
- 106 lb.
- 42.75 gal.
= 264 gal.
= 52.20 bu.
= 8C
ID.
1 cantaro piccolo
1 aalma of oil
1 carro of wine
1 carro of grain =
1 canna
PORTUGAL.
{Principal commercial city,
Lisbon.)
1 libra or arratel = 1.01 lb.
I arroba = 22 arratel8 = 22.2G lb.
1 quintal = 4 arrobas = 89.05 lb.
100 libra.sor arratelo= 101.191b.
I almude of wine = 4.37 gal.
1 tonelado «= 227.25 gal.
1 Canada . 13. 06 pints.
1 moyooftorn — 23,03 bu.
1 vara = 43.20 in.
PRUSSIA.
{Principal commercial city,
Bbki.in.)
1 pound = 1.03 1b.
100 pounds Dantzic = 103.3 lb.
I quintal. = 110 lb.
1 eimer of wine
1 ahm
1 sclieffel of graua
1 laat of grain
1 Berlin ell
1 Prussian ell
RUSSIA.
{Principal commercial cities,
St. PKTERSBLRa and Warsaw.)
1 pound (funt) = o.90 lb.
1 pood = 40 pounds = 36 lb.
100 pounds = 90.26 lb.
1 wedro of wine -= 3.25 gal.
1 eorokovy = 40 wedros = 130
gal.
1 chetwert of corn
1 arsheen
1 sashen
SARDINIA (Italy.)
{Principal commercial cities,
Gkkoa and Tl'uin.)
1 peso grofiPo (Genoa) = I2.1(J6
oa. Avdp.
1 libra (Turin) = 13 oz. Av;Ip,
1 pahiio (Genoa) = 9.75 in.
1 minaufcorn '< = 3.50 bu.
1 barileofwine " «= 16.31 gal.
113.42 1b.
= 18.14 gal.
= 39.66 gal.
= 1.52 bu.
= 91 bu.
■■ 25.5 in.
= 26.28 in.
= 5.95 bu.
= 28 in.
= 7 feet.
bar le of oil « = 14.35 „al
I P|edelipran.lo(Turi.i)= 20.5 in
f piede juaneJle " « 12 75 n
raso (ell) . ^ Jlf j^'
J ^acco lor wjne '« = 25.5 gal.
.-, . SAXONY.
(I^rtnctput commercial cities
IJRESDEN and Leipsic.) '
{pound - 17.625 „..Avdp.
1 ell i'.»75 jij.
J^c,,*,ofco.„ .-|j-
"<a„,.. Mitre „ ufA'
OMYKNA AND THE LEVANT.
} ^}'\ = 3.25 lb. Tr.
Icantaro - 127.5 lb. Tr
Irotolo =lG..^3oz Tr
1 drachm ^ 49.6 gr. Tr.
Ikillowofcorn = u"25U'l"
. SPAIN.
(Principal commercial city
Madkid.)
P'^""d « 1. 01 11^
1 arroba= 2i- pounds = 25*.38 lb."
1 quintal = 4.-rroba8 = 101.52]b
i cantaro or airoba of oil =. 3 75
gal.
4.25 gal.
Iraoyoofwine - 16 arrobaa «
08 gal.
1 botta » 38 arrobas of wine ^
•^"aarrobasofoils. 127 5„al
Ifanegaofcorn « 1.^7 1m"
cah,z= 12 fanegas- 18.91 bu
1 vara or yard - 33.37 in!
irr. ■ r SWEDEN.
(.Chxefcommer.eity, Stockholm.)
J P°""*^ - 93 Ih
* pound of iron • 0*75 lb
'ORBIQN WFIOHTS AND MBASURte.
293
1 aiun -?'"' - 20-75 gal.
1 anm = 2 eimers = 41.50 gal
P-pe=3ah,n,s =124.25^1:
tun or barrel ofcorn= 4.16 bu.
*^' = 23.36 in.
. SWITZERLAND.
(Principal commercial cities,
(^imtA, Eku.v, & Basi.s.)
110.25 lb. Avdp. ^
} lb. = ikiIog.= i 7.625 oz.Avdp.
1 foot = 0.;^ mo»^» _ 1 1 0/ .*'•
0.3 meter
11.85 in.
= 2 feet.
= 4 feet.
4.I2,> bu.
3.5 pinta.
7= ;!3 gal.
3.5 pinta.
1 foot
I ell
1 stab or staff
1 malter of corn
1 iinniir of << ,
ohm of wine
- maas << ^
TURKEY.
(Principal commercial city
Constantinople.)
Jpound,chequi,-ll..33uz.Avd.
^^^ « 14 02. Avdp.
1 pile, commercial = 27 i,i
I kilJow of corn — 7 5 <ra.\
1 fortin = 4 killowa « 30 °al*
1 almud for liquids — I.37 |al.*
^ . TUSCANY.
(rrinapal commercial cities,
i'LORENCK and Leohokv.)
1 pound « 12o2.Avdp.
}?rS -^^5ib.Avdp^
loo ''' , • , - 1 "^iJe 48 ;d:
lOOeacchiofcorn = oqi [J
bOquarn.zziofwine- loV^gal.'
1 ban le of oil «, 7 ■' g^
, UNITED STATES. '
(I^nncipal commercial cities
NbwYokk Boston, Chicago,'
NewOki.kans, etc.)
The Weights and Measures are the
1 auker of wine -. 1 n sf ' i ^*'*' ^'^'^'^^'^ ^" ^ ^^^i^nt
^^^ _ -"••^•'^ gal. I same as in England.
he same as those of Sll onh^« '^'l"^- ''^ "" "^°'*« of Sp^nro I i nz^l
United States, and of H yT^esaS ^n'S ^r^^'"^''*^'^" Provi ce . f .hl'
»^ii*,t. a« .bout 8^. ''-"'^SEu^?:^?e•«^^^^^^^^ -«!J^-
M
; !
1
f
i
291
FOREIGN WEIOHTS AND MEASURES.
llicinetrio system has of late been adopted by Spain and Portugal, to the
exolu-ion of other wei;,'hld and inea-iurcs. In lMl4, it was legalized in Qreat
i5ni|i!n; and its u^e, cither ii« a whole or in. ■'ome of its parts, has been authorizud
111 (Jreece, lloilaiiii, Italy, Norway, Swolen, Mexico, Guatemala, Venezuala,
I'.f iin.lor, Columbia, lirazil, Chili, riim Salvador, Argentine llepublic, and tb«
The following oxdinplos will etnbraoe operations analogous to what we have
already had, in addition to the exchange of weights and measures.
Ex. 1. A Montreal iiiercliant iiiiporlH from Holland 2550 ells of
linen, which he finds costs hiin 2 florins per yard. In payment ol the
tifinie, he remits throiisxh London. The amount of the remittance is
required, allowing 9^9^ premium in favor of sterling currency, that
it I exchanges for 14 florins of Amsterdam, the agent al Londoo
charging \% commission.
OPERATION.
2550 ells
2.;{ X 4 fl.
£1
$40 X 1.095 '
1.0025
$« = $2725.176 + , Ans.
% X
.3 ft.
14 fl.
£9
Analysis.— Since 1 oil equals 2.3 ft., 2550
•Us X '"i'" -i- ^i == the same in yards ; the
yards iinilti(iiled by 4, equal the whole cost
in florins, which, divided by 14, are reduced
to sterling currency ; and this in turn ia ex-
changed to dollar.'! by multiplying by 40 and
dividing by 9, and this value i.s increased
*i% l>y multiplying by 1.(195, and tinally
the brokerage is added by multiplying by
1.0025.
£;.... 2. A merchant of Toronto ,^ends lard to Hamburg at f 10 per
cwt., and orders remittance throuL^li Liverpotd, expen.se of remittance
to he paid by N. Ashley of Hamburg. Allowing !iK7 excliange for 20
mark l.ancos, and l."^^ mark bancos exchange lor £1 ; also, that the
bterimg £ bears a premium of 9 96 in Toronto, and that 105 lb. Ham-
burg equals 112 lb. Toronto. Wliat is the cost of 1 lb. Hamburg,
charges for cotmnissioo being 2 %, insurance 1 %'i
AVAI.T3T8. $10-1.105 =. price of 1
lb. Hamburg in C.ma la currency, which
X j^g or £1, flinl j.'Jg makes the re-
quired deduction in favor of Sterling
currency ; then the remaining value X
j^n, is increased by the percentage of
expense, siml thatvuluu so increased X
13^ or y ia exchanged to mark baniofl ;
ifJ^l =1.3i^ inark.s, £7 =. 96 m.irka;
and the marks X l<^ skill, k 4 fikilliogs
6-f- pfenniugs per lb., A*».
OPEKATtO.V.
105
40
109
100
7
X
10
9
100
103
96
16
4 skiilings 5+ pfennings
per lb., Ana.
EXAMPLES FOR PRACTICE.
1. A merchant in Quebec ships 2000 lb. of butter to Bremen, and
Bells the same at 12 grotea per Bremen lb. The total receipts are
remitted to Paris, and the merchant of (Jiiebec draws on his agent
there. For how many francs at 6.25 to $1 mupt he draw, allowing
hie agent in Paris charges 2 % commission ? Ana. 1 290.44 v fr.
2. L. Enrigiit of Halifax imports from Lisbon 18 quintals of raisins,
tor which he pays 50 reee per arrated. He sells the same in tht
yti . ;
■i-^;-. .vi2;?5.'."J!L"XZ^Z!!i!^_llj
FORErON WEIOHT8 AND MBA8UR18.
what we have
295
Hie .sau.e, allowing a Brommm of 8 ^' n 'T"^'^' V c^^'P?-"'' '° »^^>' ^^'^
and 25 francs to Jt I ? IZ L i • ^ t^ '^'"'J'' "'^ '^^^'"''"g currency,
that R. N. B. PoM tl e flax for's'."S ^^ "'^^ ^'^'''^ "'''^^^'•^^«' ^"^
did he gain on the total cost? ''"" "'* ^""'^' ^'^^^ P^^ °«"t-
4. Maple .n-ar is Whf]I/ nl? be rcnmted, an.I 29 % gained.
to Naplel android a ' 5 carii^i n^^^^^^^^^^^^ ^ P"""''' ^^^^^^P"^'i
tI>rou>rli Pari., the exc £1?? ?, ^ ^ ''''■> '""^ re.nutance is ordered
rateor24grui 1 (W^ ^n'^'^^' '^"'^ Paris being at the
of 5.25 francs toll A low "^ \'IT ^-'V ^"^^^'^"^ «^ ^^e rate
^-nce. etc., a.no.nf l^^^^ 1^^^^:^^^^^- £ ^^
wih'cSt^!tlJ;;t^;^r^^tft [ ^"^ that'-^SftSre
centinies. Alluui^^^riremium o jt":^ »""' "^/c;^"?- '^ '"^^^"'^'^ ^'"^
and 5.25 francs lo the dollar T i • f ^''7''^ "** ^^'^'■^'»^' currency,
advantageous,, ^^^^^^^l^^^X^^f^t^^ S'pP^^^
6. Having a ouantitv of^wLpA^ '^'l' P^ ^'^- •''! ^^"'"' «^ ^i^'-'rpoul'.
market, I .n"ake^ inmS a' i fiJ^^^^ ^? ^'^P^" '" ^'"^ ^''^^^
».ost faVorabie placera'l nLjll ^ '^'"' *"'^ A.nsterdun, the two
»..Hi it«. I find thS A Lit J % ^"^ '"vest.gate tlu ir comparative
and ren.itta. ce can £ d Icted U^^ '* conunands 127^ tlorins .er last,
to 80 IVancs, 5!20 L.u^ bet^ oSo l^"' 1 ^he rate of 37 florins
is -^J*^. 4d. 8terlin.r ner hn«»f«1 °<!^ . ^^^ ' ^""^ ** ^^""don the price
9 % ia the Ca ada^ na k T ' also t'Kt'";'"'"'^ ^T""^ * P^^'"'"'" ^^
tliruugh Paris, amonnUo 1 -' tlhtc Pr""". ^^/^^'''ittance, etc.,
5 %• =To whi^h u.arSt'shlll1\.S':„';r,.eaT?'" '' """"'"^^ ^^ °"'^
at Ig^r^t ■" feES^-S-e^^-^^^^
9%; or, tbron.'h Par s and M„5 '^ '^'''"° bearing a premiun, of
e«in per lb, anTaL'TX °L':'i'Tr»n l' *' *,'? "'""' '
f
1 1
! i
296 fiUPPLRMENT TO PROaRBSSIOHB.
STiPPLEMEiXT TO PROaRESSIONS.
ARlTHiMETlCAL PROGRESSKON (460).
50H. Case V. — Given the commnn difference, ihe numbe^ of
terms, and the mm of all the term*, to find the first term.
Ex. The iiutnber of terma ifl 34, the common difference 6, anJ the
Bum of the terms, of a series of numbers in arithmetical progression
is 3536 ; what is the first term 7
Operation. a= " - [ (n — 1) x ^ c] = -^ — 1(34 — 1)
X 3] = 6, the first term, Ant,
S09. Rule. — Divide the turn of the termg by the number of
terms ; subtract from the quotient, if the series be ascmding, oth-
erwise add to it, half the product of the common difference into
the nmnber of terms lets t e.
EXAMPLES FOR PRACTIOB.
1. If the number of terms be 22, the common difference 5, and the
sum of tlie terms 1221 ; what is the flrwt term ? Ans. 3.
2. A farmer is to receive $300 in 12 payments, each succeeding
Kynjent to exceed the former by $4 ; what will his first payment
1 Ana. 3.
310. Cask VI. — Given the first term, the common difference,
(tnd the nuinlnr of terms, to find the sum of all the term*.
E.V. If the first term of a series of numln .s m arithmetical progres-
Biqp be 5, the number of terms 34, and the common difference 6 }
what is the last term ?
Operation. I = a + [(n~ I)xc]=5-f- [(34 — 1) x «]
• 203, the last tern). Ana,
Sll. Rule. — Add to twice the first term, if the series be ascend-
ing ; othermse si^jtractfrom it the product of the common difference
into the number of terms, less one ; multiply the sum or difference
by half the number of terms,
EXAMPLES POR PRACTICE.
1. If the first term be 3, the number of terms 22, and the common
difference 5, what is the last term ? Ans. 108.
2. A man piirciiased iOO yards of cloth; the first yard cost him
40 cts., and each succeeding yard 20 cts. more to the last ; what did
the last yard cost him ? Ans. $20.20.
3. The first lerm of an ascending series is |, the number of terms
16, and the common diif. |, what is ths last term? An$. Tjf^,
^ vMK;.:7.'' :iy"n j;^igt-'-:'.-r
OEOMJ.TBI0AL PROflftSailolf.
Geometrical progression (477).
291
OPKIIATIOX
*\,r- 17 -^ ^ 3__t= 1328600, ^n,.
number uf /em«, mhtract one; divide the remainder bu the mJ
man raUo, less one, and multiply the ,uotienr^'7tJ^^^tt:Z
EXAMPLES FOB PBACTIOE.
An$. 64 miles.
»'« «y t«e rfrm«, to pid the common ratio.
mon ratio? " ^65720; wimt w ihe coiu-
Opbration. t— ^~^ = 265720 -- 1
8 — 1 265720 — 177147" ~ "'*' '^'"-
EXAMPLES FOR PRACTICE.
igjo .'"'-! '''•' *r" '"'.'*' **'* ^''''* <^rm 1372, an.? .K- - u. ,_,^
lO'jv'; viiat is ifae ratio? "" '"" ""'" '"" "^^ terras
"lanl;, in geon,«r,o«l prL/Jon of^ttah ^.^L'^ ""'°"''' W'
m
V •' T
•it 1
h'
298
LWB IM9CBANCK.
PROMISCUOUS IXAMPLES IN PROGRESSIONS.
1. A lady gare to a po<jr perKoii ..n the first dav ofthe year « 10-
on the second, $.2;l; and each succeeding day ^ 15 more U.t on
thejonner: how u.uch did thi« person receive 'on the K dav of"th:
2 For 7 day.s a captain dintrihuted Kon.e money to ifiw.ldierl^^on
he firs day he gave, hen, $.40, and on the foilouin; la^^'. '.nu"
tiplieit tliat sum t.y a certa n niunhep- finH H.Qf .,„ ,•',"*'""'
that on the 7ch dayf they received $29.) "^ "^'^ ""'"'-r k„
J. What 8um »u,.t be paid for a thermometer, who^e price inea .ml
ofl\5T' •';*"' ,'rr •'^ '^- ^^^^ ^^-^ « ^^^er .en on"t'h;ia?5av
ner .r ^ I '^:'. ''' ^^^ '^*''' *^" '^^^ ^'"- ^'^-^^ ^' "'^' rate of r cent,
per U.. ; and. ./ the .ale of each day wa. triple that o. the preceding
on'th.^?.!''' ^'V^^ ""^^t ^'"^i"^^^' * confectioner leared^J^^.
o.Uh« 7th. year he cleared ^473850 ; required the ratio of increase pei
Ans. 3.
LIFE INSURANCE.
516. Life Insur=>nce Is u contract in which a companv
*t pulates to pay a certa.n sun. of u.oney on the death 7thJ
nually. or^u/r.erirnt^rdingtofgrTement '^ '' '"^'^"'^ '*°°"^"^' ^^'"'■a-
^. The maured may designate to whom tbe amount of the policy shall be paid
u^^7'p'^^ Insurance Policies a.e of the followin-^ kmd.-
1^ An E,uhroment Insurance RAiry, that is, a contract \u which
an Insurance Company agrees to pay to the party insured a snec
biX T " '''''''' T^ '' ^° '"^ ''^'"-^^ should hi. death concur
befo e that age, on condition that he .shall pay an annual pemium
untd the policy matures ; 2nd. .1 mn-Zhrfeito,. ]ik or Z T
-^^ Pohc, IS one in which, even though the parfy insu • d .litid
fail to pay his annual premiun.s after the first, the company a xree.
l?fhY;;;ioT' '^ """^ '' ''^ ^"" '"^^^'^^ ^" ^^^ "''''-^?
The Expectation vf Life is the avarage number of yea.vs that
)\S.
the year f.lO;
more, tlian on
last (lay of the
is -oldiera ; on
'lays lie niul-
iber, knowing
Ans. .1.
price iw equal
tlie l.Jth. term
inn. 50 cts.
n the last day
ate ul' C cents
the preceding
ns. 23328.
leured $650;
f increase per
Ana. 3.
LIFE INRURANei.
299
a company
eath of the
the insured
of tbe insured,
years, when ic
:mium at the
ally, setni-aa-
shai) be paid.
nnu; kinds:
ctiii which
red ;i spec-
leath occur
1 1 premium
or End >!.■}■
lied should
any agrees
ni.iturity
years thai
etermined
In^reJ nm ;,.J» f fu P^O'"'"'" ""'^t be «uch a sura n.s will, when put at
Bnai IS easUy foand upon tho prinoipio of Life Annuities. ^
Bnv flt![°ii°.!^,''""''^^'**'"''•"'''^^*■'^° ^■^'•'«' ^howing the premium to be pai.l at
B.ny ago to scour.) ad annuity cf i^ioo, during tho rern.^in.lor of life. '
Dir1."tion"n? Thr/w'"' '' 'r^° "* '^ '^^"« °f tho polioy, and another at tho ex'
C<ul, Jo TftbrthiTn.hf '"f. '^?u"''"1 **''' fi^P^of-'ition of Life. One. called the
a^^^oVinih.fhi I M^ ^ Wig^lesworth Table. The Kxspeotation of Life,
atooraing to the two tables named, is shewn in the following
<!
1
2
.3
4
.5
6
7
H
9
10
11
12
13
14
ir,
16
17
18
19
20
21
22
23
24
25
2(1
27
28
29
■M)
31
"7? o
.3H.72
44.08
47.5.''.
49.82
50.76
51.25
51.17
50.80
50.24
4 9.57
4S.S2
48.04
47.27
46.51
45.7.-.
45.00
44.27
43.57
42.87
42.17
4 1 .46
40.75
40.04
39.31
38.59
37.86
37.(4
36.41
.35.60
35.00
.34. J 1
33.68
§05
28. 1 5
3(;.7,S
38.7*
40 01
40.73
4U 88
40.69
40.47
40.14
39.72
39.23
38.64
3S.02
37.41
36.79
36.17
35.76
35.37
34.98
34.59
.34.22
33.84
33.46
33.08
32.70
32.3.3
31.93
31.50
.•il.08
30.66
30.25
29.83
to
32
33
34
35
M
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
5H
69
60
61
62
63
33.03
32.36
31,6«
31.00
30,32
29 64
25 96
28 28
27.61
26.97
26 34
25.71
25.09
24.46
23.82
23. 1 7
22,80
21.81
2i.ll
20.39
1 9.68
18.97
18.28
17.58
16.89
I6.2[
15.55
14.92
I4.,!4
1.3.82
13.31
12.81
o ,
2'i.43
29.02
28.62
28.22
2^78
27.34
26 91
26.47
26.04
25.61
25. 1 9
24.77
24.35
23.92
2.3.37
22.83
22.27
21.72
21.17 '
20.61
20.05
1 9.49
18.92
18.35
17.78
17.20
16.63
16.04
15.45
14.86
14.26
13.66
<3
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
yo
91
92
93
94
96
12.30
11.79
11.27
10.7.:
10.23
9.70
9.18
8.65
8 16
7.72
7.33
7.01
6.69
6.40
6.12
6. HO
5,51
5.21
4 93
4.65
4.39
4.12
3.90
3.71
3.69
3.47
3.28
3.J6
3.37
3.48
3.63
3.63
c
' 13.05
1 2.43
11.96
I1.4S
11.01
10.50
10.06
9.60
9.14
8.69
8.25
7.83
7.40
6.99
6.59
6,21
5.85
5.50
5.16
4.87
4.66
4.57
4.21
3.90
.3.67
.3.56
3.73
3.32
3. 1 2
2.40
1.98
1.62
n
8M
>.' I
I
ii
\i I
i^ge at
ibsue.
14
15
16
17
18
ly
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
64
65
UFB INSUKANOB.
LIFE TABLB.
ANNUAL PREMIUM ON A POLICY OF $100.
Payments
during life.
$1.4707
1.5105
1.5516
1.5940
1.6377
1.6829
1.7296
1.7780
1.8280
1.879S
1.9335
1.9891
2.0470
2. 1 07 1
2.1696
2.2346
2.3023
2.3728
2.4464
2.5232
2.6034
2.6873
2.7752
2.8674
2.9641
3.0658
3.1729
3.2.S56
3.4046
3.5303
3.6632
3.8038
3.9530
4.1111
4.2782
4.4549
4.6417
4.8393
5.0486
6.2708
5.5067
6.7577
Payments
To cease at 6t
Payments
. To cease at 60
Payincnt.s
. Tc)ccasoat5(
Asfo nt
. i^sue.
$1.4999
$1.5238
$1.6150
14
1.5422
1.5683
1.6681
15
1.6861
1.6145
1.7240
16
1.6316
1.6625
1.7826
17
1.6786
1.7124
1.8444
18
1.7275
1.7644
1.9096
19
1.7782
1.8186
1.9785
20
1.8310
1.8753
2.0516
21
1.8859
1.9344
2.1292
22
1.9431
1.9963
2.2118
23
2.0027
2.0612
2.3000
24
2.0648
2.1291
2.3944
25
2.1300
2.2007
2.4959
26
2.1981
2.2761
2.6054
27
2.2695
2.3555
2.72.^8
28
2.3444
2.4395
2.8525
29
2.4230
2.5284
2.9928
30
2.5058
2.6226
3 1466
31
2.5930
2.7228
3.3163
32
2.6851
2.8296
3.5044
33
2.7824
2.9436
3.7142
34
2.8856
3.0657
3.9503
35
2.9951
.11971
4.2182
36
3.1117
3.3:W7
4.5251
37
3.2361
3.4919
4.8807
38
3.3692
3.6584
5.2981
39
3.5120
3.8402
6.7959
40
3.6654
4.0393
41
3.8311
4.2588
42
4.0106
4.5021
43
4.2055
4.7735
44
4.4181
5.0782
45
4.6512
5.4235
46
4.9075
6.8180
47
6.1902
6.2?26
48
6.50,38
6.8032
49
5.8536
7.4317
60
6.2470
51
6.69:^6
62
7.2061
53
7.h01T
54
8.504^ 1
55
ts
Aafo nt
t5t
. isi?ue.
14
1
15
[)
k;
t)
17
t
18
VJ
20
21
22
i
2.i
)
24
[
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
62
53
54
65
UK INSDRANCW.
ENDOWMENT AS^URA^VCR TABLE.
(Ago at Polioydua
j isgae. at 40.
I>
1
i;
■>
16 $3,356
17 3.545
IH 3.752
IS
3.978
20
4.228
21
4.504
22
4.812
23
6.156
24
5.544
25
5.985
26
6.489
27
7.082
28
7.752
2!)
8.558
30
9l
9.526
.1'
32
33
34
36
36
37
38
39
40
41
42
43
44
46
46
47
48
49
50
61
62
63
64
*5
LIFB INHtTRANOB.
NON-PORPEITINQ TABLE.
^B^^~:^j^^^;'^^^
on fnr «anh '.. V • ""«:»"^'«n. »r one-twontieth of tlio sum
1 III!
Five I Ten
Paytn'>i|P*w»n»g
i
21
.'3
21
25
20
27
28
29
30
31
32
33
31
35
$7,696
7.8481
8.020
8.193
8.374
8.55fi
8.758
8.962
9.154
9.316
9.488
9.660
9.842
10.258
|14.400|
Fifteen
Paym's
«4.294
$3,190
4.3«(;
3.2(;0
4.482
3.;! 32
4.582
3.412
4.690
3.494
4.79S
3.574
4.914
3.(5G6
5.030
3.750
6.138
3.838
6.234
3.908
6.330
3.980
6.430
4.060
6.540
4.152
6.658
4.246
5.782
4.334
Twenty
Paym's
$2,656
2. 7 hi I
2.77.8
2.844
2.914
2.986
3.002
3.138
3.210
3.274
3.338
3.408
3.480
3.558
3.640
Five
Paym's
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
!?1 0.470
10.702
10.9;!6
11.178
11.422
11.664
11.886
12.110
12.332
12.566
12.808
1.!.063
1.3.336
13.648
13.9841
Ten I Fifteen
Payra's'Pnym'd
.'?5.914
6.050
6.190
6.336;
6.478
6.612
6.738
6.862
6.988
7.1221
7.262
7.410
7.574
7.762
7.972
.•?4.434
4..-)46
4. 648
4.758
4.870
4.972|
5.0621
5.1641
5.266^
5.3661
5.478
5.610
5.752
5.914
6.10G
wenty
Payrn'j
$3,726
3.816
3.i)06
4.002
4.096
4.186
4.276
4.366
4.462
4.564
4.676
4.800
4.936
5.092
5.274
EXA.MPLES FOR PRACTICE.
$2750
OPERATION.
X .023728 = 165.252, Ans.
ANAtvam. - We multiply the
face of the policy, $2750. by the
rate <7f found opposite .SI ye.irs <a
malljr. aud obtain $65,252. the annual premium req^ufred^'*"'"' "P""^'"'' **'''■
2. A person at the age of 23 Jneuree his life for $1500 • uhat w !,;«
annual preuiium ? p^ovv , unai is hi8
•i. U hat 8 the annual payme.u on an endowment nolicv for f:■^V•n
payab e at the age of 55, i.sne.l to a person at ,be aici% vLrs? '
4 AM,a„.r2year.oId ,..„k an endowment assSLnce poitcv for
«8y0, dueatti*eaaeof50, and died when 49 ve^s oM ifv ' u
more would his heirs have reui.zed if h^ had Uk aTlife p'o c;*"; the
same amouat with p^ment to «*« at 50 ? W $266.40.
Ti, to jeouro $100,
.ind ■"hould fail to
(ml tlic othor eon-
ii .<iiin j>, liable at
t'tcr niiL' premium,
n assured, ami ao
^remiuiBj will b«
Fifteen
Twenty
! Faym'i
Piiyrn'j
.«4.4;i4
^3.726
4..-)46
;:;.H]6
4.648
3.906
4.758
4.002
4.870
4.096
4.972;
•^.186
5.0(121
4.276
r..lGli
4. .366
5.2(J(3^
4.462
o.HiiOi
4.564
5.478
4.676
5.610
4..'^n9
5.752
4.936
5.914
5.092
6.100
5.274
surance Com
»t the igsue of
B uaultiply the
$2750, by the
site .'il yeiirs -n
xpre3sed deci-
; what IS his
'. $28,197.
cy for .•f35t.U),
27 .veara ?
?e policy for
; how much
policy for the
. $265.40.
ANNDTTIB8. «-,
ft A
a"^\i.e/:r,t''!:etT"r'lh? ''"I'^rr -" '"« "^^ •• «- a^e o, 26
an.,.„„t 01 insurance iha.! ? •**'''• '"'" "'"'^^ 'e^« will ^11?;
Ant 'KO.^^r^
il/t«. $26^0.
AXNIITIK8.
is for a J.tto"„Sct"?v™s''"°' "'■'''' P'™"' "•■oo.mnuanoe
con,i:„« ilre'r""' *""""»' °' P^Petutty, is o,a. which
e»ci, pay,„e„t of an annuu/ „ a„ '" "T' '" !" ''' '■™'<oned „„
sanuMis on an, other deb,/ ' "'°"' "" """""'J. 'bo
su:':*nTh^%*s\reof,r'7*'''*' "^ "" """-"y >» -b.
became d„,, ,„yr;°aV, "S '""■""• '■™'" "'^ '-' -»'"
•.-'!\b'':„^'o*<'rpi:i71r i-T'.'^' " -"po""-' '»■
preset worth olit, floal^X TtMlf ^r""^' °' "■»
compound interest, wiU amoun »! ,1,/ ,• , "i""' P"' O"""
Ibe annuity, ,0 its 'finaUalue' '™o of the expiration of
rl-i"^- ■"•"-".-••'. ".6"^^^^
'iJ the ordia-jry rates of inter«rt. * '^'^ * «"«° omaber of y,*,)*
I
III
i i'
,M|
if r
f !)?«
JN
Hh
\lk
ii'jj
TABLE
''"'"'"5»/rL?T"**' ''^"" T^'-'J^^' "^*^ ^''^ ""'""'»• "' compound
i»fjrestforany number af y,i,in nul e:vcetding fifty
7 per oeot.
Ij 3pcre«nt. |8^ pececnt.
9
4
5
6
7
8
9
10
1)
12
J3
)4
lu
16
17
18
19
!20
v!l
y3
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
i.ouifooe
;JAl3iiU(>0
.'J.O'JOJUO
4.l.-;i(i27
5.309136
i;.4»384IO
7.(ii)ilti2
1^.892336
IU.ir)9l()6
ll.4C,H79
i2J07796
14 1 921)30
15.617790
17.0r)0324
I8,./J89I4
20.156d81
21.761588
23.414435
25 nG"5G8
2d.o7o:i74
2:*.i;76486
1 OOIIOUO
2.035000
3 ii'(;22r»
4.21494:
5 3(W4ti6
6.5.'.Uli
7.779408
9.051687
i0.36d496
II 731393
4 per cent.
45j
4H
47(J
48
49
&9
30.536780
32.452884
34.426470
36.45!)2i;4
38..553(»42
4(1.709634
42.930923
4r).-Jl9rr50
47.575416
50.01 '2678
52.502759
55.077841
57.730177
60.462062
63.271944
6C. 174223
69.159449
72.234233
75.401260
78.663298
82 023190
a5.483b92
•3S).048409
^~2'.)s6l
;d'. 'v ! . '
i^A^p ^;
OS..VJ, :;4w'
13.141992
14.601962
IJ.n3ii3o
17.676986
19.295681
20.971030
22.705016
24.490691
26 357100
2d.27:iL82
30.269471
32.32«9(;2
34 460414
36.666528
38.949=57
41.313102
42.75906{.'
46 290627
48.910799
51.622677
54.429471
.57 334502
60.341210
63 45315
66.67401
70.007603
73.457869
l.oiiui''"'
S0400UU
3.121600
4.216464
5 41632.1
6,632975
7.byrt294
9.214226
I0 5d2795
I2006I07
9 p«f oent. I percent.
77.02889r
80.724906
84.550278
88.509537
92.607371
96.848629
I0I.23S33I
105.7*1673
13.486351
I5.025s0i
16 626835
18 29)911
20.u235-:8
2i e24531
2:; 697512
25 64.'4I3
27.6TI . j}^
29.77(r()79
31.969202
34.24797U
36.6 1 7 -r) J
3<».0b2604
41 645908
44.311745
47.084214
49.9675^3
52.966286
56 084938
59 323335
62.701469
66.209527
69.857909
73.652225
77.59=314
b 1.702240
95.9703:i(;
90.4091.50
95.025516
99.826536
104,819598
110.0123/^2
M.5.4 12877
121.029.392
!26,>7n56-:-
11. r, 3509731132.945390
iV0.3^8297!i:"').^G3206
125.601»4Ci :.>.833734
1.(1001100
2.0.")0000
3.152500
4 31 01 25
5,52.')63I
6 801913
8 142008
9.549109
1 1 ,026'64
12.r)77^93
I4.20(i787
15.917127
17 7 1 -,'983
1959=632
2 1 .57e564
23.657492
25 840366
a-', 132385
30.539004
3,3.06.5954
35.719252
3b.50.52 1 4
41 430475
44 501999
47 727099
51.113454
54.669126
58.402583
62.322712
66.43::; 848
70 7G0790
75.298r29
80 063771
85.06()959
9(t,320.307
95.S36323
101.628139
<07.7W)54t)
114 095023
I.OOOiiOO
2.(60000
.3.183600
4374<>I6
5.637093
6.975319
8393838
9.d974f^8
II 491316
I3.1ci0795
14.97 1(i4:i
I6.8(i9'.»4l
I8.8-1'J|;W
21.0l.-)0i;6
23,275970
25.6705281
28.2128t<0
30 905653
120.799774
127.83'J763
135.231751
142 993339
151.143006
159.7001.56
16^.6^5164
178 119422
IH8.025:{93
198.426663
33.75999
36.7tt5591
39.992727
43.392290
46,995828
50 815577
54. =64512
59.156383
63.705766
68 528112
73 639798
79.05=1=6
84 801677
90.889778
97.343165
104.183755
I.OiMlOOO
2 '170000
3 214900
4 43:i,M3
5 7.i073!»
7 l.'.3'29l
^ 654021
1 0.25981 (3
1 1 9779=9
13816448
l57»,Joy9
17.888451
20. 14064 J
22. 5504 88
25 lJi^022
27.9=;054
30.P402I7
33 9hiyii3J
37..<7By05
40 995492
44.c(j5I77
49 005739
53 436141
58 |7o6rl
63.2490,30
68 6764'0
74.4=3->3J
80,69T(;i.»|
=7.346529
94.460786
102.073041
no •21=154
1 18.933425
128 258765
111.434780 1 3e,i;36878
I19.I2086-! 18.1M3460
127.2681 li>i J 'jO,;i3';4(jO
135.9042f/>i ti^;,,! ;ii)
45.058..'. ;' j4\.^i>i
154 761966
16,j.047684
175.950645
187.597577
191)758032
212 743514
226.508125
241.098612
256..->61.')29
.>72.9.5d401
i 130.99991 0|la2.6C70t>4[209!34797t>ja90.'3k5905
199.635112
214.609570
230.«)32240
247 776496
266.120851
285.749311
3ii(! 751763
32.1.224386
353.27(1093
378.999000
406.528929
46
47
48
49
50
TAIii.E
Showinxr the present tvnrth ,,1 ,n annu,/ r-vi .,
305
3 p. eent.
0.97087.1
J.yia47(i
t'.82dGIJ
;V7I70!W
4-.7;)707
5.417191
(».5«U-,'8'J
7.onhm
7.786109
9.-.i52(iy4
9.9.-)4004
I(».6:549.->5
ll.-<il)«073
11.9.{7!>3.-)
'■■i.ofi 11(12
I;j.l0(ill8
i:«.7r);{r,i.'}
14.323799
14.87747,'-)
15.4150'.>4
Il3.93(;9l7
Iti44;i()(;8
HJ.93r)r)42
I7.41314H
18. 32703 [
18.704108
l'J.J6S455
19.(300441
•20.000428
0.9(;r>IH4
1.89:»G!)4
2.8(»u;;!7
3.()7.'J07;i
4.r.ir)052
5.328.-.5:!
6.114541
6.8739,-()|
7.C07G87
8.3IG605
9. 00 1 r>r) I
9.663334
10.302738
10.920.-)20
n.517411
12.0.94117
12.651321
13.1896S2
13.709837
14.212403
14.697974
15.16712.^)
15.620410
16.058368
16.48 1.'-) 15
.876842 16.8903.V2
1 'J.»->noi !•» <-».-.,..„_
17.28536c
17.667019
i8.03r)7(;7
I A 392045
18.736276
.'0 338766 19.068685
20.765792
21.1.1J837
'1.487220
5l.>i32v..
22 ir.7235
'22.492462
122.808215
•23.114772
23.412400
19.390208
19.700684
20,00l)t)6l
20.290494
2'».5ro525
20.841087
21.102500
21.355072
2I.O99104
23.701359 2 l.«;J4883
23 981902122.062689
24.2542741
•24..''>|f^7!;
24.775149
V 024708
25.266707
25.5016.57
r-25.729764
'2-2J8279I
2. t9,";45i;
22.700918
22.899438
23.091244
23.270564
23.455618
".96 1. 538
1 .8r«(J09."
2.775091
3.629895
4.45182i
5.24213'/
6 0020.55
6.7.32745
7.435332
8.110896
8.760477
9.385074
9.;»85648
10..563123
11.1/8387
11.652296
12.165669
12,6.59297
13.133939
13.590326
14.029160
14 451115
14.8.56842
15.246963
15.622080
15.982769
16.329586
16663063
16.983715
17.292033
17.588494
17.873.552
18.147646
18.411198
18.664613
18.908282
19.142579
19.3678641
19.584485
19 792774
19 9930.52
20.185627
2(1.370795
20.548841
20.7ii0040
20.884654
21 042936
2I.195J31
21.341472
21.482185
1 1.9.52.38 1 1
1.1.59110
3.515951
4.329477
5.075692
5.786:i73
6 463213
7.107ft2->|
7.721735
8 306414
8.8(532.521
9..39357:{
9.6!)8641
I0.37i)6,58
10.837770
11.274066
11.689.587
o.943:{9(;
, 1.83:!:fi)3
2.72.V248I 2»;730I2
3.465106
4.212364
4.917.324
5.5s-j:wi
0.209741
6.80J692
7..360()87
7.886^*75
8..3S3814
8.8.52i;8;!
9.294981
0.712219
10.lO.5vS9.-,
10.4772(io
i.>,ij.;..;'.i!^'^~'^*''"V"-'-''''"""
2.08;>. 21 I J58Ji(;i0..3:!.5.578
12.4fi22lo ll.4{;9.12l 10.593')')7
12.821 1.53I 1 1.76-107; '
12.04 i5-<-J
0,9,14579.
I.SOMJI?
2.(;.'13|4
3.3-^72(»!»
4.100195
4 7665371
5.3?928l)
5.97l29ri
6.5I582-*
7 023.577
7.498(i(i9
7.912(;7I
8.3.57635
8.745452
9.J07S9>
.0.44663-2
9.76:!20(i
lf».059O7O
13.16.3003
13.488571
13 798642
14.093945
14.275185
12.30.3379
l-.'..55035>
I2.78.335ti
I3.003l(!(i
14.64.3034 13.2 1 0.-.34
14.8981-7 13.406 KH
15 141074 13.590721
15.372451 13.764.^31
15..5928II 13.9290.S6
15.802677 14.08401;!
16.(102549! l4.23o-'30
16 192204 14.30814
16.374194
|10.8!5527
11.061241
11.272187
11.4693.34
ll.().5.3.83
11.8257791
11.9,'^6709
12.137111
12.277674
12.409041
r2..53l814
I2.64(m55
-7')o|
12.854009
14.498^!46 12-947672
1 6.546852 1 4.620987 13.0.35208
0.71 1287 14 730780 13.117017
10.86/893 I4.84(>019 13 1J)3473
17.017041 14.949075 |3.2(;49->8
I7.1.59/ir:'6jl5.04()297
'7.2943(;8il5.13eoi6
17.423208
17.545912
17.662773
17.774070
17.88(»067
17.981016
18.077158
18. IIJ87S2
15.224543
15.3()617.')
15..383I82
15.455832
15.524.370
15..589()28
15.650027
15.707572
13.331709
13.394120
13452449
13.506962
13.557908'
1^.605522
13.650020
13.6!)1608
13.730474
13.766799
18.2559251 15.76l86l|l3.8Q0746
f
Si
< %
t i
'■> ] m
i ' VH
f' '
3M
AWWniTtRH.
u
*m^. To find the amount, or final value, of an annuity certain,
at compound interest, in arrears, or forborne,
Ex. An annuity of $400 a year remained unpaid G years ; what re
the amount due, at 6^ compound interest?
OPERATION,
$6.975319, amount of SI for 6 years. (See Table).
400
$2790.1276; " $400
NoTT.— When the annuity draws timple iuterett, the amount is found as in
amutal interest.
52T. Rule. — Multiph/ the amount, or final value, of an an-
nuity q/'$l for the given rate and time,f()uii<l in the table, by the
given annuity, and (he product will be the required amount.
52S. To Bnd the present value of an annuity certain.
Ex. What 18 the present value of an annuity of ;j80, to continue
20 years, ato^?
NOTR. — Since the present value of
an annuity is the preaent worth of its
amount, or Qnal value, the present
value of an annuity may also be
found by first finding the amount,
and then the present worth of tbi;:
amount.
OPERATION.
$12.46221, present value of $1,
80
$996.9768 ;
$S0.
5S^. Rule. — Multiply the present value of an annuity of $1 .
/"or the given rate and time, by the given annuity.
5SO. To find the present value of an annuity in perpetuity,
Ex. What 18 the present value of a perpetual leayehold, which
yields an income of $840 a year, at 6 % ?
OPERATION. Analysis. — The present value
$84« ^ .06 = $14000, present val. ^^^ ^SrSanta^ ^S
$840, at 6 per cent.
5«{1. Rule. — Divide the given annuity by the interest o/Sl,
for one year.
Note, — When an annuity is payable semi-annually, or quarterly, interest must
be allowed on the hulf-yearly or quarterly pavQieDta to tho close nf the year.
5S2. To find the present value of an annuity in reversion.
Ex. What is the pre.sent value of an annuity of $500, deferred 10
years, and to continue 8 years, allowing 6 % compound intereet ?
lity certain,
irs ; what re
ible).
18 found aa in
e, of an (in-
able, by the
mint.
tin,
to continue
esont viiluo of
mt xoorth oi Mi
I, the pro sent
may also be
; the amount,
worth of thi?
luity o/^l,
'.rpetiiili/,
hold, which
present value
a principal
ual interest of
erest o/Sl,
interest must
the year.
version.
deferred 10
tere«t?
ANKUITIIB.
OPERATION.
^ ' -"S^nnS^ P''^^^"^ ^*'»e Of $1 for 18 yeaw.
(..^60087, " ti « 10 «
$ 3.467al6, " » «
600
8 " deferrj'd 1 years.
1500
«
u
i<
to
He
$173^!.758000, " «
NATmv ^ i' '"''"'"J''"9 <'t once and continuing till the termi-
^i'^*/^yv(y /A. r/.^Hr«c. of the^e present values, h, the given annuity.
'^£:^^t:^::s^l:^:^Si;. '^"""^ ^'"''^ °^ *^' ---en-gat
ratf ^b,!;;en:^ '" """''^' '""^ P-^^'^* - ^-1 value, time and
^^m^^irX:^^^!^ ^ «^' --P-"^ interest, is
Analysis. —Since $6.209744
ate% compound interest, for 8
$623.70 will yield an annuit^
^ equal to $623.70 -i- 6.209744.
^v?/i^m.f«/'!ff/V''T' "/ -^""^ "^^"^ of the given annuity
(^ijtUepH. sent or final value of an annuity of%Vfor the aim n
■rate and lime. "^ "y wi-jyM/ in e given
EXAMPLES FOR PRACTrCE.
12yeaTi;'ut'ri"'^''""''"'"' '' '" '"""''^ jf $1300, to continue
2 A grou.Rl rent in the citv of Quebec yield-^ aT-n^nnf f f,"^^ ^ ' f
Am. |o93.86 f .
OPEKATION.
1?623.70 -f- $(5.209744 = $100.43 + .
^i
!.::
308
ANHniTTM.
5. What is the present value of a leasehold of $900, deferred 6 yr.,
md to run 10 yr., at 5% compound interest? Ans. $2804.43 + .
6. What is the amount of aa annuity of $1000, forborne for 15 yr.
at 3^5(5 compound interest? Ans. ■:'<\\)29r).(iH.
7. A widcw i,« entjtle<i to $420 a year, payable wniiarmuallv, for
18 3'ears; what is the pre.'>ei>t value of her interest, at 7 %, compound
'oterest? Ans. $42(;!.
8. A yearly pension, unpaid for 12 years, at 6%. wjmpound int.,
amoiinted to $1)550.2762 ; what was the pension ? Ans. $1 1 :!9.1 2 + .
9. What sum should be paid for a perpetual annuity of §1500, pay-
able semi-annually, interest being at 6 % ? Ans. $25000.
10. A lease, whose rental is $()00 a year, is left to a son and a
daughter. The son is to receive the rei>tfor8 years and tlie daughter
for the 1 2 yr. succeedmg. What is the present value of the daughter's
interest, allowing 5 % compound interest? Ans. $8599. 3'J -f .
11. What will an annuity of 840, payable semi-annually, amount
to, in arrears for 5 years, at 6 ^ ? Ans. $458.55 + .
12. I w>:^h to purchase an annuity which shall secure to my ward,
at 5 5t compound interest, $300 for 15 years. What must I deposit
in the annuity oflBtee? Ans. $3113.89 + .
13. A laborer agreed to work for 1 year and 6 months at the rate
of $25 payal>le monthly ; he was paid only at the end of the 18 mo. ;
how much did he receive, being allowed 6% simple interest per an
Q»'"? Ans. $469.12^.
14. A merchant being desirous to secure a dowry k>r liis son. de-
posits annually a sum which, placed at simple interest, commencing
at his 1 2th year to his 23rd., amounts to $630, and that due for dowry,
to $5580 ; find the value of the yearly deposit, and the rate %.
Ans. Deposit, $300 ; rate, 30 %.
16. A founder wishes to economise $360 in 5 years; wliat swn
Bhall he have to deposit at the end of each year so as to have the
required sum at the end of the 5Hi. year, comprising both capital and
compound interest, at 5 % per annwa? Ans. $63.16.
16. What is the amount ofanannuityof$45. payable semi-annually,
for 3 years, at 7 ^ compound interest ? Ans. $294.75 + .
17. A servant leaves his yearly salary of $250 in the hands of hi&
master, on condition that he will allow him 4^% interest, per annum,
to be added to his capital ; find how much will be due the servant at
the end of 15 years. Ans. $5196.01.
18. A marbler buys divers blocks of marble measuring altogether
4.850 cubic yards at $1 16 a cu. yard ; lie pays $122.60 in cash, and
settles the remainder in 4 annuities; what ia the amount of each an-
nuity at 4^^ interest. Ans. $445.99.
19. Find the amount of an annuity of $225 fbr 5^yr. payable every
three months, interest -dt l^% also quarterly. Ane. $5729.62 4.
20. An oi! merchant bought 32 bbl. of euperfine olive oil, fur which
he paid'yearly $190 for 1 years. If money was worth 6 ^ per annum
compound int., what was the cost of a barrel ? Ans. $43.70.
21. A planter agrees to pay $598 in 13 payments, in such a maimer
that 6ach succeeding pa.yment shall be greater than the preceding one
bj 9 6 ; what will be hu first and last pajmeot 7 Au$. Last |ti2.
red 6 jr.,
4.43 + .
"or 15 vr.
l29r).6S.
lually, for
compound
$42(1!.
lound int.,
;0.12+-.
1 500, pay-
S25000.
son and a
! dau-gjhter
laughter's
9.3'J + .
f, amount
8.55 + .
my ward,
1 1 deposit
3.89 + .
: the rate
5 18 mo. ;
set per an
:69.r2^.
is fcon. de-
uniencing
for dowry,
e, 30%.
iv\\&i som
) have the
^pital and
$63.16.
•annually,
4.75 + .
nils of hi&
?r annum,
servant ax
196.01.
altogether
cash, and
f each an-
445.99.
ible every
29.62^.
for which
er annum
$43.70.
a mai»er
eding one
l8t|62.
AffWUITnM.
309
tl^f capital deposUed wlm canifll '^^ f f '^T ' '' ^ P"' aunum on
calculateciatl^i^gyearrv ' d ff S^. '*J!1 '^T'''' ''■ '"^^est Z
18 years and UnoSf' '^ ^' ^'""^^^^^ I'^'-^^ioo of hi« life b^
24. A laborer, from the acre of Ifi ♦. «n ^"'^- ^^^^^ *2 5A.
23. A mechanic boucht tools fn,- tu^ , *-^"'- *'*15-45i.
m yearly, so as to cance] hird/bt in I ''*™ ""l f L^^® = ^^^^^^ ^'d he
pound interest ? ' ^^"^ "* ^ ^^a^^' at 5 Jg per anmim cora-
26. I have deposited $5000 at 5 <*; intPPP«* ^ :^"'- *^' ' -27.
withdraw only .$150 yearly, and tha flT ' °".«o»dit.on that I will
win be added to tj/e cap^ af wha? Vilf i!T''^'' «*" '^' '"»«^«t
years ? ^'*^""' ' "^^^^ will be due me at the end of 12
27. When dvin? a forfKo- ua . ^^s. $6591.71
a boy and a giH " yeSt oTd V, ''""^ "^'"^^^^^ *« 1"^^ twin chi Id L
deposited at 7%, If;^„^^;,,VrdtSVo?r"'^^ ''' ^^« ^oy -a«
'nterest, payable semi-annually • the IfJZ^'^^'h ^^ ^ ^ compound
bemg 13 3.ar5«wide and twicJ as S 'r ' '" 35 window^ each
$3.37 J per square yard, but oServe that a <?m ""f ' Pf ^ ^' '^'' '"^'^ ^
must be added to make up frthe head n^Ll f W' of the wmdow
in 3 instalments tb^ fl J l ^^''^^^^ ^''"'^*'- Hewdnpaid
being at 54 qi li,!, ^'* "l^'"^"^' ^"d the others yearly • interL
is to op«, 9 years he, ce how Mmch wilf nf/"°T °''^^"'^.' ^^'**^
money, if he is allowed a veaHv fi i Jii ^^*^P" ''chaser pay in ready
30. A roof of 128 smmie v nl^ -^ I '^"i'' ^'^267.41.
minous «.ment of i of an neh'^^ t '"'^ ^ ^'^ '^ ^'■'"•
The oontrastor wal paid iH W*;'^T'' ^* Z^^' ^i^. a sq. yard,
year, ex,«pt the k tTuch was nS"^'"*" ^T^^^ ^' '^' end V 3
hi^ stock it thl iate S- $93^6 an^"" '^'^'^ bearing 4^ 5,5 ; he Uier, seSf
What shall be hifyeart bco'me TZl^' ^T'"''' '". ^ "^^ ^"""i^^-
for selling his stock; 2- iX comnanv 1 ^^'.'^ ^^^ » 5« biK,kefa^
aWr^Pa go? <;,_ ^^^.'^ '"* company w4iere heseenpf^s eb» M^n-n-
32. A defctor owfs WOOIllr^i ■ iT' . ^»«- MM5.38.
could he ye.,1, j^ *;ur«ao u?'""! P"''' "I' « ' «; ™l« .wn
■'It
1 1f 1 •
Hi
310
rS^UPBRATtmB>-THRRM0Mli:TER8.
Pi .'
(■;-;■
' i !
1 1 1 1'
?8 in a Savings Bank, a,i'S^%; and continues the same for 20 yeafs,
comuicricmg at the age of 26. What will Ite his capital at the end </
the 20th year, including an income of $40 from etock bearing 4^%,
which, at his request, the bank purchased for him from his deposits
every second yenr, at the average rate of 93 % ? Arts. $12852.94.
34. An engineer who earns on an average §^2.30 a day, and works
25 days a month, spends yeasJy $1T9 for hoof?e-*ent, S«l5 for jl^mly
expenses, and .f6» for euiwiry expenses. We want to know; 1" how
nmoh he may save yearly ; 2° what will be tiie totai value of hi?«
yearly sayings by depositing them at 6 ^g compound interest, from Us
fh •*■ '^ ^®^*'' '^^ **^** y^^^^y income he will enjoy at the age
Of &4, If at 47 he eonverts the total value of his sayings into an
annuity bearing 4^96 inteffest, supposing him to live to ihe age of 76
aDd4montJ>8? Ana. 1»$135; Z'' 3808.74; 3» $94.3.Ib + .
TEMPB]RATIJRE— THERMOMETERS.
(586. Temperature is a term employed to denote the con-
dition of a body in respect to heat, or cold ; it al«>o expresses the
greater or less capacity of a body to excite i« us tiie sensation of
heat or cold.
NoTW.— Heat and cold are correlativa terms ; that is, as the former inoreaises
in a body, the latter decreases, and the converse. Tom|)erakure generally nten
to tho amount of sensible heat in a body ; eold being regarded as the absence of
heat.
SST. A Thermometer is an instrument used to measure <fce
wraperature of bodies.
NoTM;— 1. The oonstruotion of thormometera dopendi <m the prineipie, wfcieh
IS universal, that bodies are expanded by increasing and contracted 1:^ deoreusing
their tempowiture. The thermometer commonly used for measuring iempei atures
neither extremely high nor extremely low oonsists of a glass tube having a small
bore of uniform diameter, and at its end a bulb within which is mercury. 'Jihere
B aieo a scale which meMurea in degrees the length ot the column of morouiy,
wWoh by its expansion or contraction within the tube indicates the temperature
^0 whioli tbo thermometer is exposed.
2. 'Ibermouiet-ers are graduated by markin* on the Uibtv, or attached plates,
two poinrts at which the mercury stands at fixed and easily asoerlalned teniper-
ntureit the lower being that of freemng water oalled tihe freewag poia^ aod«he
higher kbot of boiling water, when the barometer stands at 2&.M inofaes (760
milikm^. ^
4*38. In the cetHiigntde thepraometer, or that of O'lsrns, the
freezing point is marked lero (O''), ^ bmlku; point, 100°; and
tiie i^tt<»uiediate spaoe is divided into 160 ecpd parts eoMed
''v^^Y^r ^3fr'"" ".'■
WMPERATTTRB-THlRMOMarmB.
idod into 180 equaip,"!" ' ""' '°'«''™' ('8"°) -s dJ^^
o'!lt?.he\S?r„r;i„v 8orr L^^^ ^r-s p--' « -rhd
equal parts or degrera. ' '°'"'"'' ''^"'« ''■"ded into 80
Jfc£tS"'o,^t': -rrr.re«--»^ „p.^ ,„„
(- 391" C, _ 39" p., _ 3ir,o r"! t''e freezing point for mercury
mercury (3481° C; 660° F ^2791^'r ^^i^^?^^ '^' boiling pointed
facrl'"*'r't? ^'^"^I^rature L> tl e" scales Tr''"'"^?*" ^^"'^ ««^««
filling the tbTo.oteSr'."''"*'"' '^'^ - ^'-''o. inlt;af of Seru^fS'^o"
Since th« interval between th. a.
* divided into 100 eqnarpartefn «,/',"« ?"'' '','"""8 Po^" »f "ater
■ahrenheifs, and 80 Mual Mrl, il'l,.*-™'*?*' ISO equal pans?'
SS,K'."i^'™- ■» ."«ktd!20.'';L"Lft„t-A»i':».-a,e t^e
<ijrraA %«e.. i»-""W<:< k<^^ 4e fAe temjieralvre in Ci,"
««. To change fton. t.^..^,,;,, ^ j^^^^^^^,^ ^^^^^
aumur's degrees ^ ^^ "'*'* *^ <^« temperature in d-
s^.f **■ T° orange a temn«rafnr^ .,. •_ , ,
^^^\- .nto the saiue as givenljFlhrUekr ^ '^" ^''''^'''^'
^"ri^m'^'tTX!!: S/r it^^^* ^-^ ^' -^ «^^ .^2° ^c,
,«^ urn «;t^/ 6. ^« temperature by Fahrenheit^,
I i i?i
r !:
i ml
V >
1 i
;
•\ !
l>!
'12 TKMP«RATUai5-THMlMOMBTIR8.
»44. To ehange fi^om Reaumur's to Fahrenheit's eoale.
o9?Y'1;~^'f '^'y f^j^^'^rees on Reaumur's scale hy |, and add
heif^scale '''^' '"'^ ""'^^ ''" *^'' temperature hy Fahren-
545. The degrees on the Centigrade, Fahrenheit's, and Re-
aumur s scales, corresponding t) temperatures differing by 10°
Centigrade between the freezing and boiling points of wat^r, are
given in the following tablo : '
Ceutigraat.
0" Zero =
10" =
JO®
30» =
40" =
60" =
60« =
70O =
80» =
90» =
lOOe =
Fahrenheit.
32^ Freez'g. =
50'^ =
68" =
86° =
104" =
122" =
140" =
158" =
194" =
212" =
Reaumur.
0" Zero.
8"
16"
24"
32"
40«»
48"
56«
64"
72"
80"
By means of the rules (641, 542, 543, 544,) the atudent can readily
extend this table above and below these limits.
EXAMPLES FOK PBACTIOE.
1. What temperature bj Fahrenheit's Hcale corresponds to 176"
Centigrade? 'Jna 348*°
2. When the temperature of a body by Reaumur's thermometer is
7» , what IS It by I'ahrenheit's? j^„g 20"'"
3. What temperature by Reaumur's thermometer answers to 834°
Oentigrade ? '
4. What temperature t)y Centigrade's soalfi norre-oorids to 45"
Fahrenheit? ' " ^ ^^^ ^^^
6 When Fahrenheit's thermometer indicates —13°, what should
ttie Ceati^fradK Mi Reaumur's indicate ?
4Wf Qwtigrade, —26" j Beaumur, ■-20''.
"^yr*^Tj^i»->g^qi|
A Mktrb
'^ KlI.OMIITK
An Abh,
«QrriVAL«.Tfl or mrthio measures.
« 39.37
— 3.284
= l.OQSfl
( '■» I
<«-^«3
C =.<
7 -ifl^-.T'-^''""'^
C — .^.953-f- yq rods _
=«= 39.37 inches......
.28-f- feet....
.09S« + yards!
313
An inch
A foot
A yard
flfj^^t 10 inches I^y^rd
A »q. yard
A iq. rod
~ n- ■(].
A Hkotaub i = 2.47J acres.
? = .0038»-f sq. mii;' T *"''°
-T- 04. miie ^ A sq. raifo
■■i:a,tet ^«i--h
^^■" Asq. foot
A Stkbk.
-^ a cubic raoter.. I * . .
..3i1[!t°;:S/a:::;."L'„":?r
— •22»'l+ meter.
= .3048-f tneior.
*" •9141-1- meter.
» .OOflilH kil,.m.
« l.609-f- kilom.
*= '834-1- cent! are
«= .2629+ are.
-= .4046-f- hect.
« 258.99-f- hect.
=-=.0006454- cent.
= .0929-f cent
=.0000163-f8ter9
«= 3.62-f 8tere.
sz .7H4-J- stere.
= ,0283+ stere.
A IdTKa.
/ ♦• * •»M«ttr« 0/ capacity , I
= a cubic dooimetcr I a
1 "= •"«8+ of a „T„^/"n:::V;- I ^ °^ f£<^'. = 23.32 liters.
•JOB I "°"""«"'r..
^oi.oi+oubicinfihes
A flKOT»i,rr«B,. ^ ■" ^•''^•'^-f bushels
' =3.a317l-loHbicfeet
AaRAJi,. ..
( ~ (35^ ^'■■*°'' ^'•°^ ^' •• A grain
C ~ i».d6+ ounce, At. Wl '
A ;.r n ., = ^H.^2 liters.
A& = 3.78+ liters.
A fluid o«. », .02958+ liter
Acu.„ich =..,M63-fr,ite'r"-
A bushel
A ou. foot
.352+ hectol.
.283+ hectol.
.0648+ gram.
A &.,>«««.... j - S?t S: l;: »S- ^° -ojr. lb. ^ .4530+ kilo.
^ - 2.679 1 Troy VV^ght ( l-^,--^- ^ -J^S^f kilo°|.
^ T^"'^"*" J r ??„1;i'»> At. Weight.....
f — i,ivi-j- tons
An avoir, lb. ;
A ton
ilog.
= .000453+ ton.
: .907+ tonneau
100 grades.
' A ton
A Gradr S **« measure of anaUii • * • u.
J =- .9 of a dog«e^^ f "S"^' «»?'« - - ,.„_
° A de^-ree =■ i n "'"■
NoTBs — 1 Th "II • '='*"I' grades.
MENSURATION.
i i
I i
'
•Mi
ij <
I i
DEFINITIONB,
546. Mensuration treats of the meaearement of lines but
faces and solids. '
547. A Point is that which has place, or position, but not
ma-jnitude. ^ ' r j
548. A Line has length without breadth or thickness, and
may bo straijrht or curved.
549. A Surface is that which has length, or breadth, without
height, or thickness. There are three kinds of surfaoes; viz
plain, convex, or curved, and concave. '
550. A Plane Surface is one, every point of which is
touched by a straight line, extended over and upon it.
551. A Curved Surface is one that ha« length and breadth
without thickness, and is constantly changing its direction.
5S-S. A Concave Surface is the reverae of the curved, and
constitutes the interior surface of a hollow sphere.
L ^??" ^?^^}h Volume, or Body, is that which has length,
breadth, and^ thickness. Length, breadth, and thickness, are
called dimensions. Henoe, a solid has three dimensions, a surface
two, and a una one.
ANQLBS.
554. An Angle is the diyergenoe
6f two straight lines from a common
poiat; as the angle A. Also read
1? ^* '^^^ ^^'^ straight lines are
called the sides of the angle, and the
common point of intersection, the wr/«E.
555. A Right Angle is an angle
formed by a straight line and a per-
pendicular to it, and contains 90°-
as the angles ABE and E B 0. '
556. An Acute Angle is one
less than a right angle ; as the angles
557. An Obtuse Angle is one
greater tiian a right aagle : ae the an-
gle A B D.
—
/
VftUNQLKfl.
Hnee, stir
n, but not
kness, and
li, without
Mies; viz.,
which is
d breadth
on.
rved, and
as length,
jiesa, are
a surface
[▼ergenoe
common
Jso read
lines fire
, and the
le vertex.
an angle
i a per-
ns 90°;
tc.
) is one
le angles
) is one
I the ao'
315
lie^??);^"*"®i.''"^««'-«^»^''««th'''t
^e in the sanie direction ; they are
other ; as A B and C D.
POLYGONS.
it. mr&c. " ^"^ "'■ " "sure is the number of equare units in
TRIAN0LB8.
56«. There a„ eev.r.1 kind, of triangle,, „.„»),..
e,L.*" """"""^ friangl,, the three sides of whioh .„
. In lie right-angild trianrie tlfj J^ """* ?"° "Slit angle.
is oaUed thehi^LnZ^ ' *" '"''' °''1'°^"« ""= --igh "angle,
fciquilateral
leoseeles.
Scalenui
NoT«.-Ih« aottod li«« «.p,^„ ^^ ^^^^^^ ^ ^^ ^^
Kight-anjled.
m
? m 11
U'
816
OF THR nrnrLi.
QUAIIRILATEKALS.
m
1 1
I I
k . I .
567. There are three kinds of quiulrilateralfl, namely :
o" ^t® Parallelogram, wliicli has its opposite sides para
o mi J'^^P^O^d) ^'I'cli li''f^ only two of its sides parall
3. The Trapezium, which has none of its sides parallel.
Parallelogram. Trapewid. Trape«uai.
^56S^ Ther e are four kinds of p;.rallolograms, nauiely:
1. The Square, whose
sides are equal, and whose
angles are right angles.
2. The Rectangle,
which is any right angled
parailf ic^rani. '
3. The Rhombus, or
Lozenge, whose sides are
equal, and whose angles
are not right angles.
4. The Rhomboid,
whose opposite sides are
equal, but its angles are
not right angles, and its
length exceeds its breadth.
ISquaro.
Reotnngle.
BhomJiUB
^<^mboid.
OF THE CIRCLE.
569. A Circle is a plane figure bounded
by a line, every part of which is equally dis-
tant from a poiat within called the centre as
A G H B C E D.
The Circumference of a circle is the line
that bounds it. It is divided into 360 parts
called degrees.
5^0. An Arc is any j.ortioii of the circumference ; as A D,
3J1. A Radius is a line drawn from the centre to the cir-
cumference ; as A, or C.
57a. A Diameter is a line which passes through the centre
and IS terminated by the circumference ; as A B.
MBIVSOIATIOV op suaPAOBB.
— 317
•rc^^f D 0°"'"' '" * ""«'" ""« J'»""'« ">« -femUio, of „.
drolei »> the ,,",t A * K A "•» P'--"""! chords of .
S79. A Lune, or Orescent .o ♦!,
fpaco contained be ween the !r^!' of . '
intersecting circles. ''' °^ '^°
whfsf L;Lf Sf: .5et'7 '^ T
pentagon ABC D E ^"''^' "^ '^*'
MKNSUKATICN OF SURPACBS.
Probf.km T.
To find the area of any paraUelogram.
■> n- , . * '^ * ~ ^ " square yards /It,,
4th ,476 00^4 ykTUlm/,'^'^ «^«-' /J- >
.-.1"5w'4'o|-,%"^.j:,^-'^«^^U.«o.^.
; )3
^
;*
i. i 1
. 1
i
li
■li
Mi
n
n
a
A E
H p
Q1Q
° «»NiUBATlON Of 8Ca»A0BH.
3. Find the area of a rectangle A B C D
01 wlucl. th. I,a.e A [i = 7 yard.H, and th^
iiltitiide A I) = 4 yards.
Ol-KRATION. 7 < l = 2H flq. yd., -!»|«.
4. What is tlie height, or allituda, of a
recta..;rle who-e l.aso is II yards, and aren,
i IZ rtquare yards?
14 =. s yards, ^«.. ^ * ''®"°°' ""»* ^°'«^»' •'hoild bo eqiml to 112 +
■dna. 1st 72 1. 5 1 i sq. yd. ; 2nd 10997.248 eq. yd., etc.
n M ^^''^"^ '^ "'^ ^'■^* °^ ^^^^ rhombua A B
L p of which the base A B is 12 feet, aad
ahitudeE D, 4 feet?
Operation. 12 x 4 = 48 sq. feet, Atu.
7. Find the area of the rhombus whoae
- 4n 99 v^ 1? n oo -.^'^ ^"'-^ »'tiMi.les are as follows : 1st A B
q^q-f'^^ y i^A^u'^ 32.,oyd.; 2nd D C = 105.75 yd., C P =
86.95 yd. ; .^rd A B = 145.20 yd., E D = 127 54 vd -4/11110 —
/)«.. UtW.n.Z(lo«i.yd.; 2nJ 9194.9625 .q.ViSfd 18518.8080
Q wu..* ■ *i ja. ■ /!»». 110 8q. ft. 10 eq. m.
.n 1*fW nf J' t'^^f'S^^fenoc between the area of a floor 50 feetsquare,
^^•n1 r ?^''''' t^*"^ ^^ ^""^ ^"^-^^^ ^««- 1250 feet. '
lU. iind the bases of rectangles containing each 19208 sq. vd
S'2 8(?v) /h 7n"f.n'''?''/r> ''* 100 y^-' ^»d 7,24 yj., 3rd
iJ52.80 yd., 4th 705.fa0 yd., 5th 940.80 yd.
M TT. 11 "^"n ,^''*- ^^^-^^ y*^- 5 2nd. 85.75 yd., etc.
11. How many boards will be required to floor a room Ifi yards
loDg by 8 yards wide, .f each board is 3.90 yards long by .32^ard
10 A -4 11 o- V „ . . ^w*- 102.56 board's.
12. A side-walk .3.) i\. 3 :n. long by 2 ft. 9 in. wide is to be orer-laid
with a nuxture ot bitume and sand. What will be the cost at $2 92A
a square foot? ^n... §283.54 + .'
l.-i. Ihere is a square whose area is 3600 vd. ; wh^it is the side of
a square, and the breadth of a walk along each .side and each end of
the square, which sliall take up just one half ..f the v-hoie'
fl ^A**- ^ Hi ^\*^.o*" the .square; 8.78+ yd., breadth of the walk.
\\ piece of land in the form of a parallelogram is 2i;4 yd. loa^'
and Its width is^j of its length ; how many bushel, of wheat will ^
required to sow it, it it takes 1 4 bu. per 1000 sq. yd. ? Atu. 43.56 bu
■K'^nsATroN OF nvHTAm,
PROBLRM n
319
aa L»
«'• I'ltiu tJie area <if .. . • i "^ *!•/"•)
32.2 feet. *'"'' '^'^^ "-'angle whose ba«e is 7fi , . . .
«-Afleldof»,.- , ' ^ ""«'"f l"«ifJi will covW
Pkoblem III
586. Rule.— I a,?^ ,,
I T . "*" "'*^'*'' "'"^ '* A"'/
•«« te ,Ae «;„,>«;„„„ '?«'« ™»( of Ihe product, which
* "~ ^^ half ,UBa . 22 — 8 s: 13.
f
320
i'
i. ;
1
1
I
i 1 '
1
1
i
i
1.1!
I. ! r
MwisuBATioif ev mKrA<m.
3rd rem. Then.
Irtrem.; 22 - 16 = 7, 2nd rem. ; 22 - JO = 2
^:?;?i^;';s5^^;- jrc ^ ^^ ^ ^ ^ ^= ^««^^ vioor^
25 fiq^^t" •"*''' ''f^''''^»g"'«''fi^ld are 49 chains 50%^^ "^^ ^"^^ .
^5.69 chains; what is its area? cnama, 50.25 chains, and
4. Whatis'theareaofanisosceJe^ ,ri„ . ^?- ^^-^^ 97 9 acre...
each of the equal sides 22 5? '' '"*"^''' '^''^^^ base ia 30, and
5. How many square vards in o ♦..: i , •^"*- 251.55.
10 ft. 4 in., an.i LOfeet ? ^^'' ''^°''' ^'^^^ «^« 8 ft. 5 in.,
6. How many arnenta arp «1,«h^ ;„ „ . ■ . '^"'- '^•^'^■^ ^q- y^'-
15 to. 3 ft, 24J to.,'^!;?.^ ; ,0 'ft ? '':i^"g"^'' fi^'^i ^vhose side, are
7. There is a triangle hi in . -I"^' ^ ^'''P' ^^■^^'■^ «q- per.
shortest .ide 9 2 f et^a^d he oS m^ uf T'^'^^ ^' '^'"^ 'fe^^' ^''^
contents? ' ^^ ''"'^'^ '^"^^ 10.4 feet. What are the
8. How many acres in a frian^i- i .l '^^' '^^'^'^^ ^- ^^et.
and 1147i yards? ^ ""'^T t'^'-^e sides are 570, m,
9. What is the area nf « t.- . '^"*- ^0 A. 3 R. 4.72 per.
35 perches? * ""^ ^ tnangular meadow, each side meafuling
Kl. Find the area of each offl,»f^ii • '^n*. 5;^0.44 + per.
Ides are : Ut illTalXd^^^^^^^^
Ans. 1st 106.28+ bo ft. 9r.A i^l'A ' ^^d 81 yards?
square yards. ^' ^^ ' ^°^ ^^^'^^ + «q- 't. ; 3rd 2840.99 +
Problem IV.
To find the hypothenuse of a right-angled triangle when
the base and perpendicular are known.
giJ'cri^eRL^a^^J^^/i^^,^-^^^^^^^ whose area and altitude are
tfi^ 6a,e. * '"^ alHtude, and douUe the quotient, the rettdt ioM gve
we^a^eJ'A^R - llf^'T^^'i ^'■'^"g^^ ^ ^ C,
to find A C. '" '''^' ^"'^ ^ C = ^S '•eet;
Operation. 203 =_400; is^ = 2265 400 +
226 = 626; V 625 = 25 ft., AC. |
2. The height of a mast planted on the brink
of a pond, ,s 144 ft., and the breadth of t^^e. 5
opposite edge of the poL? ^ '^'"^ '^' ^^P f *^« "^^^^^ to the
^ ^^^ Atu. 290.24+ ft.
fl rem . The n.
04; V4004 =
in a triangle,
16i 8q. yd.
!5 cliains, ami
.4979 acres,
lase 18 30, and
ns. 251.55.
are 8 ft. 5 in.,
64!) eq. yd.
hose side.s arc
)G3 eq. per.
15.6 feet, tlie
'Viiat are the
139 ^- feet,
are 570, 6{0,
k. 4.72 per.
Je measuring
).44 + per.
angles wjiose
.vard.s ?
J 2840.99 +
ngle when
I.
ely.
II he the hy
i altitude are
'etwU wUl g ve
>gle ABC,
= 15 feet,
26; 400 +
.C. £
II the brink
I of the pond
line which
iiast to the
►.24+ a.
3 ««-.««„,„, „ ,„^^_^^^^ ^^^
yorda: finf) ff °f " '"""S-lar field ,, ?„„,.„. „'<"•' lOl/rPfr.
4 Tl, " ■'"^'^''"<'" ' "'"""« I acre and 3 r
„:j • A, 'adder 50 feet Inn., .„:>, __ . Am. U:^^^ 007 ' ^
fiide-walk. :l?l'.^^«'''?eNit will rP.nl, „ L"'_"r ^'f'. 'acMer over to
^n.9. J4.^7I .897 yd.
'!^e other .ide c7the st'ree't l^'S,^"'^ ''> -'
tl>e^aS:oretV?iJ'^'^'^^
. ■'^. What.;nSV''f^^!-^'2^eet?
Ans. 21.1 (eet.
'^ I'ouse, in theW. ' "
,..e, if
Ans. I7.G7 ft,
on each side were 17.<
^"« 24.78 ft. ^
-'^- What would u''f'''!'!^2^eet?
feet? ^"'^'^'^''^^^'dtb, if the rafters
Proble.m V
''•'en the h,p„,|,e„„,e ^^^ one sidl „f u
'*•• i. in the rieht- " -
riven A f <.. ., "6"'
given A C ~? '>?!• '''^^'<-a".?Ied (Wangle A R d ^. ,
2 ■Vr'V''"'' '"'=■'«« i «25 - 400 = 225 . ^2-^
9n fa^t — "J f^'-.i^uuse era
/ 4l ,''^^* ,'« t'^e ba.se ? . ^.
■4n*. 06 feet.
ong. anditsoppolitevokpL^',.?* ''"^ «^ t^ie rafters be \( fl
Problem VI.
-^ "^e area Of a trapezoid.
Orijj. Rule Mth' 1
^^ t-o: the quotient wiulTtt^X'^'^-divi^^
fi !
'1
)1
I , I
. ■ 1
1
. 1
!
!
i
si'
j
Mf
J
ii
322
MBI^SURATION OF SDRFACES.
Ex. I. What is the area of the trapezoi*^
A BCD, having given A B = H4 yards, D C
= 26 yards, and D E =» 20 yards?
Operation. (34
-5- 2 = 600 eq. yd.,
26)x20= 1200; 120C
Ans.
2. Required tlie area of trapezoids who^e perpendicular heights auJ
bases are: 1st H = 16 It., B = 24 k. and 36 ft. ; 2nd B = 20.15
■>i.2f) yd. and 62.49 yd. ; 3rd H = 36J ft., B = Ib^^ fi.
vd., B
and85ift.: 4th H = 55 A yd., B = 106.iyd. and 134j»'„ yd. : 5lh
1st 480 sq.
ft.
H = 7(1^ ft., B = 145J ft. and lODj a. Ans.
2nd !)74.65u5 &q. yd. ; .3rd 2923.15 sq. ft., etc.
3. What is tlie area of a trapezoid, the parallel sides of which are
12.41 and 8.22 chains, and the perpendicular distance between Jhem
6.15 chains? . Ans. 5 A. 1 R. 9.956 per.
4. The parallel sides of a piece of land having the form of a trape-
zoid, are 2482 and 1644 hnks, and their perpendicular distance is
1030 links: find its area. Ans. 21 A. R. 39.824 per.
5. A field in the form of a trapezoid whose parallel sides are 76.28
and 60.72 yards, and the perpendicular distance 4(i yards, was sold
for $18768 ; what shall be the cost of another field o( the same kind
having a rectansular form, who#e base is 115 yards, and altitude
76 yards? ' Ans. $51760.
Problem VII.
To find the area of a quadrilateral.
500. Measure the four sides of the quadrilateral, and also
one of the diagonals: the quadrilateral will thus be divided into
two triangles^ in both of which all the sides will be known.
Then, find the areas of the triangles separately, and their sum
will be the area of the quadrilateral.
Or again,
Let fall on the diagonal two perpendiculars drawn from the
vertex of the opposite angles ; multiply the sum of those perpen-
diculars by the diagonal, half of the product will be the area.
n E^' i. Suppose (hat in the quad-
rilateral A B C D, the diagonal A C
= 88, the perpendicular D B = 27,
and B F = 25 ; what is the area?
Operation. 27 + 25 = 52 ; 62 x 88
-r- 2 = 2288, Ans.
2. In the quadrilateral A B C D, the
side A B <« 12 lieet, the side B C =>
16 ft., the Hide C D >^ 10 ft., the eicU
MENSURATION 01" 8DRPA0E8.
323
e trapezoi*^
yards, D C
200; 120C
leightp and
1 = 20.15
= 75j'(» n.
'„ yd. : 5lh
I) gq. ft. ;
r wbicb are
weeo them
956 per.
o( a irape-
listaace ih
,824 per.
s are 76.28
ii, was sold
eame kind
[)d altitude
$51750.
', and a ho
ivided into
be known.
their Hum
I from the
one perpen-
i the area.
a the quad-
igonal A C
D E = 27,
je area?
2; 62 X 88
^ B C D, the
side B C =.
t'l., the eida
AD =
1 P ft., and the diagonal A C = 22 ft. ; what ia the area ?
9 «,, , . , ^ns. 174.02 aq. ft.,
.i. What 18 the area of a quadrilateral whose diatronal is 40.25 feet
and the 2 perpendiculars 12.25, and 15.05 ft.? 4.' 549.4125 sq ft '
4. Kequired the area of a quadrilateral whose diagonal is 108 feet
b inches, and the perpendiculars 5« feet ?, inches and 60 feet 9
'"^>^|;. , ,^ Am. 6347.25 sq. ft.
.0. i;ind theareaofeachof !he follow! n^r quadrilaterals: Ist dia<'-
onal 65, perpendiculars, 28 an<l .^8.^; 2nd perpendiculars, 18 auTl
lb, diagonal, 42; 3rd diagonal, 100, perpendiculars, 35 and 30.
Ans. l.t 1998.75; 2nd 714; etc.
6. In the quadrilateral A B C D, A B = 40 yards, D C = 36 yd
Sfh " Vf-: ^ F ^ ^^'^^ y^- 5 ^'^«' F E = 8 yd.; find the area
ofthequadrdaterai. Ans. 1280.42 f sq. vd.
7. buppose that in the quadrilateral A B C D, on account of some
obstacle, we could measure only A B, D C, BF, D E, and F E which
measure respectively 26, 22, 20, 21, and 7 yards; what is the area
of tUe quadrilateral ? Ana. 585.275 sq. yards.
PaoBLEM VI i I.
To find the area of a regular polygon.
5»1. Multiply (he perimeter of the figure bij half the per-
pendicular let fall from the centre on one of the sides, and the
product imll be the area. Or,
Square (he side of the polygon, then multiply the square so
found, by the tabular area set opposite the polygon of the same
number of sides, and the product will be the area.
The following Table shows the areas of regular polygons of any
number of sides, from three to twelve, the side of each being unity, or
1 ; It also shows the length of the radius of the inscribed ci°cle
Number
of sides.
3
4
o
6
7
8
9
10
11
12
Names.
Areas.
Triangle. .
Square . . .
Pentagon..
Hexagon
Heptagon . .
Octagon.
Ngnagon
Decagon.
Undecagon
Dodecagon.
0.4330127
1.0000000
1.7204774
2.5980762
;;. 63391 24
4.8284271
6.1818242
7.6942088
9.3656404
11.1961524
Radius of
inscribed circle.
0.28S6751
0.5000000
0.6881910
0.86602.')4
1.0382617
1.2071068
1.3737387
1.5398418
1.2028437
l.b660264
i
I
1
'1 f
I'!
I '
9£4
MKNBtmATION OF SUmFAOBS.
E:v. 1, Required the area of the regular
pentagon ABODE, each of whose sides A B,
B C, etc., is 12 feet, and the perpendicular
P, 9 feet.
Operation. 12 x .5 x
f = 270 ft.,
Ana,
tbe 8id«8 =s 18
2. Find the area of each of the following
regular hexagons: 1st side, = 20, perpendic
ular =-= 15; 2nd perpendicular = 12^, one ot
3rd side, = 36, perpendicular = 27.
, o . , , ^ns. 1st 900, 2nd 675, 3rd 2916.
3. Kequired the area of each of the following regular polyfone
1 of a pentagon whose side is 30, and the perpendicular, 24°feet-
2 of a heptagon whose side is 16, and the perpendicular, 12^ feet;
.irci of an octagon whose perpendicular is 20, and each side, 22
,• w. , . , ■ , ^«»- let 1800 feet, etc
4. What IS the area of the following regular polygons: let of a
hexagon whose side is 25.40 chains; 2nd of a nonagon whose side s
^0.5o chains; 3rd of a dodecagon whose side is 28.30 chains?
. -. ^ns. 1st 1676.174841 sq. ch.; etc.
5. Uow many pavements in the shape of a regular hexagon, the side
of which IS 3 incheis, are required to pave a room 6 A yards lone by 41
y»'"'^«^'de? ^/M. 1.31+ pavenfente.
Problem IX.
To find the area of an irregular polygon.
592. Rule. — Divide the polygon into triangles and trape-
zoids ; find the area of each separately according to the Proh, II
andYl; the sum of these areas will be the ivhole area of the
polygon.
Operation.
+ 64) -T- 2 =.
= 31 X (27
AmB = 41
4464. oCD =
A/H -= 33 X
4032, GnpV
10) ~ 2 ^
Ex. 1. What is the area of the
irregular polygon ABCDEFGH
measuring asfollows: A/ = 33yd.
In = 84 yd., np = 28 yd., pq 2.
31yd,, 9D = 13 yd.; A7» = 41
yd., mo = 96 yd., oD = 52 yd. ;
H/ = 32 yd., Gn = 64 yd., Fp ==
27 yd., Ey = 70 yd. ; wB = 32
yd., oC = 61 yd.?
32 -^- 2 = 528, H/nG = 84 x (32
28 X (64 + 7) -V- 2 := 1274, F»oE
i>03.5. E«l> = I:-J -' ^n _i_ '> __ ^KK
l5o;-
X oi
EyD = 13 y. 70
455.
52 X 61
2 = 65(5, BwtoC = 96 X (32 + 61> -^ 2
+ 456 + 66C , iiU^lm - 1441.8.6 ,q. yi., or 2.M6+ Je^lt
the regular
3e sides A B,
erpendicular
570 ft., Ana.
he following
•, perpendic.
12^, one ol
3rd 2916.
T polygons,
lar, 24 feet ;
ar, 12^ feet ;
ch side, 22
3 feet, etc
is: Ist of a
rhose side 's
line?
ch. ; etc.
gon, the side
3 long by 4|
avementfl.
MENSURATION OP .-DRPA0E8.
(tnd trape-
\e Proh. II
area of the
area of the
!DEFGH
1= 33 yd.,
yd., pq «=
Am = 41
== 52 yd. ;
yd., Yp =
wiB = 32
= 84 X (32
274. FdoE
- 2 « 455,
l> -^ 2 «
he polygon
I + 1503.6
acres, Ana.
as
2. Suppose the same irregular polygon A B
follows; Am = 10ft. fin.,L = 32 ft
ft. 4 in. /« — 0/ A n • ' „ "-' ""
325
C D E P G H to measure
6 ft. 4 in., In = 21 n. 9 V:' Tp Z % l' V"-' oU = 28 ft. ; Al
■= 4 ft. 10 in.; Bm = 10 ft ;^. 7. l" ^-'.^^ = lift. 6 in. oD
Qn = 16 ft., FP - 4ft!Vk,%rJ^^- 2.n ; ^^ T '^"- ^ -'
"V ^q la ft. 8 in. ; what is its area ?
Ans. 1297.82+ eq. ft.
PROMISCUOUS .XAMPLBS I» R.CT.UN.AL .,™p«E».
4 yards high; allow-
ceilin„ ? P" ^^"^'^^ yard for Uie walls, and fin nf= e^°.
le
ceiling ? ''^ *'" "^"^'■'^ y^''^ fo' tiie walls, and 60 cts. for tlL
2. Some paper 15 inches lon^r an,i 10 • u • .'^"*- $1^5.56.
quire; what will a quire of the LmT ^^'"«^«« wide, costs 1 6 cts. a
long and 13 inches wide ? ' ^"^''^^ "'''' ^h'«'' >« ^^^ >nche«
3. The panelling of a room is 191 t^- 1 .'^"*- ^-^'il-
what must'^be paid for It Cwin^ ?hi? h' ^^"^ ^""^ ^ ^°'«^^ high:
I8a. 4d. a sq. toise, and tlie naTnJL r,f o^^, ^^rpenter'n work cSsts
42yar..s? * ^ ^"^"^'e, whose sides are 20, 30, and
„^^- ThehypothenuseofatriancJe is 4^; fo.f a ^'^"5" ^^^-^^ yd.
25 ft.; what is it3 base? "**"«'* '^ ^^ «et, and its perpendicular
32 ft. long and ISmchesZJ^^i^X 1 f''''^'' ^''^'"' ^he rolls bein"ir
at $1.75 Iron ? '^''' ' ^°*^ ^^^'^^ "^"^^ bo paid for the whole
9 What is the surface of a <^hepf nf -i 30 rolls; |52.60.
wide? uii^ceota sheet of paper | yd. long and | yd
10. The sides of three sauares Rr» q a A ^"^^ ^''^•> °^ "'i ^q. ft.
12. A 6ide.walk 6iyardslon-andlAvaHJl^!J' pavin.-tile..
with stones, each stan% has a aurfaco o 70 sauarlt'.;' ^ ^l P*^^'^
b3 the cast of the whole pavement at the rat2 of ?1h' a'' ' T^'^S^^^
etonea? ''*'' '"^ '^^'^^ ol i5>18.i)0 per hundred
J 3. What ia the area of a panlpn in tl,^ »Uo * ,"^^*" ^32.5<i.
length of which i. 45Td an/ti;';';4dtS 2f;j7' ' ^^^^-^"^' ^«
_ 14. A tjquare yard of a floor r.nQt«$9 «o • h» v' • «
*^« .i^^^^dUy. 5- yeards ; what i7the I^'t f """'^ ^ T^f^''^^
lo. A ladder 16X feet iu leu^nh stands unvlcrhr .. • . ^^i yards.
far must the bottom of it be d?awa out from f b TT^ ^ ^^'"' ''«^
the top 8 inches ? ^"^ ^^"^ "^^''^ ^•'> »" to lower
•ud 5.2o yd. h,«h, at the r«teof $i.ia tha^. yd. 7 AZ%lt88+'
326
MENsnaAxroN of surfacbs.
I'r
I
j
L
' i
17. What cost a piece of cloth 12^ yards long and I A vards wide,
at the rate of.$1.90 a yard in length? Ans. $23.15.
18. What is the area of a trapezoid, whose diagonal is 45.10 yards
long and the two perpendicular?, 15,80 and 20 yards?
,„ . , , Ans. 807.29 sq. yards.
ly. A man plastered three ceilings each 7.35 yards lono- by 5.40
yards w:de, and painted 6 doors each 2.05 yards high by L05 yards
wide ; what sum must be yet paid him, if he charges $1.22 a sq. yard
for tne ceiling, and fO.HG a sq. yard for the doors, havinir been paid
already $22.40 on account? ^
20. Find the side of an equilateral triangle equal in area to a square
whose side IS 8 feet. Ans. 12.15 + ft.
21. Find the area of a piece of land comprising three trapezoids,
and one triangle ; the parallel sides of the first trapezoid are 36
and 54 yards, altitude 19.50 yards; those of the second are 110
and 75 yards, altitude 126 yards; those of the third 186 and 141
yards, altitude 219 yards; the base of the triangle i.s 69 yards, altitude
/9 A%n u 1,,-. ^ns. 10.244+ acres.
IZ. A field whose parallel sides are 630 and 436 yards, altitude 80
yd., 18 let for $200 a yr. ; how much is it per acre? Ans. $22.70 + .
23. A room 12 yards long by 7 yards broad was floored with boards
rf yards m length ; the waste made on employing those boards was I
oMheir gross surface, and they cost $.25 per sq. yard, gross surface.
Ihe work was done in 12 days at $1.10 a day, and the nails used
amounted to $2.50. Find the whole cost of the floor. Ans. $39.70.
24. A man wishes to plant 1815 trees at an equal distance Jrom one
another, so as to form a rectangle whose length is to its breadth as 5
18 to 3 ; how many trees should he plant on eacli line ?
^5. Ihe g of the cost of a barn gate being paid, there still remains
I of that cost plus $23.40 to be paid. Suppose the barn to have two
gates each 3 yards in width and 5.40 yards in length : what cost the
square yard? ° ^^^ ^4
26. Some earth was brought and levelled upon a field whose area
equals that of a regular heptagon, the side of which measures 42 yd. ;
i^hat cost the work at 4d. a sq. yd. ? Ans. £40 1 3 + .
27. What will be the cost of roofing a building with sheet-iron at
$1.22 a sq. yard, if the roof comprises two equal triangles whose bases
are 9.40 yd. and altitudes 6.32 yd., and also two equal trapezoids
whose parallel sides are 25.48 and 16.08 yd., their altitudes bein<r the
same as those of the triangle? Ans. $392.92 +
28. The breadth of a field in the form of a parallelogram* is to 'its
length, as 5 is to 18; what are the dimensions of this field which
sowed in wheat, produced 28f bushels per acre, and 345i« bushels
"'o^"^ . ,. .. i«»- 460.24yd. in length; 127.84 yd. in width.
ZJ. iin indiviauai has a property forming a trapezoid whose parallel
8ide^ are 465 and 806 yards, altitude 550 yd. In the centre stands a
square pond whose side is 45 yd. Find I» the whole area of the field •
i" that of the pond ; 3° that of the cultivable part. '
Ans. 1« 349625 sq. yd. ; 2« 2025 sq. yd. ; 3« 347500 aq. yU.
MKNSURATION OP SURfACES.
I vardw wide,
s. $23.75.
I 46.10 yards
sq. yards,
ong by 5.40
y 1.05 yardfl
',2 a sq. yard
ig been paid
I to a square
2.15+ ft.
? trapezoids,
zoid are 36
md are 110
86 and 141
.rd3, altitude
I + acres.
, altitude 80
522.70 + .
with boards
(oards was ^
•OSS surface,
e nails used
r. $39.70.
ce t'rori) one
)readth as 5
5 and 33.
till remains
to have two
lat cost the
Ans. $4.
whose area
ires 42 yd. ;
1 3^.
iheet-iron at
ivliose bases
trapezoids
;s being the
392.02 + .
am is to its
ield which,
5J^ bushels
in width,
use parallel
tre stands a
3f the field;
10 sq. yd.
327
wlull; ^Illd'^Jd^s ^r^J^tf ITo'ir ,1> r° ^^"^^' ^^^P^^-^'ds
•qnal triangles wh..seba,;es are Ifi20^v'' i-jT V'"' ^'^^ ? 2" two
l-'ps each being lo.so v ..Ton 'hv Vv V f "^T'"^ ^''^^ ^^^ ' ^'«° '^
^l"".!,' the gutters; the'siafes wK,.?*" {!:>''*;'' P'"« ' '"'^"^ '^f'slates
0.21 7 yd.,"and ar'e ZrZo 19^ vd" h ^) ^- 'V"''\"'^' ^ ''^'^ ^y
are paid .r sundr? e.pe^ %^iSS Xfe io^stTtlKo? ^^^
4ns. $265.22^.
Problem X.
To find the circumference of » circle, the diameter being
given. °
wcf Will be the circumference.
N0T^4,« is the cireumferenoe of a circle whose diameter i. 1.
. ■^•^- ,^* What is the circnrnterenre nfo
circle whose diameter is 18 yards?
Op.R. 3.1416 X 18= 56.5504 yd., 4„,.
3. What are the circumferpnPf.a r.e ■ i ' , Io7.7106 yd., etc.
^n». I 265.46o2 yd. ; 2" 422.482368 yd., etc.
Problem XI.
To find the diameter of a nimio ♦!,« •
•luccer 01 a circle, the circumference being
594. RVLK-Bivide (he circumference hy 3.141(; and th.
qmtunt will he the diameter. ' '
1^%i'J^V''^'^'^'^''^' ^^^ «'r«'« -hoee circumference is
Operation. 25.1328 - .3.1416 = 8 yards .!««
^^^t^r^V^^f^ who. circun^,.n;es are ^
yd': Ki;2:;^;liJ22?'2o^"'^?^r?^"T"^^«-^ '^^9.2.
60 it 6' 3" ? ^ ' 4«. 1-1/0.;,'.? i '• I ^*^- ' "' *H y^- ; P"
iiw. 1 11.02146 yd. ; 2«' 24.2105 + yd., et^.
e
M
1
328
I
1
J
! 1
1
■1
1 It 1 ^M
■
* ^^^|H
■
i!
1
MKN!!5i;nATrON OP SCTllKAOliS,
PR'BLKM XTT.
To find the length of a circular arc, whea the number ol
degrees which it contains, and the radius of the
circle are known.
n^*'}J*' 1^''^^K.— ;)//(// /y,/y fJir. vinnhpr of degrees hy the decimal
.01 ^•lo, and the product arising, hy the radius of the circle.
E.v. I. Suppose the arc A B to contain
D 120 degree.-, tirui the railius A C be 10 teet j
what is tlie length of the arc ?
Oper. .01745 X 120 X 10 ^ 20.94, Ana.
2. What is the letjgtli of an arc containing
25°, the diameter of the circle licing 15 ft. ?
Ans. 3.2718 11.
E .S. Required the lengtli of each of the fol-
lowing aros: 1 1120 10',(]iainetei- 20 ; 2nd 10" 15', diameter 68 ; 3rd
670 17' 44i", diameter 25 ; 4th 60''. radius 14.
Ans. Lst 2.123 +; 2nd 6.0813 +, etc.
Problem XIII.
To find tho length of the arc of a circl ), the chord and
ridius being given.
S06. llnr.E. — I. Find the chord of half the are.
II. From 8 times the chorda/ half the a'C. subtract the chord
of the whole arc, divide the remainder by 3, and the quolieat
will be the length of the arc, nearly.
Ex. 1. If the chord A B, fig. of Prob. XIl., equals 30 feet, and the
radius A C be 20 feet ; what is the length of the arc A D B ?
OpEiiATioN. First draw D C perpendicular to the chord A B ; it
will bisect the chord at P, and the arc of the ciiord at D. Then A P
= 15 feet. Hence, AC^ — AP^ = oF^, that is, 400—225=176
and V 175= 13.228 =_ C P.
Then D C — CP = 20 —13.223 r== 6.772 = D P.
Again, A D = V A P^ -h P D2 = V 225 i- 45.859984.
Hence, A D = 16.457 =■. chord of the half arc.
16.457 X 8 — 30
Then, r^ == 33.885 = arc A D B, Ans.
2. Tf the chord A D of half the are A B I), %. of Prob. XII be
30 feet, and the churd A B of the whole arc. 50 feet; what ia'the
length of the uro ?
Ans. 031 feet.
/E^
lumber oi
fthe
he (decimal
circle.
to contain
be 1 teet ;
0.94, Ans.
containing
g 15 ft. ?
;.27I8fl.
of the fol-
er 68 ; 3rd
+ I etc.
)rd and
the chord
quotient
it, and the
9
lAB; it
rhen A P
25=176
84.
Ana,
>. XII, be
lat is the
ik feet.
MENSURATION OF 8DRPA0E8. 329
Ans. 64.42.
PttOBLE.M XIV.
To find the area of a circle, the diameter, or the circum-
ference, or both, being given.
^597. nvLE.-AIuItip?^ the square of the diartiefer by .7854.
^'^ultjply the square of the circumference by 07958 Or
Ex. 1. What is the area of a oiroie whose diameter is 12 yards?
i. Fmd tlie area of a circle whose circumference is 12 yards
OP.a. .07M8 X 12> - .07958 x U4 = U.459I ^. yi.', An..
and.h^?£*;aX°"'"'°'= """'' ™"fere.ce is 37.70 yd.,
0,ERi„„„. 37.70 X 8 _ U3.10 sq. yd., An..
low'^M^^ir, .'srvr s?iL'Si t™^
4° 86.59035, etc. *"• ^■''•' ^ "^''"i 3" '9«3-50i
PaOBLEH XV.
Oiven a circle, to find a .aiiitre i.,k,»i, .k.n v._. .
equal area.
SB
Ji?lJ:"~'- "■*" *"°""^ X -8862 = .ide of an ,^
II. f A. c,>ra^«.3K» X .288J = «a. ./■,„ eyui,^, ^«,„
«r,>|
330
MENSURATION OP SURFA0E8.
,1 i 1 n
I If
f ill 111
'i II '
,1
I:
f- 1
ill
III
• 'ill I
Ex. 1 The diameter ofaoircwlar field is 650 yards, what would
be the side of a square field of an equal area?
OptRATioN. 6o0 X .8862 - 676.03 sq. yd., Ans.
2. The circumference of a circular fishpond is 200- what is the
3)de of ;i .square of an equal area?
Opkuation. 200 X .2821 = 56.42, .4ns.
3. Find the sides of squares of equal areas to circles whose circum-
ference^-are l"250yd.; 2^ 300 yd. ; 3" 412.50 yd.: 4" 135.75 yd.:
L '«;..'!>'-"• J ^"*- 1° 70.525 yd. ; 2» 84.63 yd. ;
3« ll6.:{(i(;2D yd,, etc.
4. What are the sides of squares of equal areas to circles whose
io\ToT ff ^'^ 2^ ^^-5 2° 30 ft.; .3« 73.10yd.; 4« 45 ft. 8 in.:
o! f ^*?^ /.'^- ^ . ^"»- 1° 22.155 yd.; 2^ 26.5860 ft. ;
3" bb.5536+ yd., etc. '
Problem XVI.
Given the diameter, or the circumference, of a circle, to
find the side of the inscribed square.
5»». Rule.- L— The diameter X -071 = side of the
inscribed square.
II. The circumference X .2261 — side of the inscribed square,
Ex. 1. The diameter A B of a circle is
300 ; what is the value of A C, the side of
the inscribed square?
Operation. 300 x .7071 - 212.1.S, Ana.
2. What are the sides of the inscribed
squares, if the diameters of the circle are
1«312; 2«400; Z^ 150.20: 4° 225.,S0 yd. :
5" 170 ft. 8 in. ? ' '
^ ^"«- I'' ;^20.6152. 2" 282.84; .so 106.206 + , etc.
•• Hequired the sides of the inscribed squares of which the circum-
ipivncos of the circle are 1^ 718 yd.; 20 180.40 yd.; 3^ 368.10- 4"
1.!;).70 yd. ; 50 800.20. Ans. l^ 161.6218 yd. ; 2= 40.608 + yd! i
.-1'^' «2..^5y31, etc. '
PliOBLEM XVII.
To find the area, nf a ttt^p.tnr nf a n\To\»t
600. Rdlb.— I. Find the length of the arc by Problem XII
VII
II Multiply the arc bjf one half the rad»U9, and the prudm^
II be the orta
-f.Ti-v'i-.f'ir' '
f^^Sffifcti"
MKNSURATION OP rtUKFACE.S.
, whnt would
what ie tbe
331
,J. Find .he area era, actor „.„,, ,„<„„, ,. I'^anfufel;^;!,: „,■
5. Wl,a. i. the area of a «„ioirole i„ „,„■„, ,b. J,"„'k ilTjf "
C- What i« the area of a .ertnr „f , k- i .l ''"'■ ''53-874r,.
•nd the r.h„, of the droit 1"l7' °' """='■ "" j}^,^; '^ o'o^sVoe' k "'
Problem XVIU.
To and the area of the segment of a circle.
111. V f he segment it areaier fhnn tJ.^ • • ,
area. /.^.,A,,; L, ij. /^r L ;?Lf / /r*'"'"^'; '^/'^ '^^ ""^
either case, will be thiareareqXd ' ""'^ '^' ''"'^^ *"
Or use the following
""" '-• -: -» • "-i" ^^.hf s Of .r-e-A ^o^ rj
Operation, "^ ' " =~^=^
of C P.
ofPD.
-AD:
iiieasure
nieawure
I
26.7309, the measure
■
I
I, .1
332
MRNSURATION OF SURI-AOEH.
Jd. 20
ftniSVp^ 'n?i ^^^'^'•.a'^'"^ - 257.309, area of the «ector A D B C;
JSrvrm .,?, - //o'' CAB- aroa of Reginci.t .v D I{ ; that is.
267..^()J _ 1!)2 - 6r,.309, area ro(,uire.l. It is alnc cbvious that the
area <n the lector A D B C eul.traited from that of th "^IJh'ole drcl.
9 u ' . '^^^^ ^''^ ^"^^'^ of the wc*oP A E B C.
2. Kequired theareaofa Hej,'nient who8e arc id 220 dejiroeB the
radius ofthe circle heing 20 yanis. v. .« ^^ uegrees, ine
onP^^m'^'^'^^'* '^'*® '^^'"'''*' ^f 220" less 360° - 440° — 360° =
Vu \'»« ^'•o rectified of 220« == 3.1416 x 40 x ajja =. 76.79 yd
The chord of H0« (we Table of chords) = 20 x 1.2856 = 25 71
/ 76.79 + 25.71\
«n!l'fi^'*f V^^ f ^* ^''^''^ sejrment of a circle whose radius ia 10,
and the chord of the arc 16 yards ? '
ifl^^^'VJ'"'''", J''^ *^''^'''^ '" ^•"' ^^^'^^ fof tJ»e arc of the segment -
OfiTrA ."J.^^' ^-Z' = "^'^'' ^"' -= 106.333 + ; (3.1416 x 20 x
-- nS .^■.^^T '^f ^*^^- ^'»« °^'°'"*^ ^f an arc doubled, or [360^
--(10b«20' X 2)] - 147" 20' = 1.9193: 1.9193 x 10 == 19 193-
Lt, ^Anf' " ''■''' "- '^^ = ''-''^ sq.yd.Meaofth;seg-'
anhlTi'!!!"'!^!'^^^^*^^^'"^"^' ^^'^ '■ad'"« Of the circle being 10,
and the chord ol the arc 12 yards. Ans. 16.326 m. yd.
diameter of H T%r°^ ^''' ''°'"'"^ ^^'°'« ''*''"^^^' '« 27 and the
diameter of the circle 75 ? Ans. ] 432.3 1 + .
of the d?cTe e! **'""'' of a segment whose arc is 90^ and the radius
It T . *, nns, 28.27 + .
sf Jm„V °'f "'rV"''"' '» ^° •■*■«'' "I"' ■"■' "'" area.ofihe
'io o'j 'jioc ,. \„ ._ /ina, 1" 8.1075 sq. u. :
^" 23.3125 eq. ft. ; 3« 170.75 sq. ft., etc. ^ '
Problem XIX.
To find the area of an ellipse, the two axes being given.
9^^^ liULE.— 7lfMZ///'({/ the two axes together, and their prod-
uct by the decimal .7854, the result will be the required area.
s £.v. 1. What is the area of a garden in
the form of an ellipse whose transverse axis
.,_ . , A B >8 40 yards, and the conjugate axis D B •
*r I Ib is 25 yards?
Operation.
eq. yd., Ans.
40 X 25 X .7864 = 786.40
oA^;„^®*l"''"^'^ ^^^ ^^^^ ^^ *^« ellipses whose axes are 1«» 5 and 4 vd •
yd. 60 70.40 and 4- 66 yd. Ana. !<> 16.708 sa vd -
20 6S.1269 eq. yd. ; 30 98.1934 «,. yd., eta ^' ' '
)r A D n C}
i> ; and the
• 15; that ia,
iUH, tliat the
whole circle
degroes, the
— ^60° =1
= 76.79 yd.
>6 = 25.71
segt., Ans.
adius is 10,
segment =»
6 X 20 X
d. or [360<^
= iy.l93;
of the seg-
; being 10,
5 sq. vd.
!7 atid the
J2.31 + .
the radius
28.27 + .
reas of ihe
75 ft. ; i"
sq. ft. ;
given.
leir prod-
area.
garden in
t^erse axis
axis D E
= 786.40
tnd4yd. ;
md 34.18
1- y^' i
MBNSURATION OF SURrAOES,
Phoblem XX.
833
Given the area of an ellipse and one of its axes, to find
the other axis.
Phoblem XXI.
To find the ciroumfe, , of an ellipse, the two a«,
being given.
o„rf^^, ''"'-^-^""'f'.'/ 'he mm of the two ox,, h, 1.5708,
and the product ,„n gtu, ike drmmfjence, warly.
Op™*t,o»^ (20 + 16, X 1.5708 = 66.5483, nearly. An..
Problem XXII.
To find the area of a circnlar ring, or of the space included
between two concentric circles.
^ 605. '^m.^.-Midtiply the, sum oftke two tUnmeter-^ hi *Ji-!r
rifr'o;,""" '^''P'''^'''' «^^"^' % -7854 for the i^reanfhL
fr^)lZ '^^,^"'^*^ 'if'^<'<^^ ring, siihtract the square of the /ess
6y the decimal .7854, thejtroduct will be tht area.
<?' ''
(■i-
M
334 PROMHoiroue bxamplu in oiroular subfacm.
Ex. 1. 'I'he diameter A B is 20,
and D B is 12; what ia the area of
the ring?
Operation. 20 v- 12=32, the sum ;
20 — 12 = 8, difference; 32 x 8 x
.7854=201.0624, area ofthe ring, ^ns.
Jwefn*Il?p'!ifrr*T^''^^/"'^^^' ''^^^ ^'" be the area included
•7 w ™ ^^"^^'^ ^na 122 5224
SO v3!''^^''Q'^.?®Y!^i'y^''"'"S8 whose diameters are 1" 24 and
•SO yards; 2" 36 and 52 ft. ; 30 60.30 and 90.50 vd. ; 40 U4..36 and
ioulrtjj '5?-'^L^"^ ?«-^« ^ ^««- ^" 254.'4696 sq yd. ;
^ 1105.8432 sq. ft. ; 30 3576.8372 sq. yd., etc. '
J.
PROMISCUOUS EXAMPLES IN CIRCULAR SURFACES.
1. V/hat is the area of a circular pond whose radius is 12 yards?
2.^Required the area of a circular ^.AZ'eV'l'eS iX
3 *A ^:ro.,io- u • . ^"«- 447.1279 sq. y,i.
a sauare thJt--^^^'V" ''^^T^' * ^^"^ ^''"^ «^ ^ S'^rden in the lorm of
basin? ' '"'^^^'^^^ '^ *^ y^^'^^' ^hat is the radius of the
4 WUa»;«*i - . Ans. 11.354 yd.
7. R»d the area ofa dial ^hose diameter i,-4i/er "•""'"'•
eWne:^ni:^'ss-re,e'°ev™':^r.i^,i"Se:r °'" ^^ "-'
9 Rp/,,,;^^ fk "^".f* ^024.993+ miles, or 1G74.996 leagues.
36 and?7 v^dl ''^ '^ ^" "'^'P'''^^^ flower-garden wliose ales are
10 WhLi^fi. 1 , . ^ns. 763.4088 sq. yd.
14 fek ? ^^ '^"^^^ °^^° ^'■^ '^^^«^' '» ^ circle whose radius ia
radius e^airflL*" •''^"*'' ^^^^''^ of a circular" piece oftttdwh^se
'Son'o?rJl^r"\?'r 'f'""^ P^ '^'' ^"'•^'^^ ^d^P'^'i ^"-r ^''^ con-
iT wv/,^'^:r*yf^^ '^^'"g «"0 toises. .1 J. 2234^ arp.
who'se lV«t joVn""' . u ?^^" *^^i'P"^^i basin inscribed in a rectaiiHe
Whose base 18 30 and he.ght 20 yards? Ans. 471.24 sq. yd°
lateral Sr* t ^''J '?^^^' ^'''^'"^^ circumscribed to 1« an equi-
?K8.
5l B 18 20,
;he area of
J, the sum ;
32 X 8 X
e ring, Ans.
sa included
22.5224.
1" 24 and
114.36 and
eq. yd. ;
^ACES.
2 yanis?
i sq. yd.
eter ih 75
) sq. y.i.
he iorm of
dius of the
.354 yd.
ow whose
' sq. yd.
space of 5
65-. ft.
cupies the
U)d height
054 yd.
sq. feet,
le, 18 1.66
■ by that
eague.^.
5 axes are
sq. yd.
radius is
+ feet,
nd whose
[" tiie cori-
7^'i arp.
rectangle
sq. yd.
an equi-
is 7 yd. ;
de 18 lU
PROMISCUOUS EXAMPLES IN OIRCULAR BUBFAOBS. 335
1<
37.6099 sq. yd. ;
yd. ; 5" an octagon whose side is 18 yd. ? Ans'
2« 76.9770 sq. yd.; 3^ 183.^54286 sq. vd., elc.
iJi'v, f-f; 0°^*"'''°*' •■■° ^"'^ '''•" ''^'^^''^ '^ f^^^; what is the
length ot the arc? ^^„g '34 ^3 , ^
. l^' \f:fr ^^^'■„*'^'i ^^*''^ ^''''c'"'' «q»«l in area to ellipses whose
axes are I « 2b and 12 yd. ; 2- 30 and 24 yd. ; 3« 45 and 36 yd. • 4°
52 and 42 yd. ; 5« 62.20 and 46.40 yd.? ^n» 1° 8 83 vd •
2" 13.41 yd. : 3» 20.12 yd., etc. ^ '
16. What weight will a solid cast iron column securely support,
who.se diameter is .12 yd. in diameter and 3.80 yd. in height, if each
hundredth sq. yd. ot transversal Hection can support 666 poun.ls?
,», ■> . . „ . , An$. 75323 lb.
fn \L S'"Jw ^!,^'^* "} ^\'^ ''"''" '^''■°'« of the earth corresponding
o the 49» of atitude north, knowing that the value of each degree of
longitude, in that latitude, is 80018.43 yards.
18. The diameters of two concentric circles are 45 and 30 ; what is
the area of the ring f n-med by those circles ? Ans. 883.575.
c^ : oT*^"^ I"^7 ""P*' ^ '"'^^^^ '" '^^•^'"s, can be drawn from a tin
on li'"°j.'^^' '°"S by 15 inches wide ? Ans. 205.
20. J he diameter of the bottom of a ba,sket is .46 yd., an! the cir-
cumference of its top is 2.262 yd. ; what difference is there betn-een
the area of the lower base and that of the upper base ? Z'
.„ c' . , Ana. 0.240977 sq. yd.
^l. trom a iinc sheet 28 inches long by 25 mche.s broad, how manv
""If ^ml ^®.*i'''*w" who.se diameters are 2^ and 3^ in. ? Ans. oil. '
22. Ihe circumference of a circle is 314. 1 G yd. : what is the rac'lins
of a concentric circle half the urea ? Ans. 35.35 yd.
.ul^li^^*''?*^?.**^^*"''^'*'^ ""'"^ "'' ^ circular parterre, "knowing
that the exterior diameter of the parterre is 18.40 y.l., and the breadth
5^* ""S 80 yd. ? Ans. 44.233728 sq. yd.
Z4. W^at Utile Side 01 a. square equal in area to a circle whose
diameteria4? ^J^g 3.544 + .
25 The exterior diameter of a circular pond is 15A yard.s, the
breadth of the ring j»^ yd. ; required 1 ^ the area uf the ring ; 2« what
will be paid to have it paved in tlag-.stuues, at tiie rate of §4.16 a
sq. yd. Ans, $171.72.
26. A circular garden whose diameter is 26.5 yd., is enclosed l"y a
fli^^^if'"' "'^ '^'^' ^^"^'^> '^^^ '"*"y bundles of gras.s, each weighing'
3b. 64 b., can be gathered from this ring, knowing that when the
grass dries up, it io.ses 56 % of its wei>iht, and gives 2056 lb. of hay
27 Ihe radius ot a circular pond is 12 yd.; what must be the
width of a grassy ring around the pond, that contains the same
ftr**' Ans. 4.97 yd.
28. A triangular meadow wiiose sides are 6420, 6280, 340U yd.,
eneloseH an eliiptical pond wliu-e diameters are 195 and 348 yd. Find
the worth of the hay produce. I by that meadow, if 5056 lb. are cut per
acre, and sold at 4 cents per l.undle of 10 lb. Ans. 138246.29 + :
29. A man has a ci«tern wliose diameter is 3 ft. 10| in. ; its ed"e,
which 18 23| in. broad, is to be covered with tin-plate at the costVf
W.lOasq.yd. Find the ooet a»». *b.3ti -t- ,
ll
!■'•;
I' i r
■1
iii.
I' ri
336
PROMIBOUOTJS KXAMPLE8 TN CIRCULAR 8URFA0M.
he own .(ill ? ^ °' ^^ P™''/' '" diameto. What part doei
The field p^uMssfoolhoJh' °'^""' '"'°',"'' ^M a>"l 328 yd.
whi s^ireSJa^riirf r-""" -t i"--^ i- '«e.d
beine nart of /pS„ ^- '^^"'«"^ the arc ol" which is J70«
.h; «dtf of'.LVet^T7°/6'vr" "";■"" i™!?' ««'» i» s" and
KS^i^',?^^^^^^^^^ - ^LVthetdi^jTS
^m^:.
-itr-'''
kOEB,
.50 a sq. y<J.
iqual in area
ircular; the
id the diam-
He pays the
3. a eq. yd.
! ; the smith
$399.65.
37 a 6q. yd.
must be the
» each other
:^.351 yd.
per arpent,
he segment
le segment
13 + bu.
g 10 acres,
tt part does
I- sq. yd.
' of a circle
ad 328 yd.
bundles of
bundles,
om a field
ch is J 70®,
e produced
bundles.
a 86", and
iVhat sum
bushels of
boee angle
8 of which
d 1840 lb.
were gath-
MENSURATION OP SOLIDS.
DEFINITIONS.
thite. ^ ^'*'" '' ' "■•'«"i'"<'»"'I,i«h ha, leogth, breadth, a„d
.iafsTr-"^ P'"yhedron i. a bodj, „r ™lid contained by man,
also equal t^Ce arothe" ""' '"^"'""'^ »""'' »"g'«» "«
p£jhithte^s„:t,j:i\:Cprr"^ ^^'-^ -»>
angles are un^uT °° °"""' """^ """"^ «'"'^»
n>aneq^Cai?s^fer:ir:he:/°7 7"''^f ^"^ -
«17. Ti'«'«8»i«loM«Wr«i,.«*i«„^tt„g^,„,^
338
tJ i|
MENStrRATION OP SOLIDS.
hi
■I if
% 'I
In . >
Ri
fc
t i
e.|ual and sirailar triangular pyramids, whose vertices meet in
I lie centre ot a sphere supposed to ; iicumscribe it,
»<afes5^. 618. The regular
Hexahedron or cube,
is a solid whoso surface
present 6 equal squares.
619. The regular
Dodecahedron is a
«.S"S"'' "'■'"'""" "™'™ "^l""' l"'-* '""""S
the" jmmM f""'"f''''''''9>'l"'- polyhedrons are the prism and
„„ *?*• /■ P"™, '■■' » %iro whose bases, or ends, are any similar
cIm ?;,-,i7il.'''"°" "^'^ '^ perpendicular to the base, is
©as. An oJ^Hc
prism is one whose axis
IS not perpendicular to
the base,
624. The height,
or altitude of a prism,
in an „b„,„ „„ ,, „„,„,„ ;, ,^^ perrndiatf'r^'il'
««- r^'"' """"^ l'JP»«>enuse is the aris. "
„.;?*• ^ •"""S"'"'-. quadrangular, pentagonal, hexaKonal etc
rS^onX""" '"' '^ " '"""«'=■ aquadrilatiral, a-penL;!:;:
alle?o?r™.'* ^"»"«">P'Pe'Jon « " P™">, whose base is a par-
anS?'^],^*?"^*'"^'' 'V-^''^ "^S"™ contawed by several tri.
»m«oa verL " "" "" '" *' """° "'""=' """* "'™'' >■"» one
*«r»'*' pjrrjwiW,
P7t-<iiQi4.
f riMtutu ut' a |>/rftmid
ices meet in
MKN80BATI0N or SOLUM. 339
nn^^i- T^® ''•'^** of the cone is the
perpendicular drawn from its ton to
w»s.», ihe generant or side ofthp
»o„c ,. th. hypo,he„„se, which" by the
revolution of the riohuiigled t iaCio
to the plane of itst^aTdt 2 ■L;:,^'^ "^■» '^ -'■-<'
Small oirde. *s»« m,
635, The/.«,^:,r;i of
«'i cone, is the portion re-
maininij when an upper
section is removed.
e:56. A Spheie is a
solid, bounded by a curved
surf'icc, every part of
which is equally distant
trora a point within, called
fSie^ Ti,« J- /. '^c centre.
to a^pJ^I£fZ:L' ^f''='« '^ " '™ -i™" from the centre
thS Jtt:?: jtS;s ^ ticts -^ " "- ^-'°^
betre^tw^Lrpire;' Sh r:^";: ,i:. --™ '---
Circular Spindle is a
o VA ,1. /. ' Spindle 18 a
solid, th<; %urc or shape oi' which
IS marked by the revolution of tl-
arc of a circle about its chord, which
remains stationaiy.
(Jreat circle.
:&
S40
MSIfSVRATION or SOLIDS.
Sector.
Segment.
Spherical Wedge.
T^
Segment with two bases.
643. A Spher-
ical Sector is a solid
generated by the rev-
olution of a sector of
a circle about one of
its radii.
643. A Spher.
ical Segment is a
portion of the sphere
cut off by any piano. The plane is the hase of the segment ; the
perpendic.ilar distnncc from the centre of the base to the convex
surface, IS the height of the .segment.
644. A Spherical Wedge is the portion of a sphere com-
prehended between the halves of two ^rroat circles.
645. A Spheroid, or Ellipsoid, is a figure produced by the
revolution of a semi-ellipsis about oi a of its rxes, that axis re.
maining fixed. When it revolves about its t. ansverse axis, the
figure is said to be prolate ; and when about its conjueate a'sis.
It 1.S called oblate.
J ' = .
Problem I.
To find the surface or area of a prism.
646. EvLE.—Muffiply thepenmeter of the base by the alti-
tude, and to the product add the area of the bases : the sum will
be. the surface.
Ex. 1. What is the sur-
face of a rectangular prism
who.-e base is 3 by 4 yd.,
and altitude 5 yd. ? '
Operation. The perim-
eter of the base is (4x2) +
(3 X 2) = 14; 14 X 5 =
70 yd., convex Hurface ; 70
+ (4x3x2)=94yd.,yln».
^.r. 2. Required the entire surface of a pentagonal prism, when
each Hide ot the base is 10 feet and the heightSO.
Operation. 10 x 6 x 30 = 1500 so ft., convex surface: 10" x
tabular number, or 100 x 1.720477 = 172.0477, area of one base.
1 hen, convex surface = 1500, square feet,
lower base =r 172.0477 " "
upper base = 172.0477 « "
; I
B»4iTC sar&oc
1844.0964 «
MlNSUaATION OF SOLIDS. 341
ri^^^^^^r^UrilugC^ ?'•'«"'» whose ba«e is an
heiglit 2a feet? ^ ' '^^ ^* ^^'°»' measures 20 inches, and ii
. 4. What is the waIl-8nrfi,/>o ^r "*' ^^"^ ^^- ^- ■'''^ "Q- in.
16/eet long and 1 St fjSf ? "^^ '"l''^'' '^-"^' -''"«^ «ides a?e each
o. A rectangular Dri,sini« •? v,^ 1 r , . ^««- 71^ sq. vd.
what is 1° the conve^r, rface ^^ "^' • •'•^- ^'■^'^'^' ^"'^ « ^d. h.Vh;
Its two ba.es ; 3° he side r a ^ .. ^"""' ' • ^^ ^''^ ^^'^°'^ m,rface of
6. What extent of 8.,r/ace is ^n oVi; '^■- ^''^' '/^ ^-^"^ «q- ^d-
are hexagonals, each side ,'ea 'initio '-''7' ''f ^"'^"^ ^''^'hich
pri^n. 20 feet, and the pe WtS ofTL • '"^''''•' .^''" ^'^'^'ht of the
4^ feet ? perimeter of a section perpendicular to the sides
7. Required the entire suriace of an .,,,,^"^- ^•^•60843+ eq. ft. '
whose base is 15 and altitude 12 feet ""^j^"*' -E'Tj '^« '''^'^ «^
Prohlem TI.
To find the solidity of a prism.
fee., a^d it, l.JgfriSfeer'wi.a.t &S.:T'' * ""»*"""S ^
Upkration. 32 X 2 /iq9n7fi9 v. 1= .,,. J
2. What is the «ohdi v !f ! . " ''^'^'^^ "^ ^^'^'^ ^^^'^ ^ns.
eral triangle, eal^idf <ff whirSstes'? " f "'"^^ '^ ^ ^^-'-t"
the prism 18 inches ? measures 6 inches, and the length of
3. How many cub ft in q n^^i i. -4ns. 280.59+ cu. in
b-adU, . ft. » f„ t, fd ptS fftV „"'?'"• ""'o-'-Kli. i« 4,1. ,s"i„.,
■•■ H"» many perches of In ,,r,nr„ "' "*'"• '^"iV »ul). ft. '
5. Jow many .rallons nf u.«fl\r • ' ^*"^- 21.G76 ner
^osedimensio'nsCThe/amfas^^
6; The three sides of the base of an ^^ ^"*" *^^^-
■e V 4. A Q^.-i ^ ..„_Y ^ "^°^ "' an oblique nrism itip«o„^^ -„Z ..
whos
"«!}' 4, 5, and 6 yards, «nd the aSS „*;■?""' ?""""' '4eo-
P-u. are 7, 8, and . ,d. , .ilu«1Sl,;^''S'St! i"'
Problem III.
I. To and th. .uriace of a regular pyramid.
342
M' >
MENgnRATION OF 80LID8.
II. To find the slant height of a regular pyramid from it»
superficial area, and the side of its base.
6..,?^,?*/ r""-:? "TT^'"'''^ '/'^"'^^^' "'''"■ '"^'^^'^^ the area of th,
bct^se^ and divide the remainder by one half the perimHer of the
III. To find the side of the base of a regular p] xamid from
Its superficial area and its slant height, the area
of the base not being included.
««!?*^^; ^^j-J^'—^''!''^^ (hegmn area by half the slant height,
and that quotient again by the number of sidesf ^ '
Ea^. 1 . What is the entire area of a trian-
gular pyramid, the slant height of which ie
iO feet, and each side of the base 4 feet ?
Operation. 4x3=12, perimeter of the
base; 12 X ijjO = 60 sq. ft., area of convex
surface; 42 x .4330127 = 6.9282, the area
of the base.; 60 + 6.9282 = 66.9282 sq. ft.,
entire surface, Aru.
8n^^"n!,")Ti'^ ^r^r^'l \ '''^^".'^'" '"a"g"lar pyramid is 31.732052
sq. tt., an(i the side of its base 2 feet ; what ie its height?
-_°,lo'nr7-^,?;.^'^^^'"^^ 1.732052, area of base; and 31.732052
eter J thets7= io':ee;,'Z.' ""• '''" '' ^ '' ^^'^ '"^^ P^"""
E.V. 3. The superficial area of the sides of a regular trianmilar
Sferu'i^'Jf if "XT '"'""'' ""'°'«" ""•'"^ -'aUalrfi
Operation. 30 -^ 6 = 6, and 6 ^ 3 = 2 feet, Atu.
4. The slant height of a regular pentagonal pyramid is 40 feet anH
6. The area of the sides of a regular heiagonal DVpamiH i« qfio
.irs'i&V"" '" •"'°' "''«'" '' '^«' -l'at1,7he''ESt'e^
7. What is the total area of a regular heDtaeonal n^^rJ^ ^^^
slant height is 21 feet, and the meJnreofiKA^UZ^j ''"°'*
- ^•J^^.:?^«V^*'eg«Ja''l»eptagonal pyramid i8"483°9rMu2e W
and the side of its base 6 feet; ;^ MiUmlaoi height? ^ **
2jm. 96.17+ X
lid from itft
e. ,
• area of the
meter of the
amid from
area
lant height,
a of a trian-
of which ie
4 feet ?
neter of the
a of con vex
2, tlie area
)282 sq. ft.,
31.732052
131.732052
the periin-
triangular
I the liDear
feet, and
', and also
6 sq. ft.
ramid, the
f. 160 ft.
lid is 360
r measure
3|feet.
lid, whose
58?
3 sq. ft.
|uare feet,
17+ ft.
■■NSFRATION OF SOLIDS.
Problem TV.
343
T. am the „rfao. of a, tm.tnu of . regnU, py,.„M.
i^.r. •• What is the superficial area of th«
fill 91? , on^' "PP" perimeter. Then
(36 + 24 -. 2 = .30, and .30 x 18 = 540 vd
lflfi«Hj-;<7o „, area ot the sides. Again. 6 x 2 -iqwnTft') -1'
I5.5884.)72, area of lower base, and 4 x 2 598n7fi9 -. i n onio" =
what 18 its wliole surface ? ^•' ^".^ "** S,^ top 4 ft. •
3 What is the convex surface of the frustum of^T; f '*^-,^-
amid whose ^lant heijrht is 50 fppt ^^,.1/0^ ^.u P "^Ptasonal pyr-
of the upper ba.e 4 feet? ' '''^' of the lower base 7, and
Ans. 1925 sq. ft.
Problem V.
I. To find the solidity of a pyramid.
pentangular, etc , pyramid, from it, solidity and ha^it
and r^lrac, the sq,mre root o/,kesZ,Z ^ "''"'"'' "'"»'*'•.
in. To find the height of a regnlar pyramid from the .ide
01 tie base, and its solidity.
<*e ruuli bfS ^ 'net^mn o/ ilu ,uU ofm &,„, and mukify
hi
344
Ut^MSURATION Of 80LID8.
* I h'
1^'-
m n
Ea:. 1. Wha* is the eoluiiljr of a triangular py»amid, the h^Tgbt of
wliich is 20 feet, and each side of the ba-e 4 (Wt ?
Opkrat»on. 4" X .4330127 x y = 46.188 cub. ft., Am,
Ex. 2. Ifthesolidity.ot'areg. ocfasoiuJ pyramid be 2133. r)273088
soU-J feet, and its height 42 f«et ; waat is th« meaHur* of oae of itt
•quai eiiies ?
OfERATioti. 2433.5273088-7- Vj=173.R233792 ; 173.82^3792-*-
4.8264272 {See Table)=:36, and V 30= 6 ft., side of the base required'
Ex. 3. A rej^ulur octagonal pyramid contains 2433.5273088 solid
feet, and one of its equal sides measures 6 feet ; what is its iiei"ht ?
0PER4TI0K. 2433.5273088 -f- 4.8284272 = 504, and (504 -t 62)
X 3 = 42 feet, Am. ^
4. Find the soJidity of a regular pentagonal pyramid, its height being
15 feet, and each side of its base 2 i feet ? Ana. 53.7649 sq. ft.
5. How many cubic yards in a i.riaii.;ular pyramid, the height of
whk;h is S.CS yards, and the three sides of its "base 1.5, 1.9. and 2.6
yards? Ahs. 1.6669 cu. yd.
I. A regular pentagonal pyramid contains 45.879297 solid yarda
and it« aides measure 6 feet ; what is its height ? Ans. 60 feet.
7. How many solid yards are there in a pentao-onal pyramid, the
sirle of wluch, at the ba^p, measures 6 feet, and \U hei'jht GO feet ?
Am. 45.8794 + cu. yd.
8. What is the measure of one of the sides of a regular pentagonal
pyramid, containing 4678.56 solid feet, and having a height of 64
feet? Ans. 12.29+ feet.
9. An octagonal stone monument has a perpendicular height of 45
feet, and the linear measure of its side is 5 feet 10 inches. Also, each
side of the inner cavity measures at the base 4 feet 1 1 inches, and its
perpendicular height 41 feeU How many yards of stone does the
monument contain ? Ana. 32. 1 973 + cub. yd.
Problem VI.
To find the solidity of the frustum of a pyramid.
653. Rule. — Multiph/ the areas of the two basea together,
and extract the square^ root of the product. This root will be the
urea of a base ichich is a me<in between the other two. Take the
sum of the areas of the three bases, and multiply it by one third
of the altitude ; the product will be the solidity.
Ex. I. If the length of a frustum of a square pyramid be 18 feet,
the side of its greater base 27 inches, and that of its less 15 inches;
what is the volume ?
Operation. 27 in. = 2.25 ft., 15 in.
I-??! =]'^?25; 6.0625 ^ 1.5625 = 7.91015626; V 7.91015626 =
1.25 ft.; 2.252 = 6.0626,
2.8125 ; 2.8126 + h,W^ \ 1.56J6 = 9.4376 : 9.4376 x V -= 56.621
OHb. ft., 4f»f .
MBNHUftATIOR 01" S0U08.
346
a ad ita
tude 1^8 fee? tlh^'^-fVL^ regular pentagonal frustum, wl.one alti-
70 and i) vd r '"''' ^''' '"="'" ^^^'Sons ti.e «id.« of whicl. are
4 H • ^ V • . • ^"''- ' • ' 60484 cu. yd,
•th« t«^ '"any cubic feet ,„ a nquare piece of tin.bw, the areas of
the two ba«efl being 504 and 372 inches/and ,t. lengHi 31^ feet?
Ana. 95.44 f- cub. ft.
Problem VII.
I. To fin 1 the sarfaoe of a cylinder.
-//S.^;^' ^['^:^-~^f¥i/ the circum/crevre of the hate hy the
»ltUude, and t^e product >ri(l be the conie:, snr/ace ; and fo this
add the areas of the two bases, when the enfj.^fnce isre^Jred,
II. To determine the area of surface in a cylindrical ing.
657. Rule.— rr, the thickness of the nnq add the inner
Ex. 1. What is the entire
surf, of the cylinder in which
the .iianieter of tlie base is
10 feci, and the altitude 24
feet ?
Opkuation. .3.1416 X 10
= 31.416, circumlerence of
the base J 31.416 x 24 =
102 y imi—iRKA o- fLi . 753. ys4, convex surf. Also,
= 911 064 ^T. ft fir" °'""' '^'"'' ^'"'"- "■■■■'•'»* ^ <"*•" ' 2)
6 Wliaf io ^K^\ . '^"*- 325.6968 8q. in.
!!
t
I
( -
84S
«*««.:
WENSnRADCON Of SOUJM.
.. How much must be pmd lor the painting of the wall and oeiline
oi i\ c r«ular room, whowe .lianicter is MO and height 1.' fret, at *2.50
*«<l'.y'^-- ^TM. $o89.05.
Problem VIIT.
I. To find the solidity of a cylinder.
eSH. RvLn.—Af^ltipfy (he area of th« buie ht, the altitude,
una the product will Lr (he mlidity.
II To find the solidity of a circular ring.
650. Rule.— ^r/<7 the inner diameter to the thickness of the
ring, and mnltlpl,/ the mm b,/ the nqnare of the thickness, and
this product Inj 2.4674, the result loill he the required solidity,
Ex. \. Il'a cylinder ineasur.' 8 ft-et in diameter at its base, and 18
leet in length ; how many solid feet does it contain ?
«n ?r'if ^''■'I'N- ^* ^ -785^ = 50.2656, area of the base. Then.
50.2(556 X 18= 904.7808 cuh. ft., /Ins. *
Ex. 2. If the thickness of a cylindrical ring is 2 inches, and ita
diameter 6 inches, wliat is its solidity ?
Oper. (6 4- 2) X 22 = 32 5 32 x 2.4674 = 78.0568 solid in., Ans.
3. What is the capacity of a circular basin, the radius of whose base
18 5 yards, and altitude 2 yards ? Ans. 1 57.08 cub. yd.
4. What is the solidity of a cylinder whose bape equals 2.15 ea vd
and aUatude 1.46 yd. ? Ans^ ■^.V^% cub. yd. ''
0. What IS the solidity of a circular ring, 4 inches in thicicnees and
18 inches in diameter ? Ans. 8i;s.5248 cub. in.
b. A cast-iron rod is 4 inches in diameter, and 15 feet in length •
what 18 Its solidity in cubic inches ? Ans. 31S.087 cub. in
7. Kequired the solidity of a cylinder whose altitii.le is 1.50 yd., and
the circumference of whose base :].08 yd. Ans. i.\:-\ 2391 cub. yd
8. Ihe area of the base of a cylinder is 4 ,q. yd., ana -the perpen-
dicular distance between the two bases is 8 yards ; what is its solidity ?
Problem IX.
I. To find the entire surface of a cone.
i^^^\ ^^^^-—MuUiphj the jm-imeter or (he circumference 0/
the base by half 0/ the slant height, and to the product add the
area 0/ tiie bat^e.
II. To find the height or diametex of a cone, one of them
and its solidity being given.
HiifwimATroN op nOLriM.
34T
««1. RuLE.-/)tvir?« the solidity hy .7864; then, if (he
DIAMKTKR be reqmreJ, h, me third the. altitude al»o, and extract
the.yunre root of the quotient; hut if the ALTITDDE he required,
by the square of the diameter, and multipl,, the quotient hyH.
^ E.T. I What is t!ie entire surface of the
cone vhoHp v'ti^x is C, the radius A B of
Its l.r, ^e being j". fleet, and the side C A, 40
feet? '
Oper i-r -1.1416 X (f) x 2) = .^1.416,
«ircmnf. ,i base. 31.416 x Y = 628.32,
convex surface; 10*> x .78iJ4 = 78.54;
628.32 + 78.04 = 706.86 eq. ft., Antt.
i3'^: '^' ,^*'**.*? ^^^ diameter of the ba«e of a cone, if its solidity be
i* feet, and its ahitude 12 feet?
Opkkation. V(24-f-.7854^ V) = 2.764 feet, nearly. Ana.
Ex. ?,. If the solidity of a cone be 36 feet, and its diameter at the
base .^ feet; what is its altitude?
Opek. 36 -^.7854- .3a = 5.0i)29 ; 5.0929 x 3 = 16.278 ft., An$.
4. Acquired the entire surface of a cone whose side is 36 and the
diameter of Its base 18 feet. Ans. 1272.348 sq. ft.
, 5. If the solidity of a cone be 72 feet, and its altitude 30 feet; what
18 Its diameter? j^^„ 3 027+ {-.et.
hpi,;Ji%77."'"T"''^''f^''' •'*'" ""^ * cone is 9.50, and the slant
7^ wf ' "* ^'^^ ^"^""^ «urface ? Ana. 105 744 +
i«; 7>at will it cost to tin a circular steeple, the base of which is
16 feet in diameter, and the slant height 48 feet, at 7.-. ctn. ^er -quare
8. l?ind the convex burtace of a cone, whose slam hei-^ht is 40 feet
andthecircumferenceat its base 12 feet. '
9. If the solidity of a cone be 3684 feet, and its diameter 30 feet ;
what IS Its altitude? ^n«. 15.635+ feet
Problem X.
To find the solidity of a cone.
662. Rule.— J/«/^ipZy the area of the base bij the altitude •
and divide the product hy 3, the quotient will he the solidity. '
Ex. 1. What is the solidity of a cone, the diaineter of who^e base
18 4 feet, and altitude 5 feet?
mSnZ ^\ l-^lTlir ^P.^^^-'^q^^re feet, area of the base;
(l/.&bb4 X 5) -r- 3 = 20.944 cub. ft., Ana.
Ex. 2. What is the solidity of a cone whose side is 2.5 yards, and
the radius ol its hiue 1.5 yu4a ? .' "» •*""
fP
Tf?f
'^^sitt0^mmmemtmm
I >
V'
f
1
j
f
" 11
!
i
i 1
1
' 1
1 m
1
■f^
■I
if
^^H'
1
i
1 1 >
1
1
1
MBMHURATION 0» SOMDB.
Find first the altitude of ttie couo. The altitude, radius, and side of the aon.
2 v^l' Vd'il "I'^r =% i-^^ ~ 2-25 = 4 yd. ; hence, A = ^Th:
I ^J\ ^;IV K ¥ f ^•^'^^^ ^'l- y*^-' *^^* »f ^lie base; 7.0fi86 x
i = 4.7124 cub. yd., Ans. '
8. The circumfejenoe of the base of a cone in 40 ft., and the altitude
/■ Wk f '!»!'' ' r!,^''^ ^ ^"'- 254(;.66 ci,b. ft.
Rf TL vil '^ ^^® '"''"i'^ of a circular pyfan.id. thedia«,eter of which
at the ba,e measures 4 ft., and its height 18 ft.? Ans. 75.3984 cu. i\.
5. VVhat 18 the solidity of a cone whose height is 1.35 yd., and the
area ol the base 3.40 sq. yd. ? Ans. 1.530^ub yd
6. Requiradthesohdityofacone who.se altitude is 1.23 yd., and
the circumlerenoe of its base 1.98 yd. Ans. 0.127913 cub. vd.
altttude 4 yards ? ^„^. ^^^gyg^ ^u^j. ;d.
i Problem XI.
To find the surface of the frustum of a cone.
663. RVL^ --Add together the drmmfennas of tiie two
bases ; and multiply the sum hy half the slant height of the frus-
aZi fP'f'''' ""f *f ^^'^ <^onvex surface, to\hich add the
areas of the bases, when the entire surface is required.
A „ ^^- 1- What is the entire surface of the
/ \ Iruf^^umofacone, the slant height of which
18 J feet, and the circundorenues of the bases
S and 6 feet ?
Operation. (8 + &) x ^ = 70 sq. ft., con-
vexKurtace; B^ x .079.58 = 5.09312, lower
f"''J.n'^/'^'P= 2.86488, upper base; 70
+ 0^.512 -^ 2.86488 = 77.958^^^. ft., entire
surface, Ans. '
h.Lr T y^ the convex surface of the frustun. of a cone, the side
being .7 yd., amd the radii of the bases .3 and .95 yd. ?
s wu^tic*\. .. -4ns. 2.7489 sq. yd.
is 210 Td thlt oTZr T r ?''^*"t' vvhose diameter of the bottom
M ^lU yd., that of the tu]. 2..^0 yd., and slant height 3.84 yd. ?
A Ti, • » Ans. 26.5402 sa. vd
, 4. Ihere i^ a feustum of a cone, whose slant hei-ht is 12 leet th*,
Probi.km Xli.
To find the solidity of the frustum of a cone.
664. Ruus.-. y'kci the sum of tko areas if the two ends, mU
II.
MENSURATION OP SOLIDS.
349
I of thfl aone,
me ; let A be
■ = VT^
7.0fiH6 X
he altitude
cub. ft.
r of which
!4 cu. th
I., and the
sub. yd.
3 yd., and
jub. yd.
^ards, and
zuh. yd.
iiie two
' the/i-us-
h add the
ace of the
; of which
the bases
|. ft., COD-
12, lower
base ; 70
ft., entire
, the side
sq. yd.
le bottom
I.?
s({. yd.
i leet, the
id 9 feet ;
eq. ft.
ids, cKid
ofageometrkal mean between them ; muUlph, the i^rime hv nn.
third the altitude, and th. product Jill he tl 1?/?% '^
Ex. 1. If the diameters of the two base^ of thp frii«f,..» .*•
be 24 and 20 feet, and tbe altitude .30 feet ; wl.at iJ^t" soHj;tv^''"'
. Opkration. 242 ^ .785,1 ^ ^-.^^^^ ^^^.^^^ ^^,^|_^ ^^^^^^^ • '
.90 yd. the area of the lower base 2.25 sq. yd, and of t..e upper I "f
.{. How many cubic feet in the frnstum of a cone, whose altitude is
28 feet, and the diameters of the Li<e.s 11 and 18 feet '' ^'^'^'"^e ''^
4. Required the solidity of the frustum of a cone, the "altitude
being 6.7D yd the c.rcun>ference of the lower ba.-^ 1 445 v and
01 he upper .628yd. ^„,. .coo,.5 ' cub.^'vcf
.■^- Wliat IS the height of the frustum of a cone, the convex surLe
of which IS 84 sq ,t.. knowing that the area of ihe upper 1^ "si
eq. ft., and of the lower base 12 sq. ft. ? JfJ^,. 12 feet
PttOBAEM XIII.
I. To find tte area of a wedge.
U^?mo^t^l'^'~^'T^ ^^'^- r« '^ '^' '^^«^^' ^^l"«h is a paralle-
^A« reqmredarea. ^ ^^'''' '''''''' «''^'«« "''^^ ^«
II. To find the a»ea of a prismoid or frustum of a wedge
.TIT:-^ '.""'- ^^ "i- "'■■ »- »f "- '''•d, and n . ,0
„...! .1 "^- '°:t "«» "' '!« '"o sides: V 12' — n "- li ob
a«d 2 inclies, the length^and tre^lth nJtL 'r "" ^"^'"^"^ "« ^^
1 inches, and the lenSh <k.m fh! l ^ f"'"*" <^"^ «^ ^''^ '» ^od
what is the area? ^ '^' "^^'^ '^ ^^^ upper section 10 in. •
Op.e*«o«. !• X 2 - 20 «^ in., „ea Of Ae base; !• x l .
m
'!'■
350
MINSIFHASION OF SOLIDS.
10 sq. in., area of the section cut off; and 10 x 10 x 2 =- 200 sq. in.,
area of both faces. Then i-^-X =« .5 {„., one half the d iffer, betwee n
the thieknees of the base and the section cut off; and V 10^ — .52 =
9.98 in., the perpendicular distance between tlie base and upper sec-
tion ; and (2 4- 1) X 9.98 = 29.94 sq. in., area of the two ends. Then
20 + 10 + 200 + 29.94 = 259.94 sq. in., Ans.
.J^: ^.^^ ^^°^ of a wedge is 8 in. long and 4 in. broad, and each face
18 in. long; what is the area in sq. ft.? Ans. 2.7191 + eq. ft.
4. The length and breadth of the back of a wedge are 10 and 4 in,,
the length and breadth of the upper section 5 and 2 in., and the length
of each face 20 in. ; what is the whole surf. ? Ans. 3.26 I- sq. ft.
5. The perpendicular height of a wedge is 20 inches, the thickness
ot the head 3 inches, and its length 5 inches; what is its entire area?
Ans. 274.85 sq. in.
Problem XIV.
I To fiiid the solidity of a wedge.
667. Rule.— Multiply the mm of twice (hclenglhof the base
ond the length 0/ (he edge by the breadth 0/ the base, and that
product by one sixth the height of the wedge, the result will be the
solidity.
II. To find the solidity of a prismoid or frustum of a wedge.
668. Rule. — Multiply the sum of the areas of the two ends
and of four times the area of a section parallel to, and equalh
distant from, the two ends, by \ the height of a prismoid.
lo"^^; ^* '^'^^ ^eugtii of the base of a wedge is .36 inches, its breadth
1^ inches, the length of the edge 60 inches, and its height 18 inches-
what IS its solidity ? * '
9 7^/'"'^^^^'''; (36 X 2 + 60) X 12 X 3 = 4752 solid inches, or
-i.75 solid feet, Ans. '
E.V. 2. The dimensions of a rectangular prismoid are as follows :
length and breadt' of the base 10 and 6 inches; of the face parallel
tothe base 6 and t inches; and the perpendicular height 40 inches.
What IS Its solidity ?
Opkration. 10 X G «= 60 sq. in., area of the base ; 6 x 4 = 24
sq. m. of opposite section. Then (10 4- 6) -— 2 = 8, the length of
the central section, and (6 + 4) -1- 2 = 5, the breadth of the central
section. Ihen (8 x 5) x 4 = 160 sq. in., or four times the area of
the central section; 60 i- 24+ I GO - 244, and 244 X V - 1626 +
8o!id inches, Ans.
3. What is the solidity of a stone pillar, the base meat-uring 3 W. by
2 ft. fa in.; the top 2 ft. by 1 foot 6 inches; and the perpendicular
height being 8 feet ? An9. 40 cub. ft i 1 62 pub. io.
*:«»»««W*Jlkf .,%.wj., »,»^|j
MENBDEATTON OF SOLIDS.
35]
200 sq. in.,
}r. between
.0'
upper sec-
mis. Then
i each face
4- eq. ft.
and 4 in.,
the length
I- sq. ft.
thickness
itire area ?
> eq. in.
f the base
and that
J III be the
I wedge.
'voo ejids,
i equally
8 breadth
B inches ;
iohe8, or
I follows :
i parallel
inches.
: 4 = 24
length of
e central
e area of
■■ Hi26 +
g :^.ft- by
indicular
iib. in.
4. If the length of the ba.se of a wedge be 24 inches, its breadth 7
niches, Its edge 32 inches, and its height 33 inches; what is its solid-
'^y' Am. .'^OSO cub. inches.
Problem XV.
I. To find the surface of a sphere or globe.
C6S>. Rule. — Fiml the arm of a ci me of the same, diam-
eter as the sphere, and midtiply the same h\j 4. Or,
Multiply the diameter by the circumfireiice of the sphere, the
product W'll l>e the surface.
II. To find the diameter of a sphere from its surface.
670. Rule. — Divide one fourth the area by .7854, and ex-
tract the square root of the quotient.
III. To find the surface of a spheroid or ellipsoid.
071. Rule.— Multiply Ihe product of the two diameters by
.7854, and that product by 4, th.i result will be the surface.
IV. To find the convex surface of a segment or zone
of a sphere.
07S. Rule. — Multiph/ the circumference of the sphere c;'
which the segment or zone forms apart, by the height of the seg-
ment or zone.
Ex. 1. What is the surface of a globe
50 inches in diameter ?
OpERATioi;. The surface of a great circle
is .7854 X 602 .= 1963.50 sq. in. Hence,
the surface of the globe is 1963.5 x 4 =
7854 eq. inches. Ans. Or, 50 x 3.1416 =»
157.08, the circumfeience of a great circle :
157.08 X r)0 = 7854 sq. in., surface of the
globe, Ans.
Ex. 2. If the area of the surface of a sphere be 24 square feet :
what is its diameter ?
Operation. (24 -i- 4) -f- .7854 - 7.6394, and V 7.6394 = 2.76
an ellipsoid be 6 feet, and the
feet,
shorter 5 feet
Opkbation
«q. ft., Ama.
he longer diameter of
what is its surface ?
(6 X 5) X .7864 =- 23.662; 23.662 x 4 =- 94.248
852
MKNStTBATlON OF SOUDB.
1
It ;
;i'
,i_i
;. i.
Eat. 4. Ff the diameter of a sphere be 50 inches, what is the couTex
surface of a segment of the name 10 inches high?
Operation. 50 x ;5.1416 = 157.08, circumference of the circle,
and 1,)7.08 x 10 = 1570.8 sq. in., area required, Ana.
5. What in the surface of a sphere, the circumference of wliose great
<'''"°'«J!,« 't-'J;! yd. ? Arts. 7.4506 sq. yd.
b, 1 he diameter of a sphere is 21 inches; what is the surface of a
zone whose height is 4^ inches? Ans. 296.8812 sq. in.
7. If the surface of a sphere be 6.16 square yards, what is its diam-
Q rru , ,. ^««- 1.40 yd.
8. ihe longer diameter of an ellipsoid is 18 feet, and the snorter-
15 feet; what is its surface?
9. Required tiie surface of the segment of a sphere, comprised be-
tween two parallel plans at a distance of 1.25 yd. from each other, the
,n°^mf*^^ ^P'*^''^ ^'^^"= ^-^^ yd- ^ns. 27.489 sq. yd.
10. The radms of a sphere is 3.08 yd. ; required l" the circumfer-
ence of a great circle ; 2'-^ the surface of that sphere.
,, _,, ^rw. 1^ 19.852 yd.; 2o 119.2098 sq. yd.
11. Ihe area of a zone IS 2.85 sq. yd.; required the entire surface
of the sphere, the height of the zone being .45 yd. ?
,o 1. , • ., ^^' 12.742 sq. yd.
12. lieqnired m miles the surfece of the two frigid zones, allowing
327.1i)6.-i7 miles for the height of each of them, and 39.'^5.82986 miles
for the radius of the sphere.
I f n''*"7^° ^^^ '■*'° ^"''f'>'"'s of irregular solidB, or bodies, the following process
J jIV ^'^^"^' """^ °0'°P'>sed of plane faoes.^nrf the area of each face,
ana add them together for the whole surface of the solid; if oompo^ed ot circular
taoes, eftmcie theee tnto a number of faces infinitely great, eo thtt each might be
eonndered a plane. Then proceed as above to obtain the entire surface.
PuOBLBSf XVI.
I. To find the solidity of a sphere.
673. Rule.— Multipli/ the surface hj one third of the radius,
and the product will be the solidity. Or,
Multiply the cube of the diameter by the decimal .5236, and the
product will be the solidify.
II. To find the diameter of a sphere from its solidity.
674. Rule. — Divide the solidity hy .b2^Q, and (^.'v^ ct the
cube root of the quotient.
m. To find the solidity of a spheroid or ellippoid.
675. RULK. — Multiply the longer axis by (he square of the
shorter one, and ihe product by ihe decinvd .5236. the result wiU
be the required Molidity.
' '"taWtfi^'i
9 the coDTex
)f' the circle,
wliose great
)6 sq. yd.
surface of a
12 sq. JD.
ia its diarn-
1.40 yd.
the siiorter-
niprised be-
h other, the
9 eq. yd.
circurnfer-
8 sq. yd.
tire surface
2 sq. yd.
3, allowing;
29:^6 miles
^ng process
>/ each face,
i ot circular
ch might be
\e radius,
I, and the
lidity.
■ 'v a the
Old.
irr of (he
zsuk will
MKVSURATION OF '30ITD8.
363
IV^find the solidity of the segment of a sphere.
«T«. "^^hw..-!. From, three rime, the
_ h'ght afthe segment ; mnltlpU, the rema^l
^qnnre of the radius of'JJ.'eq^n^'lZ^'J^ tlJZ' .t
V. To find the solidity of a 7or of a sphere
«TS. Rule.-!. To the. sum of the squares of the radii a,
bJt soiUUr^' ""'^ ''^''''' ^ ^'^^^^' and the last resuLevl
, ®^®. ■RULE.-.2. For the middle zone of a sphere: I\om the
Z'ZX''^'TT'^'^''P^"^'' ''/-'^-^^ ^e zone is Z^,
snho net one third the square of its height, and multiply tU rl
mmnder hy the height, a >d also hy .7854. ^^
VI. To find the solidity of a spherical sector.
incS'does'u contn f '' "' * ^^^'^ ^« ^^ '-^-' '-- '-"7 ^ohd
Operation. 3.1416 v lo =, 5<r cooo •
37.6992 X 12 » 452.H904M^2.SI'1T9'^
12B . .5236 - 904.7808 cub. in., L^ ^ 904..fe08 enb. m. : or
^^' 2. What is the diamete r of a sphere containinj? \m soBd ft. /
Operation. «' '•"'■■■• ^ ^^~^^-
one
poHiJity
and Ihe shorter
Opeiution. (22 X 3) X .5236 =
6.2836 cub. ft., An».
"I
riii-ritrfrf-firfii---'
f
i. li
\l ill
3ft4
MSNSDKATION Of R0LID8.
E.r. ;'). What jb the ixxlidity of the temperate zone, ihe vtr^p-'fT mdlifs
beiriL' ir.8«.572H2n2fi m ies.j the low«r redins 364«.bfiirMKS8 miloK- ;
and the height 20G2.2655 ruilee?
Opeii. [(1 r,8G. .07282526)* 4- (3G48.h8750f.38)a -t ^ (20:".'2.265fi;«
X 2lK)2.2(i5;;) .-, 1.5708 -- 5587777866H cubic miles, .H?7«.
Ex. G. Tlie diameter c'f ft sphere i* 15 feet. What w the solidity
of a pector of thcf-anie, the 'ircular h%i-f. of which la 1 ^ feet distant
from the central section 7
Opkiution. 15 X 3.1416 x 6 =- 282 744 ;.]. «... the convex sur-
face of the Hector. Then 15 -~ 2 = 7^, iuciin? of the circle : 2R2.T-44
X (74 -~ 3 - 2^) = 706.86 cub. ft., An$.
T. Hwriired the aiameter of a cannon-ball weighing HO lb, knowing
that a i- >:,.!c foot of caat-iron weighs 450^ lb. Ana. 0.6973 ft.
8. If tU? ;iiar.ctfr of t'je baHC of the Pegnientol a sphere be ;>0 feet,
and the he-^^ht ..vftbe sause 5 feet; what is its solidity?
Ana. 18;?2.(i cub. ft.
9. yjh&i 's t>;e 8o]i(i:;ty of a sector of a sphere 2i leet in diameter,
the SfifmLu- jjaae of which is 4 feet distant from the r.i'ntral flection ?
Ans. l6n;'.5616 cub. ft.
10. The surface of a sphere is 55.44 square yard.-; . what is its sol-
iJHy? Ans. 38.8, '! + cub, yd.
11. What is the solid content of a spheroid, the longer axis of which
is 16 feet, and the shorter 12 feel?
12. What is the solidity of the torrid Kone, thediameU-r of the earth
being 7957.75 miles, and the height of the zone 8173.14565052
"iJe-s? Ans. 149455081137 cub. miles.
13. The diameter of a sphere is 24 feet, what is its solid contents?
Ans. 7238.2464 cub. ft.
14. What is the solidity of a spiierical segment whose height is 2
feet, and the diameter of the sphere 10 feet ? Ans. 54.4544 cub. ft.
15. Required the solidity of the middle zone of a sphere, the top
and bottom diameters being each 4 feet, and its height 6 feet ?
Ant. 188.496 cub. ft.
16. The height of a spherical segment is 8 inches, and (he radius
of its base 14 in. ; what is its solidity? Atu. 2731.0976 cub. in.
17. If the eoli(iity of a sphere be 4'.62 cub. yd,, what is 1° its diam-
eter ; 2" the circumference of its great circle ; 3° its whole surface ?
1^. Required the volume of a spherical sector, the cuxsular base o'
.which is .25 yd. distant from toe central section, and the diameter oi
the sphere .84 yd. Ana. 2.2167 1 2 cub. yd.
19. The height o{ & spherical segment 16 .42 yd., it? sarlace 1.6632
eq. yd.) what is 1° the radius of the sphere; 2<» t» ^lidity ofthe
sphericHl .sector ? ^n«. 1« .63 yd. ; 2«> .3< .; cub. yd.
'■^^- ^j)»|; '■'' the solidity of a Bone whose greater ■ v jeter is 25 ft.,
between theiu i
height
Am'
vf908 oub. ft.
Pkoblkm XVII.
To find the solidity of any regular i*oij i oil
eurpsr radlre
1bu<m mile« ;
iri the solidity
] ^ feet distant
he convex iJnu-
ircle: 'IH'LIU
) lb. V;riu\ving
8. 0M13 ft.
!re be oO feet,
12.0 cub. ft.
t in diameter,
ral section ?
(il6 cub. ft.
'hat 19 its »ol-
+ cub. yd.
' axis of which
:r of the earth
173.14565052
cub. miles.
>ljd contents ?
464 cub. ft.
se height is 2
544 cub. ft.
ahere, the top
feet ?
t96 cub. ft.
id (he radius
76 cub. in.
) I" its diam-
ale eurfax^ ?
xsular base <
e diameter o.
12 cub. yd.
jrfice 1.6632
'lidity of the
cub. yd.
eier is 25 ft.,
1 08 onb. ft.
-OIL
MISC1LLANI0U8 MAMPLK IN sOLlDg, 355
tJ^ solidity. ^ ^^^<^ed ,pkere, m,d the product will U
«?««« ";Mj/!:.i;'iv!'L'„7"i'!^;"{ any irre,^.ular body. suol. .« a «tnne, a chain A.
tnehes, Ang. ^ n'e . lone is ^7.7274 x 12^ = 346.5925 cub.
fe .m^ersedVnXnttefou'r" rl'^ '%'"^'' ^'"' -^'«'' «» object
34 gallons. WhatlsMtdSty ^^^^^^^'^^^ ^ '^- -J, ia
Opkration. 5 — 35 «: I ,t ,, *'
hence 277.274 x I.5 , 415.91 i u,^ll!'7°f "'"'^ '''^'''^-^ ««h- i«- I
W;raSror%\tSfd8 wS ,';'7 .ti.'""^'' ''^. ^'^'^*°- «hem into •
division consists in taking for the Vfirfov el ^*^''^ ^^ reckoned. The easiest
fohd, and for base the side ophite A-, n^° P^'"'"^'^' ^^' '-^'^'^^^^^ angfe of £
kinds of pyramids, is to proXoe the, h ''T J"".°°''«^' '" ^^^d the he). -hr of all
irfn thin plane board, anKrutr is /;.?!'' ''''^ " '"'^^" ^'^ '^^ base, by means
»ve (he hwghtof the pyramid. ^® '"^^^ ^"'' "^'« P^^e wilfevi-lentty
MISCELLANEOUS EXAMPLES IN SOLIDS.
anJ-th^\'id^SelVar^^^ ^™ - 71.1126 cub. vd
1*-; 2» the altitude She pritl^r^'' ''^"'^^*^ ^^ ^J^« a''^- Vth^
i What is the solid contentT^f^r IV^^^ f*" ^^- ' '^^ '^■■^^^ jd.
of whose base is 12 i^ aS it" lu t.tief 177'^?'".?! ,^^ ^^'■^'-^-
3. A room 9.25 yd. Ion- i fi^ v •) , "*" •^'-^•I'J-l cu. ft.
Papered; the rolls of tSer are^ 2 ^f ', ^"^ ?-80 yd. high, is ^^ be
{•^12.25 ^. ,d. ,,, thi^aPtu's in^|;e'3,>;;:^7^'- -^^ Allow-
be required, and what will be ti
lie C'ist at 75 ct,
lis, liowr many roll« will
L^?'^;!l^"^!:f*.''"^'^«^<^f^^cyiin.
-^ns. 20.51'! roll
per roll ?
w f-'* yil., and ite altitude 3 of ih
;^ A -...11 ■> o . . ft . ' *•"
, . 'p» and $15.38 + .
er, the ratims of who«e base
eoircunif. Am. 185.707
+. .^q. yil.
cuiuferenoe? """-"er ujwe b leet in Ipi,^,!. o,..j i ......
leet in length and I foot
Ju cir-
Ana. 96.1^76 lU
356
MIStOELLANKOnS KZAHPLKH IN BOLIBS.
I! 'I
!'■ r
6. Wliat is tiie w^iglii of a i^quare bri^ pillar whose aide is 0.7S
yani>, ami lieiglic 4.75 yards, if I cubic yard of brick inaBimry weiiilia
3(1 civt. ? " Ant. 96.1875 ib.
7. Tlie filaiu lieiiihl ol a regular he^caguiial pyramid is 8 yd., and iba
side of its base t> vards ; what is its whole surface ?
Ans. 237.5307 sq. yd.
8. A man had a wall built for $186, which was $3.20 a cub. yd.
What \s the height of that waJI, knowing that it is 14.5 yd. long and
•70 thick? iln*. 4.18 yd.
9. A rectangular basin is 12 to. long, 2.5 to. wide, and 1.6 to. deep;
how many barrels of 3! ^ gal. each does it hold, there being 231 cu. in,
in a gallon ? Ans. 2811.9 + bbl.
10. The convex surlace of regular triangular pyramid is 45 sq. yd.,
the slant height is 6 jd. } required the length of one of its side-edgee.
An8. 6.50 yd.
11. The lower base of a pile of stone is 26 by 12 yd., the upper on«
16 by 8 yd., and the pile is 3 yd. high : find its cubic contents.
12. What is the convex surface of a right cone, the radius of whose
base is 1.4 yd. and its side, the | of the circumference of the base?
Ans. 29.0167 + sq. yd.
13. I desire to get a cylindrical tub made whose depth will be 3 ft. ;
what must be its diameter that it may hold twice as much as a similar
tub whose depth h 5 ft., and diameter 3^ ft. ? Ans. (5.38 tt.
14. What is the slant height of the frustum of a cone, whose convex
surface is 12.26 square yards, and the radii of the two bases 1.71 and
2.2 yards? Ans. .998 yd.
15. How many cords in a pile of wood whose length, breadth, and
height are respectively 15.5, 4, and 7.25 yd. ? Ans. 94.81 + .
16. What mu-^t be "the radius of a cylindrical basin holding 110045
gallons, its depth being 5 yd.? Ans. 5.^39^+ yd.
17. How many solid feet in the frustum of a pyramid whose bases
are regular octagons, the sides of which are respectively 21 and 9 in.,
and the perpendicular distance of the bases 15 ft. ?
Ans. 119.20+ cub. t\.
18. What is the surface of the base of a quadrangular prism, whose
altitude is 1.15 yd., and its solidity 4.25 cu. yd. ? Ans. 3.6956 sq, yd.
1 9. Find the solidity of a beam whose length, breadth, and thickness,
are respectively 12.76, 0.35, and 0.25 yd. Ans. 1.115625 cu. yd.
20. A man gets a cemenieil cistern made iu the ground that will
hold 3000 gal. ; what will be its depth, the length and breadth being
respectively 1.8 and 1.75 yd. ? Ans. 4.715 yd.
21. What is the solidity of a regular hexagonal pyramid whose al-
titude is 3.6 yd., and the side of the base 3.6 yd. ?
Ans. 40.405651 cub. yd.
22. What is the convex surfece of the frustum of a triangular pyr-
amid whose ba-^es are parallel, knowing that the sides of the lower
bate jire 2, 3, an i 4 ft. ; the corresponding sides of tho upper base
,0.95. 1.20, and 2.10 i\. ; and the height of the three traj^zoids 5, 6,
and 6.45 feet? Ans. 40.4537 sq. ti.
23. What are the dimeDaione of a barn whose capacity is 810 cu.
elcrf '-""rail area 01 half on acre; what will bi- ih , liatn-
-7. Whali8the,«iirra(!i.nf » .«. . . 'tis. 66.50 yj.
jcal Hector who.e soM^'ifi "sX ^ ""b id"'';'.'' "^ ?• '^^V? « ^^^^^
being 1.5 vj.? ^ *^""- J^'^-' "'« railius of the spltert
,, .^^Wl.t i. the surface of the earth, its ra.Hu. I'^^^at^ ^,,
29. Find the8oHditvofaIo..9^rv/f '^"^'^'f •^.^*^-^^<^'^^q- '"'"•
••^O- What must be the th.Vkn«. r Z^- '^•^^•«»'062 cub. yd.
aruJ external surfaces a e fand ff/v.^J/ '' '"" ^P'^^'^^^^^^ internal
•■5i. A basin hold, log- 7^ ;^: 12 yards? /i;,^,. q^ .
•^2. Keqinred the convex «nrF«?. .• a 5 ' ^"'' '^'^ dimensions.
un.^ respective,, ,.«4 and /^^afltte^irhSI^^^I^,:;: :^^---
35. One no.,n.J JA i ' "<^"^ J*^"^' was the wire?
^Hect^ cylindricairwlS-w:;; •;j:^l:^,rf^'^ «-^^^ -•' -d the wire
of each part? a' Is 9^-«9^^''' ""/^^^'-^ *''« <^«^^^e^ «"rfaoe
37. What i8 the wefX" nf '^^'^ ''^•/'^'- ' 2"'' ^^-''^^d sq. yd.
thkkness, if LexS d,/. ^''PPr.'P^''''^^' «'^^^' 0.985 inch in
weight of'a ouU:Z^£^r^l^,^^ ^P'-e is 1.35 yd., and thS
oou^yt^rS:^^-;;^- eIlipticai'fisl.pond to be digged io hie
eiTiaJlaxis 12.75%.! H?^^ tliat li.h-pon.l ,3 to measure 15 yd., the
digfe^ing it, if the co u alV^chle 'l "^ ""' ^^fq""-^"V^ ^''^ ^'' ^^'
or the maaonry. at $15.45 p^cfb^d.^'s?'?^ ' " '^"^ ^^^^*
the oapacity of tus pond. P^^ *^"'^- ■y'^- ' -^ '''e whole cost; and i^
the t«^r'bls!'i8 6^'LSf SL ^.''■"^'""' ,K ^i cone who.e radiu. of
»ad itfl depth 16 inJw t'fiS^ w,thT7 '' '^^'/'^^'T/. ^^*^^^ ^' '"'^^^^'
^f that acfd. ^i, U wSlh /i'^ct'^'qurr '^^"' ^'^t,i t.if ^
' !' 'I
358
TABL» O? OHORDS.
•9 l
40. Supposing' t>»e Moon m oe a perfect sphere, what is her surface,
her diaiDeUT Lvi.-,' t/> .Ii.vt ci the Earth asH is to 1 1, and the diameter
of the Earlh I>eing 7912 miles? Ana. H(]2&158^ pq. mi.
41. A fbiiinK'r wishes to cast a semi-sphericfll lioiler whose internal
diameter sliall he (i^ feet, its thickness 2j^ in. Required the weight
oJcaHt-iron ii will lake, if we allow 10% waste in melting, knowing
tliat tlie hpecitic weight of cast-iron is 7.208 Ans. 8608.3(;+ lb.
42. The interior space of a blo' >.-..Hvt v.. nsist* of two conic frua-
tum« uniting at their larger base whose diameter is } of the height of
the furnace. The altitude of the upper frustum is I of the height of
the furnace, its less diameter is i of the greater. Tiie altitude of the
lower frustum is .^^ of the height of the furnace, its less diameter is ^
of til > greater. If the furnace is 15 yards high, what is its interior
cap-icity? y47i». 41.921 cub. yd.
43. A fountain in the fomi of the frustum of a cone is filled with
water. Required 1'' how many gallons it contains, if the circumfer-
ences of its bases are 16.95 and 15. 8& yards, and its depth 5.35 yd. ;
2° in how many hours it will be emptied, if the water is let out by
tJiree pipes, of wiiich the 1st empties l^gal. in I minute; the 2nd,
11 gal. in 8 min. ; the 3rd, 13 ^;al. in ^i^ hr. ; 3" what time would each
pipe take to empty the whole founta n by itself?
■' II
TABLE OF CHORDS.
Tn the table of chords, the radius of any circle is represented
by 1 ; and in tlocinial of the radius, is represented the length of
chords that subtend arcs of 1', 2', 3', &c., up to an arc of 180«*,
which is itself a semi-circuui^jrence.
Any chord which is not a diameter, subtends two arcs, one of
wliich is less, and the other great - than a semi-circumference;
but their sum eq As the Iroumfc noe.
In all problems treating of arcs, the smaller arc is always im-
plied, unless otherwi?? mentioned.
1st Rule.— To obtain the chord ( t any arc greater than a semi-
circumference, avbtract the degrees oj the gioen arc fro-.i .m'^ . and
find m the table the chord that corre"/ '. ms with the difference.
Ex.—Wh&t is the chord of a -.re o^ U0° ?
360° — 310° - 60°. Intl oV he chord of 60^ s 0.8452.
2na Rule.— To find the leng. of au cliord in any £;iven ci
muitxply the radius of the given circle by the chord in?
table.
ted in the
A'.r.— How long is the chord of an arc of 24o in a circle whose
radius 18 20 yd. ?
The chord of 24» in tb« table ie 0.4158; U x 0.4158 - 10.395
'f-'wismi
B her fiurface,
the diameter
8^ pq. mi.
'hose it)ternal
■ed the weight
ing, knowing
08.36+ lb.
vo conic fru8-
the height of
the height of
kltitude of the
diameter is ^
is ita interior
II cub. yd,
is tilled with
he circiunfer-
pth 5.35 yd. ;
' is let out by
ite; tlie 2nd,
16 would each
represented
he length of
arcof 180»,
arcs, one of
Bumference ;
3 always im-
than a semi-
a 360''. and
Terence,
s 0.8452.
given ci;ole,
ited in the
circle whose
8 - 10.395
TABLR OF CHORDS.
3ft9
yafr;u]!e;lsrLo%no'*1o'V' ' ''''^' '" which a cl>ord ofl?
yJi^AZ'' ^'''^ ^'' •" '''' '^^'^ ^^ 0-^502 ; 134-0.,S502 . 34.20.
ing with tUtquotuZ ' ^ '" '^' '"^' '^'^ ''«^'"* corresponl
^^^^l^ S^,t "' ^^« ^'-- «»>-' - 4-24 yd., if
4.24 - 20 ^ 0.2120; 0.21: m the table indicates 12° 10' An,
tended to any n'un.b^r ^ l^S'lX^t''''' '^ "" '""'^' ''^ *''•
TABLE OF CHORDS.
21
22
23
24
0,0175
'>,034:)
0523
0(i!)8
0,0872
0,10-47
0,1221
0,1395
0,1569
0,1743
0,1917
0,2091
0,2264
0,2137
0,2611
0,2783 I
0,2956 I
0,3129
0.3301
(1,0029
0,0204
0,0378
0,0553
0,0727
0,0901
0,1076
0,1250
0,1424
0,1598
0,1772
0,1946
0,2120
0,2293
0,2466
0,26.39
0,2812
0,2985
0,3157
0.3330
0,0058
0,0233
0,0407
0,0582
0,0756
0,0931
0, 1 1 05
0,1271)
0,1453
0,1627
0,1801
0,1975
0,2148
0,2322
0,2495
0,2668
0,2^41
0,3014
0,3186 I
0,0087
0,0262
0,0436
0,0611
0.0785
0,0960
0,1134
0,1308
0,1482
0,1656
0,1830
0,2004
0,2177
0,2351
0,2524
0,2697
0,2870
0,3042 1
0,3215
0,0116
0,0291
0,0465
0,0640
0,0814
0,0989
0,1163
0,1337
0,1511
0,1685
0,1859
0,2033
0,2206
0,2380
0,2553
0,2726
0,2899
•,3071
0,3244
0,0145
0,0320
0,0494
0,0669
0,0.^13
0,l()ls
0,1192
0,1366
O.IjIO
.,1714
0,188-5
0,2001:
0,2235
0,2409
0,2582
0,2755
0,2927
0,3100
0,3272
ih\
'4
i
ii
it-
!»'' n
P
aeo
TABLfi OF cnORnd.
D.
0'
10'
,, 20'
30'
40*
50" •
20
0,4499
0,4527
0,4556
0,4584
0,4012
0,4011
28
0.483-<
0,4-^07
0,4895
0,4923
0,4951
0,4979
:?o
0,r)l7G
0,521) t
0.5233
0,5201
0,52m9
0,5317
32
0,5.-) 13
0,5511
0,5509
0,5598
0,5025
0,5052
34
o,r)sn
0,5875
0,5903
0,5931
0,5959
0,5980
36
0,(UH0
0,6208
0,0230
0,0203
0,0291
0,0319
38
0,6511
0,6539
0,0500
0,6594
0,00 J I
0,0019
40
O.fiStO
0,6808
0,0895
0,6922
0,0950
0,0977
42
0,71(;7
0,7195
0,7222
0,7249
0,7270
0,7303
44
0,7492
0,7519
0,7546
0,7573
0,7000
0,7027
46
0,78 1 5
0,7811
0,7868
0,78'J5
0,7922
0,7948
50
0,8452
0,8479
0,8505
0,8531
0,8558
0,8584
54
0,9080
0.9100
0.9132
0,9157
0,9183
0,9209
58
0,9090
0,9722
0,9747
0,9772
0,9798
0.9823
62
1,0301
1,0320
1,0.151
1,0375
1,0400
1,0125
()6
1,0893
1,0917
1,09 U
1,0905
1,0990
1,1014
70
1,1472
1,1495
1,1519
1,1543
1,1507
1.1590
74
1,2030
1.2'>60
1.2083
1,2106
1,2129
1,2152
78
1,2586
1,260;)
1,2632
1,2654
1,2077
1,2699
82
1,3121
i,314{
1,3105
1,3187
1,3209
1,3231
86
1,3040
1,3601
1,3082
1,3704
1,3725
1,3746
90
1,4142
1,4163
1,4183
1,4204
1,4224
1,4245
94
1,4627
1,1017
1,4667
1,4086
1,4700
1,4726
98
1,5094
1,6113
1,5132
1,5151
1,5170
1,5189
100
1,5321
1,6340
1,5358
1,5377
1,5;}95
1,5414
104
1,5700
1,5778
1,5790
1,5814
1,5832
1,5849
108
1,6180
1,6197
1,6214
1,0231
1,0248
1,6205
112
1,6581
l,05i)7
1,6613
1,6029
1,0045
1,6662
116
1,6961
1,0976
1,6^»91
1,7007
1,7022
1.7038
120
1,7320
1,7335
1,7350
1,7304
1,7378
i;7393
124
1,7659
1,7673
1,7086
1,7700
1,7713
1,7727
128
1,7970
1,7989
1,8001
1,8013
1,8026
1,8039
132
1,8271
1,8283
1,8294
1,8306
1,8318
1,8330
136
1,8544
1,8554
1,8505
1,8576
1,8587
1,8598
140
1,8794
1,8804
1,8814
1,8824
1,8833
1,8843
144
1,9021
1,9030
1.9039
1,9048
1,9057
1,9065
148
1,9225
l,923i
i;9241
1,9249
1,9257
1,9265
152
1,9406
1,9113
1,9420
1,9427
1,9434
1,9441
156
1,9503
1,9569
1,9575
1,9581
1,9587
1,9593
160
1,9696
1,9701
1,9700
1,9711
1,9715
1,9721
164
1,9805
1,9809
1,9813
1,9817
1,9821
1,9825
188
1.9S9')
1,9893
1,9896
1,9.899
1,9902
1,9905
170
1,9924
1,9920
1,9929
1,9931
1,9934
1,9936
172
1,9951
1,9953
1,9955
1,9957
1,9959
1,9961
.174
1,9973
1,9974
1,9975
1,997
1,9978
1,9980
176
1,9988
1,9989
1,9990
1,999.
1,9992
1,9992
179
1,9999
1,9999
1,9999
. 1,9999
1,9999
1,9999
180
2,0000
-i
CULLING AND MBASUllINO.
861
50' •
0,4(>H
0,4!)79
{),fhm
0,5052
0,5!)S(;
o,G;n'j
o,(]Gi:t
0,6t)77
o,7;{o;?
0,7027
0,7'J48
0,H584
0,9209
o.;)82;5
1,0125
1,1014
1.1590
1,2152
1,2699
1,3231
1,3746
1,4245
1,'4726
1,5189
1,5414
1,5849
1,6265
1,6662
1.7038
i;7393
1,7727
1,8039
1,8330
1,8598
1,8843
1,9065
1,9265
1,9441
1,9593
1,9721
1,9825
1 9905
l',9936
1,9961
1,9930
1,9992
1,999»
Culling and Measuring of Timb.r, Masts, Spars, Deals.
Staves and other articles of a like natari.
(Pioiu the Consolidated Statntes of Canada. Cap. 45.)
^ Doals^-. A Quebec Rtn,i,]a,d D.,,! h 12 fc-t !on- 11 inches
broad and 2^ inches thick, and contains 2. fr » i„ G^ts ^hi^
?"4Kd'a?r'''" Standard contain 229 'ftr's i^^cihTc o";
u;;ill7ttchThi:k'.""''"'' '' '''' '-'' '^^'''^^ ^--'1
One Quebec Stunl.rd is 100 pieces oP 12 ft. hv 11 i„ hv 21
in an-ys equal to 1 hd. 1 c^r. 16 pes. of St. Potcrsbur's idLi^
and 240 Quebec Standard Deal, are equal to 11 loa.Fs '
1- tt'lf t'f 'Ii'''"'"';'l ^"•^'■^ '^ oquaUol20 PCS. c^
A Load of Deals is 600 square feet by one in'^b in thickn,«.
equa^to^SO cubic feet J or 300 square fit oV 2 the' oV4^^
ar/andllinntl II t'' (^'''l^'^ inches, Quebec Stand-
ard and equal to 36^ St. Petersburg Standard deals.
t^K ^ °:T'"'^ Quebec Standard Hundred into St Pe-
30 TrXters. ^ '^""^'^ ^' "'^ remainder, divide U hy
i«ct: "^"miir '''''-'' '*^^"' - ^^"^^ ^° ''' ^-^ 9
^(PZ ^."'^^•i/"d seventy-five Standard St.aves are equ«l to
Owing to the vari«tion.s in breadth and thicknass of Staves.
to KSr'^ °'' ^^'''"' ^'"^"° ^^^""'^^^^' *« t)e equal
h=..^^lwS^"~^"' ^''^ of Latbwood is 8 feet long and 4 feet
fiigii, iiingiish measure. *
■n
rf Hi
1 ;
'I'.'l
I'..
•l) ,*
U
M 'jHIi
i
I' :
1
1
J .
1
362 CTJI-tlNG AND ME.ASURTNO.
CUSTOMARY ALLOWANCE FOR FREIGHT AND
BROKEN STOWAGE.
Deals.— A Hundred St. Petersburg Standard, at twice the
cliiirged rate for timber per load.
_ Staves. — A Mille Standard, at six times tbe rate cbnro-ed foj-
timber per load. A Mille West India, at twice the rate charged
lor timber per load.
Lathwood. — A fathom of Lathwood, at the same rate as
charged for timber per load.
FREIGHT AND SHIPPING.
To find Freight measurements, or cubical contents of pnckages,
Rdlk. — MuUiphj length, breadth and thichness together /for
surfaces, length and brctdth only.
For Stowage.— 97 quarters of Wlieat, or 140 barrels of
Flour, or 80 barrels of Ashes, are considered equal.
For Grain.— 42 oul)ic ftet equal 1 ton of shinping. One
bushel is equal to 60 lbs. 2218^ cu. in. are equal man Imperial
bushel. 8 bushels are equal to one quarter =17745 cu. in., or
1Ot^^0 cu. ft. Therefore, 1 ton will take 4rV quarters 1 bushel
being = 60 lbs. ; 1 quarter = 480 lbs. ; 1 ton = 1968 bs. A
ship of 200 tons measurement can, therefore, carry 820 quarters \
but it can generally carry much more. ^^
CUBIC OR SOLID MEASURE.
42 solid feet equal 1 ton of shipping.
40 solid fett, round or unhewn " 1 ton or load.
.50 solid feet, hewn or squared timber.. " 1 ton or load.
50 cubiefeet " 1 barrel of flour.
8 barrels " 1 ton.
5 quarters " 51 J cubic feet,
5 quarters , ,. " 1 loud.
SQUARE MEASURE {seep. 118, 119, 120).
Engi.ish. ' Fhgnoh.
36801.7 Square Feet equal 1 Square Aipent.
0.845 " Acres " 1 «' "
2.471 " " " 1 « Hectare.
i " Foot " 0,0929" Metre.
»!^^7it-iiyy. fW!-'~
iiSSm
■M
6PE01PIC GRAVTTT.
!G3
T AND
twice the
hnro'ed foy
te charged
le rate as
rpnckages,
efher ; for
barrels of
img,
One
n Imperial
on. in., or
S 1 bushel
68 bs. A
) quarters ;
f shipping,
r load,
r load.
\ of floor.
)ic feet.
ENOH,
re Aipent.
Hectare.
" Metre.
1
3 955 Prchcs .. u j ^^..^^^
The side of a s,,,^,re acre is 69^ yards i„ jen.tl,, and is ofton
.,>.'-t^d by Irench-Canad.ans as a unit of length I'or short Iv
1 French foot is equal to 12ff) English Inches.
104 lbs. arc " to 112 " Po^ndg
I Canadian Minot is " to 1.054 Imperial Bushel!
The following rules for Timber Calculations may be
found useful by the trade. ""'"^y "^^
Sqm're^''^""' ^*^"'''' ^'"'^''' "^ ^"^^'•«"t ^^^es, to an Average
contrnts of (he whole fo parts ; divide 'he product by the total
^alfeet; the square root of the quotient will he L average
sgu'ire, in inches. "I'c/ci.ye
To find the Cubic Contents of Round Timber.
^/wy''7"Ti'^"'"V''V^'r*'''''' '^"^('Pf,y (he product hy 11 and
tT 'I 'f "^''^^.^ '^' result by the length of the. L ■ ^hen
TABLE OP SPECIFIC GRAVITIES.
In estimating the weights or specific gravitfes of bodies rain-
That n '' 1-"T"^ l'^^" "-^ '^'' ^»'''"^="'^- ^^^Poriment has show
that a c..b,c foot of rain-water weigh. 62^ pounds Avoirdupois'
OOsfieVsurV^' We follows that- a'cubic inch wei^h;
" bo V h n 1?- "5 "^ ''r"f • V' '^''''^''''' ^^' ^"^^^ific gravity" of
ci bod) bo muluphed by the above decimal, the" product r.ill be
whicTm tt^r'^^r.' :;^'^^ '^'^ in poundTirolrdu o^
dupoi:: nsibs' Trot ' '' '''' ^"" ''' ''^- ^^^"■
f ; vl^rti -n V' f ^Tb'^«^t of«"J one of the
- "in^ ariicies ic in uutices Avoudupois.
lii»»
h.
SPECIFIC ORAVITY.
11'^
Woods (Dry).
Ash 845
Apple ,. 793
Box-wood 1031
Beech 852
Birch 567
Butternat 376
Cedar 561
Cherry 715
Chcsnut 610
Cocoa, ,....,.. 1040
Cork 240
Cypress 614
Ebony (American) 1331
Elm..... 570
Fir, White 512
Haokniatiick 592
Ilazcl...., 860
Hemlock 368
Holly 760
Liirnum vitaa. , 1333
Lime 804
Logwood 913
Mahogany (Honduras). 560
Maple 750
Maple, bird's eye 576
Oak (Canadian) : 872
Oak (English) 932
Pear (i61
Pine, White. 554
Pine, Ptod 590
Pine, I'ellow 461
Pine, Pitch 660
Plum 785
Poplar 383
Spruce 500
Taraiirack 383
Walnut, Grey 671
Walnut. Black 550
Willow. 585
Liquids, Metals, &o.
Alcohol, pure, 60°,
Brer
Brandy ,
Blood (human) ,
Bees-wax
Brass, c;ist
Brick, fire ,
Coal ( Anthracite)
Coal (Newcastle)...
Coke
Copper, cast
Earth, onmmon
Glass, window
Gold, 22 carats
Granite (Scotch). ..
Guttapercha
Honey,...,
Iron, cast
Lead, oast
Lime, hydraulic...
Marble (Vermont)
Milk
Petroleum
Plaster of Paris. ...
Platinum, native....
Quicksilver
Salt
Sand, common
Silver, pure cast....
Soap, Castile
Starch ,
Steel Plates
Tallow ,
Tin, pure „...,
Turpentine
Water, common....
Water, saa,. =„,.„,
LZinCj roUed.t»«t....
794
1034
924
1054
965
8396
2201
1436
1270
1000
8788
2194
2642
1748<:
2625
980
1450
7207
1825
11352
2745
2650
1032
878
1176
16000
13568
2130
1670
10474
1071
950
7806
941
7291
870
1000
1026
7iyi
iS, &0.
794
10H4
924
]Uo4
965
8396
2201
1436
1270
1000
8788
2194
2642
17486
2626
980
1450
7207
1825
11352
2745
2650
1032
878
1176
16000
13568
2130
1670
10474
1071
950
7806
941
7291
870
1000
1026
7iyi
BOOK-KBEPINa
neyiNiTioiw.
1. Book-Eeepiug is a syatema tie record of buameeg trane-
actions, or the art of keeping aocounts.
Every penon, engaged in busines 6 for himself, should ke^) a book of some kind
m which to record all his buBin«>8S transactions. The mechanic, the farmer, the
)>r»'cf8ional man, etc., should keep an account with every person with whom
thty denl. For no one should trust transaotionB of a pecuniary nature to his
memary atone.
2. All business transactions consist in an eschangc of values.
3. There are two methods of Book-keeping in general use,
distinguished as Single and Double entry.
4. The Double Entry is conceded to be greatly superior to
the Single Entry, particulaily from its more excellent tests for
deptermining the correctness of the work.
15. Single Entry embraces only the accounts of persons, and
consists of 6)<^ one debit, or one credit.
6. Double Entry is derived from the fsct that every business
transaction must be entered to two or more Ledger accounts, as
two or more persons or things ar^^ affected thereby.
T. Two books appear indispensable in Single Entry ; via., the
Day Book and Ledger.
8. The three main books used in Double Entry are the Day
Book, Journal, and Ledger. The Day Book aud Journal are
sometimes combined in one.
O. The number and char.j'^ter of the auxiliary books depend
somewhat on the nature and extent of the business, but more on
tiie amount and kind of information desired. Those most in use
are the Cash Book, Bill Book, Invoice Book, Sales Book, the
Oommission Sales Book, etc.
10. The Day Book is that in which are entered the busineai
traneactions in the date and order of their occurrence.
This book should be plain, ooncise, and unequivocal in its statemeatc. Ab the
records in it are supposed to be made whan the transiietions and all the circum-
stauMes connected tberewith are fresh ia the mind, it is tb* only book allowed in
court, Ml oases of litigation.
11. The Journal is a book in which the buMness transactions
rreordcd in the Day BoiMcare prepared to be entered in tiie Ledger,
by ascertaining the projKJt debits find erodits involved in each
ii j'.n.^action. This process is eallfAjmumaUvmg.
1*. The Ledger is the book of retuh*, — *he final book of entry.
1
$ li
f. 4
BOOK-KBRPtNO.
rn this book, nndor approprirrte h&a*. ocUfed R<roiints, are awanaed all the
facts neoos-ory fw a full and satisfii 'tory statement of the business ; Including,
not only an ejditbitiofl of the present resouroee and liabilities, bnt a distinct record
of partioul.iT gains and losses. The proeeeB of transferring to the Ledger \e called
pottmff.
IS. TlieOashBaok is that which shows all the sums of
money which we receive or pay, with a short explanation relating
to each sum.
The entries, in «ils book, are made immediately on reoeivin,^' or paying the
of
transactions.
14. The Bill Book is that which shows a description of all
the notes or acceptances in our favor or against us, with their datec,
credits, when due, and amounts.
The notes or acceptances in our favor are entered under the head of ReaeivaUt,
and those against us under Payable.
15. The Invoice Book is that in which are copied all bills of
gootls bought, and all invoices of goods received into our posses-
sion.
From the Invoice Book the entries pa«B into the Day Book, either daily, weekly,
or monthly. This book is sometimes made of coarse paper, and the original in-
voices pasted into it.
16. The Sales Book gives a full description of all goods sold
Of passed from our h;mds, or out of our possession.
From this book the amounts are tranferred to the Day Book, either daily,
weekly, or monthly. At the time the purchaser selects his goods, they are de-
8;^ribod in tlie Sales Book— quandty, quality, and price ; and from this book wo
make out his bill.
17. The Commission Sales Book contains a minute descrip-
tion of the merchandise sold by us for others.
Tiio entries in this book are drawn from the comnnon Sales Book, and from it
we make tho Aeeount« of Sal** that we may have to r*«it to those for whom we
have sold.
18. An Account is a statement of facts pertaining to some
persoti, species of property or cause, \riiich enterh into the trans-
action, producing a debit or credit, and designated by u name,
which appears upon the Jjedger.
19. Every account has two sides, a DiAtor and a Creditor ;
each contiiiDing the resulte of separate traosaotions.
*^0. in avcry transaction the sum of debiu und oredlte must
be equal.
\ aob liodKeT aooavnt, by the uira of tbeee teraM, >• made te ibow as important
rMuUo( itself.
trang«d all tfa«
ten ; Inoladinjyt,
.distinct record
jedgor \e called
he sums of
tion rehiting
or paying the
'cash on hand,
k at the end of
the next day's
iption of all
1 their datee,
i of Recfeivable,
ed all bills of
3 our posses-
• daily, weekly,
the original in-
11 goods sold
c, either daily,
[e, they are de-
n this book we
nutedeeorip-
ok, iind frotn it
e for whom we
ling to some
to the trane-
by a nanie,
a Creditor ;
oreditfi must
m ae importaot
BOOK-KEBPINO.
il" \ ?^??S?® •' '"""y ^"'^ ""^^^'^^ belonging to the concern.
tt' n ^.^^H"y '"^ ""y '^^^^ '^wif'S by the concern.
-*». tasa IS the title to (losignate money.
ite?^itWl SuJ^Vmon^'L. ^''^ !^'^^'^'''"^ f''^ '^" ^^''^'P" '^ <^'"', and cred-
tima, oxhibUare^mfrl^f ih '^'^^''^noe between the two .idee must, at any
of rL=h „. a roeouroe of the exact amount of cash on hand. The croJit aida
1 Sn^T^5r°°' "°''' ''' "''■'' ""' "'''-' '■■'"'' ''»'"^°' bo paid out than
24_ Bills Receivable are written obligations ofwh'itever
heZ'cHved!' P^^^^^'*""' ^""^ ^^'""^ ^ ««'"*^^" specified amount is to
th^ debS a5/L I • ^^"-^ /"'lu""'' °^"°''«'^- The oxceg., if any. must be on
trie debit side, and will indicate thnt portion of our rosouroes consistinj,' in note.:
„T??' ^^*^?/?yable are written obligations of the concern, for
which a specified amount is to be /nld.
B,Mhtilitiir.tT<i\T ^h«<"f 't-^''l«. our notes and acceptances M8»ed,
ttiiaontneaobit side, such of them as have been redeemed The diffHron^n 7?
the^be any. must exhibit our outstanding notes, or ourSility ta untdeJmed
2«. Merchandise i^ a tern, which usually implies all prop-
erty purchased or owned by the concern for purposes of traflBc and
remaining m store. •
Merchandise generally embraces all such property, unle.-s the menshaut bein*
curious to know h.s gains or los.es on a pa,. ^1^ kind, opens a seiTrate i,^^
with that particular kind, under ts own <n«nial HHa tk!. .,„„ . -
'*" r^'4've titlas, is debited with th?ooro?'t''""..>p^e; 'rrTse'n^ed'Ld
credited with ite returns. ^ ' "^P™«»ntea, and
27. Real Estate relates to such property as houses and lands
and the account is similar in its objects and teachings to that of
Merchandise.
38. Bank Stock, Railroad Stock, etc., are not accounts
dissirniar to Merchandise and Heal Estate, inasmuch as stocks of
all kinds are bought and sold at their market value, rather than
the value written on their face.
2». Shipment or Adventure is but another h ime for Mer-
chandise, and is used to distinguish bpt,veen property in store and
out of store.
<,.,fh^l"/'"'*P^'''^''"*'''''r^^'>^'*'^'*!^'»y " '^g«°t fo' "*. we should disdn-
guishufrom our merc-..ad>'e;u store by ffivine it a siirnificRr.t .,«,»« mT.
"Shipment to Halifax. ,>r -SLipment I lrofrliIent?or""tn^r^?"t^''ch1
With their procoeds."the oiflereno^'being'a gair;r ir«I:' '^'' '^ '^'^'*^
SO. Feraonai Accounts, that Is, accou.its representintf per-
sonal indebtedness, and designated by the uropei nameb- of such
•11 /
18' ''f
llllk'
bfel
BOOK-KGEPINO.
fi
■ii
! 1
1}
'
'•t
...
persons a^ sustain relations of debtor and creditor to the oonoera,
aro capable nf showirts: either resources or liabilities.
Personal Accounts aro liebited with such suras as, from time totlme, the persou
miiy become indebted to the oonoern, or the concern has pidd them, and eredhea
wttli what they have paid the concern, or the concern may have beoome indebted
to them.
♦51. Stock, used as a Ledger title, means simply the proprietor
of the business, or the stockholder.
There would bo no valid objeetion to using the proprietor's name inatead; but
as nfl real good would result from the change, authors, taftchers, and praotio«l
accountant?, accept (he term which custom has suggested.
This account is usually the first opened in the Ledger, and ia important to show
the nut investment. It i^ generally credited with the whole investment, and
debited with snsh liabilities as the concern assumes to pay for the proprietor.
The difference is the not investment, or what the concern owes the proprietor.
Fiotii the fore<roing remarks, we derive the seven principles
which follow, and we believe that every student who will thor-
oughly finiiliarizc himself with thera, will have no diflGloulty in
deciding upon the proper debits und credits involved in any business
record which he may be called upon to make.
PIUNCIPLES.
1. — The Proprietor^
The person or persons investing in the business should be creel-
ited, under some title, for all such investments, and also for his or
their share of the gain ; on the other hand, he or they should be
debited for all liabilities assumed by the concern for hiin or them,
for all sums withdrawn from the business by him or them, and
for such loss as he or they are entitled to share.
2.~C(Juh,
Cash account should be debited for all oash receipts, and cred-
ited for all cash disbursements.
3. — Merchandise.
Merchandise, and all species of property, bought upon specula-
tion, should be debited, under some appropriate head, for the
cost of the property represented, and credited with its proceeds.
4c. — Bills Receivable.
Bills Keceivable account should ba debited with other peopla's
notes, acceptances, and other written obligations when they beoome
ourss, and credited when they are paid, or otherwise disposed of.
> the oonoern,
ime, the p)er80Bk
in, and eredtted
>eoome indobted
he proprietor
ae infltead; bat
, and praoUoftl
portant to show
]vegtment, and
the proprietor.
> proprietor.
m principles
ho will thor-
diffioulty in
any business
uld be cred-
so for his or
y should be
ill! or them,
r them, aod
BOOK-KBEPiNo.
^.— Bills Palpable.
Bills Payaole account should be cr«^few «♦!.
anoes, or written promises to n«v »T!^ !u ^^ ^n^ notes, aooept
itecl when they ar^ paid or^d':eU " *''^ "" ^«^' ^^ ^^
^•—Persons.
or the, get „u, „f „„ ^R "'""' "' ''»°»°'« i»<lebted to them.
7. — Expense, etc.
^^"^^^^'^'^^^^^ the out.
^credited und«r omc name L the a^^?!;^"^ ^^'"«' should
The foregoing princinles al. I ! I °?.* ^^""^ Produced.
^ g pnncipjes are all embraced in the following simple
FORMULA,
Debit what oosta the concern valup • an^ n j; ,.
the oonoern vake. '-^ra value, and Credit y^)xtix produce*
I
s, and cre(^
)on speottla-
xd, for the
proceeds.
her people's
hey become
sposed of.
BOOK-KEEPING
<> »
I
■T
IDOUBLE3 El^TI^Y.
SET 1.
(INITIATORY.)
DAY BOOK, JOURNAL, AND LEDGER.
RKPRE8EKT1NG THE BUSINESS OP A SINGLE PROPRIETOR.
WITH KXPLANATIONS FOR JOURNALIZING, STATEMENTS, BtO.
INSTRUCTIONS FOR SET I.
The following set comprises the most simple transactions in
business ; the main purpose being to illustrate the foregoing prin-
Biples, and to initiate the student more fully into the proce'sses of
Book keeping. The general instructions given in connection with
this set, will apply with equal force to the succeeding ones . They
ghould, therefore, be properly heeded.
The transtictions are first recorded historically in the Day Book,
in the order of their occurrence ; from thence transferred to the
Journal, and from thence to the Ledger. In journalizing a traas-
action. the first thina* tn Yu^. annaJAoraii la tV,a nr^^~^^„ »- tu:
affected ; next, m what manner aflfeoted ; and 'aslaj, the proper
application of the principle. The check-mark (V) is uinde oppoiHte
the Day Book entry, immediate^ upon its b«ing journaUted,
IT.
DGER.
:ETOit.
rs, BTO.
3sactions in
egoing prin-
processes of
lectioii wJth
ones. They
! Day Book,
Ti-ed to the
sing a traos-
'D or Lx^Uig
the propor
ide oppodto
T>AT BOOK.—SBT I.
ftilness, and notE t ^' '"''' ^°^«^«''' a°d constant watch-
errors in postin. = "^"'^ '°™"^°° ^'*»> "^w beginner, thaa
«?h^Sg^:tt*Llt "r -f'tH*'^ •'°"^"^'' -^ -•»« >*
the debit or'crediljol^U ^PP^'^^' ^e in
mg side in the Ledcrgr u^ino- 1. • "^ '* °" *^^ correspond-
entry. Suppose fofeiannle th." "''^'T''' '^'' ^PP^^'^^ J«"^°«'
disc Dr. To Cash '' T^ i ' *^'J°!^^"a ^"try to be " Merchan-
Merchandise is to be debh^dTndT ".''"^^^ 5 «<^""«' ^^^^^
chandise account in the Led .'er on P^!'t T'^-?'^- ^^^'' ^^'"
Cash," and carry the amounftn fi? ' '^'*'' f'^'' ""' ^^^' " To
Cash account on^heV.T /^ we^r^^Bf.r-. ^i" ^.''''
carry the amount into the or ,}Z^?' -^y/^^erchandise," and
Journal, be careful to en to in , hi. i ^'"'""- u ^? P°^*^"g ^'^^ '^^
thep^ge of the Ledger to whlhT"'"" "I '^' ''^^ °^ '^^ «^°^^"°'.
t>pon ill being entered in The tedger ^''''^' '"^^'^^^^^^i
DAY BOOK,— SET I.
(JPEBEc, January 2, ]67i
''^ r ^S'„L7.o '.". ':"'"•' ""^ ■'•^ C..1.
^''°'tTLf;r°»^'"-'^'"-''»^'p'ij
-Bough, of A. L,„<,l,|.„, (,»,!,,
$4500
350
16731
it
1 ^-
.1
i
1 1 i.'«f
i>AY BOOK,-~SBT I.
JuBBEo, January 12, 1871.
V
V
V
V
V
V
V
Amount brought forward.
Sold Jos. Murray, on fc^
16 yds. Biack Cloth, (a) $6.5'J
17
Bought of N. S. I'ower, on our uoie due Feb-
ruary 22, next,
21 yds. Black Satin, /S) $i. 10
20
Accepted R. Green's draft on us at 16 days' eight,
favor of M. Duval,
26
Sold J. N. Benson, on hiw note payab'e Fel». 27, next,
86 yds. Canada Gray Ciulh, fd) $5.40
31
Paid Ca«b m follows:
Fc\- .''-■.;■: ting of Store,
Eci r ;;,,',■ ;iy Expenses,
Fus S'Vu'. of Store, one month,
February I
115.75
42 60
30.00
Received Cash of Jos. Murray, on %j
Bought of Myler & Lee, at '?, months,
432 yds. Irish Linen, (d) §.45
Lent Cash to D. Murphy, until 15th inst.,
6
Sold W. S. Reid, 84 yds. Gray Cloth, /® $5.50
Received in Payment,
.3 Shawls, rti) $60, fl80
His Note at 40 days, for 200
Balance on 5i^, »2— 462
Paid our acceptanc*, ftivor of M. Duval, in Cash,
|720!>
97
86
360
302
8d
60
194
120
462
70
60
10
40
35
350
$9310
40
46
"^■X'-
|720!»
97
70
50
86
3dU
302
10
4-0
88
60
194
120
462
35
40
DAir BOOK,.-43BT I.
Quebec, FEBRUAar 10, 1871.
Amount brought fory,ard, \
Beceired Ca.h of Joe. Murray, ia full of %,
_ 15
"*'th'io«t^°'^' ''"'*'*'"' '" '"" '"^ "^"° ''
18
Gave my Note ^ 60 clay«, for 250
Bounce on f„ 245_645
22
PuiJ^CuHh for mj Note in favor of N Power, now
25
Exehanged Notes with L. White for our mutual
accon.modaticn, each drawn at 40 days,
TfSTo
47
120
645
50
27
Received Ca-h for J. N. Bencon's Note pdvt due,
■ «
Bought of I.. A. Tavlor,
500 yds. French Merino, /® $.75
bave in Payment,
Ciix ^^''''^ ^""^^ ^^ ^^ ^^^^^ ^""^ ^'^^^
Order on W. S. Reid, in full pf «fe, _J5-375
__ 28
Paid Cash for gtoie Rent to date
" Family Expenses, etc.,
$30
48.50
86
300
302
376
10
40
78
$11264
50
95
" h
35e
$93101 45
^^^o.
IMAGE EVALUATION
TEST TARGET (MT-3)
y^
1.0
I.I
w^
12.2
WUu
id. 116
=d
<^
/).
Phntnorpnlnip
Sciences
Corporation
4.
■^
iV
<v
33 WEST MAIN STREET
WEBSTER, N.Y. 14580
(716)872-4503
^
::«»
^
A
h
o
'^%
II I
JOURNAI^,— SET L
Quebec, January 2, 1871. Dr.
Ct.
1
1 Ca^h Or.
$4600
^ To Stock.
$4500
Ml
;!
ti
Stcck is the dtle chosen ropresent the
tierpon mvegtinsc; in this case, A. J. Hall.
It IB ere I, ltd with the investment according
to /■rmmple 1. Cash is here reeeivcd bv the
oonoem, and is made Dr., acoordinj: to Prin-
etpU ?.. *
350
1
I Stock Df ,
r
' To R. Green.
1
3S0
.;t.'>^k is debited for the liability assumed
by thL' eonpern, Prin. 1. R. Green is ered-
iteii according to Prin. 6.
ft
lei.'t
i
* MtRCHANDfSB Dr.
i
' To Cash.
1673
Merchandise roH $1673, and is debited,
PriH. '}.-Giwh was paid for merchandise,
and irf credited, Prin. 2.
8
686
70
1
Cash Dr.
2
To Merchandise,
Cash is debited for its receipts, Prin. 2
Merchandise is credited for its proceeds,
6S6
"
12
97
fiO
3
Jos. Murray Dr.
2
To Merchandise.
Jo«. Murray Dr., Ptnm. «.— Merchandie*
Of,, Prim, .3=
97
50
1
$7307
20
$7307
''
10
Or.
;f45()0
350
1673
70
686
TO
50
20
97
$7307
51)
20
JOURNAL,— SET I
QuKBBo, January 17, 1871. Z)^
AiERCHArJDISK
Ancunti brought forward,
Dr.
Tfi Bills Payablr,
Crl%"°?'" Dr., Prin. 3._biiu Payable
20
To Bills Payable.
have ««ncW«rf our inJobtedness to him by
prom.MO« to ,,ay the amount to another
pe^^on whom ho has authorized to receive ir
new h .bi ity thus assumed, Prin. 6.
,»,i . "^ ^ *'.'"'"8^ wrought in our affairs hy
ih u transaction is the transfer of a liability
^^11 a ,,ersona: account to a note. We
rT °";i"l^''' "^" Obligation at its matu!
protUIeS* ^'^'"""'^ ''■^ ^"'°S our paper
26
Bills Receivable Dr.
To iVIerchandise.
•1
BxPKNSi;
Dr.
To Cash.
fc;«p«'j» Dr., Pr.«. 7.-Ca8hCr., Prin. 2,
■ February I
CAtitJ
Dr.
To Jos. 1VIURRAY=
CMh Dr., Prxn. 2.~Jo$. Murr.y Cr., Prin. 6
u
I7307I 20
8G
10
Cr
$7307
86
20
10
302 40
m
i
— ii
1 I
•r
i:
in
\ > < I
i, ■'
\l I)
JOURNAI^— SET I.
Quebec, February 2, 1871. Dr.
Amounts brvvght forward,
Mtt ^OHANDISE Or.
To Myler & Lee.
Merahandise J>r., Prim. 3— Myler A Le«
Cr., Pnn, 6,
D. Murphy
To Cash.
D. Murphy Dr., Prin. «.-CaAOr., Prin. 2.
6
Sundries Dr. To Merchandise.
Merchandise
Bills Receivable
W. S. Reid
Merchandise Dr., Pnn. 3. Bills Reeeiy-
able l>r., Prm. 4. W, S. Reid Dr., Prin 6
Merchandise Cr., Prin. 3.
The term Sundries is here used for the
first time. It means, simply, Sundry Ac
ooimtt, and is convenient as a Journal ex-
pre.-'. ion, and to avoid the necessity of enu-
inerjiiing the items which comprise the totals
cafncd to the Ledger accounts.
— 7
Bills Payable
Dr.
To Cash.
Bills Payable Dr., Prm. i,.-Cagh Cr..
Prm. 2. '
10
1 1 Cash
3
Dr.
To Jos. Murray.
o^« '*'■•• ^'^- 2— •'<*• Murray Cr.,
$8184
194
120
180
200
82
06
40
350
47
50
$9357
Or.
18184
194
05
40
rjo
462
350
47/60
?..!.. mill, imui yiwiii jju^A.,-
l«
t
96
$9357
95
SS*SfS^^^^g*5^^!^
pp^tsh^^^-,,-^^^,^
Or.
18184
1»4
Ofi
40
120
462
350
47i
S9367
60
»6
!' ■ I Ill U llr II I J I IJJi l j
JOUBNAL,— SBjx l
QlTEBEO,'PBBBrAaT 15, 1871. Dr,
Atnoxmf i-rought forward,
Br,
Cash
To D. MuR«>Hy.
Sane Pri* as for the preceding entry.
18
$9357i ;».•)
120
Memchandisk Dr. To Sundries.
To Cash.
"' Bills Payablk.
" C. Phelan.
Merchandise Dr., Prin. 3. — Cash Cr
Pnn. 2 Bills P„yabIo, Cr.. />«« 5 j d'
Pheian Cr., Prin, fi. '
22
Bills Payable
Dr.
To Cash.
Bins Pay. Dr., Prin. S.-Cash Cr.. Prin. 2.
25
Bills Ukceivable Dr.
To Bills Payable.
B. Rec. Dr., Prin. 4.-B. Pay. Cr., Prin. 6.
. 27
Cash j),.^
To Bills Receivable.
Cash Dr., Prin. 2.—B. Kec. Cr., Prit. 4.
((
Merchandise Dr. To Sundries.
To Bills Receivable.
" Cash
" W. S. Reid.
Mdse. Dr., Prin. 3.— B. Reo, (.'r Prin 4 •
Caah Cr.. Prin. 2; W. S. SeiJ Cr:'. S^^'.V.
28
EXPE.NSE
Dr.
To Cash.
BzpaD8« Dr., Prim. 7._Ca«h Cr.. i>rMi. 2.
18
646
86
10
300
302
40
376
78
50
$11264
y
a*.
!j!y357
120
95
150
260
246
3ft
10
300
302
200
140
35
40
78
60
$112641 96
S'fv ^^t
i^sfl
' iHn^^l
■HHI
liEDOER,— SET I.
(5
f I
I
i I
]. iii.
§e
IS| 2 1
o w
n
s^
M
;&
■*
s
-
IS
?0 ^^ eO r^ r-l O
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13
K a
5J
o
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a
It
e
a.
— NW^ST»l>^^r»<
ei 00
Si! c,a
1-5 £ti
^5
d
I o w
.£3
OS
„ C3 3 -M ri.
M : 5 : 5 : 3
lftl-^^^-0C?^^»OO_
o s oo o o
o t- o o s «
IS
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1
c
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« i-i N CO Tf Tj(
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2S
45
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5^ ^1
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«5
IS
1
OS
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CO
r"
! -^'■V^^ijjfv^.^n ,-. ■
•«s^<auWUKS^|^
LEDGER, —SET I
*
1 =
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1 <o
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c^
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i:«£!DQ£}JEl, -SfiT I.
3
2S§i I2i
« O 3 S I O
00 o .o = I 55
r*::
N N ^ ■*
a
> a>
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ja
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««• O 30 m
>-H CS -^ T^
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LEDGER,— SET I.
a5s
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3 1 =>
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PROOEWS or CLOSING.
I'ROOESS OP CLOSING.
3r)0
570(;|fi0
80241)
"131; I oi
3,-)0
9700
166 Soi
120
«2
Steele,
Casli,
Mcrclmruliae,
Bills IJeceivablf,
i'ill.H Payable,
H. Green,
Jos. Miiiray,
Expcn-^e,
Myler & Lee,
I^. Murpby,
«'. Phelan,
VV. S. Reid,
11264 95j[ Equilibrium,
!onc usivo cvidptieo tl,,, •,! ,1 „ . ■ ''^""•"•'1; ivliicl. ;ilK>nls
^ the Le,j''T::i:i^T;'s::^:r^j^^ ^^^^y;^y
now proceed to cToi:''rtyn:c rn^^'^^'v^:^'' 7^^
for-otten that the object of closin- t T o i • ^'' '^ "°^' ^^
pi-opor manner both f ],« « T" J • ^'^*^"'''" >^ *« pi'oscnt in a
resources and liabilitie^^amM « ; i"^" ^^ * ^'■'^* ofits
and losses. "'''"'^''"' '^"'^ '^^ P'ogrcss, by a list of its gains
Bj an examination of the fants ,> v-i!' V -p-. n d
are shown by an excess of the Dehii side of K??t ^"'"«''<'^»
LiAB.MT.Es by an oxce^ of thV^.w / ^j r^» accounts, and
and that Lnsss are Twn K '^'^ ''^" of Rkai. accounts:
^lu^TATim accounts, and G't.in* by an excess of the Credit
21
h '-*'^ s
I
M
iimK ii
PR00E88 OP CLOSING.
side of RkprEsentativr accounts. This will su2:a;eHt the pro-
priety of opcnitig two accounts for these general results: one to
contain the rcsouiccs and liabilitie?, and the other the gains and
losses. We will now open these accounts nndor the titlrs of
" Loss and Gain," and '• Balance," the former to contain the re-
sults of the Ueprksentative, and the latter of the lli:AL ac-
counts. Before proceeding to elose the accounts, we must ascertain
if they are all ill a condition to show the results desired. The
Merchandise account, as it now stands, shows an excess of the
debit side, and would therefore represent a foss, if the merchandise
were all sold. The account itself does not show whether the pro-
perty is all sold; aiii the only means of ascertaining the facts in
the case, is to take an actual inventory, or a valuation of that
which remains unsold. This we now proceed to do, with the fol-
lowing result :
INVENTORY.
Merchandise remaining unsold, February 2S, 1871.
ISC
93 yards English Black Cloth.
l&$5
$ 465
21 ♦* Black Satin,
«' 4.10
8(5
10
432 " Irish Linen,
« .45
194
40
86 " Silk Velvet,
" 7.50
(i45
600 '« French Merino,
« .75
375
3 Shawls,
" 60.00
180
$lii45
50
Hence, we see that the unsold nierohandiso is worth Si 945 50,
which amount we enter on tlie credit side of Merchandise account
in red ink, * and transfer the same immediately to Balance ac-
count. The accounts are now in a condition to close ; and wc
will take them in their order. The first account (after Stock,
which is the proprietor's own account) is Cash account. This
aooount represents a resource consisting of cash on hand ; the
debit side showing the money received, and the credit side that
disposed of. We close the account by entering the difference, in
red inJa, ou the credit side, and footing up the sides, drawing
double lines underneath. The red ink entry, or balance, is trans-
ferred immediately to the debit side of Balance account. The
Best account, Mcsrchandise, shows a g'ii», and the balance is trans-
* An entry In redink on the Ledgor, denotes that the amount thus written it
to be ir<tMf'err«d, either to aoine other ocoount, or to another position under the
s&me acoounW Ked Ink entries are always traiwfcjrred to tlie oppotUe aide from
wbn« they ftrst appear, f»r the roacoa tbat they indicate an oxoesv of that lide.
12
1 eutrs;est the pro-
] results : one to
lier the aaina and
dor tho titl(\s of
to contnln tlic re-
>f the Kkal ac-
tvemust nscertain
ts desired. The
i an excess of the
' the merchandise
^vhether the pro-
ining the facts in
valuation of that
do, with the foi-
!8. 1871.
)
$ 465
t.io
80
10
.46
194
40
r.5o
045
.75
375
).00
180
$11^45
50
worth Si 945 50,
chandise account
7 to Balance ac-
to clo?e ; and we
it (after Stock,
account. This
1 on hand ; the
credit side that
the difference, in
sides, drawing
balance, is trans-
! account. The
; balance is trans-
lount thus written m
ir position under the
e oppotUe aide from
oxoesti of that lide.
PBOCWfiS OP OLOSINO.
«oa„ balance., and we close it by simply ,-uli„„ the do ,2 1 ne"
*ow, a «<,„„., .„d is .ransfened to thelj.VoV BaL V.'^rn"
.helc- d TrT *" 7f'-' °f."Ji "■" "<"=»""'» exhibited unJ°r
been plerlv r? ^1' 'l^ "''"""''■ "»'' '^ '^e balances have
« next take . T-iai Balance of ^^^'ZoJ^^^
SECOND TRIAL BALANCE. Dr, Cr.
Stock,
Loss and Gain,
Balance,
I
$4500
340 60
989 40
.tt:;: Z !;^t"l?tr Sd rfff^^r^
side, decreasing the investment The S.A '°''' •" ""' '*"''''
the capital invested inc'aaed b> ^'^^IZhZ'TJT''"
equal tho/,fMra( worlh, as shown hv the R J , ' »' <"""■*.
now close 'stoclc account in^ Bala/ce whwTusI?""/ '^'
eju ,b™„ „f the Balance account ; a^d cotlct" i 't^^^-t^unT
t.iy euurd 01 resources and liabilities. " ' " -account,
b Jness ,hich it occupied'atr oil ;:C^^^^^^^^
the not investment, or net intae- of tile pIv^Li ' ' "'"«
I
, !
ORDER OP OLOeiNQ.
ORDER OY CLOSING.
Th« student will <\o woW to observe particularly, and to follow
out in prnctioe, tlie foUowin- order of closin.i,' tho Lcd,;?er.
First.— Open ;in account with " Loss and Gain," (if not al-
ret.ay opened,) and aaotiier with " Bulanco " ; the former to
exhibit tho losses and gam-t, and tho latter the renoarces and ha-
bxll/ie.t.
Second.— Ascertain from the inventory if any property remains
unsold ; and, if so, credit each account lor which such property
was oriu'inally debited with the value of that unsold, makinp; the
entry in red ink. •' By Balance," and transferrin^' the amount
directly to the debit side of Balance account, making this entry
in black ink, " To Merchandise," or "To Real Estate," or any
other account from whicli tht^ amount is tranaferred. The Ledger
accounts will each show, now, one of tho four following results;
viz.. a Resource, a Liability, a Gain, or a Loss.
iThird. — Omitting Stock account, (or Partner's accounts,)
commence with the first account in the Ledger. First ascertain
which of the above results it shows, and make the closing entry
accordin"-ly. If the diiference represent a resource or a liability^,
enter upSn the smaller side, in red ink, «' To " or " Bi/ Balance "
as the case may be, and transfer the amount in black ink to the
opposite side of Balance account. Tf the difference represent a
gain or loss, enter on the smaller side in red ink, " To " or " By
Loss and Gain," and transfer the amount, in the same manner,
to Loss and Gain aocount. Close all the accounts (except Stock
or Partners',) and transfer the balances as directed. The Loss
and Gain account will now show, on the debit side, all the losses,
and on the credit side, all the gains, the difference being the net
gain or net loss. The Balance account will show on the debit
side all the resources, and on the credit side all the liabilities,
(excepting the result of Stock or Partners' accounts,) the differ-
ence being the real interest or present investment of the proprietor
or proprietors. m • i -n i
Fourth.— Take a " Second Trial Balance," or a TriaJ Balance
of the remaining open accounts. Stock or Partners', Loss and
Gain, and Balance. If the balances have been properly trans-
ferred, the debits and credits of these accounts, taken together,
must be equal. .
Fifth.— Close the Loss an;! Giin account into Stock, or, it it
be a partnership business, into the partners' accounts, dividing the
gain or loss according to agreement. Tho Stock or Partners' ac-
counts will now show the original investment, increased by the
gain, or decreased by the loss ; the difference being the jyvesent
24
j^, and to follo\»
Lcd,2;er.
lin/' (if not al-
the I'ormer to
Honrces and Ua-
roperty remains
I such property
old, iniikinnj the
[ill the amount
iking this entry
h]st;ite," or any
i. The Ledger
lowing results;
ler's accounts,)
First ascertain
he closing entry
ce or a liability,
" Bj/ Balance,"
')t<ic/c ink to the
ice represent a
" To " or " By
e same manner,
:s (except Stock
ited. The Loss
le, all the losses,
ce being the net
iw on the debit
II the liabilities,
ints,) the differ-
of the proprietor
• a Trial Balance
ners', Loss and
properly traas-
taken together.
Stock, or, if it
mts, dividing the
or Partners' ao-
noreased by the
)ing the pruent
PRACTICAL EXfcROISKS.
condition Ko uSnos, '" ""^""'"^ '""''' "" «»"' P^^"'
PRACTICAL EXEllCISES.
MEMORANDUM L
bu^-ne"s"wftTTi'*?r'-'' \^- ^^'•""' «—ence.l the Dry good
^T " 000 ■ li T"'' ^^'^■''"r«^'^= 350 yards Elbeuf Cloth, a
ai lik ;2^t-^'S:- ;!"::' at ■ • ' V ''" r*^- ^•"^^''^'^" Cloth
and the balance, at GO dav^i 1 1 1^,^'f ,,f \'x,.„' ' «' Vi"
at 40 day., 28 yd. SilktlVet* at £2 0^ ;u"-^Jo\^,i:V ^," •7,»'>t«
30 Vds. Clotfn,. Val,.-.t „» ,:. <. i' . .« " ",,'3-. *— >"J''1 l>- ^t. Just.
Received
ance.
s. 6d.
ceiled in pa,n,en., cihr^f 10, alid'tirriaC"' «' I'l;.;::'- ,"«"
100 yds. Cassiinere, at 8s. H!,l _!« C3„i,i ,^ y, v i '
ca«h, for l,al. ot account n.^- due, £6 7 ti.-lS. Aooeuted C. Vt7;.
kin's Draft
Received of E. G. Ir
on me at 8 day.-^, in favor of A. Svk
vine, cash, on %, £1 5.-~31. IJ
epted C. Har-
e.-J, for £8 8.— SO.
on ,ny note at 2 months. I0,s v,].. Dutch I
K Aiid.bert 140 yd... Elbeuf Cloth, at £1
!i, at £i I
!o't ofS. McGill,
lien, ut 28. 8d.— 16,'«. Suld
uote at 16 da., for £150, and cashVor the
S 5.
Rec'd
in payiu't iii.s
26
bal.~84. Takeu from the
i')
Il
niAOTICAL EXERCISKS.
Store for my own use, '4 Silk hiinclkerchiefa, at 8s. Gd. — 35. Sold
D. N. Fatten, 28 yds. Silk Velvet, at £2 15. Received in paynnent,
100 yds. B!- e Cloth, at 15*., and ca-li for the bal. — 30. Received
of B. Morency, 50 yds. Yellow Cotton, at Is. 4d., on %.— 37. Bo't
of D. St. Just .'50 yds. Sedan Cloth, at £1 2 G.J. Gave in payment
his note of the 12th instant, for £10; the balance on "/c — 38. Lent
F. Audibert, cash, £12 10, until lOtli of February next.— 30, Paid
cash for acceptance fiivor of A. Sykes, 19th inst.; on the same day,
received cash of \V. Dixon, in full of ^. — 31. — Paid cash for sundry
expenses, £G 10 t.
Take the detailed Inventory of the Merchandise unsold on Jan-
n&ry iiisty and quoted at the cost price, the amount of which is
£872 6 e.
£ 2G6 11 2
Net Gain realized on January Slst,
My Net Capital
M
(I
1465 6 2
\ '■
I !
if
timtstt
Mi
'i
MEMORANDUM II.
February 1, I continue the same business with the following,
resources and liabilities, shown in Balance account oflast month'
Ledger; viz.. Resources: Merchandise, us per Inventory, $1489. S3.
Cash, $2982. SG; Bills Receivable, MGGT.oO; E. G. Irvine's account,
§3.70; B. Morency's do., ^235.41 ; F. Audibert's do., $50 ; Liabiu
ITIES : Notes outstanding, for !?4SG.83 ; Bedard and Jordan's acct,
?35; D. St. Just's do., $'J5.25.— 3. Rec'd cash of F. Audibert, in fub
payment of the oan of last January 28tii. — 3. Gave D. St. Just,
an order on B. Morency for $G(), to be p li 1 in cash. — 4. Paid cash
for Insurance in the Ruyal Insurance Co., un Merchandise amounting
to $1400, at li% premium.— O. Sold Kelly & Shea, at H months,
20^ yds. Elbeui Cloth, at $5.60 ; 217 yds. Belgian Linen, at G2icts. ;
57yd3. Cassimere, at$1.70; 69 yd^. Indian Cotton, at 22^ cts.— 7.
Rec d cash of L. Newton, in full for his note of $1067.50, due this
day.— 9. Sold H. T. Perry, 65 yds. American Cloth, at $2.70; 24^
yds. Gray Cloth, at S2.75 ; 20| yds. Merino, at $1.45; 31 j'ds. Yellow
Cotton, at 82^ cts. Received in payment his note at HO days,'' for
$150, his order on F. Audibert, for $80, and cas)\ for the balance.
— lO. Rec'd of F. Audibert, in payment for his note of January 28,
last, amount'g to $600, and due this day; viz., 82 yds Silk Velvet, at
.^9.80, and cash for the balance.— 11. 'Bought of A. Gibb, 218 yds.
White Flannel, at 87^ cts. ; 195 yds. Red Flannel, at 92 cts. Gave
in payment my Draft, at si^ht, on B. Morency, for $150; the bal. at 1
month.— 13. Sold G. S. Convey on %, 7iyds. Silk Velvet, at $10.70.
— On the same day, sold to sundry persons, lor casli, 8, yds. White
Flannel, at $1.12 ; 87^ yds. Blue Cloth, at $4.20.-14. Rec'd for my
portion in my aunt's l>equest, $■•60.75, in ca-h, Vrhio:! I !;ave depos-
ited in the Union Bank. — 15. Paid in ca.^h my note in favor ol H.
Simon & Co., for $120, due this day.— 17. Sold C. R. McGruth, :u
8 days, 8 Silk Handkerchief-, ai 85 cts.--lJ»-. Bo't of A. Lane & C--..
2i5| yds. Black Watered Silk, at $1.86. Gave in payment H. T.
Perjy's note in my favor, for $160; my note, at40 days, tV;i tsOO ,
26
Gd.— 25. Sold
I'ed in payment,
—30. lifccived
%.-27. Bo't
hive in payment
%.— 38. Lent
ext.— 30. Paid
the same day,
cash for sundry
! unsold on Jan-
nt of which is
206 11 2
465 6 2
ith tlie following
of last month'
itory, $1489.83,
[rvine'p account,
0., $50 ; LiABiij
1 Jordan's acct,
Auilibert, in fuh
rave D. St. Just,
I. — 4. Paid cash
mdise amounting
a, at 3 months,
linen, at 62^cts. ;
, at 22^ cts. — 7.
1067.50, due this
1, at $;2.70; 24i
5; SlyJs. YeUuw
at ;-iO daya,'' for
for the balance,
te of January 23,
is Silk Velvet, at
. Gibb, 21Syds.
at 92 cts. Gave
150; the bal. at I
Velvet, at §10.70.
ih, 8J yds. White
14. Itec'd for my
i«;i I have dopo'-s-
ote in liivor ol H.
I. R. MoGrath, tii
of A. Lane & C'..
n payment II. 'i\
days, f« taOO ,
PRACTICAL BXERCrSfcS.
and cash ibr the balance -ai» *
- ;ack watered Silk, at '^^ i\ * ^•'^'^•-24. Sold f^^r cu^^h ,i' vd.
yJ"- Sedan Cloth, at .s' 30 ^0' ^^ ^'^'- ^'^ ^'^""^1- at .^1. o'-^2i
anee of 20th in.'t, ftnr^r /'f'"'^''^-^' Di-^courit.d mvaccep
«ale at auc;;^-o Tl :*£'Sr^"' '" T'' - the?:t proc^^d'of'te
Store on the 24th i sL-38 R^c'd ^^^ '"■'" *!i« «^« ^'"^^ destroved my
cash, $1400, amt. for wh^h my \li' h^" /''^ ^°^?' ^"^"rance Co., J
"ly^viert'liandise was insured.
BALANCE ACCOUNT.
MEMORANDUM III.
March I f A J h 11 i
-^7, to my Dry Good bu.sfne^s Mv r' ?^ J"'"^^ F^-^^uce and Gro-
'allows : Cash on hand, £755 3% .fc. '""['''' ,^"'^ Liabilities are as
^^ per Inventory, £486 7 G ■ V 's j^'^'^" »'«"^. ^75; Merchandise
Notes outstanding amt'e to £r7; 7;, ^r^ "'^"'^ '»« on %, £11 is'
and C. Pheian, £61 5 io„ f ^"' ^ «^e Mvler & Lee £4S 9
yds. Sdk Velvet, at £2 2 6 _o u '^,'^^"<^" Merino, at 48. 6d • 5'
I bbls. Superfine Flour cPu»„ J ' , "'^- ^^'^a Pour, at £1 J. «
pV;"? ^0 bush, i'eas, at 4s 6d • '^n 1 1 ^,' , °^^^' Oatmeal, at
^"glish B ack Cloth, at £1 16 s- vVl «, P^^"*' ^^ %, 12 yds.
tco 'J^^^t ^"P^^'^"^ *^Jo"r. atii 6 2 ^""^'^r^^PJor Flour, at
r^n^''^^^'^!'^"' ^ Jo^en Fet hats JT**:,,^/*^^^- Crawford
I !
i
l!
1
PRACTICAL EXBBC18M.
Maurice fov Ca«h. 1 bbi: fi»t.a Snr>eric.r Flour, M l9.-0n the pa.ne
day, Accepted Myler & Lee^s DrafY on in- at 10 .lays. »" J^^^r of 1.
lJ.el,fbr£;^7 10.-8. Reo'.i of J. B. Davi"- ?;ri' •,""-,?;,/ "J^'
-Onthe8amr.day, 13o'tf)rca.'.h<>fSMUth & O'Ne.l ..0 lbs- coffee^
at Is. 2d.; 20 U.S. Tea, at 2h. fid.; 60 X,3. Brow"^u?ar at S^.h ,
16 lbs. Chocolate, at 1h. .5d.; 24 lb.. Cboe^e. at '-i'l-^' S^J^p,^'
Rolland, at one month. 15 yds. Iri.h Linen, at 38. ; .30 yd.. Red Flan-
nel, at 4m. 4d.~10. Bo't of A. Haniel & Co. .54^ yd.. Alpaca, at is.
Id. : 1 LSI yds. F»ench Me»no, ai 53. .Sd. ; 6 Carpetbags, at 5.s. 6d. ;
3 doz. handkerchief, at lOs. 5d. Gave in pay"^"<^^njy note at 90
daTs, fori:20 10; Uie bal on %.-13. Rec'd of W S. Reid, m cash,
£11 15, in full of %.-!». Paid £3 H 9 in cash for the purchase,
oartage etc., of 2^ curd, of fire-wood.-ll. Sold B. Jones on hi8 note
at 2 months 70 vds. Red Flannel, at 4s. 7d. ; 15 y<i«.^B"gl>;li Black
Cloth, at £1 16 9^: 28 yds. White Flannel, a^/^-Jf •-:1%^°,'*/
for cash, 16 lb'.. Butter, at U. ; 5 bu. IJarley, at 68. n;l--l«- B^« ''
of J. B. Davis acheck on C. Howard, for£17 1, payable to the l^earer,
which was paid me this day, in cash, in full of ^.-IT. .^old ix. i.e-
niay, 2 bblsT Superfine Flour, at £1 7 ; 2 bbls. Extra buperiur Hour,
atil 17 8:1 barrel Oatmeal, at £1 1 1 : 40 lbs. Butter at 1 id.
Rec'd in payment, cash, £2 10 6; the balance on acct.-lO. I aid
L. Crawford & Co. cash, in full of %.-SO. Paid cash for acceptance
favor olT. Lebel, 7th inst.-31. Paid cash for a horse and harness,
£43 5.-22. Bought of F. R. Meredith, 6U yds. Cassiniere, at 9s. 3d.
Paid in cash, £18; the bal. at 20 days.--2a.. Bo't of Myler & Lee,
78i yds. Woolen Carpet, at 2s. 7d. ; 85 yds. Printed Calico, at lO^d..;
18 pair Cotton Gloves, at Is. l^d. ; 15 yds. Welsh Llannel at 2s. bd. •
6 Silk Umi<reUas, at 18
ltd. Gave in' pavinent, cash. £6 4 6; an
order'on G. Lemay for £5 ; the b:.!. on %.-24. Sold J. Bell on %
1 bbl. Extra Flour, £17; 5 bush, peas, at (.s. 2d. ; .3 l^elt Hats, at
58. 6d.— On the same dav. Sold to sundry persons for cash, 5 yds.
French Merino, at 7s. 4^d.: 1 carpetbag, Hs. 4d.; 2 Black Caps, at
9b. 8d.— 26. Sold B. Nolan 40 yds. French Mermo, at bs. .sd..*. Reed
in payments bbls. Apples, at £1 2; and cash for the balance.-27.
Sold S. A. Hunt, 15 yds. Alpaca, at 3s. 4d. ; 1 doz. Handkerchiets
129. 6d.: 25lbs. Cottee. atls. lOd.: 10 lbs. 'lea, at 3s. 5d. Reed
in payment his note at 40 days, for £3 11 2,^; and cash ior the bal.
-On the same dav, Paid cash, 3s. 6d., for carta-e ot the above sale.
-38. Rec'd of Gauthier & Barry, Montreal, as per their Bi 1 ot In-
voice of the 2bth inst. ; viz., 5 bbls. Rye Meal, at £1 7 ; oO ou-^hels
Indian Corn, at 4s. ; GO bu. Oats, at 3s. Dd., which I paid, pursuant
to their order, to J. Rogers, their agent, as follows: b. Reeve s note
due April 17, for £15 10 4; and «ash for the balance.— On the same
dav, Paid cash for freight and oiher expenses of the above Invoice,
£13 7.— 8». Paid cash tof 1 ptjir of pants and I overcoat for my
own U3- £5 10.— 30. Tafeen from the Store for Family expenses
durkis the month; via.. 8 lbs. Butter, at H^d. ; 5 iba. Coffee, at Is.
2d. : 3 lbs. Teft, at 2«. 6d.— On the same day, lant A fcwnth, m cash,
dSlO 12, 6, previous to babticing my accounts, »ivi whose entry I had
omitted —31. Paid cash for sundry expenses diiring the^ month
via., for Rent of 8tor«, £6 10 ; for Family expenses, etc., i* 6 «
28
PRACTICAL KXER018E8.
—On *he name
in favor of T.
n %, £V1 10.
.')() lbs. coffee,
-^ujiar, at 5^(1. ;
-9. Sold W.
ydo. Red Flan-
, Alpaca, at 28.
jagfl, at 5h. 6d. ;
my note at 90
i. Reid, in cash,
r the purchase,
ones on his note
Engli-h Black
2 id.— 15. Sold
^.1.— 1«. Rec'd
(letuthe hearer,
7. Sold G. Le-
Supei'iur Flour,
iiuter, at 10. id.
cct. — 1«. Paid
,1 for acceptance
'i?e and harness,
iinere, at 9.s. 8d.
t)f Myler & Lee,
Calico, at lO^d. ;
,nnel, at 2s. 6d. ;
ih, £6 4 6; an
d J. Bell, on^,
•^ Felt Hats, at
for cash, 5 yds.
Black Caps, at
It (is. Sd.-'*» Rec'd
i balance.— 37.
Handkerchiefs,
3s. 5d. Rec'd
cash for the bal.
f tlie above sale.
their Bill ofln-
l 7 ; 50 bu^^hela
I paid, pursuant
S. Reeve's note
e. — On the same
! above Invoice,
overcoat for my
Fanuly eJipenses
bfl. Coffee, at Is.
. Swnith, in cash,
diose entry J hud
ing the n»onth
etc., i*' 6 «
£578 16 I i. ""'"'^''' "* '^« co8t pn^, the avwuni of which it
Net Loss on Miirch 31
M/ aet capital " <<
£ 30
1061
5 2^
6 04
MEMORANDUM IV.
U^Z takJrTl ;YeS e " ni:"'^ the following Resources and
cent.; viz., Caion 1 uL »2?'fl7 r^^^^ ininuaafew
^2:515.3S;'Noua on h'^d Alt J} ^^^'"^'j^f'l *« P^r Inventory,
T^uuiydo,$8.96. J rtTl iiit' ^- <J^" 'H ''^'^''»"®^25; G.
outstandiniamte ta^4'M(?'T . ^' h^"'''^'J?-* ^^^'^'^' ^Wb
C. Phelaa fn?." A w 1 'A^"^*?* foWowa: Myler & Leo $88.90 ;
o R j! *'*^'^' -^^ Hainel & Co. $72.47; F. R. MereciithSil ^l '
^8h 2ft S);£^M^''''^7v'^^5 '^^^'-- Mackerel, at$7.20.-3.Bo't for
Cheese, aSld'cts -« SoiJ P% & ?\'''?.f*'5 ^'r ^t Z^^"' ' 24 lbs.
ve> on his note payable U the rnrin';; '''r^: ^^^"' ^- »• Col
-On the same day SoMP L f ' ^"^.^^.thout interest, .>f60
Bank Stock, at ^^ .t!on he^TeTaV R. ''.^''' *? i^'^'^^"'^ ^^^''^^^^
in full of acct.->10. Sold J M f if ' '^u- T^' ^'■'''" ^^- ^^^''-^'H
Superior Flour, at" 12.45 •'> hbi^Fw ^''pf '*^^'"^'^"'^' ^ l^bls. Extra
perfine Flour J6.40 1bbi. Oatmeal ?s'^^ ^,'*^^' ^ b^'' S"-
40 lbs. Brown Snea,' at iii o^t Tl m' 1 ^ '"'' ^^''''''^'' ^^^^-m;
in payment, 100 bu. potatoes at'4linl""oT'i'"- " ' '"' R^^c'd
the balance,-On the^samedkr pLt{' o'^ ^Jf "«^ «* 60 days for
the above Invoice in cash S2^^^ ^1 ^o ^f*"^ Jrunk for freight of
in full for his Sof Mu ci^2> -i^"s Jl^^^ i^ I' «: Merfd.th,
Black Cloth, at $7.72 i- yds" RkTw Q ^'"' ''^.'^ ^^ >'*^«- ^"g'isS
Velvei, at J8.65 "5 Fd hLs afll •',) vi *n ^^'^^S ^^ ^^- ^ilk
in the Un.on Bank.-l4. Rec'd of PrR^f ?T''^'^ ^^«^' °'«h,
if-
if
i li
PRACTICAL EXER0I8B8.
$17.28 on the Union Bank, in payment of his account. — 20. Rec'd
$84 in cash for 6% dividend on 14 Shares Montreal Bank Stock.
—21. Rec'd of J. Beaudry, Sorel, loO bu. Oats, at (iO cts. ; .'500 bu.
Rye Meal, at 90 cts., which I Hold immediately with fHO profit, to
E. Stephens. R*c'd in payment of the latter, a note at 2 ) days, lor
$200; cash, $120; the balance on %.— 23. Bo' t for cash lu bWs.
Extra Flour, at $4.80; .T) bbla. Fancv Flour, at $4.70; H bbl.s. Su-
perfine Flour, at $4.60; ■i bbls. Oatmeal, at $6.— 24» Lent cash to
P. Fremont on hia note at 40 days, and without interest, endorsetl by
A. Sauran, $65.-25. Rec'd cash of G. S. Convey in payment for his
note of the 9th inst., due this day.— 20. Sold C. A. Simpson, 8 Simres
Montreal Bank Stock, at $112. Rec'd in piiyment, 128 yd«. Eibeiif
Cloth, at $6 ; and cash which I deposited in the Union Bank.— 27.
Sold N. O. Day on his note at 2 months, 35 bu. Peas, at $1.13 ; 17
bu. Barley, at $1.29; 20 lbs. Cotfee, at 30 ots.; 4 bbls. HerringH, at
$7.85.— -28. Paid cash for Myler A Lee's Draft, in iavor of C. May-
nard, $62.45. — On the same day, Gave the carpenter an order on
N. Graham for $5. 10, for repairs of Store Fixturec^.— 30. Sold J. S.
O'Brien, 200 yds. Irish Linen, at 90 cts. ; 40 yds. Silk Velvet, at
$9.20 ; 12 Felt Hats, at $1.98| ; 12 Black caps, at $1.90. Rec'd iu
payment, Neil & Roche's note, at 40 days, for $240 ; cash, $203 ;
discount allowed for the payment in cash, $3.80 ; the bal. on ^.—
On ihe same day, Paid canh for sundry expenses; viz., Taxes and
Gas, $5.63, Family expense.^, $24.35; Rent of Store, $26.
Take the detailed Inventor}/ of the Merchandise unaold April
30th, and quoted at ihe cost price.
The Merchandise amounts to $22^2.96.
The Shares of the Montreal Bank Stock, to 624.00.
BALANCE ACCOUNT.
t
BKBODBCKS.
■jr,
LIABILITIES.
S 840
^■j:
(
Cash,
$ 83,'
Bills Payable,
10
^H ' i
(
1 M«rcliandise,
2232
95
C. Phelan,
245
00
^H M
$1
1
Bills Receivable,
1285
45
A. Haiiiel & Co.,
72
47
^■1'
J. Bell,
14
86
J. Beaudry,
3(;0
00
^^^^^^^H !
A. Smith,
42
50
Stock,
•4821
0',^
^^^■f-' '
Montreal Bank Stock,
624
00
^H liH
I \ B.Nolan,
26
98
[ Union Bank,
1 H. Collins,
910
46
72
90
^H . i
Hi
N, Graham,
i i E. Stephens,
125
\l\
00
■1 " IIL
'-
^ J. S. O'Brien,
1
147
85
59
5
%
^^^^^H '< i*G^^H H
] 1
$6338
$6338
59
u
L_
;
9
SKT I[.
DAY BOOK, JOURNAL, CASH BOOK, BILL
BOOK, COMMISSION SALKS BOOK,
ACCOUNT SALES.
it,.]
DAY BOOK,— SET II.
QuEBKc, April l.st, 1871.
J. Byrne and F. O'Reilly Imvc tl,i. ,Iay ontore.l
BTRNfc, & Reilly, toconrluct a Produce, Grocery
Domestic Shipping business, and for l.uy.n" IS
8el mg Real Estate, Steamboat Stocks, etc : ~Tl e
parties to invest equal amounts of net capital ad
to share alike in gains and losses. ^ '
J. Byrne's Resources are as follows :
une-half d the Tow-boat Nestor, valued at 7800
One-iourth of the Tow-boat Levis, *' ««
6400
His Liabilities are:
A Note, favor of Barclay & Co., due April
II th, which the Finn assume,
J. L. Eraser, amt. due him.
Making his Net Capital $20200.
$8750
250
20200
1
If
m
00
9000
00
s
DAY BOOK, SET II.
Qr.f.Hiso, Apiul 1st, 1871.
V. O'Hcilly'fl Resources are:
Casl) on liathi, $19600
A Note in liis favor, drawn by 1.. Clint,
due May 25tli, 4230.60
His LialiiliticH, which the Firm assume, are
Young & Talbot, anit. iliie them
R. Fisher & Son, " " "
Makinfj; his Xct Capital $20200.
fl068
2.502.60
1
Deposited Casli in the National Bank,
2
Bought of C. Ross & Bro., Storo ami Fixtures, at
Paid thern,CliPck oil National B'k, $2000
Bond and Morlgiige for balance, 4000— $6000
Solil i of thft Tow lioat Nestor for cash dl•J.o^ilfd in
the National Bunk,
Bonjiht of L. II. O'Connor & Co.,
IFiQ bhlH. Snpwfine Flour, ^ !?
120 ♦' Extra Mfjsa Pork, "
720 " MfSH B.'ef;
\'l!
Piinic Beef,
(iO «< Bed llamH,
6(t " Pearl Ashes,
8 hhde. Sugar, 8800 lbs.,
(<
(1
Gave in payment.
Our two Notes— 1 ^> 10 da., fur
1 ® 3 nio., for
Our Check on the National Bank,
for
Balance on ^,
:"). to
10.00
12.00
!).00
KL.^O
.').50
.07i
$2000
4000
$810
1200
Hfi40
1 1 2.5
9!)0
27.5
H60
.3700
4000— $ia700
Drew Cash from National Bank, per Check,
32
2.S830
3630
60
60
18000
6000
00
00
4200
00
1.3700
00
4C9
00
DAY BOOK,— SET II.
QuHBEc, April 6, 1871,
Paid cash for \ Repairs of Tow-boat Ley is,
90
00
a.H r?sk, ' ^^""■'^«'' '0 be eol.J on our ^
200 bbl... Mess Beef, ^$12 2400
•^0 " Prime " <( ij 270
4 hhd8. Sugar, 4400 lbs., " $.07^ .S30-3000
4
Paid drayage on same in cash.
8
Bo't of E. S. Pierce, a House, 24 St. Louis street, for
Gave in payment,
A of Tow-boat Nestor, for $2200
Uieck on the National Bank, f:)r 1.000
liond, secured by Mortgage, payable
'" <• nio'ill'f^, tor .S.S00~700n
Received per Ora„d Trunk R. R., from L. Sha^v &
Co loronto, to b,^ sold on their % «..,! risk,
(•00 bush. Wiieat, invoiced /?» .fl.do
"00 •• Corn, »• «« (ig
4200 Iba. Butter, '< <« "14
Paid transportation charges, in casli,
10
W Z nf f "'"' ?" ^f '?"*' ^^"'^' ^f Lewis &
Wright, of this city, (heir Bill of Exchange at
«.gl.l on Watson & Co., Montreal, and reimtte
the same this day to Young & Talbot, in full ol
Faid ,n cash, i % Pretn. for the Bill, *^"^2.C7
.■?00i
7000
00
00
9.0
00
1070
II
.! I
DAY BOOK,— SET 11.
Quebec, Apku. 12, 1871.
Rfoeivr'i ifii.'l' ''•nee (Imt the Tow-l>.iaf Lovn* Mink
^estenlaj in tl, St. Lawrence river, near i. ""en
Inland, uml lia> Jicen dt'livercilover to the Under-
writers.
The boat being insured fnr $21 ')00. we liave reci'iv-
ed ill Casii, (wliicli we liave deposited in the
National Bank,) rmiu tiie Qnol)ec Ins. Co.. nnr
\ of same, $5:17;'). !.s« Expenses $110, = f52t»ii
Lost the Bal. of our Share ol'the cuat of
eaid Boat, ($5400 + *l)0 - $52(j.')) = 225
13
Rec'd per Steamer Anna, from F. J. Ray, Halifax,
N. S., to be HvUi on liis % and risk,
400 lil.ls. Codfish, invoiced ffi) *4.r)0
(iOO " Mackerel, " " 6.50
500 " Herriogs, " '* o.OO
Paid Freight and Insurance, in cash,
15
Bought of A. Stars & Co., per Check on National
Bank,
30 Sliarea National Bank Stock, ^ $48 per S.
16
SoldB.W. Hardy, for cash, from L. S.
ConsigDuient,
4200 ll- Butter, i9 $.\6
800 budb. Corn, " .80
& Co.'s
$(172
640
Cloped L. Shaw & Co.'e Consignment, and rendered
them an Account Sales of the same.
Our charges for Storage and Adver., $ 20.00
Our Conn-iiasion on Sale?!, 64. IM
L. Shaw & ' ';.'8 net proceeds, 2152.87
Boughl, at Aucuon, I- :)f ot^amboat S' rel, for
34
5400
0(1
150
00
1440
00
1312
00
^
2237
6400
00
00
DAY BOOK,- SET II
QUKBKC, APIML 17, 1871.
"I'M)
()(i
1.^0
00
1440
00
1312
00
22,-^7
6400
00
00
(^>avo ill payment,
The Note or L. Clint, favor of P. O'lteillv an.l
.liie 2;, 1, i.r.xiino, .':;42;{0.7lO
Our chpoko'i National B'k for inoo.OO
tu^li U,f Sal. inclmJHjg tlisci,
•^"N.ie, GfH;.l!)-642(i.7!i
The di^ct. on Note, $4230.60 for .'{8 day.s, is
it
Gave oi.r Note, ^ 40 day,, to the QneI.ec In.s. Co
^i'riTl'\''Y ■^'""''' *^^^''" Stea.Mbout Sorel, fur
*0500, ^ 2 ^ = $i:;o, a,„| Policy )?[.
18
^ W fr '"^''i^-'b^^-'^t Alfre,!. a„.| coM.i,ne.J tu
% and risk!' ^"^'''"' '""'''"' '^ ^^ ''^^''^' «» -"r
50 bb!s. Pearl A.^hes, fron) Store, valued
f<2>$7
!? im
4 hhd*. -1400 lbs. Sugar. " <•
I 600 bblH. Mackerel, (F. I. R'^ Consi..„.
Paid ca T' V^ *^5" ■ ° 4500
i-aul cttflh lur Ins.^Preujium and Policy, 20
19
The SteaMiboat St. Alban, on which we shipped
puds to McLean & Co., Montreal, got on fiS a
her , rnval in p..t. and our go, J.,= which w'i
resc .; ,„ a (hunaged condition, and upon which
there was no in.surance, were sold at auction lor
2H 79
Shipped, per St»>an)boat Glory, to W. S. Kellv
^iniiJrr' ^tt^^ ^^ ^"^ ''''^''^ -^"^ -^^ i''^ %
•'0 bbls. Superfine Flour, /a $ (5.12 3GG
■■50 '< Extra Mess Purk, " U.oo 650-9IG
Paid drayage on same in cash,
131
00
5266
00
2500
00
920
00
m.^
in
i i
■lit
6
DAY BOOK, -SET IL
Quebec, April 20, 1871.
Sold E. G. Henry, for cash,
400 bbls. Codfish, (F. J. R'8 Con.) ^ |5 2000
500 '< Herrings " " '< 6 3000
Closed F. I. Roy'a Consignment, and rendered him
an Account Sales of the same.
Onr clirtrires for Storage and Advertising, 50.00
Our Commission on sales,
287.50
F. I. R. net proceeds, remitted in cash, 9062,50
22
Sold to J. L. Fraser, 25 Shares National Bank
Stock, at fn) $52
Received payment as follows :
Canceling tor our indebtedness to
5''"'. $250.00
Iiilcrest on same allowed by us, 1.50
Cash for the balance, 1048.50—1.300
23
Received from G. Doyle & Son, Ottawa, to be sold
on their ^ and risk,
1000 bush. Wlieat,
SOO *< Oats,
200 bbls. Tallow,
Paid i'^reight in cash,
24
Sold our House, No. 24 St. Louis street, toR. Fisher
& Son, for
Offset, as part payment, the am't which we owe
them on %, $2502.60
li^cM their Note at 1 8 months,
fieciired by Mortgage on Prop-
^ ^r^y. for 5000.00
And Cash, for the balanoe, 437.40—8000
25
'\
Sold E, F. Andrews, at 40 days, on %
200 bbls. Tallow, (G. D. & Son's Cons.) /© ?8
5000
00
9350
1300
00
100
8000
00
Od
IfiOO
00
SS
l»te«,. due o„ sSrialr'^ *»"£»
' 0.75
27
Cash paid,
I»ificount off- to May 1 7 ' '^^^■^'^
29
Received advice from Price & Tr. w .
pale of 50 bbls. Pearl A.i '.^'"S^'o"' o^the
-;j 600 l>bi.;MackLet'S:iLl'^V'"'"^^'-'
ISlhinet. ' snipped ihein on the
Net proceeds remitted in casli,
30
1000 bush. Whear <^pn t, o .
/a $1.40 ' ^^- ^' * ^^^'^ « Coneignment)
CJofieiJ G. Doyle <fe «?nr,'a n
Q. Doyie i Son's „« proved, jjjf
~- . <(
^••0-Rei,„„.3dra„-„ cash for p„>,^„,,^
8758
00
Pa.d sundr, expenses this month, in cash,
JOURNAL,— SET II.
QuKBKC, Ai>iuL 1st, 1871. Dr.
Gr.
• The term "Mortgage Payable » i« but another name for BilU Payable : the
ad'ount! mZ b" kept ^separate or together. There is a dist.uctjor, between a
SomiSorrnote nnd^ mortgage on real estate ; and the majority of business
■to would pr»fer to h«T9 U»»t distinction prwwved in tbwr aooouHts.
Sundries Dr. To J. Byune.
S29200
00
National Bank
$16000
00
Tow-boat Nestor Stock
7800
00
Tow-boat Levis Stock
5400
00
J. Byrne Dr. To Sdndrie*.
9000
00
" B. Payable.
8750
00
" J. L. Fraser.
«
250
00
Sundries Dr. To F. O'liKiiXY.
23830
60
Cash
10600
00
Bills Rkckivabie
4230
60
F. O'Reilly Dr. To Sundries.
3630
60
" yocNG& Talbot.
1068
00
" R. Fisher k Son.
«
2562
60
National Bank Dr.
18000
00
To Cash.
2 .. ,
600(
00
18000
00
Real Estate Dr. To Scindries.
" National Bank.
200(
) 00
«' MobtoagePay.'
i
•
400(
1 00
Gr.
00
00
00
00
129200
00
60
60
00
8750
250
238:^0
00
00
60
00
00
1068
2562
00
60
18000
00
2000
4000
00
00
r BillB Payable : tha
listinction betwoen a
majority of busineas
MOOUBtS.
JOURNAL,— SET 11.
Quebec, Apiul 3, 1871. ypr
Or.
Nationat, Bank /;,.
To Tow-boat Ne.stou Stock.
4 _
Mekchan
DISK Dr. To Sundries.
To BiM.s Payabi,).:,
" Nationai, Bank.
" L. R. O'CONNOK & Co,
— •■•- _.
5
Cash
Dr.
To Nationai, Bank.
<i
Tow-boat Levis Stock
Dr.
To Cash.
6 _.
Shipment to Montuk.m, * Dr.
To SuNDlilES.
" Mercfiandise.
" Cash.
8
Real Estate Dr. To Scndries.
To Tow-boat Nestor Stock.
" National Bank.
" Mortgage Pay.able.
* " Shipment (o iMontreal " i'? » ~ ~ '
enterprise, and although it relates t'Jfm!?ih''"V"P'"'^ '°'"ep>-esent <^ particular
IS as
though wo had sn.'d
same in this advent
aod cash credited
our m
tire.
c'^Jnn,? ""i" f'*^ distinction. It
norchandi^e for 7 nn ) f '-'^^ ""''''""f'
invested thi
80
cost and morohandiae
■f
w- ' —
1 1 )i
;; i-
i
JOURNAL,— SET II.
Quebec, april 9, 1871. Br.
8
L. Shaw & Ce.'s Cons. * Dr.
To Cash.
10
SCNDRIE3 Dr.
YOCKG & Tai.bot
Premium
To Sundries.
ToIa onal Bank.
.« Cash.
11
BiLLK Reckivabi.e Dr.
To L. Shaw & Co.'s Consignment.
12
Sundries ■''**•
To Tow-boat Levis Stock.
National Bank
Loss and Gain
. 13
F. L Ray's Consignment Dr.
To Cash.
15
Or.
$ 95
National Bank Stock Dr.
To National Bank.
1068
2
00
1020
00
G7
$ 95
00
62G5
225
150
1440
00
00
00
00
1068
2
00
1020
5490
GO
67
00
00
150
00
1440
00
rKoae. m effect, as wouia db au a^ receive, as comm ssion morchaots,
•t:';;ir"'L''t:a7C'efore ff Kur^ -count ^th the ,-.
% Ih. pro^rty, we d«bU it onij with what it haa eoBt u..
40
JOURNAL,-SET n.
Quebec, April 16, 1871. /v.
To L. Shaw & Co.'s Cons,
<<
I- Shavt & Co.'s CoNsioN. Dr.
To Sdndiues.
" Storage & Adfertisino.
" CoMMisaio>f.
" L. Shaw & Co.
St'NDRlES />». rr,^ o
'-'^' io Sundries.
Steamboat Sorel Stock
DlSOOONT
To Bills Receivable.
" National Bank.
" Cash.
Steamboat Sorel Stock Dr.
To BiLr,8 Payable
18
Shipment to Kingston
To Sdndries.
*' Mdse.
" F. I. Rav's CoNriGw
" Cash.
"Jeir CoDeignmentlocounf . " ^^*'*'* '*' ^'^r business wit"h'^h"''* tbe aet amt.
their nronertv a/i\ "^ ""* "«ef^ «'> »how fhl #■ ? "° '^^™ «<> f*r ; and m
When iKS'o:,^ °3„d "^f '" '^ '''8'^r^nce Se7n T/'^-h''*'^ ;'^ ''"tUled to!
-ui. to the a.sw«ir,i'-i- '^^ coLgi', ru;t!"::d?;4-:^-
-u't.totheac=^'g^J':,^-
41
;
\i
1 1 I
I [i
JOURNAL,— SET IL
Qdebeo, April 19, 1871. Dr.
Cr.
Cash Dr.
$2500
00
To Shipment to Mont heal (1)
$2500
00
W. S. Kellt (2) Dr. To Spnoribs.
920
00
'* Mdse.
916
00
" Ca3B.
4
00
90
t
Ca8h Dr.
6000
00
To F 1 Rat's Consignment.
6000
00
«
9360
00
F I. Ray'8 Consignment Dr.
To SCNDBIES.
" Storage & Advertising
50
00
" Commission.
237
50
•' Casb.
9062
60
•>2
Sundries Dr.
To National Bank Stock.
1300
00
J. L. Frasgr
260
00
Interest
1
50
Cash
1048
60
(1) Shipment lo Montreal is treated precisely as any property or represent-
ative aocouni ; baviog been dabiled with itn costs, we now credit ii witii its
proceeds. The difference will be, in this case, our losf.
(S) Here the good« are not shipped for our account, but for the account of
another party who oxtered them. This is therefor* a regular sale.
42
"•acfteaiu.
Gr.
10
00
$2500
00
!0
00
916
4
00
OU
00
6000
00
00
50
237
9062
1300
00
50
50
operty or represent-
» credit i( with its
for the acoouDt of
rtal*.
6
JOURNAL, -SET n.
^Quebec, Aprm. 23, 1871. /)^
TE.
G.DOTI.E& Son's Consign. Dr.
To C^sH
■ 24
i/r. lo Real Esta
H. FisHKK & Son
MORTGAOK HeceiVablb
Casb
■ — - 26
E. F. Andrews ^„
To G. Doyle 4 Son's Cons.
26
$ 100 00
2662
5000
437
1600
Or.
$ 100
8000
Shndries Dr. To National Bank.
Bills Payable (];
Interest
60
00
40
00
00
00
J 600
27
Bills PATABLM2)i)r. To Sundries.
" Cash.
" Interest.
8760 00
8 75
00
8768 76
2000
00
1993
34
66
wrlti^i^n'ttS^'^^t/ thf J'ar':*^',!" '"' ^'"^'"'^ '^-^ credited with the ....
est wi h'-.h^^* "'^'«^'"-« debit Bi'ls Payabl JithtS'^""'*?!'** P^y. *» ordor^
est with the amount we pay for Interest. *°*' ''^ ^° "°*e' "Wd inter-
arioyg"eKrp:;^',r,lV'$%*i^'r'V^*^^" ••• «Fe.aedvaiue a. w.
here debit BillSPnvublowkh the fapf' T^'f'' " **•" >«S8*^han iJC "w.
;^Jtbe.n«t.e amount produced by ir.&^'t^'irv'^;':^'^^'^:;:^
4S
il^;,
^mi
JOURNAlw, - SET n.
QuEBKc, ApiiiL 29, 1871. Dr.
CA(?n Dr.
To Shipmkxt to Kingston.
30
$5100
00
Cash Dr.
To G. DoYi.K & Son's Cons.
G. DoYi B & Son's Cons. Dr.
To SrNDKiKS.
" Stobaoe &, Advertising.
" Commission.
" G. DoTLE & Son.
u
F O'Reillt
u
EZPENSB
Dr.
To Cash.
Dr.
To ClBH.
1400
2900
00
00
200
ISO
00
00
Cr.
$5100
00
1400
30
75
2796
00
00
00
00
200
150
00
00
We have omitted the Ledger in this Set, believing the student
to be fully capable to post the accounts without assistance of this
kind. Wo shall adhere to this plan hereafter, except in cases
wlicie some new principle or application may be otherwise more
clearly shown
The student wHl make his Ledger conform to the following
Trial Balance, and close it in accordance with the Statement
hiob follows
w
'. ^■^^»-ft?;iff^:^^ff,-.
ving the student
issistiince of this
, except in cases
! otherwise more
to the following
the Statement
rooi-ing.s.
23098125
140U
TRIAL BALANCE.
LEbGKJi ACCOUNTS.
J- HVIIIL-
National Hank
Tow-boat Ntvstor Slock
low-boat Levis Stock
Bills Payable'
•»• L. Fraser
Bills Receivable
Cash
Youni;; & Talbot
H. FJHlier & Son
Real Estate
Mortgage Payable
Merchandist
L- li. O'Connor & Co.
Shipment to Montrtai
L. Shaw& Co.'sConsi.r,,
Premium, Disc't, & [..t
L0H8 ami Gain
F. I Ray's Consignment
National Bank Stock
i^toragean,! Ailvfrh,^,,,;:
Coiiiiiii8ision
L, Sliaw & Co.
Steamboat SoreJ Si,oc4f
SliipmeiU lo IiHj.u«icn
W. S. Kelly
<;. Doyle & Son's Cons.
Mortgage Keceivable
i^- F. Andrews
G. Doyle & Son
Expense
INVENTORY OF Ux>^SOLD PROPEKTY.
T.)t:ll
2:)2(i()
2;v>;:{(i|i;i)
2(i;?(;(;
(>i()(i
5l!)()
J4syi
2o()
423(i|i;i)
31)50 7J7()
1()()S
2oG2|i;()
HOOO
7;^()()
'I (it; 2
40(10
2500
2332
11500
1300
100
376|(i:-!
2152S7
Uulanoeg.
202001
20000
4i;^l
7300
4000
100
370
03
5100
3000
2152 87
Merchandise,
I ofTmv-boat Nestor Slock,
Keai Estate, '
I Steamboat Sorel Stock,
5 Shares National Bank Stock, ^$30,
$9325
1050
6300
6531
250
00
00
00
00
00
,4
45
$24a56JU0
STATEMENT,— SET U.
LOSSES AND GAINS.
^^^^^^^^^^^^H!
^^^m
I:
r TTT.
1
225 (
504
33 Oi
166 00
150 00
1645 58
2723 r.3
«. Qaini.
Tow-B(i,\T Nksto« Stock,... i'ro«et!ds from rales. 6400
Valuf of unsold 1950
8860
Cost 7810
65t
)0
1300
. Gain 650
1 00
on
Tow-B/)AT Lkv»8 Stock, Coat 5490
^H'
Proiceedg from Ins 5265
Lofs. 225
^^^^^^^^^M
1
f
(
I
i
1
t
Real Esjatr, .....Proceeds from siiles..''000
Value of Unsold 6300
14300
Cost 13000
OnAn 1300
1
t
1
1
.MRRGBANDI3R li'roceeds from B.ileo 4662
Mdaeun3.(porInv.).9325
139S:
Cost 13700
287
»
110
100
376
i
2723 f
i
00 1
^^^^^^^H '
Gain 287
fcHIPMBNT TO AlONTBIiSAIi,. ....Cost 3001
Proceeds 2500
Loss 504
^^^^^^^H '
Prkmium, UISO'T, l.\TEREST,..Oosr. 3'J 71
Proceeds 6.f)6
Loss 33.05
^^^^B 'J
Natjonal IJA.NK Ktook, Prooceds from sales.lSOO
Value of unsold 250
1550
Cost 1440
^^^^^^H
^^^^^^^H
Gain no
00
^^^^^^1
STORAGE AND ADVERTiaiN0,..PrOC6edS
90
^^^^H '.H' SUl
C()M,MI8S[0N, "
33
^^^^V ' ^'jHHI
Shipmr.vtto Kingston, Cost '5266
^^^H tfli
Proceeds 5100
^^^^^H S^H
Loss , 166
^■■■■M ! iJiriMM
Jfc.XPKN«B^ Cost
^^H 'if WW
Net gi»in •
1
53
^g^^g
46
Lamm.
225
00
Qain
550
00
130000
287 00
504
33
GO
05
110
100
376
166
150
1645
2723
00
00
58
fi3
2723
00
00
63
IIESOTJRCES AND LIABILITrES.
'''■"'" ''W'en/oriM of Unmld Property.
Jifi- Liul.il,
Tow BOAT Nebtob Stock,,
HkaI, ESIATR,
Na no.vAL Bank s;ock:::. "■^•
Steauboat SoREt, Stock,.."
63
From Ledger Aoeountn.
CASH '"'" ^'"'"""
MOKTOAUE PAVA8I.R..;:;::0utsta
hand.
'Hiinj' Notes.
l' iuZvn^"*" ^ ^^«-'-We owe them
w. s. kkllt,..:.. ";;::;;:::J™° '^"^
G.^.ov-u:A«uN We owe th;-;;:::;™:::::
' ' <japitarmvested(net) 202()o;0(i
ni9 half of net gain... 822.7'J
His present interest in
Ike concern 21022.71^
$1950
fi.'JdO
9;i2.0
250
6531
23098|25
1020 I
6230,20
920
5000
1600
4131
7. '100
<1000
2152
*'. O-Rkilly,
"Capital invested Cnet) 2020U.00
l>rawn out 200.00
His half of net
gain 822.79
622.79
His present interest in
the eonoern- 20822.79
87
2795
21022
79
62224 45 62224 46
20S22
79
his B.Lce a Juft ;hLV;o ei^/i'V^-i-f 'V 'f""- -
.ouroos a.d Liabilitios therelLwa, ">e bead of lie-
4T
I'M
V
s
1 I
CASH BOOK,
Cash Ukciivbd.
4l
ti
ti
i(
April; !;To ['\ O'Reilly KecM of him as cupital.
" I 5i " National IJank, . . . Uec'd of it.
" 16 " USIjdw&Co'sCon-
sigiiineni,.. . ilecM for fale of this date.
" Ship't to Montreal,. Rec'd for sale at auction.
" F. I. liay'wCoiidign-
nienl, HecM for gale of lliifi date.
" iVtit. Bank Stock, liec'd the lialarice of sale
of this date.
*' Keal Ef-tate, Rec'd for Lai. of s.ale.
" Ship'l to Kirigstcn, . Keo'd tor sale of ciwda.
•' G. Doyle A Son's
Comigtiiueiit, . . Kec'd for sale of this date.
To Balance, Kroni old %.
BILL BOOK,
Bills
No.
WUon
n'c'd.
Drawars.
lit whose
favor.
For what
received.
Where pay.
1
2
I.Sil
April
• >
1
11
L. Clint,
H. VV. CooiKf.
F. O'Reilly.
Ourselves.
Investment.
Merchandise.
Our Offioe.
BIIJ.S
No
When
iM(l
Mat.
A pill
Drawer^
18'
)vriit',
.1, I
Ourselves.
In wliOhe favor.
Hurjlay & Co.
L. R. O'Connor & Go.
u
Quebec Ins. Co.
48
For what
given.
To Hal. «;^
Md
/t-
.»e.
Where
payable.
Quel>ec.
Insurance.
u
ital.
f 19600
<Iate.
400
1.312
ctioii.
2500
dale.
5000
I'Hale
1048
50
e.
4S7
40
ds.
5100
date.
1400
*:?()7!>7
90
C230
20
Where pay.
Our Offioe.
. (< <<
wliat
'en.
il "■'.
aace.
Where
payable.
Queliee.
u
-SET n.
Cash Dlsbursed.
" , ,. '"."■■•",«""vi-.Sl..d<..P„Tl for rfoair.
li
ti
((
n
u
It
<(
<<
lOi
);{
Ii7
18
19
20
2;!
27
;!()
;{u
■M)
' ai'l (or Drayaijc.
Paitl K:»r net j)riiceevl3,
'^nipin t to ]iin<»s{oM PiM / .- i
" W. S. Ivelly, = ^"'l.^"' ''Jf i'l.-nrance
\\ !;'• f- ^''f^ conVi^',, ■
tr. Doyle & Son's Con
Hills Pavable -M./br Freight.
F. O'Keillv '''."'"'"• Note Xo. 2.
''expense, p,,;, " "" ^i'
^'^"c«; ::::::::: ;^;^^""-'T.'-^pe...e..
—SET II.
Reoeivabli.
':"« I Time
of Note. to run
April lu GO days. j,,^ |,T
^^-, -; .i^..^..^ .'.-,v,.ip.-Hi,.-g:A-jfJ^
»feB
Dr.
COMMISSION SALES
L. Shaw & Co.'s
i
1871
April
u
<i
/)r.
1871
Apr I
Invoice, Per Gratul Trun]< R. !{.,
of (iOO l.u. Wheat, m .il.40
8(Mi Ini. Corn, iTt) .(io
4200 lbs. Biiiier, /a) .U
To Cash, Paid Frei<;lit
" Storage & Aiu'triTisiNo,
'* CoAtMissiox, -I'^'-^onis-l^-n
" L. SiiAW & Co., Net proceeds
Due by Equation May W), 187!
F. I. Kay's
l;<
Invoice, Per Steamer Anna,
ol 400 h\)U. Coillish, m .?4.50
(500 " M;icK-erel, 0) COO
HI o ^ .,, '^"'^ " Herring."-, fd) 5.00
lo Cash, Paid I<reij;lit & Tnsurauoe
" SToiiAaK & Advkktisino,
" CoMM'ssioN, 2\% on $'jr)00
" Cash, Net proceeds remitted
Dr.
G. Doyle & Son's
$ Hf)! 00
I'd I 00
t;i
21.VJ
$2;JH2
S7
00
$ 1.50
5(1
2:^7
90G2
$9500
OG
00
50
50
00
1871
Api-i
It
a
((
•n
Invoice, Per Kichelieu Co.'s Line,
of 1000 bush. Wheat,
800 " Oat.s,
200 bbla. Tallow,
To Cash, Paid Freight
" StOIIAOE & AnVEllTIPINO
*♦ Commission, On $3000 f(b 2\%
" G. Doyle & Son, Net pro. due May 20, 1871
^ 100
HO
75
2795
$3000
00
00
(JO
00
00
* The calculation for avernging'this aoeount, to ascertain when the uot proceeds
60
ifeMM
'"""^"^*"^'*^^^i^i*^^^im^i!^
05
'20
GO
00
c.ij i:;
21,VjI S7
S2;5:^2 00
$ 150
00
50
00
2:^7
50
90G2
50
$9500
00
$ 100
00
m
00
75
00
i71
2795
00
$8000
00
3U tile uot proceeds
BOOK, SET n.
Consignment.
Cr
187)
April
I By BIU.S Ilv:c«ivAui.;,, Suld H. W. Cooper on If I
Ins Note at CO days, i
16
QftVR
" CA.H, Sold B. w^^' :- W^^-tr^"$1.70: J $1020
'^««n[^-S"'^''''®*-^6 $672
a«0 bu. Corn, i® .80 640
1312
$2332
00
00
00
Cqn.sionment.
600 bbls. Mackerel, /© $7.50
'"^'S :; giB!^± f Voo' 12000
^P- 25 Bv E. F. AxoH.ws, Sold hi.n, ^ 40 day«,
■ " Cash, iS) bu'" Wh"T' f ^? II ^^^^^l 00
iuuu bu. Wheat, fa> 1.40 14QQ
" 30
•re due. will be foo^U in the Com
tneroial Arithmetic from p. 2fi«to 279
61
ACCOUNT SALES,— SET U,
Account Sales
-!,
600 bii. Wheat, )
SO) " Corn,' > on % and ri»k of
200 |l>s. Butter, >
L. Shaw & Co.
I, :/■
!' il- !
1871
April
11
16
9
16
ii
Sold H. W. Cooper, on his Note ^ 60 days,
600 lin. Wijeat. <® §1.70 $1020.00
Sold B. W. Hardy, for cash,
4200 lbs. Butter, r® $.16 672.00
800 bu. Corn, fed .80 640.00
2332
179
1
00
<«
<< .
Charges
Paid Freight, in cash, 95.00
Storage «& Advertising, 20.00
Comiiiiseion, 2|% on $2.S32, 64.13
1.8
L. Shaw & Co.'s net proceeds,
Due by Equation, May 13, 1871,
E. E. Byrnb & O'Rbilly,
Quebec, April 16, 1871. Per J. Maguire.
$2152
87
Sales of Goods by order and for % of F. I. Ray.
1871
April
II
II
II
n
18
20
Taken to our account,
600 bbls. Mackerel, ^ $7.50 $4500.00
Sold for Cash.
400 bbls. Codfish, (d) .*5 2000.00
500 " Herrings, rd) $6 3000.00
-Charges .
Paid Freight & Insurance, in cash, $150.00
Storage & Advertising, 50.00
Commission, 2^ % on $9500, 237.')()
F. 1. Ray's net proceeds retuitted
E. E. Btrnk & O'Eeiily,
Quebec, April 20, 1871. Per J. Maguiri
52
9500
487
$9062
00
riO
50
md risk of
00
I
00
00
2332
00
00
00
13
179
IS
*2152
87
re.
I. Bay.
00
00
00
9500
00
00
no
4M7
■)0
$9062
oO
'ri'.
i(f^'??^--*'"^!,>i.. ■!•;•:«'■
PEA0TIC4L EXEROrSES.—SRT „,
Sales of 5 200 bbls. Tallow, ) « «/ - „ ^
I 1000 bu. Wbeat. ( ^°^ ^ 0^ »• Doyle & Son.
April 2;
•' 30
u
u
u
SI 600.00 li
1400.00
23
30
Sold E. P. Andrews, fa) 40 davs
200 bbl.s. Tallow, ra)$S' '
oold for cash,
1000 bu. Wheat, /® .$1.40
Charges
Paid Freight, in cash,
Storage & Advertisinsr.
Commission, 2^^ on'^ISOOO,
G- Doyle & Son's net pro. due May 20, 1871,
E.&O. E. Byrne &0'Reiu,y,
Quebec, April 20, I87I . Per J. Maguite.
$100.00
.30.00
75.no
MEMORANDUM.
the prosecut on of a vrodurp o-i,!: ""^ "'^'» Oj tiAi.L & Guifkin, n
and^br buying and Sri^/nTS/cf T'^ ^"^'"^-'
the Capital &s agreed. A. J HaH i/ f i * ^^'7- ^''*' *^ ^'"'•"'•^»'
Griffin, twcthirlsofthegaL or OSes 1'7 H ii "L^' ^'"^ ^^- »•
Liabilities are taken from tL Ral a *^* "^"^"^ Resources an.J
April, Memoran,lum IV, ;" so R rrwr-""!/'' ^'''^ ^^^^^S^"- ^"
bihties are as follows; Cash Ssr.^T^n" i'r , " ,^^e^"»rces and Lia-
at 40 days, L $150 ^he balance L 7'"' ' '''''' ^^"*^''^'* ^«^^
Sold J. Morgan & Co J 50 bWs 1^. p "lontks.-Un the same dav,
^0000 ibs.. a^6i cts ' R^ ^fin pav,^:ent'hYf ?-'^ ''''''''' '^'^
at 6 cts. ; R. S. Griffin's note tlS Zor 1 J''^'' f P'"', ' "^^^ i'^'''-
commencing business, due 2t th S foSlS ""^ ^''' l'^'' ^''•'^' ^^
eale and for discount on note .f 2^T7'-, n- ^^^ ^ ' an'l cash for bal. of
for 27 days is $6.76.-3. SaveR l^Li.^'^V ^'" ^- ''^- ^'^^'^'^ "ot,
Hull's note thei. favor, due this dkJ^TJh,*.?^?: ? Pa^'^^ntof A. J.
cash for the balance, 5r^30 _ffih« 1 ^ ^''^'•f ^'^ ""''• > and
meucingbusi^es., date^Fe^ ,fary" t 'atfl l^lS ^^ '^' ^''"J' ^ «^™'
Amu of Note, $738.36. Theint for 9?,1 fLJ VI' '^''^^ "''' ^'""''^ date.
44.~Onthek.nedayBo'tofO c^^^^^^^^
fine Flour, at $4.25f'l00 bWa E^^trk M ''^/,^^,"^ ^^^'' ^^ira S^pe^
53
f
irriPT -n— —««-—»■
J'
i1
PftACTIOAL BXRR0rSE8^-r-8«T II.
Hamfl, at$16; 50 bbls. Pearl Ashes, at $4.30. Gave in payment,
3 bbls. Codfish, at $3.60 ; 100 buphelfl Potatoes, at 48 <tia. : 14 hhde.
Su^rar, 15 tOO lbs., at 7^ cts. ; and cash for the balance.— 4. Shipped
per^Stoiamer Prince Arthur, and consijrned to Rlanchard & Kelly,
Haliiax, to be pold on our % and risk, 125 bbls. Extra Super-
fine Flour, at $4.25 ; 200 bbls. MeP? Beef, at $11; 15 bbls. Fancy
Flour at $4.70. Paid dravage in ca^h, !?11.25. Passed our notf,,
at.SOdayo to the Quebec' Insurance Co., for S2800, at \\%.—S.
Rec'd of S. A. Hunt, in payment of his note of March 27, amounting
to $14.21. due on the Sth inst. ; viz., 2 bbl.s. Herrings, at $6 ; and
cash for the balance.- 7. Paid cash for repairs of Store, $25.— On
the same dav Bought of J. S. O'Dowd & Co. on %, 200 bbls. Mess
Beef, at $1 Li2i.— On the same day, Shipped per Steamer Champlain,
Capt. Belleau. and consigned to R. J. Wilson, St. John, N. B., to be
sold un our % and risk, 50 bbls. Pearl Ashes, at S4.:!0; 200 bbls.
Mess Beef, at $ll.l2i. Paid oaali for drayage, etc., $7; aleotothe
Mobtrnal Insurance Co.,- for Ins. oa $2480, at Ij fo and Policy i&l.—
8. v.eo'd of B. Stephens, in full of ^, hia note At 30 days, for * 1 00 ;
and cash for the balance, $20.—©. Disoounud, at the Omon Bank,
Neil & Kr-i,he 8 note, favor of J. S. O'Brien, for $240. Diset. for .3d
days, ^1.40- c&sh received, $238.60.-10. Paid C. Phelan cash in
fulKf^.— 11. Rec'd ptii Qrand Trunk R. R. from Fisher & Lee,
Toronto, M-ise., previoaely ordered by us, viz., 3 J hhds. Cuba Mo-
la^^sea, HOOOgala. at 25cta. } 30 hhds. CubftSugar, 30750 lbs. at4ict».
Pi^id in cash for freight, drayage, etc., $96.— IS. Bought for cash oJ
a. fiyor.9 & Co., their JJill of ICxcliannre on Hamel & Norris, Toronto,
and remitted the same this day to Fisher & Lee, in payment of am t
due them, $2133.75. Paid h % premium for the bill.— 14. Bo t of
C. L. Murray, on our note at 4 mos., 2500 bu. Red Wheat, delivered
on board the Steamer Victoria, Capt. Barry, at $1.03 per bush., and
fhipped the same to N. C. Moreau, Pictou, to be sold lor our % and
ri«k. I8=;ued our note, at 15 davs. to the Quebec InHiraiice Oo., lor
Itif. on 92608.61 at IJ ^ and for Policy $1.-15. E Sleplens' note
(or $200 is dup and not paid.— lO. Renewed R Jones' nole for
fl 98.06, now due. Rec'd his new note a1 141 days, for .f 150. and
cash for the bal. and 144 days int. at 1%.—V7. Sold (o Carroll &
Samson. 20 bhds. Cuba Molasses, 2000 ,cals., at 27 cts.; 100 bbls.
Prime Beet; at $9 ; 100 bbls. Mess Beef, at $11.50 RecM cash in
part, $1295; their note at 60 days, for balance, including discount,
$1 .S08.74 The lisc't on the note is for 63 days.- IS. Accepted J. S.
O'Dowd & Co.'s draft on us, at .^0 days' eight, favor of E. L. Tessier,
for $1000.— 19. B. Nolan 1ms this day renewed his note, favor of
A. J. Hall, for $50, assumed by the Firm, by another note for the same
amt. and time, endorsed bv J. Kerwin, and paid cash for 43 day.s' int
on the nfw note, 36 cts.— 21. Bo't. of H. Collins, 120 bols. Middlings,
at $4.20 ; 60 iibls. Rye Flour, at $3.60. Gave in payment. 35 bbls.
Mess Pork, .at :>10 ; our check on the Union Bank, for!?250 ; bal. on
"/c — 2;J. Sliij)i)ed per Steamer Laval, to S. Larue & Co., Caspe, for
their %, and pursuant to their order, 150 bbls. Mess Beef, at $11.50.
Paid CH.'^h lor drayage, .$4.75.-34. Sold to ndry persons, for cash,
3 barrels Herrings, at $7.50 : 3 bbls. Mackerel, at $8.40; 10 bW*.
«4
- 7
$7 ; alsoto the
PBAOTIOAL aX8K0l8B8,— 8«T «.
oil the 14th i„st.,wa. wrecked 1^1^; a ;!.'''°A^%™^« »» Shipm't
20th in8t.,-Steamer and Ca/.o to^f In il^^L Lawrence o'the
ceptance of the 18th i, st at ?0 li ^'?T*«- '^''^coiintefj o.ir ao-
Bal. paid in ca8h.-28. Paid R q rl^fflf ?', """ '^^*^'^*^' '-^ «*-l7
-On the same day. .old ^. How!'. lo C F 'p P^'^^*^ "''«' '^^OO.
Red Flannel, at 80 cts., and 2' v^i!'r1o V" a.-^''"®*' °" %' -^^^ yds.
Stea.uer Victoria, which was Sreoft • W^ ^'"/i*" ^^^^^li inst^ per
'\^. 20tl» inst Amoul^S'luTed $2608%] '«?" .1^^- ^-^"enc'e'ia
which we received our note of l!«l • . -^^* I« ^ = $2(>0.86, for
ca.h l:.r balance.-orthe 'ame d.v '" " '?'' ''*^'' ^^'^-^'^ ? ^ "^
i- J. W.isun, St. John N. T of PeLHT^ ^" Account Sales'from
the 7th mat. Net proceeds #2976 If Iw? T' ^^f «^"t him on
by them, on Viger & Roy, ^t eight Vfo; ..frt n . f t-^^^' '"'"'•"^d
paid in cash $I500.-.3O Rec?l «n a ^ P'-'^^eeds) which has been
& Kelly, Halifax, of 2?0 bbfs Mess Bfet'Z? «^^«^<•'•om Blanchard
of 4th ,n.t. Net proceeds, $2;/80 86 -On ^1^^'"^' ? ''"^'^ '« ^''«"'
dry persons for cash, 15 ibs. Brown SuTar^iM'?'" '^^^' ^"''^ ^^ ''»»•
at 30 cts. ; 44 lbs. Butter at in^^fb'h T f-'n ^^'' Chocolate,
3 bbls. Beef Hams, at $18 • 2 bb??" l?v, ^* ^"^'.^° ^^'•"' ^t ^0 cts. j
-31. Paid cashVor Rent of S^rel'! ^1"^''^^ Jl""'"'^ ^' ^^^'^'
Laborers, $38. ^^ **^' ^^^i" Clerk hire $100; for
INVENTORY OP UNSOLD PROPERTY.
Merchandise,
Shipment to Halifax, balance of Mdse
Shares of the Montreal Bank Stock, '
The net losses, May 31, am't to
?,^ry*'^^^'^- Hall's third Is
AndR s Griffln-.two-thirda,
A. J. Hall's capital is ^
«. a. trnffin's capital is
fl477.22
4!>2.4l
i^«4.HI
432H.6I
8457.23
$275381
601 76
20800
$3563166
6ft
LI. '•
''M
SET III.
JOURNAL DAY BOOK,
INVOICE BOOK, SALES BOOK, COMMISSION
SALES BOOK, ACCOUNT SALES,
FORMS OF NOTES, DRAFTS, LETTERS, ETC.
PARTNERSHIP BUSINESS.
BsMABE. — The Se«e of books thue far phown in this work, have all
been condwcted upon the IlraUan method of hi»towcal Day Book, with
separate Journal. We did so ou account of its greater eimpliciiy, and
not to distract the mind from more important considerat-ions which it
was neoesffiiry to inforce. The student being now more thoroughly
grounded m the science, we shall henceforth give a little attention to
the more practical forms in use, and to a greater variety of entries
than heretofore. We wish him particularly to note the peculiar form
of the Journal Day Book introduced in this Set, that he may be able
to express, in this manner, any conceivable transaction, combining
all the eaeential points of the separate Day Book and Journal. Where
mo»e severely practical forma — for the purposes of condensation — are
not in use, the Journal Day Book meets with great favor, ae being
both plain and practical.
In the transactions of this Set, we have introduced a new featuie ;
vi«., Mdse. Co. transactions. It will, of course, be understood that
by "Merchandise Companies" is meant the temporary copartnerships
existing between the consignor and consignee, having reference to the
sale of particuter conpignments of merchandise. The nature of this
epecies of eoRartnership differs from, that of a general copartnership
only in its duration, and the manner of conducting its sales. In Mdse.
Co. business, one of th« partner s — the consignee — is the commission
BQ^vchaat, and, in that capacity, receives and disposes of the property
66
I!
^OXmHAL DAT-BOOK,— TOT
HI.
•8 he would (rf a wmple conatonmpnr . A. ^i ^ur,
he IS mterested in the ssAns^tl ^ ^^ drfftwnce being tJiat
^ »e^ and which are^^ly mt 2^" -^ ^ '^""^ '^''^'^' ^'"^ '^
$Pfn»ng and closing eni-Z? In I« i' ^'^"* f "'^ ^ '•^g^^^s the
Mrse. 5o. a,^^,^ t fr^^. In th^ n^ethod-exen^^ified by
Lorhe & Bro. an inveice to be «o f "on • " / J^''" ^' '"^^^'^e from C.
A " With the invoice and exSn«io • '"^ ,^' ^^ ^l^bit " Mdse. Co.
cost of the invoice, til nEom?! ''■'^" '^^^ Consignors with th^
^ though it were kli our ofn °T e IT-'^'^^"''^'^ ^^^ ^^^^ Property
the 6a„,e principle, will beTo de J L Si?"'' !^*''^' **' recognizing
ohandise. In the second rnefhod tl^p%£ ' 'f ^"^''*' °'^''^* o^'l^e mer-
^'r of the property is reZ„mbIe ^tT^^' ^f ^Snized is that the
C.Lortie& Bro., mdse to beS . • -^"^ when, we receive from
A ' witb o«r ot^Xre only a^d^J';! ^^' ^^ ^^^'^ "^dse. Ca
««•'« entry, in this case, tf m2de ^o of'^ '^'' consignor. The .consign-
debt us for our share, and u |,j-L*;n?rp'^ ^''^* T'^ ^°»'J be°to
•hare. ' " oiiipment in Co. to Quebec " for liis
»re!cep?bytre/?rsShortl^^ P^'-'*' interested, if the accounts
^euSs/co. aSnT;- M'tettir'e'c'sf"^' ^'°"^*^' ^ before debS?
credit the consignor with their f?uIlT-~'V'''''^ ^'^'^ expenses-and
«ha.e, aad any ^other ^frty ^ ^1 \ e/S"? ^"^ <3onsi|nor's) joint
consignor would, in auch a case dSf Jl '?'' *^^'' «^««'- The
Bhare, and each W the othorTaV^Jt,' .?-''"''^"l' ^^'^^ their joint
other parties would, if makLTnentrv?/'' "' ^^f «^*^'«- ^he
ejgnee and credit the consignor t^oH^v^ correspond, debit the con-
Where there are more tC ^ ^""^ ^'^ ^'^^ "^'^re.
are kept by the «eco^rf7ne hod 7he^'n''-'"'"''l^'^' «»d the accounts
Co.>ccount/orAwot;nS.td aK^^^^^ '^'^'^' "^dse.
consignor for his (the consignee's Zrpf ru '^'^'-g^^' and credit the
liand, should debit each of the n«r f f ' u^^ consignor, on the other
; Ship't in Co." for hfs own share F«^^^^^^ «^«r««' and
debt "Shipment in Co.," and c'dit f^^^^ ^^^^^ parties shouJd
•hare. ' ""'^ ^^^^^*- the consignor euoh for his own
JOURNAL DAY BOOK,-SET HI
Quebec, Mat 3rd, 1871.
offgrLSSd'stfni- ^?^-,^-«' P--ticles
B^tsranTlrlfc?^^^
5r
ma
1 t
I
\\>
I I
u
. I
%p
JOURNAL DAY BOOK,-SET HI.
Quebec, May 3rd, 1871.
SuNDums
Dr. To C. S. Mitchell (1)
For Effects invested :
Cash Deposited. $9000
Bills Receivable Notes in his favor ; via., one
""*' drawn by P. Racine, duo
May 28, • . 1^00
Another drawn by S. Lewis,
due June 6, WOO
Balance of ?i^. _^
$12000
P. Allard
oe
a
SrNURlES
Dr.
Cash
Bills Receivable
MeIIC'HANDISE
A. RlNKUET
For effects invested •.
Deposited.
To R. A. HuDON.
$8000
Ship't to Montreai
To Merchandise
'« Cash
Nolo in his favor, drawn by
D. Aylwin, due Juno 1 1000
As per Inventory, Inv. B. 2700
Balance of %. _^
_ 4
Dr. To Sundries.
12000
12000
00
00
Shipped per Steamboat Quebec,
and consigned to G. S. Walls,
Montioal, to be sold for our %.
Inv. of produce, as per S. B. $573
Paid Freight and Drayago 2
12000
575
06
00
S. White & Co.'s Consignment
Dr.
To Gash
Paid Freight and Drayage of nn
Invoice of Flour, as per I. B.,
amt'g to §1018.25, rec'd from S.
• White&Co,tobosoldoDthefr%.
575
0(1
00
n\ TW« l« .uuTMMod 10 b« two ooUbu- lor doIUn aU o«»-rided llnoa £w
II.
1)
ooo
500
000
600
6120C0
06
ON.
iOOO
1000
2700
300
12000
12000
00
00
TGS.
ebeo,
k'alls,
$573
2
12000
575
08
00
of nn
I. B.,
omS.
675
0(1
10
00
fit»— reded lines for
Pi«t of roouj, ^
JOURNAL DAY BOOK,-SET HI
QuBB-Ec, May 7, 1871.
Dr
8
To SUNDRIEH. 156l{l0
Mkrchandme
Kao'd perSteamb. Champlain.from
i>. C. Peachy & Son, Montreal,
and consn^ned to u.. for our aoot.
an Idv. of Wines, as per I. B
jTo D. C. Pkachv & Son For amount of
" Cash
$1549.60
Paid for Freight & Dray. u.5i)
. 8
National Bank
To Cash '
Dr.
156110
Deposited.
«
Spndriks X)r.
Cash
Dmooittt
To Bills Iieceivable. I
Discounted D. Aylwin's note, far.
K. A. Hudon, due June 1st.
10000
looobo
Proceeds of note
Amount of 24 ds., at «^
. 10
$•90
4
L. DOUOLAS ic Co.
[To Mdsb.
'< Cash
" Commission
100000
^r. To Sundries, | 1272
Forwarded per Grand Trunk R R
pursuant to their order, an"ln-
voioeofAJdse., as follows!
Sundry produce, per 8. B. $1240.00
Paid Freight and Ins. 30.20
For Expedition ud Ins. 2.48
■ li -
1272 68
Bills R,gnEfyjiBi,B
To S. White A Co. 'a C
Dr.
iONSIONMENT.
62400
Im
JOURNAL DAy BOOK,— SET HI.
QuKEKO, Mat 12, 1871.
Cami
Dr,
To S. White * Co.'b Consionmbnt. [
For RaU) of Flour, as per C. S. B.
S. Whitk a Co.'s Con. Dr. To Sundries.
Cloaed S. White it Co.'s Consign-
ment, an' I rendered them an
Account Salea.
To Storaqb & Adver. Our charges $ 18.50
30.20
1149.30
" Commission 2}% on $1208
*• S. WniTE & Co. Their net p»ooeed«
14
Merchandisk Dr. To Sundries.
Bo't of L. MoCord, produce, as per
r. B.. amt. $2581 90, and paid
OS follows :
To P. Am,ARD Oar order on him, for $300.00
" National Bank Our check, for 750.00
" Bills Receivable S. Doran's note of the Hih
Inst., for t)24.00
" " Payable Gave our note, at 30 d's, lor 500.00
" Discount Allowed on the bal 12.30
« Cash For balance* 895.60
" 15 .
C. S. Mitchell, Private Dr
To Cash. Drew oo private ^ .
16
Dr.
Mdse. Co. a.
To SuNoriES.
Rec'd from C. Lortio & Bro , Hali-
hn Riild OP our joint acct.
to
and risk, each i, .Mdse. as }«r
I. B., amount $3550.
To C. LorTIB & Bro. Their invoke as above
Cash
Paid freight
60
$35J0
40
584
09
1198
00
1198
2581
00
90
2681
30
.S590
90
50
00
3590
r
JOURNAL DAY BOOK. -SET III
Qdkibc, May 17, 1871.
8- W»TB ,k Co.
To Shipiukt to Montbkal.
Received an Account t<aio8 of tha
Uase. sent him on the -I thinat
18
Dr.
To Bills Patable.
650
40
1149
30
19
SlTKDRIM
Dr.
To Sqnories.
10 bo gold on joint aoot.,eaoh i,
At:n%^are-«-'-^*^2«;'^^
^"•ati^, on$1290 i.-Jjl
M. BlancHET & Co. For their 4 -h. • . "^^289:20
«or tneir ^ above inroloe $644.60
SWPWaNT IN Co.
T« Merchandisb
" Cash
1289
1289 30
MbSE Co. B.
To SUITDRIBS.
ToO.Qo«K&Co. Forooritoroioe
" ^^" Paid Freight
61
wires, If,. Gary i Son, and our-
selves, each *. an Invoice of
■3sP
•WPIHW"
t*
• ■ I
11
m
JOURNAL DAY BOOK,— SET III
QuEBKO, May 22. 1871.
■•5
Ship't to Thiibe RivEits Dr. To Si'Noku;3.
Shipped per Brig St. Maurice, and
oonsigneil to J. N. Oarbray/l'hree
Rivord, to be sold on our aooi.
and risk, Md:<e. ns por S. li.
To MHRCHANiiiaB
SuNOHIiCS
Biu.s EbCKiTABiii!:
Casb
Invoieo of proJuoe $30(5. 09
PiK 1 expenses 4.50
23 .
Dr. To Md9e. Co. A.
Sold 0. Martol, MJpe. Co. A., as
per C. S. B., auMunting to
$4140.
His note at 15 days, for $2000
For Balance 2140
i(
Mdsb. Co. a.
Dr.
To SUKDRIKS.
Closed sales in company with 0.
Lortie & Bro., and rendered
them da Account. Bale-,
To Storage & Auver. Our charges
" OoMMlSfilON 21% on $41110
*' C. I.QRTiE & Bro. Their i net gain
" L«S3 AND Gain Our «• •<
_^__ 25
$ 12.00
103.50
217.26
217.25
M. Blanchkt & Co.
Dr.
To Shipment in Co.
Roc'd an Account Sales uf Mdso.
shipped them on the 19th inst.
Our not proceeds as above.
310
60
310
4140
ftO
00
4140
00
550
660
00
610
60
tia
._„.
1
v,s.
310
60
md
ree
JOt.
.oe
.60
310
50
A.
4140
00
, as
to
000
140
4140
00
ES.
650
)red
2.00
^50
r.2£
-.25
660
00
Co.
610
60
dso.
□St.
JOURNAL DAY BOOK,-SET III
QtnjDKo, May 26, 1871.
To Shipment to Thi-.ke Riveuh
flecd of J N. o.irbray, Throe
iJ"!*:"' ? iiheck fit .-k'ht on tho
proceeds of the Aldse. Mpxml
St. AIa-.ri,^e. Tho shii hayi,,*
ft'nk.ll,oMd.o.,whiol!w<.J„o''t
insured, was saved, but much
cJamagod, and ,o,d at auccion
28
D. C. PfiAUHY & Son
Dr.
To Mdsb. Co. B.
(I
Cash
Dr.
To Biixfi RecEiVABLK.
«
Mdsk Co. B.
Dr.
Closed Mdse. Co. B., and readered
Account Sales 01' the same to G.
Qu«nn & Co., Montreal.
To St.m^aoe&Adver. Our charges
" COMMKSSION 2f. on $1273.50
" «-QnmN&Co. Their net proeesd.
" E. Cabt a Son - .. ..
Loss
andGain Ow J not gain
$ 3.65
, 25.47
402.46
405.46
18.70
115 00
1273.50
Ifiojlb'
To Sundries. 868 64
868
<«
64
li
't
'^^^immme^mm^
•^^^i 'lK;:^"^^-r,"tMj-^' '■^-*
V ta
■
1 s
If J I.
lilJM'iJ: I
m^
if i!
r^;
iiil
8 JOURNAL DAY BOOK, -SET HI.
Quebec, May 29, 1871.
Interest
Dr.
To Cash.
Renewed S. White &, Co.'s draft,
for $1 149.30, whicli we accepted
on the 18lh inst,, by our note
for same amount, to the 1st of
July. We paid cash for int. on
our note $0.32.
30
Bills Receitablg
Dr.
To L. Dotoi-As & Co.
Rec'd of L. Douglas & Co., their
Bill of Exchange on A. Simms
& Devauz, London, at 60 days'
sight, for$1272.68, in full of aoct.
((
sukdries
Gash
Disco DMT
Dr.
To Biu.s Receivable.
Sold L. Douglas A Co.'s Bill of
Exch., our favor, for $1259.96
Lostl'^ 12.73
Sundries
Bit. 1.8 RECErVABT.E
DiacODNT
D. C. Peacht & Son
.31
Dr.
To Cash.
Purchase of N. Caron's draft, on
MoUon, at 8 days' eight, $260.00
Paid 2.25
«
Dr.
To Bills Receivable.
For N . Caron's draft, our favor, sent
them in payment aoct.
Expense
Dr.
To Cash.
For sundry expenses.
64
^2
1272
«8
1272
1272
262
262
260
68
68
26
26
00
4S
30
TRTAL BALANCE.
C. S. Mitchell
R- A. Hudon
Cash
Bills Receivable
Bills Payable
Merchandise
P. Allard
A. Rinfret
Shipnient to Montreal
8. White & Co.'8 Consi^rn't
htorage and Advertisin "
D. C. Peachy & Son °
National Bank
Discount and Interest
U Douglas <fc Co.
Commission
S. White & Co.
C. S. Mitchell's private %
Mdse. Co. A. ^
C. Lortie & Bro.
G. S. Walla
M. Blanchet & Co.
Shipment in Co.
Mdse. Co. B.
G. Quinn & Co.
Shipment to Tiiree Hivore
Loss and Gain
K. Gary & Son
Expense
f 1 1
INVENTORY.
The Mdse, remaining unsold, May 31, 1871,
araounts to $3530.26,
u
r:
li'i!
t^wiw-agy.ij?^^ I
BBS
1
<D
•iH
ffl
u
PQ
CO
ffl
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n3
CO
d
BQ
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s
at
pq
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CO — e« e<i -^ o
CO
en CO t- CN m >n
lO
-* -H !r) o5 o ' t-
'~0 t- t~ -rf CM
a>
— TC 't
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en
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«
tC5 tfS
bfl c^i t—
.S »s cfl e<i
"S 2 .< - - <^ »o
5;2 '^'«^
B Oi "^
O^- «. -. S3
^ ^ -Q,- -
OB «i 5
B-- « S
Cfl . «« S
'^'52 2 c: a.
^t i."
S ^ H
KM
'^ r . a. ^.
•Q 2 c "-' <"0
oT t^cq ^ |J -J,
>. £ OJ = "^ c- tJ
il^OjCOj/joJ
fQQdotaooa
1
00 m
1 '^
-"tOIMOOOTj-Cvl
1 ^
Oi C5 i-O
— ■ CD fo >n lO kO
t-ooc>»ecc^?fiie^
(M fC IX OS 1— 1
•— (
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2= -^^^^ £-3-
— -SO TT
§ - § .= . --S .2 2
at 0) 0) a>
CO « «
C C ^ C B
c^ ■; . ^ •* c8 <fl «*
OS c3 03 0] c8
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6
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Jleceivab]
landise,
lard,
nfret,
nal Bank
Walls,
ancbet k
J? X "p .r! S -2 r/ Oa
2 ^ oJ . . c« . .
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Adve
^ ~ r
andise
ent to
e and
crj
iOO
rch
pm
rag
c • •
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©"^■a
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f— 4 <m4
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^•5::
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rest,
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bj— -
B 4, £
§11
Poo 00
1
66
M.H.
M.E.
INVOICE BOOK,— SET HI.
Quebec, May 3, 1871.
lNVEvroR7 of Merchandise advanced bv R. A.
Hudon, as Capital:— ^
740 lb8. I.ard, fS>$.\0
Jy«'» " Ham,
60 bbl8. Apples,
66 " Extra Superior Flour
4b " Fancy Flour,
60 bags, 7000 lbs. Coffee,
8 ca.sks Bordeaux Wine.
120 hollies Champagne Wine,
22 gala, Cyprus Wioe,
.13
3.72
5.50
4.50
.15
" 50.00
" .80
" 5.00
(I
$ 74.00
247.00
186.00
330.00
207.00
1050.00
400.00
96.00
110.00
Quebec, May 1, 1871.
Signpd R, A. Hddon,
Invoice of Flour sent per Grand Trunk R. R
and consigned to Mitchell & Hudon, Quebec, to be
sold on our % and risk:
80 bblt?. Superfine Flour, fS) $5.00
70 " Oatmeal, ^ 6.10
45 « Rye Flour, " 4.25
$ 400.00
427.00
191.25
Ottawa, May 4, 1871.
$101S.25
S. White & Co.
Into CE of Merchandise shipped per Steamboat
Champlam Capt. Ricard, consigned to Mitchell
fu i°"' S^^^^°> pursuant to their order and for
tnejr %, viz. : —
50 bble., 1600 gals. Coal Oil, ® $ .60 $900.00
20 660 •* Linseed Oil, " 1.00 660.00
15 Herr.ncrs u 535 7375
Herrings,
— Charges..
Insurance (8) ^%oa $1650, $7 ?<;
Montreal, May 6, 1871.
$1538.75
10.8,5
D. C. Pkachy & Son.
"^7
$2700 00
If
1549
fiO
i X! W
U itf
> '!
; i!
}
I
o .
M.H.
M.H.
BODS
INVOICE BOOK, -SET HI.
Quebec. Mat 14, 1871.
Quebec, May 14. 1871.
Messrs. Mitchell & Hcdok,
Bo't ofL. McCoRD.
1600 bush. Red Wheat, td f.90
1200 " Oats, " Mi
360 «• Peas, " .80
42 tubi, 1846 lbs. Butter, " .15
$1350.00
675.C0
280.00
276.00
Received lajiuent,
16
L. MoCoRD.
Shipped per Brig Victoria, consigned to Messrs.
Mitcbell & Hudon, Quebec, to be sold oo joint %,
each i, VIZ. : —
250 boxes, 5000 iba. Soap, /© $ .07 $ 350
160 " 4000 " Chocolate, " .20 800
30S " Sperm Candles, " 8.00 2400
Halifax, Msy 7, 1871.
$3560
C. LORTIE & BrO.
21
Shipped per BngVaudreuil, consigned to Messrs.
Mitchell & Hudon, Que-jec, to be sold on joint %
of E. Gary & Son, Rnd themselves, each ^, viz.: —
36 bbis,, 1441 lbs. Plums, ^ $ .08 $ 115.28
90 '♦ Green Apples, '' 3.60 324.00
176 " Gray •' " 4.12 721.00
Montreal, M>iy 14, 1871.
$1160.28
Q. QuiNN k Co.
M
B
12581
9v
L.
MJ
mmmm,,.
*■■■ •"- VS._1,
12081
9v
M.
SALES BOOK,— SET in,
Quebec. iMay 4 1871.
QuZ''Sa''n7r K'n"'"'^' ''■''PP^'^ P^'- Steamboat
MontSl^rf U u"'' "°^»'"»«'' to G. S. Walls,
aionireai, to be sold on our %, viz. :
3 bbls., 620 lus., Lard, /5)$.10
'='' Apples, <« 3 5Q
20 bags, 2800 ibs., Coffee, •' .'is
—Charges.
$ 62.00
91.00
420.00
$573.00
M.4H.I Drayage,
Mitchell & Hudon
Quebec, May 4, 1871.
— ■ iO
2.00
676
L. D.
A Co.
M.4H,
Invoice of M.rchand.se sent per Grand Trunk
Li2 ,v, • ^^''^'g"^'! '0 L. Douglas & Co., pi,r ^^
S t^lheir order of the 4th inst" and for thS7%,
6? '^' Extra's"' """"n '^ * -16 $ 262.40
22 bags 3088 JIv'^'pT ^''"'" '' ^'"^ '^-^^O-OO
oags, dU8S Ib:^., Cotiee, '« .20 _G17.60
-Charges. .^
Paid foi Drayage, $ ,^^
Insurance, roi 2% pre-
niiuni on §1245, "^ 24 90
Our Coi«in,8. for Ins. an J Exped._2A8 ,S2.68
$1240.00
Quebws, May 10, 1871.
MiTCHKI.L & HCDON.
$1
61
II
i
"
1^ ';
I
i: -
SALES BOOK,— SET HI.
QiiRBicc, May 19, 1871.
Invoice of Merchandise shipped per Steamer
dirtier, Capt. Roy, and coni?igiied to M. Blanchct
& Co., Pictou, to lie sold on joint %, each i.
Z9
e.AG.
40 bbls., 1200 gals. Coal Oil, fa) $ .60 $720.00
20 " 560 " Linseed Oi>" 1.00 660.00
$1280
9
00
Chnrgps.
Paid for Dray age, $2.76
" »• Ineurance /a ^ijif on $1290 6.45
20
$1289
•20
s
MiTCHfcLL & HdDON.
Quebeo, May 19, 1871.
B. B.
biTOicK of Merchandise per Brig St. Maurice, consigned to J. N.
Carbray, Three Rivers, to be sold on our % and risk.
J.N.C.
40 sacks, 160 bu. Red Wheat, rd) $.90 $144.00
90 " 360 " Oats, ' '' .45 162.00
$ 306
00
Charges.
Paid for Drayage, etc.,
Mitchell & Hcdon.
4
50
$ 310
5t
Quebec, May 22, 1871.
1
B. E.
FW*"*-
1%
mier
cbot
0.00
0.00
$1280
00
2.75
6.45
9
20
•
$1289
20
nslsneiJ to J. N.
and risk.
I
o
o
pq
CO
o
M
GQ
o
a
<0
o
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M
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o o
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5.0
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^
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(C
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Or! <M
-H
cS
2 ^^ r i ^
-
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4^ U
« .a <^
03 a
ABLE
000 1
4000
atf
perm
.45
..o«
5 to oTcZ) '3^
- 0)
3 ■* wT "^ ^^^
ec'd his
, for tb
ri-g^S^g"^
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o
03 <^ — M
t-
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e^
*•
— t^
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005;!
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^
O O O lO c^ C-l
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>0 Tf — O — -— 1
•*
lO — . CJ Cv|
1— »
cc
t
€^
^
m C.
sold
each
2 to
rges.
gain.
CO w
C4 "0
^ K ^ £ O ^ 2i n
»ndered May
'a net procee
ay 29, 1871.
-< H o . o
Account Sales n
C. Lortie & Bro.
767.25. Due M
E. E.
O ,. ^ > « V.
m
«o <. en ^ ^ ^
— " N ^ - -
I S* 3 3 3 3 3
72
'^-^'"•^Aj&kiiUWi^MH
cc
03
C4
Ol
^
l>H
o
<i
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UU
a<
-^
-3
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C
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a
OS
Ki
O
Pi
01
a>
L3
03
r/1
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r!
•
^
^
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^
«o
^o?:
^
I:
*i-
;
I B ti <-j. 4> u
X JS « -"•
Q ffQ oj ,^
62'
2 >• £ £
o; O
a; i •— o8(/}
o o
o o
or
'o
>
aj3
m
= !:! ^-5
So
> 00
C — I
a
'3
oj <" ir
tc a
. "^j-r-go
'» 33 ,_, !r /','- —
>• », Q CM --
" ^^W OJ
a.
I 00
O
3 03 Ci 1^ >ii;rf3 ■«! re
!00
«j ;a
>* T*<
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00 o o
c^
-*< ^
^"^
09
•^
S
S-.
T*
«i
a,
b
,^
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-c
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c
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w
S"^
m
i^r/}
y.
r.-^
Is'
1~.
00
ca
'';^;
!'l
.**«^*a«itefe4fe.
Aooonnt Sales
C 80 bbls. Superfine Flour )
of <45 " Rye <• J
. ( 70 " Oatmeal )
I 80 bbls. Superfine Flour
Rye <' ^ for aooonnt of
Oatmeal
S. White & Co.
1871
May
it
11
12
Sold S. Derail, on liia note at 40 dayn,
80 hbls. Superfine Flour, fti) $6.00 $480.00
20 " Oatmeal, " 7.20 144.00
Sold C. Lcc, for ca-li,
60 bbls. Oiitmeal, ^ $7.00 $350.00
46 '« Hye Flour, " 5.20 2H4.00
Chiirges.
Paid Freiglit and Druyage, ii» cash,
Storage and Advertising,
CoiiimiHsiou, 2^% on $1208,
f I 0.00
18.50
30.20
S. White & Co.'h net proceeds, due June 4, 1871
E. E. MiTCHKi.i. & Hmdon.
Quebec, May 12, 1871. Per J. Madison.
624
684
1208
68
$1149
Of
9
00
70
30
Account Sales of Merchandise, on joint % of C. Lortie 4
Bro., and ourselves, each ^.
1871
May
23
16
23
(ii
I*
Sold 0. MarteV
250 boxes, 5000 lbs. Soap, /g) $ .08^ $425
160 " 4000 '' Chocolate, " .22 880
300 " Sperm Candles, " 9.45 2835
4140
372
00
Cash, S52140— Note at 15 days, $2000
u
II
II
Paid cash for Freight, $ 40.00
Storage and Advertising, 12.00
Commission, 2^ % on §4140, 103.50
Our \ net gain on Sales, 217.25
76
C. liOrtie & Bro.' 8 net proceeds,
INVOICE,
250 boxes, 5000 lbs. Soap, /d) $.07 ^350.00
160 " 4000 <' Chocolate, " ,20 800.00
300 " Sperm Candles, " 8.00 2400.00
4 net gain, 217.25
$3767
26
Net proceeds as above, $3767.25
E. E. Due by Equation, June Ist.
MfcCHEI.L & Hi'DON,
Quebec, May 23, 1871. Ftr J. Madison.
u
r aooonnt of
1
.00
.00
624
Of
.00
.00
584
e
1208
00
.00
.50
.'20
58
70
871
*1U9
30
'on.
C. Lortie 4;
425
880
835
.00
.00
.50
.25
4140
372
00
76
.00
.00
.00
.25
.25
•on.
$3767
26
ACOOUNT SALM.
Sale, of Merchandise on joint account of G. Qulmi ft Co..
E. Gary & Son, and ourselves, each |.
1871
May 28
u
«
21
28
<<
It
■ Charges.
Paid Freight and Drayage,
Storage and AdvertlHingT
Commission, 2 {jj on $1273.50,
E. Gary 4 Son'a net proceeds.'
^ur i uet gain,
$ 2f
.i.fK-.
25.4 .
405.46
18.70
G. Quinn & Co.'a net proceeds,
INVOICE,
36 bbla., 1441 lbs., ^$.08 $115.28
175 n r "" ^PP''*'' " •'^•^0 324.00
175 Gray w w 4.,2 ,21.00 1160.28
Your and our g invoice.
Your i net gain,
Net proceeds as above,
773.62
18.70
$792.22
E- E. Due by Equation, Dec. 5.
Quebec, May 28, 1871. M.tchekl & Hcdo..
60
$ 792
V'l
n
" m
n
o
S-5-:
<*J o
cjd
isi-
.S c J
3 «» »
a-S a
g-ffi-
■o-^
II
S ^"3
B I fe
" a o
I
Q 5-S^
«r5P
J<J
o ^
^
S3 O'
o ^
o «s ^
O T3
O C
J2 ej
-•-5
00 .S
V
.5-3
B 4*
•^ e
w
cc
M 1 S », t"
h
tQ
4
CO
eS>
®rJ ea
|5
nt
00
S=l '
78
II :
the
7b
r
•@
2
«e
X'^WS''
as
RECEIPTS, NOTES, DRAFTS, &o.
UECBI1»TS.
(Prom traiMuotion of Jm. 31, p. 8.)
Quebec, .Tiinnary 31, 1871.
:^::i°'l'±± """' ''l"'V Dollar., in full f„r o„e ,„o„th'.
rent of Store, up to date.
E. R. T HI' DEL,
$250. ^
(Frwn trangaotlon of Feb. 18, p. 9.)
Quebec, Fel-uary H, 1871.
thisdav <h5r''t'^''^^y\'^"^ ^*"' I'i-H'iotea m.^yday., dated
mis day, for J wo hundred & fifty Dollars.
v." Pn*r .AW.
NOTES.
$1500. ^%
(Prom traneaotion of May 3, p. 58.)
Quebec, April 25, 1871.
^, I n^y^^^y, *^^^^ ^^^^ ''^*®' ^ promise to nay to A J Hall
order, l-iileen hundred Dollarn: vil„« ....;., J^ ■■ '"^"'
P. Racinb.
or order. Md^pn I.^.^jred Dollars'; value received
Due AJay 28, 1S71.
£62 10
(From transnotion of Feb. 18, p. 9.)
Quebec, February IS, 1871.
C Phelan ^Ifl f^^ ^™c- '^^''' ^ P'^"''^'" ^'» P^^ ^^ the order ol
Due April 22, ly 71. . , „
A. J. Hall.
11149. ,!y)^
DRAFTS.
(FrMD transaction of May IS, p, 61.)
Ottawa, May 15, 1871.
Fl^v.n 1 f * w^!i* *^^^^ ^'"^^ P^-^ ^ tl'e order of J. Raymond
7b if,7cAe« ^ ^udon. Quebec. ^' ^^"''' * ^"•
77
t ';
LETTER B 'OK, — SET in.
No«.— Pot the acoeptntion, Mlfichell A: Huelon have writtoo aorogs the
Wlowiog words : " Aooepted May 18, 1671," under which they havo signed.
(From traneaotlon of May 20, p. 83.)
*115. Three Rivers, May 26, 1871.
At sight, without grace, pay to the onier of Mitchell A
Budon, One hundred and fifteen Dollars, value received, and charge
to account of
To F. T. Parron, Cashier,
National Bank, Quebec,
J. N. Oarbrat.
1;
i. I
!
n
m
i
lf|:
i
f
BILL OP EXCHANGE.
£36 5 6
Quebec June 2, 1871,
Fifteen days after sight of bhifi our first of exchange
(second and third of same tenor and date, unpaid), pay to the order
of Mr. D. Saucier, Thirty-six pounds Five shillings Six pence, value
received, and charge to account of
Your obedient servant,
Ih Simms ^ Devatuv, Bankers, C. S. Mitchell.
Wellington street,
London.
LETTER BOOK,— SET IIL
Remarks. — This book is used for taking copies of all business let-
ters of importance, written to or received from others. Hut letters
received are usually filed away.
We give herewith letters in connection with he transactions of Set
III. But we do not submit them as absolute models in their way.
It would be as difficult to afford a model o'' a bu^ness letter, that is,
one which it would be proper for evi-xy one to copy, as it would for an
artist to produce a cast of features that everybody would consider
perfect.
To be able to write a good bueinesB letter is no small accomplish-
ment, nor can it be acquired uv studyina: models, altliough much aid
may be aetured in tliis way, pertaining to form, arrangement, and
even style, if undertaken with no undue surrender of individuality;
for a good business letter sJk..; ill l>e neither more nor less than the
transcript of a man's thoughts, or what he vvoulil say were he to speak
with care and deliberation. As no ( o men ever think or talk exacU*-
«like, so vo two men oorild be expected to vnrrte alike.
78
LETTER BOOK, — SET III,
ttoa Rorogs tko
idvo signed.
May 2fl, p. 63.)
V 26, 1871.
■ji' Mitchell A
1, and charge
Urbrat.
lie 2, 1871.
of exchange
r to the order
pence, value
"vant,
1T0HB1.L.
I bweiness let-
Hut letters
actions c^Set
n their way.
letter, that ia,
i would for an
)uld consider
1 aocontplish-
igh niuch Hid
igenient, and
Individ uwity;
less than the
'e he to speak
r talk exacU**
There are, in bueinese letters, certain qualifications which are
equally essential to all, and with reference to which, general instruc-
tions may he given. We will enumerate a few of these points:— let
Like all other documents in manuscript, a business letter should be,
chiroirraphically, well written, so as to commend itself at once to the
reader. Ne^itness and legibility are the chief requisites in a hand-
writing. 2nd The grammatical construction should be faultless; and,
above all, nodocument should be disfigured with misspelled words.
3rd The subject matter should be immediately apparent, stated with-
out circumlocution, and in terms not to be misconstrued. A business
document should be written in brief terms, and yet explicitly.
There is no qualification which will more surely commend yowig
men to the favor of an employer than proficiency in Business Corres-
pondence.
(Circular.)
QvvAu c, May 1, 1871.
G. S. Walh, Esq.,
Montreal.
Sir:—
We, the subscribers, respectfully announce to you that we
have formed a copartnership under the firm of Mitchem. & Hitdon,
for the prosecution of a wholesale Grocery, Wine Business, and
General Commission. We take the liberty of assuring you that all
business intrusted to our care, shall receive from us, personally, prompt
and faithful attention ; in a word, that we will correspond to the coa-
fidenoe placed in us.
Very respectfully,
Your obedient servants,
Mitchell & Hcdomt.
Messrs. Mitchell 6f Hudon,
(Quebec.
MoNTRKAL, May 2, 1871.
Gbntlemen :— In reply to your circular of tlie 1st inst., I beg
leave to solicit the favor of your patronage fur a general commission
business, and pledge myself for the strict <<bservance of vour commands,
and fHitlit'nl porlonnanoe of my duty.
Hesptfctfully yours,
G. S. Walls.
79
LETTER BOOK, — SET UL
G. a. IVaUs. Esq., Qdebko, May 4, 1871.
Montreal.
Siu:— Enclosed we remit to you Bill of Lading and Invoice of
Merchandipe, amounting to S575, which we consign to y^n per
Steamboat Qaehec, to be sold for our %■ You will do H8 the tavoi
to uee all possible despatch in making sales and rendering account.
Yours,
MiTOHBI.l. & HCDOV.
1..
Me»«r8. S.
White Sf Co.,
Ottawa.
QoEBBC. May 6, 1871.
Gentlemen : — We have the honor of informing you of the
arrival, in good order, of your Consignment of Flour, pursuant to our
order, and of which, your favor of,4th inst, gave us a>lvice.
We find it conformable to the Invoice, amounting to $1018.25,
which we hvve placed to the credit of your %.
We beg leave to assure you that we will pay all possible
attention to your orders. Offering you our sincerest thanks, we
remain,
Your obedient servants,
* Mitchell k Huoom.
Messrs. D. C. Peachy dj- Son, Qumeo, May 7, 1871.
Montreal.
Gents : — We are in receipt of the goods you consigned to ue,
pursuant to our order of 3rd inst., and of wliich you gave advice by
your favor of oth inst. Save a few barrels of Herrings whose quality
appears to us inferior, the rest is satisfactory.
Your account is credited for the amount of Invoice, $1649.60.
Very respectfully yours,
Mitchell & E0OON.
Messrs. L. Douglas <fr Co.,
Toronto.
QuBBEC, May 10, 1871.
Gents : — Enclosed, please find Invoice of Merchandise amoun^
\ng to $1272.68, which we forward to you per Grand Trunk K. B.,
pursuant to your order of 4th inst.
Be so kind as to credit us for the saiuc.
Truly youriH,
MlTCHlClI. Jc HWKW.
80
LETIWR B0OK, — SBT HI.
May 4, 1871.
and Invoice of
gn to y^n per
do \iH the tavot
?ring account.
& HUDOV.
May 6, 1871.
ing vou of the
pursuant to our
ilvice.
ng to $1018.25,
)a7 all possible
est thanks, we
tntH,
& HUDON.
May 7, 1871.
sonsigned to us,
gave advice by
;8 whose quality
ice, $1549.60.
mrf!,
& HuDON.
y 10, 1871.
handise atnouD^
d Trunk R. R.,
urct,
QTBBBf, May 12, I9tl.
''Messrs. S. mite <f C-a.,
^e forLX-";;T;or42?n;t.'"t,f ' f^^^""* .^"'f ^ Mer«han
^•■J^ll4:t.:^0. "^ "1 4W1 int.t. Mie net proceeds, d«e on Ju«e 4,
• Re,H{)ectfully yours,
MlTCHEL), & HcDOf.
Halifax, May 7, 1371.
i»s o« ti?e1ri i^t'' Te^lt™'?' T''^ "*' ^^^^^'"^"^ "^"^'^^ between
Very respectAiDy,
C. LoRTiE Si Bro.
MoKTRKAL, May 15, 1871.
Mgasrs. MitchdL ^ Hudon,
Quebec.
ijv^iee a,.';r.„r:,.r>'e:,i;'s'; wis r^Lre-t it'^f
Your obedient servant,
G. S. Walls.
QuEBjcc, May 19, 1871.
Messrs. M. Blanchei ^ Co.,
Pictou.
l.H.e debited ^ .oK'rhe'rtl"; UUif" "" """' *• ^'
y«ur outtulile 8ervant«,
MiTCHELL &, Hrdon.
1 [
bCYSDR BOOK, — 8BV IH.
Mtsart. Aikcheit d^ Hudon.
' Quebec.
Montreal, Ms^ 14, 1871,
Gents : — We acaept witli pleasure your proposition t© j«iii in
a Company Speowlatio«. We, accordingly, ship you, per Schooner
Vautireuil, wliich is to saU to morrow, Mercliandise, as per enclofeed
Invoice, to be sola in joint account with yourselves, B. Oary Jc Son,
and ou/seives, eaeh one tliird.
We kave debirca you ft: 4 of Invoice.
Witching you c«Mi|»lete success in the salea of them, we beg t«
subscribe ourselves,
Very truly yours,
G. Qdinn & Co.
J. N. Corbray. I'jSq.y
Three Rivera.
Quebec, May 22. 1871.
Sir : — Youss of the 16th inst. is at hand. Your proposiUoae
are gratefully accepteii. In accordance ilierewith, we phip you per
Schooner St. Maurice, 40 bag? lied Wheat, and 90 itags Oats, as per
eneloHcd Invoice, amoniifelflg to $810.50, which we consign to you
to be Bold on our % and rif<k.
Hoping yoH wiM study our beat interests, we remain, sir,
Your?* respectfully,
Mitchell & Hudon.
.> S;
Meisrs. C. Lortie Sr Bro.,
Hclifax.
QoEBEr, May 23, 1871.
Genti.bmkn: — We send you enclosed. Account Sales of the
Merchandise forwarded on 7th inst. We have been quite successful
in the sales of tliww, and we are of opinion, from actual appearances,
that the good jwarket s^Jiall continue for sometime. If you think
advisable to risk a new conf^ignment, we shall be happy to join you
in it, or to sell for you on Conmiission.
Very reepectftillf,
Mitchell k HuDoir.
Pi«*oi!, May 23, 1871.
Ms»srs. MUdiell S( Hudon,
Quebec.
Gkvts: — E-nclosed, please find Account Sales of the Mer-
tshandine y«u shipped us on the 19th inst. Your aei proweds i«
92
»y U, 1871,
)SJtion t» j«in in
ju, per Schooner
as per enclofeed
E. Cary it Sod,
them, we beg U
X3,
DINK & Co.
May 22. 1871.
'oiur proposiUoM
we phip you per
nags Oats, as per
9 consign to you
remain, sir,
fully,
L & HUDON.
May 23, 1871.
)unt Sales of the
II quite succesHful
tnal appearances,
e. If you think
appy to join you
IV,
L & HcDoir.
May 23, 1871.
ilea of the Mer-
r Bfli proseeds is
r-KT-fFB boor:.— SBT in.
ToaIu \VV."^*': '•'""' ^^'''"*'''" '^' ^he sale of the like goods.
Please iivil u'JR^r •'"'" ^'?f",^'" ^'" ^^^ reasonable amount.
F lease au vi.se u,- thereupon, and believe us,
TjTjly yours,
M. Blanchet & Co.
*HREE Rivers, May 24, 1871.
i^ssps. Mitchell ^ Hudon,
Quebec.
but vonr p"' '"■'" ^'''''' *^" ^'"^ -''^ '•-'«^- ^'he car.o war avo "
proceX ' *"^^^»^<='^' 0" National Bank for |I15; ae n.
Yours respectfully
J. N. Cakbray.
QrEBKc, May 26, 1871.
•. A'. Carhray, Esq.,
TfiTHj Rivers.
b^gof J;.?c;r„/roe?r£LT ""'"■""•« *'' '"'' -^
Bel,e« us «er disposed to hoDor you .ill, our c.nfl,lence,
Truly yours,
Mitchell «fc Hrnox.
Quebec, May 28, 1871.
Messrs. G. Quinn (f- Co.,
Montreal.
.oieeo^s^^n::it'°'^^^*°^^''' ^^^^""^ ^^'- «^^-- ^n-
Hop
ing you will fipd iJ.e reH4,!t satisfeetc
eciuibe ourfielves, Gentlemen
we b
•eg to sub
Very fcr uly youBs,
I
I
sit
88
iMMiiMUHil
.M^^^...
Pi lCTIOAL EXERCIH18, — SET III.
Messrs. L. DougUts ^ Co., Qckbkc, May 30, 1871.
Toronto.
Gknt3 : — We are in receipt of v'uir favor of the 27th insi.,
oontainihg a draft at sixty days oi» A. Siiii.ns & Devaiix, Tjoad(jii, foi
$1272.6H, which is placed to your credit.
Please accept, Gentlemen, the pinctre thanks of
Your obedient pervants
MlVtHEI.l, & ili DON.
Meaarif. D. C
Peachy ^ Son,
Montrt'i-L.
QuEBKC, May 31, 1871
Gents :--Enclosed, yon wir find a Dalt at eight days' pi^jht on
N. Caron for ^'260, tor which cou vvill plea.se to credit us.
We Lave the honor, Qeia.s^Meii, to remain,
YoiivK gratefully,
Mll'CHELb & HUUON..
t I
M']\
Efi
MfiMORANDUM I.
June 1, We, Mitchell & Hudon, continue our business w*h the
Re^-oiirces and Liabilities taken from our Balance Sheet p. 66. — SS.
Receiv'ed advice ffom Douglas & Co., Toronto, that they have pur-
chased, as per agreerwent, KO bbls. Extra Flour, to be sold on our
joint %, ( ich i, and that they have debited us for ^ the cost price
which, as per bill, amounts to $585. — 3. Shipped per Brig St. Hu
bert, and consigned to S. McManus, St. Johns, Newfoundland, to be
sold on our % and risk, produce, (S. B.) amtg. to $1864. Passed our
note No. 3, at 6 mos., to the North Insurance Co., for ins. on !?2010,
at 14 %, and paid m cash tor Policy, $1.25. — Rec'd per Grand Trunk
R. R., frorn L. Dion, Montreal, Bordeaux Wines (I. B.) amounting to
$120 ; and accepted his draft oa us, favor Jones & Co., at 20 days'
eight, for the amt. of invoice,— 4. Gave Merchandise (S. B.) in pay-
ment of an order from P. Allard, tor $369.20. — Exchanged eur note
No. 6 with E. Gary & Son's, for our mutual accommodation, each
drawn at 30 days, for $320 ; discounted theirs at the National Bank,
and rec'd in cash, $318.24. Discount was taken for 33 days, at 6 %.
—5. Bo't on joint acct. with G. S. Walls, each ^, 5000 lbs. Chocolate,
at 25 cts. We are to receive 5 % c»tnmisslon on the sale. Paid in
cash for our half, $625. — 6. Rec'ii of S. Lewis, in payment of Ins
I for tIOOO, due this day, Merchandi.se (L B.) utnlg. to $500,
XT_
UULC i.1IU
and cash fo" the bal. — T. Rec'd pf"* Hrig Culumbia, Capt. Riif^se.!^
fc-om C. A. Mtlson, Limewck, pm^i- nt to our order and for ol • ?-!
Mdse. (1. R.) due in Liaierick on . . let next, amounting to i JO,
Gave our bonds to th« Ctutom-house for duties, at 3 and 6 moM., ??
84
May 30, 1871.
jf the 27th inst.,
iiix, LoadiJii, foi
of
infs
& tl! DON.
VRAGTrnAL RXERCI8EH,— SF.T HI.
^l t40 ; jni.J Freight
in eash, $74. RecM at tl
mu,e]:r:,f Columhia from C. A. Mol
an>t. .¥;!(■:>, to be 8oM on h
le f-'amn rinip bv the
C'listo
son, 50 ca«k-s Sicily Wine (L V,.)
F.
(C
Laru
S. B
'1 : hou.se foKlnties at l^
IS % and risk. G
av(.' our bond- (o the
months, for 8160r,.40; paid Frei^'l
:.7()— « «!,i,i v'j, ■■"" ^\ ."" '-^'a""-*"; paid l'reit,'ht m
vhe 5 '^^sh q •, T' "'" •';^""^*' ^^ 2 n.o.., endorsed by
Xli
ilay 31, 187!.
It days' pi^jUt on
t us.
HUUON..
upiness w*h the
beet p. 66.-2.
'. they have pur-
be sold on our
^ the cost price
per Brig St. Hu
foundland, to be
34. Passed our
ir ins. on .*2040,
er Grand Trunk
!.) amounting to
Co., at 20 days'
! (S. B.) in pay-
lianged (jur note
inodation, each
National Bank,
33 daye, at 6 %.
lbs. Chocolate,
e sale. Paid in
payment of his
.) atiug. to,f500,
, Capt. Ri'iJse.l,
' and for ot ■ % ,
mting to f JO.
and 6 mo*., 'b?
''S. B.) iuuUr to «2^« 7^ o I T "^"-^ ^vicrciianiiise Ironi our Store
. "•■'.•"'"«• lo ^^i)«.75, and an Invoice of Oaf ^ /T «: n \ i^?* />
O. Mane 1 wmir;;, '■'',".""• *'2(i ; an.l ca-l, lor ti.e b»I.-I3.
.l.eh- drnli;™ Upai 1 Ga ',, "f r iir,';!;'" n "■■"■• '"■ ''?-''"''"" °'
we ii.ive g.ien our ncceptance, at 40 days, due
J.xpc.MM for loading, etc., aint. CoSloli. -Our
July 2(i, fur .'^.OOiid.
cou.nmsion is $77.33 -1 J rJ „t „ ^^' ^"'■\''.'"'- ^o !?lo(,. • Our
Bradv each ' Ml V .t ,"> x ^'^^*"*^^"^'"' ''" J^'"t»<^connt with P.
ui^i)' f ,t 1)^' 1 '*■ ^^' ^^•>' ^'"'S- to §«)700. Our A purchase in
Co -i i pIh r? f"' "'"■ ''«<=^P^^^"«<^ at ;;0 days, iJovclmut &
dt th^' •lav.-lT'B^ro'H'e.riv^- ^^'^ ^I-^^^Cord. for$.foo*
ainfinn „i • i •? ' Healy & Cameron, the Bri'^ MaWa f.r
Bla:2h;;i'?^.:^'^|?^S;^l!:^-= -- draaat 30 days' ^iJJ'S M^
on National B^nk for the^.fl-^i « "t" f ' 'r ^'^^-i^ ^"'1 ""'"^'"^^'^
S. White .t f\. n. ; ^'^'-—IS- Sent per Grand Trunk R. R., to
C A M'« r ^'''^' P"'-''"^"^ to .«heir order, Mdse. (C. S. B.) of
No. 2, in their fUvor fi ^ m% ^n t { n '" '^ '" P^^^ ment, our note
al -Itt vl^U n■{I^ f '^^'-^.-^.-^O^ and their note at 40 days, for the
lrPn^\fL j^' for .repairing Brig Maria, ^33.10.-30. ShioDed
n '^ ot 'hh?, .?f R^'h''^ 1° ''•.^- '^^^^^-^^ Limerick"to beS
»n .1 ic /c of himsclt, H. Brook, ami ourselves e'loh ' ' - "
h-om x\ld.se. Co. E -.^^ - ^ —- ■ .- • ,'. ':''.'^" 3
bal
per
on J
Suifa.
etc.. .$20.60
amt
at 2 u)o.a
. o.o-> ,. o. lOT. Wi.ite
to .VtS.;0. Paid casl, fur loading,
, lorin.s. on .i;.JOOO, at ^ %. Our
com>ni,s.sion on^^iS? ) 6' at " ^j^ .^MVai' "" •'"""•''. ''^ ^ %• Our
at ' <^ ;. «iVrn w I -. .^ ^^^;onrcommssonlbriiis
at , %. 1^ * 1 2.;.0. We charged for the Frei-ht hv onr Bri.^ M-rh '"^i'
H. hruuk-.s ^ i« ;>] 703.285- ; C. A. Moi^^on^ I '^iliVi }li^5 '
$1703.2S|.J!2i. I„,ured%'ur Bri^l^i^ "S in th! G U f *' """^ ''A""''
ii:e'Fiti-b;^5t i^tr otr 2^,^ i/^;:^!;; .?^"t: thr
amounting to *^97.7'J. Our i i««jj.n hT „ ] •' '^ ** ' t'le proceeds
o *> ^i.< ;. uur i 18^448,85, and our net gain, $156.35.
i
9: ■'; i'
I
i ' !
I !
I
(
•
j
i
j
(
f
1
m\
1
1
i^'
PRAOTICAI- EXERCISES, — SET III.
—34. Rec'd of S. .McManu^, St. .Tohnp, Newfoundland, Acaount
Sales of the Mrlse. consi.stncil to Ihiin by Brig St. Hubert. Not pro-
ceeds anit,2. to $2120, Reo'd in payment an Invoice of Fish (1. B.),
anitg. to §2120. Paid for l-'rei^ht. and other expenpes, in caah, Sfil .34,
Clo-ed our Invoice to St. John'p witli a .cain of $229.25.-35. P;iid
casli for our accpptance of L. Dion's draft, favor of Jones <fe Co., for
$120.-30. Sol<lJ. Merault4000 lb<. Chocolate from Mde. Co. D,
at 35 cts. Rec'd cash, 8800 ; the bal. at 2 mos.— Sold R. Woods, on
his note at ?.0 dav.^ 1000 \h^. Cliocointe from Mdse. Co. P., at 40 eta.
— S7. Closed Mdse. Co. D., and rendered G. S. Walls an Account
Sales of the pame. Our charges for Storage. Advertis-ing, etc., $23.60 ;
our Commij^sion. r,% on $lsOO. G. S. Walls' net gain, $21R.20.
Onr ^ net gain, ;■> —38. Rec'd from C. Lortie & Bro., Halifax,
Account Sales of the Mdse, shipped them from C. A. Molson's Con-
pjgnment. Net proceeds, $2962 for which wo rec'd their draft, at 60
(lavs, on Hamel &, ]?ros., which was accepted. — Taken to our %, at
2 mo.s., the remaining 10 casks, of C. A. Molson's Consignment, at
?I28. Closed C. A. Molson's Consignment, and rendered him an
Account Sales of the same. Tlie expenses for Duty, etc., to this day,
amt. to $1725.85. Our Commission on Sales, at 5 i^, is $354.10 ;
Storage and Advertising, §12. Net proceeds due C. A. Molson, on
, $4990.05.-30, Rec'd from C. Lortie & Bro. an Account
iales of our shipment of the 10th lust. Lj Brig Victoria. Net proceeda,
$843. Rec'd also a draft from them, at 10 days' sight on Garneau &
Co. Pail carfi for clerk hire and other expenses, $104.75.
BALANCE ACCOUNT, JUNE 30.
BE30TTRCE8.
1
70
LlABU.lTIES.
'•
Rills Receivable.
$ 4415
Rills Payable.
$13266
90
Cash.
14185
58
G. S. Walls.
192
80
National Bank.
1210
00
D. C. Peachy & Son.
16
10
Merchandise.
12000
00
C. Lortie & Bro.
5359
25
P. Allurd.
569
20
E. Carv & Son.
405
46
A. Rill fret.
300
00
1 G. Quinn & Co.
792
22
M. Blanchet & Co.
55
20
C. A. Molson.
4886
K\
L. Douglas & Co.
156
35
G. Morin.
180
00
N. S. Robertson.
5233
C. S. MitcheU.
13500
97i
H. Brook.
1703
m
R. A. Hudon.
13531
474
Brig Mctria.
1 0000
no
Sh'pt to Limerick.
1703
J. Merault.
600
00
■
1
.•P52131
931
$62131
93|
86
Klland, Acaonnt
nbert. Net pro
> of Fish (I. B.X
in cash. .?fi 1.34.
'.25.-35. Piiid
Jones Si To., for
3m Mil p. Co. D,
)ld R. Wood.", on
Co. P., at 40 eta.
^alls an Account
ing. etc., $2'!. 60 ;
t gain, $218.20.
& Bro., Halifax,
\.. Molson's Con-
their draft, at 60
ken to our %, at
Consignment, at
rendered him an
etc., to this day,
5^, is!?3r)4.10;
!. A. Moleon, on
3ro. an Account
1. Net proceeds,
[it on Garneau &
04.75.
— ■»
$13266
90
192
80
Son.
16
10
5359
25
405
46
792
22
48H6
7(;j
180
00
13500
97i
13531
47i
$62131
931
praotioa: exercises,— set m.
MEMORANDUM II.
panSip'^I ^^:^l^;,^T^^ir 'f/ -»-- -to CO
h^'l L.Moore's invc«tme„r i . u T 'T^^ mve-.tmont is on
Bo't of F. Belmonrhi "SI fote 5^" T " "^^'-'^ ^'''"'^•-»-
niortga^.eonf]iepronert.for$%Too S r /" 'i^-X'"^"'' ^^^'^'Hned
to date «12(^ ; pa^l Jasl >o the barV^^ t r' 'f '^^ "" '^''^'IP''^
on %, 10 hhds; Surrar 1 rAn il * *«l-''t.— Bo t oi Fremont & Co.
.S.3^30; 15000 l«/e ,i'it'' ^fc «-lia'rca'l'%^''" '''''' f*
work and painting, $1 12 ".O -i Ro^' . J ^^ ' ^^"^ carpenter's
Toronto, to be sold on o, r"7(ifnt ^/ ':^ ^'T '^^""'"- * S°".
Extra Flour, at $6; l.?o ml pt/v l""^ P'J^^ ''''^' ^' ''"" ''b's'
same, in cash, ^t^O.-Re^ iro^;?^ i^^ ' Pi^''' '"'•^'■ghl o.
300 bbls. Extra PIm r ?i^i^ o . *"'^' "" ^"'^ "'^^e at ,".0 days.
Pork, (Mdse Co A.' 'at iTs'^lciosn'^ "' ^'■'' ' \'' ^'''- l'^^"'
& Son, and renderp/j .'^*'^— Closed company sales with Bennir,^
for Storage n;Stnr«l?.T""-"^'^%^"T ^" «''^^4 «
our ^ net 2ain S '?"^R ' Conimission 2^ ^ on sales $ . .
company with J. Arnold A Tim if; '* '''^•35.— Closed sales in
Acciunt Sa'es. Our chat e/ for ^^'"S'^**^"' ^"'1 /f "d.ered tiien, an
himself P T? nL i ' ^ ,'^' , ^^^' ^o be so d on joint ^ nt
SSruLV;, pS^'tTl''. ™ cTlr^ '"■"'.'' ^' per oon,?4'
p^
"&
e s a net gain, ;j;510 : P. E. O- . v'
o«rCo,nm,...,;.24<«o„.lles,?;i75.0^j:n
gam $5 -ir.. Sold W. J. Lyo, h, for clsh
i&n',K^ <>*— !«• Bo't of Jorda.' '^'^'' ^
30000 lbs., at 9 cte. • p^jd in cash
vs 4 net .rain. *519:
our J net
Ian & Sewell, 30 J.hds. B
hhds. Su'-ar, 11250
'rown Sugar,
11200; bah on i:i,S.S
I
I! >
PBAOTIOAL RXBROIBIS,
m.
cai?h as follows : for wlt-ek hire to
^., $225.-30. H.A. (Jliakners
15tV \x\nU, $T6 ; t* L. Moore, •n
< ■** 3 it ' , di«ooui)tetl hie note
111 our favor, du. July 12th ; proct'eds «i'tLc lote *149fi.68 ; (MecouiU
off, for 22 ilayn. ^ti.'H).— RecM of '• ArnoH k Bro., an Aocount
SaleH of rt»e Mdse. t<ent tivxn on the 7th Mist, to be sold on our
joint %. Our i ne< gain, ^15u.— 22. Shipped P. E. Onslow, Sorel,
to he sold on jnint % of h»inBelf, J. D. Roe, Montreal, and ourselves,
each i, HO hluls. Brown Sugar, :^0000 !bfi., at 9| cts. ; paid fireiglit
in cash. <Mi Panie $75.-85.' F. Belmont has drawn ^r, tv- Quel cc
Bank, tor pert»onai exreoyc. >^3()0.— Paid J. .'v.lu •; bi>>'H (h -t
on us, favor of C. RukpoII, per check on Quebec Bank, for $1453. 12.—
28. Rec'd cash fur rent of part ol our Store ■^«2;7(). Per statement
rendered this dav, our share of earnings of lust trip of Steamboat
Eupopa, ai.its. to *.H75.— 29. Paid cash for sundry espenees to date,
38.50.— 30. Ro'd from P. E. Onslow, Accouut Sales of the
Sugar shipped him on the '.'2nd met. Our ^ net loss, 3172^50. P.
Beknont has h= i day inve^aed in the firm, irn cash, $40o,n.35.—
July 1st. Rc3 d irom C. R. Kerney, Halifax to be sold on hi*i and
■ ui- joint ^, «ach i, 150 bbls. Mackerel, invoiced at $7 : 40 bbls.
Ilepnngrt, invoiced at ^'4.50 ; 75 bbls. Lini-e«d Oil, invoiced at $40 ;
puid Freight per check on Quebec Bank, $75. Deposited cash in
the Qnebto Bank, $1-2750.— 2. Shipped P. Gilmonr & Co., St. John,
N, B., to be sold on our joint %, each ^, 200 b.ls. Thin Mess, at
$*.S.5b; paid Dravage, i'n cash, $27.-3. Sold R. S. Venner, for
cash, 150 bbls. Mackerel, (Mdse. €o. D.,) at 87.50. »> Effected iti-
.-urance for $750(», at | f^' on any property that may be in our
warehouse, $50.25.— 4. Shijped J. O'Regan & Co., Montreal, as
per t^ieir order, at 60 days, the folIowingMerchandi.se; 75 bbls.
Linseed Oil. (Mdse. Co. D.,) at $45 ; 40 bbls. Herring.s, ^Md.^e. Co.
D.,) at $4.50.~Closed Mdse. Co. D., and rendered C. R. KerH( m
Account Sales of the same. Our charges for Storage, Adv- rtising &
Insurance, $15 ; our Commi.ssion, 2^ % on Sales $ C. R.
Kerney for his .i Invoice, $2115. and net gain, $? ;.50. Our ^ net
gain, i^ —5. Paid by check Quel <i Bank, Ivertising bills of
Morning Chronicle, $225.-6. l.eo'd from Kane Ok- Joly, Hamilton,
to be sold on joint % of themselves, A. C. MiHer, and ourselves,
each J, ]50lihds. Brown Sugar, ir-oJ'-.ed at $60; paid Freight per
check on Qiulec Bank, $,,')0.— /. l.'ec'd from T> Ma,«s(»n & V).,
Sandwich, to be sold on theirs and our joint acct., e&ih i, 500 bbls.
Prime Porft. at $13.50 ; 250 bbls. Lard, 50000 lbs., at 7^ cts. ;
paid Freight per check on Quebec Bank, $750.- '..>. Sold J. N.
Miles. Quebec, 150 hhds. Brown Sugar, (M'^' e. Co- K.,) ai *;f6.
R"c'd in payment, J. Mountain & Go's, note, ad ' irch 3, 1871,
due one d.iy after da'e, for $7500 ; due to dat- i Sfc note $lS5.'i0 ;
and cash for balance— Close<! Mdse. Co. E., ad tcidered Kane &
Joly and A C. Miller, each an account of th^ sales. Our charges
for Storage, Advertising, etc., .'?75 ; otir Commission 2.^ % on sales,
$ Kane& Joly's net prMO€ed8$338i.25 ; A. C. Miller's, $3381.25;
our net vain, .?38l.25.— f* Rec'd cash for N. Harris' note, due tuie
■day, $49i'0.--lO. Depo'iited cash in the Quebec Bank, $6000.-12.
89
t(« L. Moore, •n
jouoted hie note
9fl.68; iHecouut
a., an Account
be sold on our
Onslow, Sorel,
, and ourselves,
I. ; paid freight
\ on t*-" Quel cc
1« i lii'o's dr. 't
for $1453. 12.—
Per statement
ip of Steamboat
spensea to date,
it Sales of the
9, » 72.50. P.
-h, $4():')«.35.—
sold on bhs and
at $7 : 40 bbls.
n voiced at $40 ;
posited cash in
& Co., St. John,
^. Tliin Me8s, at
S. Venner, for
0.»> Effected in-
niay be in our
>., Montreal, as
ndise ; 75 bbls.
ngs, #lMd>e. Co.
J. R. Kerm. an
;, Adv. rtising &
y $ 0. R.
.50. Our ^ net
vertising bills of
foly, Hamilton,
and ourselves,
)aid Freight per
Map'-c'ti & Mj.,
ftih i, 500 bbls.
bs., at 7^ cts. ;
*». Sold J. N.
o. K.,) at $15.
\*arch 3, 1871,
note$l«o.20;
videred Kane &
!. Our char>?;es
n "i.j 96 on sales,
ler's, $3381.25;
i' note, due taia
ik. $6000.— l*
PRACTICAL EXBR0r8E8.^„ ,„.
•flltOO ()7 ^- * • *' '^'^ Jays sicht fL J, •''^ Sold our draft q,^
;-"i^red li. Et-„ l\^-'l^\ '• cts.-Closeci AmS '^^ «¥''' ''."
t>'ir cliarL'es fl.rQ* ' ^*"J'^'«h, an Account «ii ?',*^-' '^^'i
fi;? o„X,f "B%i«n^««' etc.T7^'/'tr Cof """"
$li)50utJi'n ^*-^'» ^^"^ i'- I. Nolan's n.?*''V''! *""'' ^^ «cot-
^!:^^^C'W^'^^^ ^^^"O^t^i^ bbls S£
McGinn I- • Kernel's note on , « .,? ™ P/""""*'" »1200._3e
S" f: ."""i?,"" ''■■", ».wi..-8y''S ,"«'"■ '»'"'°'^"
amr. changed to . '.l^^^' ^""'""^ '-^ I•^ "hn^rf '! ^cfV^ '^^''''^" *
'1^- a..:t. cC4a to 'T'^ ^'"^*- P^^^^'i o St k ace? rrir *^«
JNVE ,RY, JULY 31.
Store, valued /©
r!f "»bo^^ Europa Stock
fntfrest due us , n V...„ .
fn 7 J '^"ropa stoc i
&t;,il- -\^ote. I21..95 ,
-1.37 {
21.
REsoaRCfis,
i^ess, interest due from us
BALANCE ACCOUNT, JULY 31
$22500
15000.
00
00
192.68
Real Estate.
Cash.
QMeb, c Bank.
Bill? Heceivable.
Interest Receivable.
Sieaiub Europa c,--i-
gtearnboat Europa.
f. (xiknour & Co.
LuBir.iTifcs.
Mortgage Payable.
Bills i'ajable.
interest Payable.
J. D. Roe.
I*. E. Onslovv.
Kane & Joly."
A. C. Miller.
E. Belmont.
L. Aloore.
I 6750
11>17I
21
8010
00
50
37
00
2932 ,> a
1 1 .
I i ! i
SET TV.
JOBBFNG AND IMPORTING BUSINESS,
EMBRACING AS PIUNCIPAL BOOKS,
CASH BOOT{. DOMESTIC AND FOREIGN INVOICE
BOOK;>, SALES BOOK AND JOURNAL;
AND AS ATTX1UARIB8,
INVENTORY BOOK AND BILL BOOK.
WITH A ROI'TINE TAKBX FitOM AN EXTENSIVE BUSINESS HOCSS.
1,1- '
3i? ,
Remarks. — Thr partionlir feature of this set consists in the
manner uiid form of original ontrios, wliich are made in separate
books, — cNcwhero used as ;iuxiliarie3, — from which they are
either jonrnilizftd, or passed directly to the Ledger at stated pe-
riods. Tiiis method has many advantages over consecutive en-
trios ill the Day Book, an'], in one form or other, is adopted gene-
rally in till largo establi>hiiients. The labors of the Book-keeper
are thu.-; divided up, and the separate departments of the business
receive such special record as to present all the facts in their
clearest light. Thus, if any particular information is desired res-
pecting purch.ises, all the facts can be found at once in the In-
voice Book; in the sime manner, the facts and condition of the
sales can be found in the Sales Book; the receipts ;ind disburse-
ments of casli, in the Cash Book, etc.
In thi' previous sets, those books are represented ; but they are
used only as auxiliaries, the entries of the business being made in
the other books without reference to them. This plan, it will be
evident, although possessing some merits, involves a large amouiA
of unnecessary labor, whieh v.ould prove a great objection in ex-
tensive houses. The special l.onks themselves, however, are so
essential in evtry well-regulateil h;,isiness, that they would receive
favor, even at the expense of this additional labor. If, t refore,
K^as HOVSK.
'«;;r-un> their adaption. ^■'^^''^'- ■'''•g^'ncnt woi.l.] b. „oe,lo,T
AW sales and Durchases .o/lTrt ' ^ *^'''.""'''''''^''^ ''"-'•^"or
*° ^'^ ^^^'^-r J «'l others, iZkoLAS:^ '"'" *'^"« ^-'''^«
ROUTINE FOR AUGUST ]87I
NOTB Tosctthpfnl I
and reduction of curronnil. u-^" '"*'"'«o '''ook, involt n,, ^ '""'^'<-''f- T'"'
fended with the inv "ice b .^ "'^''""««. which beirur ,.a rJ n"* u ° '"'^•'' "'■"
'sporting houses thn H^lr '""^''"^ ''"""» tlio Ca^li hIoI ,''"'''• "^^' ""' ''x-
tbe CashVk ' "'"'^"'"'^ '^^« "ote.tend.u in tht {, voice '^f^T' '" '"■"'v
°"" "^'^1*. but only in
Cooic copled-Cash' ^7''' "'^ P^-* ^^^ -Journal entrv .T
fee ved per Sto,„„ ke" oSau LT^*;,?^*' C- B.-B ij jiiV
I
JOBBING AND IMPORTING BUSINESS.
$15.60, (C. B.— B. B.)— 20. Sold Stein & Co., St. Mary, P. Q., oc
their note, at months, Invoice of Prints, $1425.48, CS. B.— B. B.^
Paid T. J. Colston on private acot., $100, (C. B.)— SI. Sold
Mdse. for cash, per Petty Ca<h Book. *102.50, (.C. B.)— 88. Paid
cash in full of note, favor ofG. H. Shills, $3800, (C. B.— B. B.)— 25.
Sold Bvrne & Son, Kajrionraska, for cash, Invoice of Gk)ods. $-100,
(S. B.— C. B.) Stein & Co.'s note discounted; Face of note,
$1425.48. Discount ofT, &50.44, (C. B.— B. B. . . Rec'd per steamei
Apia, from J. A. Knis^lit, Dublin, Invoice of Goods, $440.14; Paid
liities in cash, $105.(53, (For. I. B.— C. B.) Bo't of L. Power &
Co., for cash. Invoice of Printp, $893.63, (D. I. B.— C. B.) ...Paid
clerk hire in cash. $50, (C- B.)— 37. Sold Mdse. for cash, as per
Pettv Cash Book, $160, (C. j3.)— 88. Sold C. E. Lawson, Sorel. on
his note at 8 months, Invoi',e of Goods, $171.04, (S. B.— B. B.)— 29.
Paid C. S. Mitchell, on pri ate acct., $130, (C. B.)— 30. Sold Mdse.
as per Petty Cash Book, .*f2, (C. B.)— 31. Received cash of W. E.
Gray, in full of acct., f 14 •10.20.
•
ROUTINE FOR SEPTEMBER 1871.
1. Sold A. M. Roonej & Co., on their note at 6 months, Invoice
ofGoo'is, $14:'.2.H9, (S. B.— B. B.) ...Paid cash for Drayage and
Porterage, eiT-nO. (C. B.)~2. Lent L. Morgan, $600, (Q. B.)— 3.
Sold Mdse. a:? per Petty Cash Book. $70.20, (C. B.)— 5. Di.^counted
our note, favor of A. G. Cook; face ol' note $1500. Discount off.
$29.75, (C. B.— B. B.) Sold S. D. Hig^ins, Quebec, on liis note
at f^ nios,. Invoice of Goodn, $527, (S. B.— B. B.)— 6. A. M. Rooney
& Co.'s note discounted ; face of note $1432.89. Discount off, $49.60,
(C. 13.;— T Sold Mdse. as per Petty Cash Book, $150, (C. B.)— 8.
Sold J. F. Nestor, St. Thomas, on his note at 8 months. Invoice ot
Mdse. $752.57, (S. B.— B. B.)"— 10. Reo'dper steamer Africa, Glas-
gow, Invoice of Goods, $14.^.?. 19. Duties paid in cash, $276.10, (For.
I. B.— C. B.)— 12. Sold Mdse. as per Petty Cash Book, $218.50,
(C. B.) Paid cash for Drayage, $7.5, (C. B.)— 15. Sold 8. R.
"Woods, Ottawa, on his note at 8 months, Invoice of Goods, $908.29,
(S. B.— B. B.) Paid R. A. Hudon cash on private acct., $140,
(C. B.)— 17. Sold Mdse. as per Petty Cash Book, $302.40, (C. B.)
-20. Rec'd per .steamer St. Patrick, from J. Bailey & Son. Live?*
;>ool, Invoice of Goods, $188.62. Paid duties in cash, $2«.29, (For.
I. B. — C. B.) . . .Bought of Bell & Archer, on our note at 6 months,
Invoice of Cloths, $1926.14, (Dom. I. B.-B. B.V . . .SoldN. B. Roy,
Levis, for cash, Mdse., $923.40, (S. B.— C. B.)— 23. Sold Mdse. aa
per Pettv Cash Book, $1S0, (C. B.)— 25. Sold E. Curran, Richmond,
for cash^ Invoice of Gloves, $460.75, (S. B.— C. B.) . . Paid Postage,
Porterage, etc., in cash, $12, (C. B.)— 27. ^old Lee & Strang, To-
ronto. on their note at 8 mos., Invoice of Mixtures, $3303.71, (S. B.
B. B.) — 28. Sold T. Hoss & Co., King.^ton, on 8 months note,
Invoice of Goods, $578.52, rS. B.— B. B.)--30. Sold A. R. Jacob,
Batiscan, o« note at 3*months, Invoice of Goods, $100, (S. B.— B. B..)
' Sold Mdse. per Petty Cash Book, $125, (C. B.) ...pAiJcasb
in full of Drayage acct., $20.75, (C. D.)
98
BOMISTIO revoiOE BOOK.
WMESTIC INVOICE BO0K.._SKT IV.
This book contains copies of .,11 ; •
chased from importers anrotSers „ nr"'' ^^ "^^^chandise par
t'ons of all such purchase. fZI .*'"', "^""^^3^' ^^^th the condi-
by sorue peculiar marL which Ts "f ^'f'"' '"« distin.uisred
^^''v.n. an important purpo e in ch i!^'"''! '' '^' ^^^'^^^ <hus
disputes, etc. ^ 'P°'' ^° ^^^^^ing the articles, adjusting
QuiBEc, AuaiTsT 1, 1871.*
A. C.i
B.
S. B. Madden,
2J S2' "'° ^""*«'
19133
1935
18863
1029 20613 of 75 .,
'■'^•^ 1332 '
J 262 158 12
n08 i222
1276 17152 58-, •
^^ 482.9l(
Amou
ri .{.'7
I' "
9f. :s!
I
DOMESTIC INVOICE BOOK, -SET IV.
QtJBBEc, August 10, 1871.
C.
794
800
834
704
Amount forward,
P. McHucjH & Co., (6 months.)
40p9.DuokDrilIing,141ia/a>17c. 239.9(5
^K' '* " " 13892 " 18 250.11
36 « J5rowii " 14153 <' 25 353.88
42 '< W. li. Diaper, 21691 " 7^ 162.69
Note at G inos. from Aug. 10.
.^ II
N. Casey & Bro.
(8 months.)
750
751
753
754
CM.
K. A.
Vj. a.
D. C.
E. N.
EG.
381)2
5788
6202
4187
5630
5685
4 cases 4.4 Bleached Shirting,
40 17322
40 1736
40 1755
40 17312 6955 yds. at 9i ots.
Note at 8 months from Aug. 11.
26
L. Power &. Co.,
52Print8,973 1858
52
1)65 1834
53 " 967 1895* 5587 Vd.® 8c. 446.98
51 " 972 1924«
49 " 968 19542
49 " 971 1920 5808 yd. /®8ic. 49.3. 6S
Discount off 6^
940.66
47.0;i
C. B.
893.63
Purchases on time (taken to Ledger),
Cash jjurcba6es (entered iroiu C. B.),
Total for the month,
1303
76
893
1006
64
660
73
63
1667
2197
.3864
:;7
39
76
9*
ET IV.
303
76
1006
64
660
73
393
63
1667
21 DT
3864
:!7
76
DOMESTIC INVOICE BOOE,_SET IV.
QUKBEC, SEPTf-MBKR 20, 1871.
Beij. & Archer,
i(
(6 nionthe.)
I88?!.M ""«'";: °"™"=. I «»'
1178a
1137
1094«
11513
1268
1J68
1279»
12618
}906|.0Sebastopol Checks, 11 683
12452 = 14191 vda.
^I'Hg. $1915.78
3.00
189630
1915)28
190.3 o'O a
1737 .3 World's Pah-,
I77o.i0 it
1823 33 a
1834 33
1845 30
«
Cooperage
Note at 6 mo-nths.
To.al^„,3se for ae„„. (taken .0
t.
■ I
B
t
a
O
B
=: I ::
<»
(M
B
o
g
to
B
o
"»
OS
o
3
I!
o
O
PQ
«tj
CO
CV5
"C
o>
CO
«o
O iO I rr, »o
00
ff<l
CD vc i'j o lO cq c<i ^^1 o M M
««
ec CO tJ< t— 1 r— c cvt in
iTfl pfl fC •<* re >o
o
-*
00
I— 4
c
02
CC OC n CO
o o OS CO
C^ C^ r-l VO
1—1 ^
QD cc m '^
9^ Cfi (^ ^ '^ "^ <^
en
u
a,
>
o
u
•13
@
o
ai"
so
o
w
«o «o
00 OD ^j t^ IK a? («
oi o m c^ — e^ 'M
CO >0 O to r-C -^ C^
@
a
s
^ 1
s
— ^ s^^
o
a^
^ ""
•z; - - - ^ -
to
4>
00
Ol
S
1
2
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•* s*
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tn o oi
e<i e<i ir<i
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03
ev
•"Id
o
•85
ic
•a
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lit
OB
CC
-2
03
<£
OQ
-4-*
C
o
S
IM
9*
o
00
1"; iffl
» n
•— '
-5
t
Ti
u
oj
fc
^
«£
-ei
CO
^-
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•95
^
o
o
s
_c
<:
o
o
"2
>ft
•a
m
cS" o '|'"o
e<i ?c f 30
00 00
a*
to f >o «o 1
:: 1-^^ 1
F-l
-E
«■
8:
^
«>
■a
ts
e
«
w
s
^
o
m
aa
s
»
00
—I
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<J
■
•
a
a
o
o
->
^O
■ «-.
5^ .^
•
■c
■■«
^-^
J*
«o r
2
^S
0/
«
"
"o r
KlO
2i W)
M
t: jn
t,
gpH
^
go —
u
K 9J
I)
ai
A
£ «s
J
o
ee
«;
'■■if
8ALM BOOK.
SALBS BOOK.
This book contains all the reo;ular pales, either for cash or on
time ; tiie cash sales beinsj extended in the inner column, are, of
course, not included in the amount for which merchandise is cred-
ited from the Sales Book. These sales, to<rc'tlier with the ]><■■ y
sales not entered on the Sales Book, are posted from the Cash
Bo<)k. The total credit of the merchandise account for the month
will agree, in amount, with the monthly leeapitulation in the Sales
Book.
Quebec, August 1, 1871.
R.
F. p.
AOe.
192
1289
71
46
46
1
€
68
100
101
L. Beacdry, St. Thomas, P. Q.
1 case Black Velvet,
796 yds. at 36 cts. $286.56
10 pea. Fancy Cassimeres,
275 yds. at 70 cts. 192.50
110 Robes, at $2 220.00
Note at 3 months from Aug. 1.
12 ..
F. Peters & Co.
Three Rivers.
25 dot. Ladies' Whit* Cotton Ho«e,®$l $25.00
20
29
I
1
4
2
8
6
6
1.25 25.00
1.13 32.7'
Pearl Spun Silk Hose, 8^ 8.00
" " 9 8.00
Black " 9 $7.50 .38.00
Pearl *< 20.09 40.00
Ladies' Lisle Gauntlets, 4.60 36.00
" " 4.75 23.75
" *< 9.00 45.00
Note at 6 noe. frotn Ang. \%.
A«)0unt forward.
699
0«
273
91% 6%
§2
br cash or on
(lumn, are, of
ndiee is ored-
rith the pc y
oni the Cash
Por the month
n in the Sales
699
OS
273
62
97)68
SALES BOOK, -SET IV.
QUEB
'W
iF .
'li
SALES BOOK, -SET IV.
Quebec, Septembbu 1, 1871.
A. M. RooNET it Co., Montreal.
U.M.
62
I bale Brown Sheeting. 663» yards at
14 CIS. $ 78.89
.00 doz, GeuV^ Linen Hdkfs., at !?5 2.'i0.00
R.X.
2.S1
1 case Cotton Damask. 540 yds.,
at 20 eta. 108.00
Ifipcp. Black Bombasin, .558 yda.
at 11.25 710.00
1 case Silecia, 2200 yds. at 13 c. 286.00
1432
89
Note at 6 ino«.
S. D. HioofNS, Quebec.
231
10 pcH. Black Boinbagiin, 350 yards, at
!PM0 $385.00
19
20 pes. Duck, 710 yds. at 20 cts. 142.00
527
00
Note at 8 mos.
ft
J. F. Nestor, St. Thomas.
1 bale Stark Brown Sheetings, 829 yds.
at 10 cts. .i; 82.90
130
1 bale 4-4 Shatvr Finnuel, 3372
yds. at 5i) ai'-. 168.75
12 pes. Grei; Vfj; Barege, 200
yards, at B.) ets. 70. UO
1066
I case Solid Check Ginghanns,
2394 yds. at 18 cts. 430.92
752
57
Note at 8 mos.
1ft
S. R. Woods, Ottawa.
4 cases Harop Prints,
M.
481
246 1332
G.
491
1262 15812
M.
509
1108 1222
M.
97
1276 17152 5851 yds./® 12 cts. $702.12
2 bales Brown Globe Drills,
1141 10.328
1147 1029 20613 yds./® 10 cte. 206.17
908
29
Note at 8 mos.
9.0
N. B. Rot, Levis.
9 oases Cotton Bama^k, 4868 yards at
20 cts. $972.00
5 % off, 48.60
923
40
Received cash.
Amounts forward,
923
40
1
3620
76
ifta
SALES BOOK, SET IV.
QtTEHKo, Sbptembib 25, 1871.
Amounts <^»rwaril,
of';- ^J'"/*^' RicJimoni,
5 n ^^",'J'<'8'I'i;>e Gauntlet.", ^$5 *450
1432 89
S. i
Krd (jlovoi,
5% Off,
Reaeiyed ca.sli.
27
00
*7 36,00
485.00
24.'25
923
40Jj .S620
4(>0
76
527
00
m' V\f . \^'^' Toronto.
32|»0i ''< (< nucK 1^
oo dO» 1 1. ooj./. 1 .
V/irtn9 // '^•^^' '49.
9K A/l« rw 2^653 14 c.
dO put! s.plnoM.Miatijre?,2«772 27 c.
Note at 8 nionfefae.
41.-).fl«
416.2?
415.1ol
4I.'i.24
41.5.17
776.y2J
752
57
— 28
T. Ross & ( 0.,
4 ps. White Piques, 75 1
)
130,3
71
674 I 18
19
64|60| ps. Larellas,
15
30281
fa> .?
Note at 8 montlis
Kingston.
(iH $75.25
1.25 18.75
• I'i 484.52
30
908
29
923
923
40
40
3620
76
A. R. Jacob,
Bati.<:
f '^'^f • '^ie^'B Nov,- Silk Shirts, ^'S $10
I
5786J
a
tt
«
n
It
26
30
35
Note at 3 months. —
Sales on time, i
Sales for caeh, entered here anrl nn«^.^ I
iroTii V. u ' i
lOOOO
iroTii C. a
Pettj sales entered al
on« on C
Total sales for the
loi"
^%.
.^. w.
^7'^%^o.
IMAGE EVALUATION
TEST TARGET (MT-3)
A
[/.
1.0
I.I
■ 50 '•"^"
Ui
u.
|40
2.5
2.0
IL25 ■ u
iiiiim
6"
1.6
Photographic
Sciences
Corporation
23 WEST MAIN STREET
WEBSTER, N.Y. 14580
(716) 872-4503
V
iV
>^
M
^9)
V
•^
^
^
^^
?
.V
i/..
CASH BOOK,
This ifl the mos<) convenient form for a Cash Book to be kept
in connection with a general merchandise business ; the feature
of special columns may be extended, if desirable. It will be .een
that all cash entries, debit and credit, are taken to the Ledfrer,
either through the Journal or directly, from this book, toiretb-3t
with all accounts producing or costing cash. Tho amounts difr
tinguiahed as *- per petty Cash Book," are entered here from a
Dr.
Cash.
[ (> ., j
1' '■'
JJ .!
1871
Au '
e
8
14
JI5
'18 V
,21
25
2h
27
30
31
Mdsb.,
6. R. BOTCK.
Loam,
6. K. UoYep,
MrsE.,
BiLi,8 Rkc'bi.k,
Mdsr.,
Bills Ubo'blk,
Mdse.,
Mdsb.,
Bills Rbo'blc,
AIdsk.,
Mdsb.,
W. B. GBAf,
Ammmt on hand.
Sales, per Petty C.-Bouk.
Reo'd on acct.
Return from J. B. Law-
rence.
Rec'd in full of acct.
Sales, r,er F<itty C.-Book.
J. N. Galt'a note duo.
Sales, per Petty C.-Book..
S. I. I'erron'snotedi^c'td. '
Sales, per Petty C.-Book. i
SoKI Byrne &Son, (S.B.)
Stein & Co.'s note disd'td.
Sale.^, per P.Uty.C. -Boole.
Sales, per Petty C.-Book.
Rec'd m full of acct.
Mdte.
Mdte. Sales tot Cash
Total Cash reo'd during '
the month
97
120
110
102
400
IHO
72
50
00
50
50
00
00
00
1032 50
Snndr.
600
00
SCO 00
1440 00
1264
soo
1426
1480
78U»
1062
8872
00
00
48
20
rt8
50
18
BfU,
7380 50
8872
10252
18
68
104
3ASH BOOK,
— SKT IV.
Book to be kept
est' ; the feature
It will be ^een
to the Ledcrer,
is book, toiretb^
ho amonnta difr
ered here from a
J500JC. The coJuim, headed " Balances " will I . r /
oonvenipnf f^n ti "'^uues, will be found very
■""k,, i„ A, „„,„„„ • »»^i Th. Chcot-
D«lized. Were th.,. '"I™" have been jour-
Were these ,m„„„t, p„s,ed directly to the Ledger th,
I.ea«..p,,e w„..a be written i„,te»d of the Cheel-,,..;," ' '
Cash.
Smdr
600
00
c<^00 0(1
144U OU
1264; 00
800 00
1426
H80
7609
1U62
887;
48
18
Bai.
7380
50
8872
18
1825268
3V
3V
EXPRNSK,
Loan,
«
«
6 V EXPHNSK,
^H p. A. Hall,
7K R. »'. Davis,
10 . Mdsk.,
'2 V JJxPKNSK,
'5 AIdsk.,
18 V Intrhkst.
20 V T. J. (:or.8TON,
23UlBiLia Payable,
26 Mdse.,
26 IMdsk,,
(26 Wexpensr,
25 V Intkbest.
|29lv C. S. MiTCHKLL,
Madden'8 Invdce, p,r Dom.
Pai'l A. Miller',- bill
Lont .'. E. Lawrence for one
PoJ4«Staa,p.s,$2,.Drayage,
Paid him on Private ncct.
PaulhirainCullofacct.
i^'ities, (K> per Foreign I, B
J^f'ijase and J'oitenic-o '
I'lUies, as per JA,roign 1. B
D..conntonPorr.n'rnote
Un P.wvato asct
Note favor rt.n".v.-i,i,|,,j„^
iJinics, por i-'oreiijn f U
Ck'rk hire, $;^0; $20
Discount on Stein J^ Co. '8 note
On private acct.
Mase. purchased for Cash
^m'^n?h'^^"''^'"''"'"°S">«
BaJanQe on hand
105
Bi Fi
Dr.
IR71
Sopt
1
3
'i
7
12
17
•20
t.{
25
3U|
Belanee tm hand,
Mdsr.. Sales, per Petty C.-Uook
iNTBRTTgT, Disc'f on note fav, A. G. C.
Bnii.8 Kro'blk, DiPc-t A. M. Kooney k
Co. 'a note
MDSfc., Sa as, per PeMy t -Book
Mdsb., Sales, per Petty C.-Hook
Mdsi., Snles, per Petty 0.-13ook
M i)8«i., Sold N. JJ. Roy, per S. B.
MosB., Sales, per Petty C.-Book
Mdsh., Sold E. Curran, per S. B,
ftlnsB., Sales, per Petty C.-Book
' Mdae. Salefl for Cash
Total Cash reo'd during;
the montb
Oach
Mdte. SwMlr. Bal.
70
20
L'SOjOO
21S!50
3(52 40
923!4I»
180'0l
4(i0|75
125! 00
29
1432
2i90
25
1462
2490
3962
89
8031
8S
3Hft2
12584
89
72
106
Oach
Simdr. Bat.
29
1432
1462
249U
3952
89
8631
83
Sv*.*)!
12684
8»
TJ
Book.
1871
Septj 1 V Bjcpbnbe,
2 V Loan,
fi V Bills Patablk,
0|V jlNTlRBST,
0( j.MDse.,
V iBxpRNan,
V fi- A. HoDu.t,
AIdsk.,
V KXPKNSB,
} Porterage
Paid Drayage.
«8.50
Lent L. Morgan
Diso'td Note favor A. Q. Cook
LUsoonnt ou A. M. H. A Co 'b
note
l>ulies, at per For. I. B '
Pnid Drayajje, on aoct. '
Pmd OD privHte acct.
I>utle?, as per For. I. B
Paid Drayage in full
Mdae. purohiised for Ua*h
Total Cash paid for the month
timance on htmd
304
1760
600)00
150000
49
1200
20 76
2414
304
2719
12584 '
BILL BOOK,
The Bill Book can never, with advantage, be made a principal
book, from which to post The form presented below is the best
Bills
No.
1
2
3
4
5
6
7
8
9
10
11
12
l.S
14
When
Keo'd.
Aug.
(I
Drawer or Endorser.
W. H. Ellison.
D. Atkinson.
H. AI. & Co,
Sept.
1
5
H
15
J.
27
H
2H
30
1
1
1
12
14
20 J. R. East.
28j H. M. & Co.
<<
it
a
J. 0. Moss.
H. M. & Co.
Drawee orlMaker.
J. N. Gait.
S. T. Perron.
L. Beaudrj.
F. Peters & Co.
Hazel & Poy.
Stein (t Co.
C. E. Lawson.
A. M. Rooney & Co.
S. D. Higgiiis.
J. F. Nestor.
S. R. Woodis.
Lee & Strang.
T. Rush & Co.
A. R. Jajob.
!' I
Bills
Nil.
When
Drawer or Endorser.
Feb. 20 G. H. Shills.
April 1 S. A. Pugh.
May 1 2 A. G. Cuok.
Aug. 1 P. McHugb &: Co,
" UN. Caeev & Bro.
Sept. Bell & Archer.
108
Drawee or Maker.
11. M. & Co.
u
«
BILL BOOK,
—-SET IV.
nade a principal
below is the best
for general purposes, althou^rh the
example is more comprehensive.
arrangement in the former
Receivable.
e«oriVIaker.
> or Maker.
Date.
t.
1871
on.
Feb. 11
■y-
April 12
&Co.
Aug, 1
^oy.
" 12
3.
" 14
'son.
" 2n
ney & CJo.
" 28
;ins.
Sept. 1
<< r.
or.
5
da.
" 8
ng.
" 15
Co.
" 27
b.
" 28
" 30
When and How dipposed of.
PaiJ.
Discoiintod.
Difioounted.
Discounted.
Payable.
It9
hi
INVENTOIiy BOOK.
Ths book is used to ermmernte the different articles of unsold
merchandise, at such times as ,n.y b., deemed desirable. It is
on hnn !"k •"''•' T:;^^, ^' f"^"'"'^- tho amount of merclw,ndise
on hand being included m the opening journal e„try. Inventories
are frequently copied into one of the Invoice Books: but a sep-
arate book is preferable. ' '
M -de. on hand, August 1, 1871.
Marks.
H. M.
R
L. B.
V. P.
A. B.
R.&X.
N. A.
Nos.
192
1
8
197
2.S1
19
1289
62
M.
190
4
B. S.
130
1066
4595
3624
1 bale Brown Sheetings
I case Black Velvet
1 case Paper Cambrics
21 pairs Wliitc Blankets
41 pea. Black and White Tweeds
21 " Fancy Cassi meres
17 •' Black Satinet
1 case Woolen Shawls
20 pes. Black Bombasin
37 « Duck Canvas
2 bales Black Wadding. . ,loz.
lIORobea
1 case Cottonades
10 cases Cotton Damask
150 doz. Gent's Linen Hdkts
160 pes. Diaper
60J Play Linens
1 case Black Alpacas
1 " Opera Flannel
100 doz. Men's Gloves
140 « Ladies' Lisle Gauntlets
6 " " Kid Gloves
1 bale Stark Brown Sheet! nir«
1 " 4-4 Shaker Flannel
12 pes. Green Veil Ban ..rp
1 case Solid Check Gin;:iiun>-
25 pes. Coburgs
1 case Silecia
1 " Linaeys
1 " Corset Jeans
1 '' Delaines
1 *' D. Bege
110
Yih. : Prioo.
7!tfi
2()0f)
l.Sf)93
576'
469
60
900
i;^92
80
687^
5400
19313
910
750
829
3373
200
2394
625
2200
i2(;6'^
17251
3(1(1
864
.11
.263
.06 1
3.43
25
.60
.522
4.89
.872
.15
.22
1.50
.222
.16
4.50
.90
.17
.272
.372
2.50
4.46
6.25
.082
.45
.29
.14
.60
.091
.172
.06
.25
.11
Amount.
fil
212
125
7-'
342
345
24 G
293
787
208
17
165
154
864
675
135
328
98
93
Of)
03
37
75
22
+0
50
80
60
00
63
00
00
00
35
250|25
281 25
25000
624
31
7U
151
5M
3;:!5
2G2
208
221
lOH
325
85
40
25
46
.S8
00
n;
ou
50
64
5!
00
04
8299 4(
firtides of unsold
dcsinible. It is,
if of meiclwiiKlise
try. Inventories
ookfl ; but u sep-
t71.
s.
Price
' .11
. Amount.
:]
61 9.S
f.
.26'^
2I2!);i
.OG'
12.
■) 00
3.43
•7 .
J 03
.)'
' .25
34i
J 37
S'
.60
■m:-
> 75
i
.522
24 C
22
3
4.8y
29;-
+0
)
.872
787
50
)
.15
208
80
)
.22
17
60
1.50
165
DO
•1
.222
154
63
1
.16
864
00
4.50
675
00
.90
135
00
a
.17
328
35
.272
250
25
.372
281
25
2.50
250
00
4.46
624
40
6.25
31
25
.082
7U
46
a
.46
151
S8
.29
5S
00
.14
3;s5
16
.60
202
ji)
.091
203.
5G
.172
221 (
i4
,06
103;
)1
.26
325 1
)0
.11
95 04
i
)299 4
rC
JOURNAL,— SET IV.
QuKBRc, August 1, 1871.
Cash
Mkrcha.noise
BiM.s Rec'ble
Store Rent
S. R. BOYCE
W. E. Gray
Resources ,,n.| Liabilities of A. .J
"all,O.S.Mitci)ell,an,iK.A.H„:
??.'?• r"^[f"«" in tho firm of. 'llnll.
MchellA Co." doing n,-ene,;
Jn )l,ing and Importing l,u8ino=^
n.m 'th'"S f ^'""'«°^ - '^^^
Amt. on hand, per 0. Book .$738(»..')0
" I"''' " S2i)».4i1
Notes on hand, per Uni » 2084.00
Advance payment for rent 1600.00
Balance of account 2040.00
«
JJ80.20
22864ir
To Bills Payable Notes outstanding, per B. B. 8500.00
" R. P. Davis B.alance of account
A. J. Hall Net Investment
" C. S. Mitchell " «
" R. A. HlIDON " «
31 __
Mercbandisb
To SUNDRIKS.
To Bills Payable For the fniirmin™ r
=. ror ine to h, wing Invoices per Dom
i'lie ""lO ""^ ^- '''^"""gh A Co.,
From .\. Casey & Bro. A ug. n 660.73
"l667.3r
22364
2,574 98
JOURNAL,— SET IV.
Qdebrc. Aiioust 31, 1871.
HiM-a Rkckivabt.k
To Mkrchandise.
Snlet for tho month, perSalM Book :
L. Beiiudry, Auj;. 1, $fl99.0«
K. Peters A Co., " 12, 273.52
HaielAFoy, ■- M, 869.38
Stein A Co., «< 20, 1425.48
0, B. Lawson, " 28, 171.04
<(
Cash
To SCNDRIES.
rr, ., Keceipts per Cash Book :
J o MD8E. Total Sales for Ca>h 1062.60
S. R. BoTCE Roc'don ncct.,$flOOi $1410 2040.00
^■'''*^ Return from J. E. Lawrence MOO.OO
" Bills Rec'ble Received on Notes, *12(J4;
$800; .$1425.48
" W. E. Gray Iq full of acct.
3489.48
1480.20
Sundries
Mdse.
EXPENSI
Loan
A. J. Hall
R. P. Davis
Interest
T. J. CoLSTOK
Bills Payable
C. S. Mitchell
To Cash.
Disbursements per Cash Booi :
Purchases, etc., for Cash 23i'2.0«
As per Items, ,'$15.25 ; $7.50 :
$25; $50
Lent J, E. Lawrence
Paid on prirate aact.
In full of acct.
y7.75
80U.00
8U.00
175.00
Per items, $15.ti0 ; $50.44 66.04
Paid on private aoot. 100.00
Hn^lcotned noto favor G. ]].
Shills 3800.(10
Paid on private acct. l.'^O.OO
112
.345)8
48
3438
8872
48
IS
8872
18
7620
86
rc'ifl
85
JOURNAL, -SET IV.
QiiKij|.:o, Skptkmbkk 30, 1871.
Mdsk.
To Bii.r,8 Patabi I- ? ■
'^ATABr.fc Involoe per Pen., l. B '
'• W. MeadkAPo !''"""':l'''^^'"'".-«"Pt.20 I»2«.I4 '
iiEADfc&Co. Inv..fi!e,.t.,0.,,e,F.I.U. N6;U9
" J. Baii,kv&S()n "
20,
188.62 ! 3667
BiLta RecjcivABi-B
To Mpse. I 7602
Sales for the month, as nor S. D. •
A. M. Roone.v A Co., Sept. I, U.f2.S9
J- F. Ne.^tor
S. K. Woods
Lee ifc Strang
T. Ko.<:s A Co.
A. R. Jaoob
<(
" 5, 527.((0
" 8, 762.57
" 15, 90S.29
" 27, 6393.71
" 28, 678.62
" 30, 100.00
Cash
7602 93
To SnNDRiEy. i 3952'
Rppoiptf., per Cash Book :
Trtal Suli's for Oiish 2490.26
To MnsE.
" ^'"■'■•' ^^'^"''"'^« R'-'-l - "0*- 1432.89
SrN'jr^RiBS
Mdsk.
fixPBNSE
Loan
Bii.i.s Patabi
3952 89
nifburgeiiient.s per Onsh Book :
Porch.'.ee^ oto., for Cash 3(14.39
I'er Items, $17.60; $76; 112 •
$3«.76 ' ,25 26
Lent L. Morgan ^OO 00
To Cash. 27 IS 24
E
Inti
lltJES'l'
R. A. HcD
Disc'W note f«r. A. 0. Cook 1500,
"iso'tonA.M.R.&Co.'8note
.00
ON
raid on private aect.
49.80 '■!
!
140 00 !;
113
.Dr.
HALL, MITCHELL A OO.'S
Balances of their Resources
in
Casu,
Mdsk.,
SroitK IIkvt,
Uii,i,s Hkc'ule,
Loan,
T. J. Colston,
Resources.
Balance on hand.
Hularice on lian I, per Inventory,
Advance payment.
Balance on liand.
Balance due tliein.
Balance iu liieir favor.
$9865
7810
16011
818M
600
100
128 16.'
48
61
00
09
00
00
18
Dr.
Balances of their Losses
I
J'
\-r^
Lossen,
EXPENSK,
Interest.
A. J.Ham/s
C. S. MlTCHEl,!,'s
H. A. HuDOJj's
Loss.
Loss.
9 net gain,
i net gain,
s net gain,
Net Gain,
$1661.05
1661.05
1661.05
$ 22.3
85
00
89
498;i
$.J292
15
Oi
114
ELL & CX).'S
eir Resources
'their Losses
$ 223
00
85
89
1.05
1.05
1.05
498;i
15
$.^292
Oi
BALANCE SHEET, SET IV.
and Liabilities.
Or.
VV. Meadb & Co..
■'. I!aim;y & Sun,
J. IlAi.r.'s,
S. MiTC'flEM/s,
A. Ht'DON's.
iJalunce in their favor.
Halance in their favor.
Share of capita),
SJiareofcai)ital,
Share of capital,
Net Capital
SG.TIO.?')
<i26().7.5
6250.76
and Gains.
Cr.
lift
BOOK-KEEPING
|ii^ ill
BY
Ilsra-I-iE] EUSTTIR/Y.
Ii <
M L,
If [
REMARKS.
^ Thouf^h we have introduced Double Entry Book-keepin: before
Sinjrle Entry, yet, vre admit that books may be kept by sinde
entry by those unricquainted with the priiiciples of double ontry;
but the mere keepin,:,' of accounts is not ali that is required. We
gave the precedence to the method by double entry, as it is con-
ceded to be greatly superior to that by single entry. In fact, the
simplest settlement of Partnership accounts involves the principles
of double entry ; and, if the commonest Enirlish education in-
cludes a knowledge of Arithmetic, Mensuration, and even of Algebra
and Geometry, n ought surely to include a knowledge of accounts
BuflScient to make a partnership settlement between two mechanics.
The following set in Single Entry Book-keef«ng, though shortj
exhibits such a variety of transactions as is necessary to an illus^
tration of it.
The principles of Single Entry are so easy of comprehension a«
scarcely to need explanation. Accounts are kept only for persons
who alone have accounts in a " Ledger," and become debtors and
creditors as they owe us or we owe them.
The principal books of entry are a " Day Book " and a
I' Ledger." Besides these, there are other books tern)ed " AusiK
iaries," varying, as in Double Entry, in nu -.ber and form accord-
ing to the b'jsinees.
AH transactions requiring a debit or credit to any f.erson with
whom you have dealings, are entered in the Day Book. The form
of entry is very simple, thus: " Paul O'Neil Dr. T*. 5 yds. Linon
@ 1^5 cts.," or ^' Peter Howard Cr. By ish on %, $8.00 ; " in
every case specifying the details which constitute vhe debit or
credit. This is the only book from which poets are made to the
Ledf^r.
116
^P^^ll^^^'2^'^-^ ^-n the ..Auxiliary
«ngle entry sot, we write TnlTS^lTr.'^'- ^ '^'^' ^oH
otherw,.e be shown io the oXdl^S^J^: ^^''' '"' ^^"''^
Quebec, July 5, 1871.
318 09
Or.
J- ViKoBKT, Levis,
B7 700 lbs. Butter, ^ 15 cents
Or.
Tomjr„oteonhisday^,n,onthioA,]Iof^
n
P. Clark
To C«eh lent to him
106 01
loslot
Dr.
20000
8136
Qcrii'^Ko July 12. 1871.
.1
I I
1 !
I .!
■■ li ■ ! _
S. Frasbr it Co.
Cr.
By 60 bbls. Oaimeal, fS) H."0
Dr.
To Cash on % |; 60.00 i
" my note of this (lay, at 2 raos., for 120.00
I 37s;
00
13
C. I. Lake,
To my note at "0 dayp, fbr
" Capl Ml full of %
Dr.
$180.00
20.00
16
J. Gleason,
Cr.
By 18 bags Java Coffee, 1044 lbs. net, f& 16
ctfl., received per steamer Florida
L. P. Clauk,
16
ByCash, mfiiP r loan of 11th inst. $200.00
" lent hiui this day
Cr
).0(
75.00
17
8. J. Pierce, j^
To 12 bags Java Coflfee, 696 lbs., fd) 20 cts.
—^ 18
L. P. Ckakk,
To Cash, in full for loan of 16th inet.
— 20
Dr.
8. J. Fierce,
Or.
By bis note, at 40 d^«, on % for his purchase
of 17th met. for |ieo.OO
" Cash in full of 5K 39.20
11
A. T. HVGHXS
Dr.
To 50 bbls. Ry« Flour, /© K.IO
U8
170
00
200
00
167
04
275
00
139
75
00
139 20
308
00
at 65^, '" **<^'-> =»-^0«, whh intercut
ut 6^,
Less interest added
•^' A. T. Hl-gh.«,
% Casli oil ;%
1 j C. I. Lane,
^y 40 l.blfi. Fancy Fiour, rci ,$7
■ ■ . 26
S2I0,0.S
2.08
' -^ pi ss„fgi:!' -,--.:
3 1 A. T. HcGHE8,
By his Draft at 3 davM «,«!,► r r^
accepted " S'^'' °» ^' Dplorma,
To Storage o» 30 lb)**.
OommissiouoDlISO, at 4 ^
To Lit* Draft on u- <»♦ in -lo
L- Water, accept'e? ^"^^ ^'S'^^' '^ ^^vor of
lp:%
\ I
i .
mi
CASE BOOK,— SINGLE ENTRY.
Dr. Or,
1871
July
• 4
<«
l<
il
(I
u
Aug
18
20
22
2H
26
t«
31
Amount of Cash on hand at commencing
bui^inees
Paid for 300 bu. Wlieat, /TO 72 ota.
" for Freight and other expentM
L. P. Clark ao a Ioun
C. I. Lane on %
for Freight ami Dra^age on an
Invoice of apples fron* G.
N. Rollaud
S. Fraeer & Co. on %
C. I. Lane on %
for Freight and Cattau'e
RecM of L. P. Clark, for loan of Uth invt.
" of L. P. Clark as loan
•' for eale of 1 2 bbls. exlra Flour, /© |7
Paid for Advertising, etc.
*' L. r Clark for loan o» if,th
Kec'd of S. J. Pierce, (or balance ol %
Paid for Stationery
Kec'd of A. T. Hughet^ofi %
" for Sales ol Roilaud'*. apples
Paid G. N. Rollaud in full o(%
Balance on hand
13000
(I
«
It
Balance from Julj 31, 1871.
200
76
84
39
liO
180
c.
OO
3698
00
00
00
20
00
00
216
2
200
81
6
50
20
3
Q.
00
CO
00
25
50
00
00
40
2
75
50
00
30
293fi
20
35
39
2996
3698
30
36
20
120
'RY.
I>r.
Of,
c.
3000
Oft
200
75
84
39
vm
180
3698
00
00
00
20
00
00
20
35
21 b'
2
200
81
6
50
20
3
2
76
39
2995
3698
e.
00
CO
00
25
50
00
00
40
50
00
30
30
3ft
20
Q il«
! t
h ^il
III !l 1
i
Vif
►o
%•
Cj
C4
s
n
«*
^
^ CM
R-
r- 00
00 3 '*
d
tf
d
8
O)
(33
CM
1S71
July
<= = o
CM O f^
§1
t» ec c.
r-4
o
00
r- CC
fc M ec
Q)
So
u
M «, s
•"« t- £ '£/ t?
esi to
o -
CO ■*
00 's "-
2 1
X 3
COO
coo
c
o
OCX
o e>4 o
■X
«»
www 1
c
a
C!
5
rs •
08 '3
^3
W - <M
»-c - W
00
3- 5
128
I
■^ 11 f^
Q a
^ I) S II 3
•3
on
CQ
s^
I
r-l
n
-1 ►.
X 3
— H-
C C: O
c
ceo
c
o o oc
■X-
o e^j o
»-
1— C-4
er.
^
•»
C» M C<l
1
!•
l"9
- e
Nf
^«
^.
^S5-
s^.
o e-
o>. -
H- -
c<i - e>«
It
— " C<l
- >.
1
59= 5
-•Hi
ll
'ti:'mtti0k;h'!s^;i
iitlW^T
8TATBMENT
II 'i,
BHOWma TH£ OONDITION OF THE BUHIITISB
I
On tho 31st of July.
: i I
il
i I
.-.,]
Resourcu.
1. From Ltdgmr /4ccott»»to.-— Balance due bj
A. T. Hughes
%. From Cask floo/c.— Balance of Cash on hand
«. From Bill Book.
S. J. Pierce's Note, due September let
A. T. Hughes' Draft, due August 8
4. From Jnvmtory. —Merchandise on hand.
. Liabilitiu.
I. From Ledger i4c(>.iHite.— Balances du4 to
Ct L Lane
J> K. Eirouac
J. Gleasoa
t. From Bill Book.
Note faror R. J. Vincent, flue Aug. 1 2
" " 8. Fraser & Co., " Sept. 13
" " C. I. Lane " Aug. 15
" " S. Fraser & Co., " Sept. Ist
Present worth or net capital
Mj capital at oommeDCing business wac
Net gain rwJieed July Slst
80
2995
100
105
1188
0.
00
36
oe
00
93
4469
2S
80
318
167
105
120
180
210
00
00
04
00
00
00
08
1380
13089
13000
89
12
IS
00
U
124
CHANGING SIN-GM?. TO DOaBLB ENTRY.
to Doulh Entry,
PrEPARATORT STATEMlflT.
•o'^Ta^;r24.'"''' ''"°"'°" ^"'^ ^biW., «Ucen
< le.|| $
Btsourct$.
— LiabiixtitM.
BnJ!"p^^ Accounts Payable (already postod)
clJtS?.*''''' out8tanding,pr BilJ Lok ^
tapiUl at commencing business
Net gain realized in buMons
SOfOO! '
29953S
20500
1188
93i
565|04
HlolOH
3000 00||4380
4469|2«
1)
80 18
will lack Just the ai^ o'^'n^et'l^VsTietof ^^^^^^^
Opening ,a the j^edger an accountVii; nami J J^T""-?'
credit, my capita at commencin^r h,L^/ f' / ''"**''■ ^« »*«
ment of a Double Entry Ledger ^^'^^ *^' commence-
Merchandise, and Bills Payable Thl; nf- ' "' J^^^^'vabie,
Je" change'," and will 8eC%eA Se„Tv,rrr*%T '*''''" *^
iSft
I %c
O TO
3 "5
CO
fC
— -5
CQ
00
m
s
«»
tx
I
u-5
O
<»
O
0)
o
CQ
lO
€»
OC —
»
a
a
0)
c3
w
n
-1 K
— ^
t: ^
2 s
30 ~'
126
Ne
-HACTicAi, EXEncis.s I^^ si.r«x,.,, ei^thv.
'^"RTUit Isf, lJi7i r i> M I
' ai, n ouHl, as follows : to W uTi / l '* P'""* ^^^ '-M cents -4
^r^akle, 2 da^s' Work at 5ci. %' ' a *''^ ^^'''^ ^' ^'-Sf) to H
• ^ai,l them m part in Cash ft5^ D^r P'"' a"'"nr.ti„.r to »5'> o
■» '^ighte 10 by 16, a -25 ct s!^- ^'' p'" ^•'^"'^™«- '^''^ forG zi„'
per Hgxeement, $15.-15 Gar 'a J>'r'^"° '^ ^«'^«'«- ^ Coa h a^
Grand Trunk R. R. Co* for *H it* ^/i«H,*,^°- *» o'rder o, the
Paint at 25 cts — ■« t/ ^ f;"""''^- Rec'dca^h for 17 IK^ j.
at «f'*'?ii^L*««' "^ ^^-SO^Paiif H lilt '"'^ ^T ^ ^'>'^^^ ' '> ^'v
atfi.__ao. Rec'd cash of T R.. i^^V'^' ^ ca'-h, 6 days' \V',,rir
cte.-.Paid ca.h for Cair« of Shon S vJ ^!^ ^^'' ^^ite Paint u I
Glover, for Stained oC as ,' J „ '*''^' ^^ follows : '"V J
painting Church, $210.-l2S^ V*' *'"'*"f' i^^'^- ofC. HaniV,;,;
New Sash at Ma'nLact^ry t feV « ""^ ""'^"'^ *"•' ^i*' = for ,;! J
'6, *t 9 ct8. ; 1 -jy Liffi'o W^ agree.nent, to wit. 56 Li^l.t. ' |^?
110 Wioduw Frames, at 46 cts^fyLttn' P '"'"'"♦ ' '^ ■"'
' , lor fainting Reception Re
JonesGdays' Work, at,?l,
Walter, 5^ day.s' Work,
tor Pa in tine
'?P-,^ndry, 4 plays' Work
$j;j.iS*^,^ Cloth tress Coil
»t$1.50jioH.Te
t" H.
leakle, 5 days' Work, at .*l
at 75cta.~27. B
'o'tof L. S. l;
P-- J « ^"'" '^'■«*8 Coat, $16- ] PfliTni , r> ' ^- '^- ^-'gers,
1^ iw ounoiy Jobs, m i>er Rill, ir
127
per Bill, in
PlAOTtCAL KXRUCfWES IN SINGLE KNTRT.
OMh $22.fin._as. Paid ciVHh for I ft ^aN. Linflpp.! Oil, at $1,624.-
a». Reo'd ouch for Tin Sij^n, $10. Pai.l casJi for Tin and Jaf^nntng,
f4.26. — 30. Uur ly A fJulj owe riip for Painting i Hico. as per a^r*^
ment, $80.— Pai(l H. TcakiW, in i;a«h, f. .iays' Worlt, at *!.— 31.
r^id (or Kent of Shop one m«; "»b, Id oahIi, $16.67.
Balances of the Resources and Iilabilitles.
If .
! I
t«. .11
; I
y ,;
Resoiircu.
Caah, balanoe on hand
Stock oftoolii, as per In-
ventorjr-Book
Stock of paints, etc
H. Young
J. WilHon & Co.
Grand Trunk R. R. Co.
Citj Hall
Hardy dc Gait
1540
08
7.-)
00
65
50
1.3-1
l:i
•)
00
1
8
61
16
('0
70
00
911
31
Liahilitiea.
L. S. Rogers
J. O'Farrel)
W. G. McLean
Balance. — My net capital
16
3
140
159
751
.38
00
00
.38
9.3
91131
'^'huat
My net oapjtal, on Sept. let, i.•^ $7;-)!,
" " " at commencing husinc'88 was only 575,
93
00
My gains in bunnesa hare been
MEMORANDUM IL
$176.93
Sept. 1, 1871, I eomratnce businesp with the following re^
souroei: Cusb, $Bol..34; Mtrehaodiie, $5120; Bills Receivable,
$1386.60 ; E. S. Burronghs owes me. on %, $167.04; L. N. VeMon.
$120.98; T. A. Maguire, $96.40 ; C. N. Darid, ^1.64.-1 owe a/5
follows: On Notes, $350 ; to Poston dc Co., on ^IJ, .;>.:. J. 12; to Gar-
neau ARoy, $180.88.— Paid L. l^avis, forrepairson t i.' S( , 18.74.
—Sold C. N. David, on cr«lit, 2 bbls. Flour, at V.2o.-'Z. ;JoId L.
N. Veldon, on %, U gals, of Sperm Oil, at $1.60 ; and 50 lbs. Pow-
dered Sugar, at 10 ds. per pownd.- 3. Bo't of Poston A Co., on %,
8 boxes Havana Sugar, 3284 lbs., net wtight, at 74 cts.— Paid in cash,
'■;• a Set of Account Books, $20.50.-4. T. A. Maguire ha« paid me
\ \ 03 hi8 old aooonnt— Sold D. S. Raymond, on account, 60 lbs.
Cn; \ t •ucsur, at 10 «t«. ; and 100 lbs. Brown Havana Susar. at SJ
c*t.- ". i?o'< (ri'Garnftdu t Eoy, on % Goods amounting 10^*406.58.
I'Md l-m v:.iOO in ms'h —8. Bo't of W. C. Lord, for cash, Merchan-
dis..' ^aiViPting to$2k^* ...lU.— L. N, Veldon has paid me !?40 on %,
-^. C. d. Dftvid h'j Utn |>ainting in tb« store f* wvh kL $1.26, for
128
60
r.
at $l.62Jj|.~
1(1 Ja[«tining,
as per agre**
, al $1.-31,
itles.
16
3H
:i
00
140
00
159
38
pital
751
93
911
31
751.93
575.00
176.93
bllowing re-
Receivable,
, N. VeMon,
I.- -I owe as
12; koGar-
. !8.74.
Z. Oold L.
50 lbs. Pow
; Co., on %,
^aid in eaali,
hsM paid me
)unt, 60 Ibfl.
5u2ar. at 8J
to !i;406.58.
h, Merchan-
■ !?40 on %.
ut $1.26, for
"»v Note at '2 ,,. L r- a'"onntiri.' io ^•tflQ, ,''"''' '>f ^
eS atts;?®-""^?^'^ ^' ^' ^^fcn mi. 7u^^"'' ^«'- Clothing,
■uay, amountin,' (,, >;(J3
Note, dated
I vu.
■>a;o.
•{olj's Note, No.
2, ^Y:
on, I „i- " ^ •'• ^•^- liurroii,
li in
urrou^hj
^ft.'y^^^as.fss £r "^±-;."-;-i;^r
-as- T. A. Ala".
Note, on demand,
week amounted to
^590.;i2.
. , .^. *5lJ — ao n ""' ^""'^u "e ii*| pre-
I2d
-HO. Paid
■■*^^^^tej»saa
PRAOTICAL BXER0I8KR IN SINOLE EN'TIIT.
Popton & Co. $100 on account, in casli.— Paid my Clerk's salary for
the month, in cash, $60.~Cash Sales for the week", $338.96.— Having
taken an Inventory of the goods in the store, I find the amount to be
$5086.41. I have Nates ai^'ainst various persons, amtg. to $1 127.46.
I owe Not*8 amounting to !fir)14.36.
On September 30th, my Net Capital is $7528.73, and my Net Gain,
$!■;«. 73.
t s
MEMOFUNDUM III.
Oclober 1, 1871, W. S. Drum, Cabinet-Maker, ast-'ociateswitli
himsHf T. A. Graham ; — Drum transferring to the firm sucli portion
«>f his resources and liabilities as is mutually agreed upon, and Gra
ham investing tlieir equivalent in cash. The parties are to share
alike in gains and losses.
W. S, Drum invests in tl)o business, as follows: Cash, 100; Sun
dry Notes which he holds against other.s, per B.-B., $700; E. Miles'
balance of account, his ftvvor, 81I1.50; J. R. Nesbitt's balance of
account, liis favor, $74.80; Materials and Unfinished Work, as per
Inventory, $71:5; Stock of Furniture, as per Inventory, $420.86 ;
Stock of Tools, as per Inventory, !ji>302.40. W. S. Drum owes; viz.,
Sundry Notes, as per B.-fe., amtg. to $842 ; L. McTntvre & Co., bal.
01 acct., $1.34; N. Percy & Son, bal. ofacct., $150.40. T. A. Gra
baiu, invests inthe business, in cash, $1206. 16. — 2. Bo'ttorcash ofC.
Vallee, Planks, as per Bill, *i5I.2ti.— ». Sold K. Miles 2 Hair Clotlu
.Mahogany Sofas, at $20. Rec'd iVom the same on account, in cash)
$120.-4. Sold Mrs. C. Nelson, on acct. ; viz., 18 Mahogany Chairs,
Cane Seats, at $1.25 ; 12 Mahogany Ciiairs, Hair-Cloth Seats, at $3 ;
4 Cherry Dining-Tables, at $G ; 2 Maple French Bedsteads, at $4.25;
2 Maple Low-Post Bedsteads, at $2.75.-5. Sold P. McGee on acct.,
per wife, 2 doz. Windsor Chairs, at $12 ; 1 doz. Windsor Chairs, for
$15; 1 doz. Windsor Chairs, for $10; 2 Spring-Seat Black Walnut
Sofas, at $21.-0. Paid for Wages, per Tuny-Book, in cash, $15.—
8. Sold for cash, 2 Bureaux, Maliogany Veneered, at $22. Paid as
follows: A. Patry, for repairs ot Shop, in casli, $103 ; S. Jones, for
Painting Shop, in cash, $44; L. Mclntyre & Co., in full ofacct., in
cash, $134; lor Glazing 2 Lights of Glass, cash, 70 cts.— 9. Rec'd
•ash for B. Motley's Note, Drunrs favor, $250. — Bo't of N. Percy &
Son, Lumber, for $270. Gave in payment our Note at 30 days, in
full of all acct. — Sold E. Miles, per daughter, on acct., 2 Black Wal-
nut Footstools, at $1.50.— Sold C. T. Renaud, on acct., 6 Patent Pivot
Chairs for Otnce, at $5. — II. Sold for cash, 2 Arm-Chairs for Office,
$10. — Sold E. Miles, per wife, on acct., 2 Black Walnut Extensio.'i
Dining-Tables, at $40.— 1». Sold P. D. Flood, on acct., 4 Children's
Higli Dining-Chaire, Maliogany, at $2. — Sold Miss Anna Roy, on
acct.; viz., 6 doz. Windsor Chairs, at $11 ; 2 Rocking Chairs, Sec-
ond-Hand, at ^'J.— Paid cash for Wages, 87o.—l«5. Sold for cash 2
Pints of Varnish, $1. — E. Miles assumes P. McGee's account, trans^
ferred to him, for .$91.-10. Boudit of L. Mclntyre & Co., Paints,
Varnish, Brushes, etc., as ner Bill, anitg. to $350.52. Paid to them
eash, in part, $100,— 17. keceived |i)r Staining Cupboard, in cash,
130
T.
rk'fi salary for
8.9G.— Having
! amount to be
T. to? 1127.46.
inj Net Gain,
ist-'ociateswilU
I) sucli portion
pon, ami Gra
8 are to share
sh, 100; Sun
00; E. Miles'
tt'a balance of
Work, as per
ory, $420.8G ;
n\ owes ; viz.,
re (fe Co., bal.
. T. A. Gra
L for cash of C.
2 Hair Clotii,.
o>Mit, in cftshj
oguny Cliaira,
Seats, at $3 ;
ads, at $4.25;
jQee on acct.,
:or Ciiairs, for
Black Walnut
1 cash, $1"). —
^22. Paid aa
S. Jones, for
ill of acct., in
Ls.— 9. RecM
3f N. Percy &
at 30 clays, io
2 Black Wal-
I Patent Pivot
lirs for OtHce,
mt Extendion
, 4 Childrea's
Lnna Hoy, oa
Chairs, Sec-
j!d for cash 2
3Count, tranS"
■ Co., Paints,
aid to them
mrd, in cash,
HI>TS AS TO RESOUHOES AND LIABILITIES.
'•-h2 0,..oma,^, u$7-iJS,'F"f,f''''''--^' '' ^''■~^^- Sold S
■ •• • ' ^J"- ^''''' J*--- Miles, per aon, on account, 2 Hat-
, ... .lu, ^ nocKini' u lairs. at .«!I9. o a>
iJr.un's Nu.e. F. Walter's Lor 1%. P^^"^f"^ ^^^OO.-Pald cash for
'•■•OM. da.e, ,0 Dec. 0th an^um^^^to ^^ i'i'^P '^^ D''^^^""'
acct., ,n ca.h. *20.-Bo't of I l/h, ^3.-^.{. Pa.,1 W. S. Drum on
•*1 92.80.-24 Paid oZu o /i*. "=' ^" '>^'Cotinl, Lumber, ner Bill
^ct., 2 MahogaV Bureaux, Sit^hSIa^^f-a?*', ^^ ^VJ ""'^' ^»
Wap:e«, a, per Time-Book, S73.30 -20 ^j' -r^^', ^""^ <^^'' ^r
hogany Hccking Chair« I'i ,< ;. , ^•^'•' <«r cash ; Tiz., 4 Ma-
MapIeFrenchBtd8(eaT'a/^0 2 ''^^^ at$l2.o0; 2 Birds'-Eye
f 4; 2doz. Child's Hl'-hCliiV.^ ;;'=^^,^;."«t:?'^^'""^Chairs/a
Chairs at ^ps.-P.idoaahasf ho;,: for B^i/of ^^^^ ^"^'^'"^
to T. A. Graham, on acct. SJO- fnrR» Vr ^"^"'"gfJSl.go-
to Mis. Anna Uo;, onaoat iklZfT''^''^^''^^' .OOct^-Solj
P. D. Flood, oaLt.. TbILoI W:te'[r,„f;^7«»,^33.-.ao. Sdd
j^BuaRo/haa returned the Maho^av B^fl' . if' *^=^''^- Mis«
lastaBt, beoaitsa it wa- too large f^rLr^^^^^^ ^'^^ ^'^'h
The Stock of furniture on hand am't. r
;; ;; ;; ««.«„ .„a3atuS wS,'?.'- ''^'■- ',? «'^j-'-^»
tools, depreciated br use - ., '*^^-^'*
Tbe'«mount ofBilla Roc. in possession of thoH " 283. 'JO
Jiilia Payabla outataadiog m ., ^^^^-OO
' " 862.40
dlNTS AS TO RESOURCES AND LlABrLlTlMs.
;i«r::.:fs;;5;i^;j^.::^i^^;^;;- -- e.t.siveiy in ,,. .ea.
business has been forcibly 4t beS L f .''"° "rV" condition ol tTse
tliat certain Ledger Aocour k • i ! '^'l''"'^' ^^'^ ''^s been tau<'in
oUiers to show liabilhS and thai' u.e'co"" 'T'^^"' '''''' '''^^"
, ttnu tiut the correspondence between the
HINTS AS TO RBSOUROiSS AND LTABILITIIS.
repourceB and liabilltien thus shown must agree in a certain sense,
with the accounts phowinf» gains and losses. Any careful observer,
however, must be aware that all classes of resources are not equallv
valuable; and that,' in the course of trade, persons may become in-
debted to ue both on note and account who will never pay ; the re-
source thus represented bein^ absolutely valueless. In estimating the
condition of a concern, therefore, it is well to know whether the books
are truthful; that is whether the rt$ourcea exhibited on their pages
art' a'tisolute or fictitious. The liabilities are always presnmed to be
genuine.) The importance of this precaution will be apparent when
we consider that al gains in business, as shown by representative ac-
counts, are predicated upon the integrityof the resources. Forinstance,
suppose we sell A, $300 worth of Merchandise, and take hie note for
it. In recording the transaction, w« credit Merchandise, and debit
Bills Receivable. In estimating our gains and losses, we, of course
include among the proceeds of Merchandise this amount, which adds
$300 to our gains. Our Merchandise account is closed, and the result
finds its way into the Loss and Gain account, thus having an impor
tant bearing upon the apparent prosperity of the business. But sup-
pose this note should prove toorthleaa. It is now evident that the $300
credited to Merchandise account was not a legitimate product, and
that all gains predicated upon it are necessarily fictitious. But tliejo
are other resources represented in the Ledger, the exact value of which
is uncertain, — they may be worth their face, or half of it, or nothing.
How shall they be treated in a general exposition of aflUirs? Shouli],
we consider thein all valueless, and close them into Loss and Gain
the error may be a« great as to permit them to remain and represent
actual worth. The most approved method of diaposing of this class
of accounts, is to permit them to remain upon the Ledger, but to neu-
tralize their effect by opening an aooount showing fictitious liabilities
of the same account. Aa appropriate title for this account is ** Sus-
pense." When therefore doubtful resources exist on our Ledger, and
we do not wish to represent anything more than actual gains, the
process should be to debit Lose and Gain, and credit "Suspense"
with the amount of the doubtful resources. If any of these are after-
wards paid, or their value becomes tangible, it is very easy to restore
them by debiting Suspense and crediting lioss and Gain. This method
is far preferable to the more usual one of closing up all doubtful ac-
count into Suspense. The Suspense acc«unt in the latter case would
represent either a loss or a resource. If a loss the amount may as
well go at once to the Loss and Gain aooount; and if a resource, it
had much better remain under its own more appropriate title. But
the chief objection to this course would be the exhibitng ot accounts
as clo&ed, which are yet owing and may be paid. If Mr. A, forin-
stance, wliom we thus consider doubtful, ahould desire to see hie ao-
count i?i our Ledi^er, that he may pay it, it might be awkwaid to
iulbrm him that, iwving considered his account worthless we had
carried it into Loaa and Gain. He might not desire to change ov
estimate of the value of his iodebtedneee.
>ITRS.
a certain sense,
careftil observer,
9 are not equally
may become in-
<}er pay ; the re-
[n estimating the
hether the K)ok8
;d on their pagea
i presumed to be
B apparent when
epreeentative ac-
es. For instance,
take his note for
mdise, and debit
es, we, of course
lunt, which adds
d, and the resnll
laving an impor
inesH. But sup-
ent that the $3(iU
ate product, and
ious. Bat thei'c
:t value of whicli
of it, or nothing.
atfairs? Shoulfj,
I Loss and Gain
in and represent
?ing of this class
dger, but to neu-
titious liabilities
ccountis "Sus-
our Ledger, and
tual gains, the
lit "Suspense "
f these are after-
Y easy to restore
n. This method
I all doubtful ac-
atter case would
amount may as
if a resource, it
riate title. But
itng oi accounts
If Mr. A, forin-
tre to BM hie ao-
be awkward to
trthleas we bad
to Changs om