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I
FRAUDULENT OFFICIAL RECORDS OF GOVERNMENT.
SECOND SUPPLEMENT TO THE (!ORRESPONDEN(;E WITH THE LATE LORD FREDERICK
CAVENDISH, M. P.. PUBLISHED WITH THE CONSENT (^F THE RIOHT HON.
THE .MARQUIS OF HARTINOTON, M. R, SECJRETARY OF STATE, WAR
DEPARTMENT, JULY, ]88+.
AN EXPOSITION
OF thp: principles and methods employed in the fabrication
. OF certain
United States and Canadian
ANNUAL TRADE TABLES,
S^i'oin ISOT to 18S45,
TOGETHER WITH THE
MATHEMATICAL, FORMULAE
ox WIIK II THK FABRICATION IS BASED; AS DERIVED FROM
JAMES BERNOULLrs
BY
HENRY YOULE HIND, M. A.,
Brilhh Sciitilific WilnfSi at Ihf Halifax Fislitry Comti isioii, ami Official Compiler of tlu Analytical Indtx to
the Documents of the Commission.
( Formerly Professor of Chemistry and Geology in ihe University of Trinity College, Toronto. }
.olonistto the CANADIAN RED RIVER KXI'KDITION OK 1857.-111 charge of the CANADIAN ASSIN-
BOINE and S.VSKATCHEWAN EXPEDIIION of 1X58.- -Author of Narrative of the Canadian Expeditions
in iho North West, 1860. — Exijlorations in the INTERIOR of the LABRADOR PENINSULA, 1863.—
Oftitial Report on the (ieology of New Hrunswick, 1 865. -Official Reports on Waverley, 1869. — Sher-
brooke, 1870. — Mount Uniacke. Oklhani and Renfrew Ciold Districts of Nova Scotia, 1872, &c., &c.,
&c.— On the Fishing Grounds of the Northern Labrador, 1876.— Official Papers on— The effect
of the Fishery Clauses of the Treaty of Washington on the Fisheries and F'ishermen of
British North America; Parts I and II, 1877. — Recipient of Gold Medal and Diploina,
Pahs Exhibition, 1878, for Maps and Chans illustrating the Fisheries of British
North America and the movements of Fish in the Sea
I
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CONTENTS.
Lctler lo ihc HonDrnlilc the Sccrclaty uf Si;\ic', \V:i',liiri(;tiin
I^Hcr lo the Mcisl lliinnrahli: the Mnrqiii!i of I,nMscl.>«ni-. Covi'iniir ( iriural of (anncla •■
IM'RDDrc'TION.
A Brief llistury iil tlie lit'tnuiilli Talilc
The Interchnnijealili' ijuamilics in ihf Kerncnilli Talilc
The Imerchanijcalilc Kignrcsof iho I'niii-d •^i.iius ami Canadian U.-ciinls nf Imeriialional Trailr
The Tables I, li, 111 an.l IV
What ha'i Iwoinic uf ihe DiilieKr
The Maihemalical Kurmula
I be Collon anil Woollen " Inipons" and " Knlrics for Home Consunipiion" in Caninlian Trade TablcR groU|«ul in Ihe form <>f an
Kndlc^s Aritlinirtiral ''rogre«^^lll^
TAHI.l- r '
Kriini lames Hernoulli's Treatise iiK Aktk Tiimkii amu.
Iternuulli> 13th I'roperty.
8th
TAiii.i-: II.
Statrment No. I. -The forged f'anadian Iniiwrls from iSrty to 1.S7;.
Staiemrnt No. II. -The origin ■ f the " Fire-brick and Clay Series ;" so nanieJ from the .subsliiiilion of 11,184 i.ollais
worl 1 of '* Fire-brick and Clay" for Fish.
Statkme.nt No. III. Thi- ■• Kirc-lirick and Clay .Scries."
STArE>lRNr No. IV. — The items grouped, shoning that all ihe larger icnna are stims of the smalh-r lerrai.
Statf.mknt No. V. The " Fire-brick and flay Scries" in the form 0/ an indelinite .\rilhmetical I'rogression.
I'Ai;r.
V
vi
vH
vii
I
Statrment No.
Staiement Nn.
VI.
VII.
TAWLK III.
-Dr. F.dwaid Voung's I'nitcd Sales Ooniestic anil Foreign Fish F.\i'OKi> for the Fi-cl Vent 1.S72-J.
-I>r. FMward Voung's Kximrl Fi.sh Trade Figures arranged in the order of Mtgnilude.
Stclicii A'<i. /- Dr. Fdward ^'oung's li.sh Trade Figures in terms of the ' Fire-brick an.l Clay Series."
Stilion N0. 11 His Fidi Trade 1 igures grou|)ed, showing that the larger terms are sums of llie
.smaller terms.
Srilion Ko. Ill - His Fi^h Trade Figures further grmiped, in the form of an indefinite Arithmetical
Progression —F"irsi, with 10 asa I'oinmun Dillcrence : Second, wiih 100 as a Common Difference;
Third, with 1000 as a Common Difference. These Fish Trade Figures being reciprocally
inlerrhaiigeablr willi the Canadian *' Fire brick and Clay Series."
Statement No. VI U.
Staiemrni No.
IX.
lAH.'.F IV.
Pr. F:d«,iril Voung's I'niierl Slates l-'i»li and Fish i>il IMI'rtUTS Irom llrilish .Anieiica for the Fiscal
Vcar 1872-73.
Stdion No. / -.Showing that Dr. Fd«aid N'oung's United Stales Inipiirl Fish Figures from llrilish
America are maile up from sums of Dr. Fdward Voung's F..\l'OKT Fish Figures 10 Hrilisli
America.
SnUmi A'o. //. -Showing that Dr. FMward Voung's Cniicd States IMI'DKl Fish Figures from
liriiish .Auieiica are sums of the terms of the Canadian " Fire Iwirk and Clay Series."
-Dr. F'.dward Voung's llniled States KXl'OKTS of Fish, Shell Fish, Fish Ciil and I'roducis ol ihc Sea
lo British America for 1S73 74, with the Canadian reciprocal siaienieni of IMl'OUTS from
the United Stales, by J. Johnson, Canadian Commissioner of C'lisioms.
Stiiiim Afti. I. -Showing that the United Stales Fiwh Trade Figures are siiniii of the Canadian
Fish Trade Figures, and that Ixiih oi these are interchangeable with the " Fire-brick
and Clay Series," from 1807 to 1873.
CIIAI'TFK I.
Statkmrnt No. X.
The Canadian diflerc i lieiwecn " Im|wrts" and " I"ntries for Home Consumption," fi>r the year
1878, in respect of Coitons and Woollens —grouped.
Stclien /.—In the form of a continuous Arithmetical Progression »
SeditH //.—In terms ol the "Fire-brick and Clay' Series 3
Srclioti 111.— In TeriiLs of Dr. IMward Voung's Fish, Fish Oil, Shell Fish ami Protlucts of the Sm,
Unitol Slates Exports to liriiish America in 1873-73 3
The Bernoulli Table 4
The Relation between Bernoulli's Column IV, Dr. Edward Voung's Fish Trade Figures of 1872-73 and the Canadian " WHri
ences" for 1878 5
Section IV. — ]
Sectioh \i.~ Exhibiting the relation,! 5
Section VII. — j
An Important Properly of Bernoulli's Table ft
li
'MK<'i!Hi^<«. •
'/
ciiArrKk II.
rin. KlXOkli IIV I'KOVINCKS.
The Ucciiiil liy I'riiviiices as 'li>iiiii;iiislifil (mm tlic IWiinimipii Kcrtpnl year 1S78 .
TAiii,:-; A.
Com|inrisiin luMwcen llic sviins cif llic Diflt'ienccs .
I'Ar.t.
7-16
16
(IIAlTKk III.
The Krinlinn lielnffn Bernoulli'* {'nliimn IV. and tlie I Hflcrcnccs l>ei«cfn Coiion ami Wnullrn " Inipori.'." ami " H ilries fur
Home t'( tisviinption,'' for the year 1878, and !hc Malheinatical Kurnuda shewing; iheir itrif^iii.
The .Slims of ilif final I lillerenres lor Coiion'. and Woollens in Table A, in Icrms of Uornoulli's Column IV
ThK MaIHRMMH AI l''i)KMl'l.A •■;
IlluMrJIion of ihe fniiid Smie> Fi.sh Trade Figures in delail, »ilh Dcnuminaiions in ihe form of the larger (|uantilies being sums
of ihc Mnallcr ipmnlilies
17-18
18
CIIAI'TKK IV.
THE CAN.\D1.*N TRAljE TAUl.KS OK 1883.
Provincial and I )oniiniitn IJifTerenires
Comparison lieiween ihe Sums of (lie Differences .
TAIil.K li, 1883.
a3
CIIAI'TKK V.
The I'
The F
The V
Talile
Tahle
Tahic
THE CANADIAN IKADE TABLE.S OF 1885.
'tovinCial and iMininion I)itTcrences for Cottons and Woollens 2$
irst Order of I hHcrencc.s for Coitons in 'he (onn of an Arithmetical Progression,—
1st — with 10 as a conui.on dilTerence 37
2d— .. 100 .. .• '8
3d •• l"X) . II ; • ^ •■ ^^
iist Order rjf OitTerences for W\«>Ilens in the form e>f an Arithmetical Pr.Tgression with 100 as a Common Difference 39
sliowinj; that the larger terms of the Firs: Order of Differences for Woollens are sums of the smaller terms .30
showing that the larger terms of the First Order of DilTerence^ for (Jottons are sums of thf- smaller terms . 3*
showing that the 1-irsl Ordrr of DifVetcnces lor Cottons ate the equivalents of the terms ofthe " Kiredirick and Clay" Series 32
taulf; c .
Coiuparini'ii lieiween the Sums of the I lilierences
32
CHAPTFK VI.
The Monderful accuracy ofthe Figures in Ihc United States and Canadian Trade Tallies . 33
The alleged Custom House Finlries for the year 1878, 1883 and 18S5. in the form of an endless Arithmetical Progression 33
The Kipiit^leiit Canadian Dill'eiences tor 1878, 1S83, and 1S85, i.i terms of Dr. Kilwnrd Young's Fish Trade F'igures, taken from
the United Slates lommerce and Navigation Keport lor 1873 36-37
The Fire lirirk and Clay Series in Terms of Bernoulli's Columns, Nos. Ill and IV 38
A Mathematical 1-ormuia lot obtaining any desirable Ratio between two Series 39
A general Mathematical F'xprcssion for the terms of .any one of ihe vertical columns in liernonlli's Table . ...' . 39
A .\Iathemaiical Process lot cuiivertiug Ikrnoulli's Formula into the " DiflerenlinI Method" of expressing the Sum of a Scries 40
A SlAIHMKNT AMI CoNCI.L'sroV 4I
EliH-A-TA..
Table I. In the Formula lor l!erii,.ulirs Sib Pr.rperty insknd of 2'' read j"-' .
Page 4.— Second line friuii b tlom. lor t liapter II read Chapter III.
I. 5.— 15 hues from liotlom after the words "of DilVerenrcs " insert ** with their signs
" 7. — IJ lines from top, for "al ihc end of ibis Chapter" iea<l "in Chapter III.'
" 18. In Section III for 16 read 10.
" IS. - 7 lines Ironi lnuiom omit. . .".\ + "
" 28. -27 lines from bottom, for IS75 read 1SS5.
diangcd."
T
""•^^mmmf
I KTl KR lO rill, SI.CRKrAKV 01' srATK, WASHINGTON.
To I'HK HONOLKAIILK
T/if Stfri-tiiry of St.Uc. Wasliiiixli'H ■
SlR,--
No pcrifxl ran be more favourable tlinn the present for me to furnish the niathenialiral exposition of the fallacy
which iinilcrlies disc iissicms in the l.ei^islatiire, or in pul)h( ioiirnals, Iwseci on certain nftiii.il n-rords. and relating
to tilt coiiimeicial intercourse hetween the United States ;ind ('anada.
The continuance of the secret dceptions in public Records which give rise to this fallacy, renders the attainment
of just legislation (;overninK the intercourse between neighbouring peoples, absolutely hopeless, besides endangering
good neighbourhood.
But when these deceptions ( learly disregaril the doctrine which lies at the bane of modern civilization, that all men
are equal belon; the law, they give unequal power to those who protit and to those who lose by them.
The exposition embodied in the following pages possesses an unusual feature. It rests upon a mathematical
foundation, and therefore cannot be ( onfutcd. The conclusions drawn Irom the fabricated figures may vary, but that the
figures are fabricated is incontestible.
It is needless to say that the subtle c harac ter of the process, the dil'tieulty up to the present lime of furnishing
absolute proof of its use in Records of (iovernment, the frequent (hanging of (iovernmcnts and heads of Departments,
have rendered it in the highest degree improbable that the heads of I )epartments were ever properly informed ot the
device, if, in some instances, informed at all.
James Bernoulli's works are written in Uitin, and are scarcely ever referred to. The " Francis Maseres '
translation ( i ) is a rare book, and not likely to be consulted except bv those who, like myself, have been officially placed
on a track which, if honestly and unremittingly pursued, promised to lead le discoveries useful to mankind.
Perhaps the best practical illustration I can offer of the hopelcssne.is of arriving at just legislative action respecting
reciprocal trade in any form between the United States and Canada, is to be found in the "Vikws of the MlNORirv,"
submitted by the lion. Mr. Rict on June 7, 1880, from the ('ommittee on I-'oreign Affairs, i:oiic.erning a "Reciprocity
Treaty between the United States and the British Provinces."
Seven pages of that Rei)ort are occupied by Official Statements, purporting to show the value of trade in different
commodities between the United States and Canada, from the year 1854 to the year 1879.
The following pages, substantiating prior communications, ivrove incontestibly that large portions of the alleged
official Records of Trade of both countries for the years specified and for the articles named, are in reality nothing more
than the sums of selected co efficients of the successive expansions of the iiinomial ( 1 i 1 ) to the power of n, where n is
ecpial to 1, 2, .V 4i 5. ''. 7. 8, iVc, to any number of terms. Thev prove also that the figures of the Records of the
Ciovernments of two ilifTerent nations are interchangeable.
I'urther examination, fortified by other communications, 'will display much greater deviations from correct repre-
sentation than are given in the following pages, besides disclosing the fact that as far as Canada is concerned these
misrepresentations continue up to the present time. I'urther examination will also expose to view a system of secret
misrepresentation, based on niatliem.itical forf^inl.e, unexampled in history, and dangerous to the mutual goodwill of
nc ghbouring peoples.
Permit me respei ll"ully to point out lo you, Sir. that I »r. ICdward Young, recently appointed United States Consul
at Windsor, Nova S<-otia, and carrying on the duties of his office within view of where 1 now write, is tamiliar with the
secret process by which he has grievously burdened the Record of the Industry of the people of the United States for
many years, when .acting as Chief of the Bureau of Statistics of the United States.
Dr. Edward Young is familiar with the subtle process by which he and his colleague, the Can.idian Commissioner
of Customs, J. Johnson, so cunningly fabricated the Canadian Records of Trade with the United States and Clre.at
Britain for the year 1H78, that, as shown on page 5 of this book, the differences between Dr. Kdward Young's United
States Official Fish Trade Figures for 1S72-73 and the Bernoulli Series, 1 70 years old, give the Canadian diflerences
between "Imports" and "Kntties for Home Consumption" for Cotton and Woollen Coods in the year 1878.
Dr. Edward Young knows the secret I have discovered, and which I now disclose in the interest of nations.
He knows the secret by means of which Mr. Commissioner Johnson has moulded the Records of Trade between
Canada and the United States, and Canada andOreat Britain, in the Latest issue of Canadian Trade Tables.
(|.> I. A translation nf the three first Chapter-, (if tho seotiid part, or H.ioli, of Mr. j.imes Heriioiilli's excellent Treatise inlitlcil
AkS CONJECTANDI,
or
" TMr AVT OF F.iRMISC I'tlOKSBLB ('oX;i^iTl'miS l\l\( tiUMNti EVKNTS THAT DtlrBNtl ON CtlAS"CH."
Publiihcd in a small t^uart.i Volume ill Uasil. or Da^lo, in Switierland, in the year 1713.
II. The l>,Kirine of I'eriiiiltalions, and Conibinatiuns, hcina an essential and fundamental iXlrt ot the IKK fHlNK t»K ChaniRs; ii.s it is ildivered hy Mr. James
Bernoulli, in hii. exiellent Treatise on the Ooctrine of Chances, intitlcii *' An Conjectnniii," luid liy tho cclchrat.-d l»r. John Wallis, of Oxf.>rd. in a ITact intllled frtini
lh« Subject, and publiKhed at the end of hii J'realise on Alijebra : In the former of which '1 racu is contained A Uem jn&lratiun of Sir Isaac N«wlon"s famous lllnol.iiial..
Theorem in the cases .>f Inte^'ral Powers, and of the Keciptucai^ of liUfgrat I'oweri,
together with
Some other useful Maihematirul J lacts.
Pnhlishe.} l.y Kran< is Maseres, Ksq..
Cursitor Baron of the Court of Exchequer,
l.ondon, 1795.
JiflgCl?'
ffJiBWWBB ^w^raeis
This secret must also bo known to a ffw United States nnd f .maili.in suhordinato officials. It is a power which
a few individuals ounlit not to [losscss unknown tn ihc general |ml)lic. who liavi- sutferfd, or do suffer, or may sulTcr,
from its palpable abuse, as exhibited in these pages.
Without liirthcr reference to the fundamental doctrine amoni; freemen, that all men are ecjual before the law, and
the indisputable claims of justice and comity, may I very rcspei ifully entreat, in the interests of good neighbourhood
between two kindred peoples, bound lojiethir by many a lie, such a just and open examination ijito this matter, that
the well'.ire ot' Slates and I'rovinces, of t lasses and Communities, shall no lonj^er be subject to a secret process
of wrong-doing known to very few individuals, but deeply afl'ectini; the bust uiterests of both nations, and at present
conlinuing in imdisturbed stturily.
I have the honour to be,
Vour obedient servant.
HKNKV VOn.K HIND, .\I. A.,
Officiitt Compiler ,</ the Analyticai /mitx to tht Dvtununls of th< tliiUjax Fuliencs Commission,
VViNDSoK, Nova Scoiia, Dec. lUth, iS.S(>.
l.l-ri'ER TO THli GOVKRNORC.ENERAl,. CANADA.
To THE Most rioNOl'MABt-K IHK. .MaRQUIS OF l.ANSlJOWNI.:,
Goifinor Central of Canada
My Lord, —
The discovery by me of the mathematical proof of the fabiicated construction of the Canadian Trade Tables
temoves the last objection which can be urged against public inciuiry into the whole matte
It may be argued that as long as I failed to exhibit proof if artifi( ial construction, based upon mathematical
formula;, it was luting that you should continue to receive the Annual Trade Tables from the Minister, just as the
Minister continued to receive them t'rom the Commissioner of C'ustoms.
The- Minister says : —
" The undersigned has the honour to present to your Excellency the I'ables of Trade and Navigation of the
Dominion of Canada, for the fiscal year ended ,^oth June, 1885, .as prepared from Olficial Returns and laid before him
by the Cominissioner of Customs."
I have now the honour to submit to vour ICxcellency the mathematical proof that these same tables, togahcr with
those of many prior years, have been secretly manufactured by means of a mathematical fornuila, which converts them,
in resiK'ct of the Eish Trade with the United States and in respect ol the Differences between "Imports" and
"Entries for Home Consumption," into the ecpiivaleiits of the sums of selected co effii ients of the successive exjiansions
of (i + t) to the power of n.
Vour Excellency is aware, from numerous acknowledged < omnlunications addressed by me to your predecessor
and yourself, that this subject has occupied my attention for many ye.-us, as an outcome of official work, and that
I h.ive not failed in my duty in bringing it under your special notice, and assigning proper motives for the ,ut.
It is with a certain feeling of regret that I am ikjw able to furnish your Excellency with the Formul.'C which jirove
the deceptions and make it ini|)Ossible for the matter to be any longer evaded. I have always had before me the
interests of millions of unsuspecting and loyal people, the well-being and good-neighbourhood of contiguous States,
and the claims of honest dealing, which together outweigh all other considerations.
I have the honour to be,
Vour Ex( ('Henry's obedient servant,
HENRY YOUI.E MIND. M. A.,
Official Compiler of the Analytical Index to the Documents of the Halifax Fisheries Commission.
WiNDDOR, Nova Scotia, Dec i6th, 1886.
■■.-rTtST-'-rE-
vM
INTRODUCTION.
A Hmif HisioKV OK iHE Bkrnoui.i.i Table.
J.1IIH.S liirnoiilli was a Swiss hy t)irili. lie was txirii at Basel in 1654. In 16S7 he was appointed Professor of
Mathcmatirs in the University ot Hasol. He was an exeelleni dassieal scholar, am] thoroughly ronvcrsant with the
Krench ami (lernian languages. As a tnalhematitian ''he is well deserving of a place by the side of Newton and
Leibnitz" (I'^n. Brit., 9th Kd.) His mathemaiifal works are -
1. JatoH /itrnoiilli /liisilunsis Ofifia,i.\ent:\\c, 1 744, i tf>ni. 4'° : —
2. Ars Conjtctandi, opus poitltumum : aaeiiunl tnutalii<: df Seriehus Infimlis, H t^stola (Galliee scripft) de Ludo
Pilu Reticularh, Basilix- 17 13, i toiii. 4'".
" Like another Ardiimedes, he requested that, as a monument of his labours and an emblem of his hope of a
resurrection, the loj;irilhmic spiral should be engraven on his tombstone, with these words—
KAPEM MLTAIA RHSUKdO.
Nearly one hundred years since a portion of Bernoulli's Treatise, Ars CoNjEciANnr, was published in English hy
Francis Maseres Ksq., Cursitor Baron of the Court of Kxchequer. The part published related to the properties of the
Table which is designated 'I'able I in this Kxposition of the structure of the Canadian and United States Records of
the Industry of the people, for the years named and the articles of trade specified.
The .iinomial Pheoicm in Its application to all powers, positive, negative, integriil and fractional, was discovered by
Sir Isaac Newton about the year 1665, but 111 this extended form the jjroof does not appear to have been published until
1685. Mr. Henry Briggs, the computor of the Logarithms bearing his name, used this theorem with respect to the
jKJsitive powers of (a+b)" and jjublished it in his Arithmetka Ltixdrit/imua in 1624.
I'rior to the year 16S5 Dr. John U'allis, I'rofessor ot (leometry in the University of Oxford, published an " Arith-
metick of Infinites," in which is a very curious table, possessing in some particulars properties similar to the Bernoulli
Table. When the series in this table are read in a sloping direction they are found to be the co-efficients of the succes-
sive expansions of the binomial ( 1 + 1 ) to the [lower of n.
This table was reproduced in 16S5 in u published " Discourse of Combinations, Alternations and Aliquot Parts," by
Dr. John Wallis.
In describing his Table Bernoulli s.iys : —
" Habet hicc tabula proprietates plane eximias et admirandas ; prteterquam enim qu6d Combinationum mysterium
" in illft latere jam o.steiidinius, notuni est interioris geometri.i; peritis, prtecipua etiani to'ius rcliqua; matheseos arcana
" inibi delitescere."
The NlASKRhs translation is as follows : "I'he pro|ierties of the numbers exhibited in the foregoing table are
truly curious and surprising, for it not only contains in it (as we have seen in the foregoing pages) the clue to the
mysterious doctrine of combinations, but it is also the ground, or foundation, of most of the imiiortant and abstruse
discoveiies that have been made in the other branches of the mathematics, as is well known to those persons who are
skilled in the higher parts of geometry."
TnK In iKRCiiANoKAiiii-; Propkrtiks ok thk (JiANriTii:s in ihk BERNOUiit Table.
The leading property of the (|uanlities in the Bernoulli Table is their interchangeable character.
.Ml the ipiantilies present in the Table can be put in the form of other quantities also present in the Table, and
these again in the form of other ((uantities present, and these again in the lorm of others, and so on down to the
natural figures.
This is the leading property of the Canadian and United States Records of Trade submitted and ftnaly^ed in the
following pages. Their praclUal identity, as far as properties are concerned, with the Bernoulli Series is shown, and
consetpiently their fabricated < haracter proved.
In order to present the relations between the official United States and Canadian interchangeable figures
purporting to represent 'Tr.id; Records, I have carried out Bernoulli's 'Table to 60 terms, in other words I have
construe ted a 'Table of the sums of the coefficients of the expansion of the Binomial (i+i) from the power of unity
to the power of 6a
On page 5 the successive coefficients of the expansion of(i + i;iVom unity to the power of 48 are given with respect
to the 4th term of e.ich successive expansion -thus forming column I\'. of the Bernoulli fable I. The intercalated
figures 6, 171 and 969 are |)rinted in italics.
Any person can form this table without knowing even the first principles of algebra.
Each succeeding number is formed by adding together the number above it and the next horizontal number to the
left, lor instance 6188 being the 18th term of the \lth column, is equal to the sums of 4368 and 1830. The
quantity 14,310 being the i8th term in tiie !.\tli column, is equal to 12,870+11,440, and so on in every ca.sc.
.Among the many important properties of this table the following may be enumerated : —
The quantity 24,310 is equal to the sum of the Series above 11,440, being the figures covered by the movement
of a Castle in chess to the extremity of the board The quantity 24,310 is also equal to the Series above it, viz.,
12,870 and the sloping column to the left, or the figures covered by the movement of the Bishop in chess, always to
left and to the extremity of the board, or to c oluum I.
This equivalency holds good for e.ach and all the quantities in the 'I'able.
Tlte,'i*ifl3
'
Agnin, lakinR for an cx.inipli' any (iiianlity. 37. ij*. being tin- sotli icrni (if ('nhiiiwi \'n. This iiiianlity is also
found to occupy tht place of ihr joih term in Column XIV. It ran, thircfore, be represented by the following series :
J7,i3i =■ i8,5(>4 ■¥■ 8,568
= 8,568 + 18,564
27,133 is equal to the sum of the following series :
I
6
ai
n»
•4M
I
•3
9'
455
1820
6188
18564
J7.'3'
43«S
6188
8568
»7.>3»
It follows from these pro|)crlies, that if any one of the 20 horizontal columns be moved one s(|uare to the left, the
figures in e.ii:h s juare are the sum of the entire series above it. I'his holds j;ood fur any niiinlier of vertical and
horizontal columns, 20, 40, 100 or 1000.
It will be observed that every one of the ijuantities given in the above series is also the sum of a scries preceding it
For instance the quantity —
8568 is the sum of the series in Column V, beginning at 2j8o
6188 " " 1820
4368 •* " 1365
3003 U U ,QQ,
And so on to the top of the column.
And this character holds Kood for each and all the figures in liei.. ulli's Table. E.ich and all after unity are
sums of precedmg series of linures given in the table. Hence the applicability of Hernoulli's legend, the conception of
which he derived from the Logarithmic .Spiral and applied to himself—
IvADKM MUTATA RKSIJROO.
If figures i . .tny square be selected, such as 19,448, being in the 18th horizontal and Vlllth verticil column, then
the sum of the figures covered by continuous movement one square to the left and one square upwaids, always to
the left and to the extremity of the Hoard, will be e(jual to the ((uantity in the second sepiare below the square from
which the start was made — less unity. Hut if the square oci:u;)ied by the figures denoting the number of the
horizontal column be occupied by cyphers and one step more be made the sum will be equal.
Example. .Startinj; from 19,448, being the 18th term in the Vlllth column, the .Series is—
19,448 6.188
12,376 2,380 1
8,ooS 1,820
4,368 . 5O0
3.°03 411, ■
1.36'; *•§:■
1. 00 1 j),!-
286 13
78 I
66 I
II 11,628 the 20th term column VI.
I
So>387
The aoth 'erm in the V'lIIth column is 50,388.
Numerous other pro|)erties are pointed out by Bernoulli, and mathematically proved. .Mso m l-'rancis Ma.seres
translation many curious features are noticed and subjected to mathematical analy.ses.
At the close of Chapter VI, I have introduced a formula which brings Hernnulli's formula and Table within the
range of any one familiar with the elements of algebra. But it is the Interchangeable property possessed by the
quantities which gives them jiresent importance.
The following Formula is derived from Hernoulli's 1 2th Property. It develops some remarkable relations, and
is especially Uicful for obtaining any desirable ratio or approximation to that ratio in the form of two series of
numbers —
The application of the letters is given in Table I.
s
1 X n
Therefore S X a = I X n
And S : n = I : a
• .' ix
which, heing interpreted, is: The sum of the Scries Is to the niiinhor of terms in titc Scries, including cypher", a«
the last term of the Scries is to the nmnbtT of the vtrtic al roliiinn.
The otiicr proportions arc sflltvidcnt, ami whrn two Scries arc taken the n|)plication of these projxirtions comes
prominently into view.
The lNTKKrlIAN(iK.Ahl K rKOI'F.RriK.S OF Al.l. IHI' I'lMlll-s IN IMK L'NITKI) STA IKS AND OaNAIHAN RKCORPS OF
Tkaiif. roK AkTici.KS and vkars si'kcikiici) in llIK K0I.tOW|N<; l>A(;^^.
It appears from an analysis of licrnonlli's 'I'ahlc that its leading fchtlireis are the intcn hamjjvnblc properties of
the (juantities or co effi< ients produced hy the expansion of ihe liinomial ( i + i ) to the power of n.
These ake the leading KEAruKKs ok the (Canadian and United Siates khohds ok Iniehn ationai Thade,
to which reference is made in Ihe following pages. I'liey jnintlv cover the ve;irM frnui 1867 to |8H^.
The f'ANAiUAN I'isM Iuahe Rkiokds kkom i«07 10 1H73.
If therc.ider will turn to Table II he will find that the alleged representation of ('onadian Kish Trade with the
United Stales from |H(>^ to 187,5, is, in reality, nothing more than an artificial series of figures possessing the properties
belonging 10 the figures in Hernoulli's Tahlc. The most impoitanl property is that ihe difiVrences between tlie agrc
gates given, when dissecteil and traced to the original denominational figures in ihc annual trade returns, (01 m, when
properly grou|)ed, an indefinite Arithmetical I'rogrrssion.
When fiirther analyzed, these original dcinjiiiinational figures are tound to lie nothing nioie than the sums of the
terms of Hernoulli's Column No. Ill, as shown in Cliapter \l.
These original denominational figures are also found to possess the property of Ihe figures in liernoulli's Tables
"hii h enables all the larger (pianlilies to be put in terms of the smaller (luantities. In other words the larger (juantitie,
unis of the smaller (piamities, as in Hernoulli's Table. It is to bo remcmbereil that all the figuies possessing these
properties in common with those of liernoulli's I'abli! are denominational cpiantities, and are su(>posed to represent
Custom House imports, on w'hich duty is paid, fir Custom House exjiorts to the I'nited States, Canada, or other
countries.
The title of this Table is : —
Table II- "To illustrate the Principle and leading Properties of Rcrnoulli's Tables as reproduc .d and applied in the
Manufacture of Canadian Annual Trade and Navigation Tables, signed H. S. M. liouchette. Commissioner of
Customs, and J. Johnson, Commissioner of Customs ; also as reproduced and applied in United States Annual
Commerce and Navigation 'i'ables. Signed, — Edward Young, Chief of Piireau.
Referring to 'I able III., we find that the United States Records of I'rade, under the siiiiervision of Dr. Kdward
Young, also consist of figures having like properties, and, as shown in Table IV., they are interchangeable with
Canadian official figures.
The United States Records of Trade with Canada in Fish, Kish Oils, Shell Fish and Products of the Sea, for the
year 1872 3, are specially introduced lo exhibit their artificial character and their relation to Canadian figures. It is
important 10 note how accurately these figures fiillow properties of the Hernoulli .Series, of one of which they arc
the ecpiivalents to a certain number of terms, the form being alone changed.
A careful inspection of 'Table III. will suffice to satisfy any one respecting their artificial ch;vracter.
The title of T.ible III. is:
Dr. Edward Young's Official Figures of United States Fish, Fisli Oil, and Products of the Sea Exports to British
America in 1H72 -3, grouped. /•irsZ-ln terms of the Canadian "Fire-brick and Clay" Series. Saotid — In
tabular form, showing that his larger quantities are successively and continuously sums of his smaller quanti-
ties. Third In the lorm of an Arithmetical Progression, identical with the .Arithmetical Progression of the
terms of the " Fire brick and CI .y" Scries, The whole being properties belonging to the Bernoulli Series,
obtained by the expansion of { 1 + 1 ) or ( 1 - i ) to the power of n, arranged in the form of the Bernoulli , 'Table.
In Table IV., the United States Imports troin Canada are given and an.alyzed with like results. Their inter-
changeable relations with Canadian Official 'Tr.ide Figures are well represented. In fact it may be said that both
United States and Canadian details of Trade there represented are nothing nuire than the visible result ot mutual
agreement between Dr. Edward Young and Mr. Commissioner liouchette, and do not represent the Trade or industry
of two nations. It is important to note that the greater portion of these Imports are dutiable, and the record of duties
being a [)ercenlage on these fabricated figures, that record is necessarily fabricated. 'The ciuestion arises, what has
become of the duties ? How is it possible that duties received from scores of Custom Houses can form an arithmecical
progression, and be put in terms of Bernoulli's 'Table?
This question derives larger importance from the proved fact that the 'Trade Records of a vast number of other
dutiable articles are subsequently recorded in such forin that they also can be put in terms of an arithmetical progression,
or proved to be interchangeable with figures in years far apart, extending tq.theyear 1885. They can also be put in
the equivalent forms of terms of Bernoulli's Table. . " '
The title of Table IV is.— • ■ .
Dr. Edward Young's official Figures of United States Fish and Fish Oil Imports from British America in l87^-73;
also, his official Figures of United States Exports of Fish, Fish Oil and Products of the Sea to British America
in 1873-74. Showing, /"/«/.• -That his dutiable Import Figures of 1872-73 are nothing more than sums of his
Ex|)ort Figures. Second —Thai his dutiable Import I'igures of 1872-73 are nothing more than sums of the
terms of the Canadian "Fire-brick and Clay" Series. 7%»rrf.— That his Export Figures of 1873-74 are
■vv
noiliiii- mure than sums of llic Can.i.lia,' (liitlahlo ami Vn-c I'ish ami l-isli Oil 'in|M)iis from the United States;
also llial llicy arc sums of the tirms of i.'ii- ran.icli..ii " Kirchrlck ami Clay " Scriis. Fourth: Ihat all the
l-inures arc iiitcrihanjiiMl.lL- ami icrivx-il (as siilisciiurnlly provcct in ciclail) from licrmmlli's Column No. UI.
anil llcrnouli.'s C()lim\n No. IV carriod out to \C tfrms.
WiiAP riAs iiKco.Mi. or niK Drnts.^
Wli.U has lnMome of the duties? and Ahat is the nature of the artual Trade which has taken place betwren
Caii.ida .ind ih.- I'nited State' in respect of I'rodiuts of the Sea, as cnmiiared with the artifii ial Record ol Mr.
Kou(hcitc, .\lr. Johnson and Dr. Young.'' These questions are of overwh|;lniing imporiancc at the present tune.
There can he no doubt whatever that the United States Records of Covernmeni m relation to this Trade with
Canada h.ive been jjriatly falsifietl, and there (an be no doidit that the Caii.idiaii Records of Trade with the United
States ha'.e also been greatly falsilied. The (igmes pur|Kirtir.g to rcoord this Trade are malhemalii ally related -a thing
im|)(issible in the ordinary course of Trade. 'I'lie i|Uesii,)n of Duties is, beyond .ill others, .i (lueslioti ol vital interest to
both nations. The iiuestion of the l''isheries is another s'.ibjctt of great importame. Hut these are overshadowed by
one of still greater moment to Canadi.ins, which is involved i;i the proved statement, that .\Ik. CommissioNKR John-
son COSriS't'liS THK S^MK I'KACTICKS IP lO TIIK PKK'iENr llMK.
The Chapters which suet eed the Tables prove beyond (piestion that in other branches of Trade between Canada
and the United Stales, and Canada and fireat Uritain, the s.ime method of fabrii:ation has been pursued up to the
last issue of Canadian Trade and Navigation 'Tables in the year of Crace iS«6. /Date of the letter, Dec. 22nd, 1885.)
Cha|i! proves that the Canadian Trade Tables of iS;S were fabricated, with respect to Coltons and Woollens,
according t • method «hi. h had been pursued foi so m.iny years with respect to 'Trade with the L nited Slates in the
Products ol ilic Sea.
In Chapter I, it is proved that the dilTerenc es between "Imporls" and " iMitries tor Home (.Consumption, 'with
respect to Canadian Trade in Cottons and Woollens with the United Stales and (ireat Hriiain are, like the lish Trade
Figures, capable of being |)Ut — •
First: Into the form of an .■\rithmetii:al Progression.
Second: — In terms of the " h'lrebrick and Clay" Series.
Third:— \n terms of Dr. Kdwatd \i)migs United States Tisb, Shell I'ish. lish Oil and Tioducts of the
Sea 1-Ap.)r!s to I'rillsli .\merica in 1.S72 _v
Fnirt/i : In terms of the Differences between Uernoulli Column No. 1\'. to .pS terms, and Dr I'.dward
Youngs I'ish Trade fr^ures before specified. (See page 5 ol this book.)
The Table on pa^e 5 is a startling lei-nrd. Subtract Dr. Kdward Young's United States Fi.sh Tr.ide ligures
of 1,^(72 7,i from James liernoiilli's Column IV'. to 48 terns 1 70 years old —and you get the Differences between
Can.iiiian 'Imports'' and " Kntries for Home Consumpiion " for Cottons and Woollens in the year 1.S78. Wh.at
a tale of deiepiion this Record unfolds ! V it has been the motive underlying it and Mistaimng it ? The duties are
levied on " I'-nlries f )r rinine Consumptioi .uul these Kntrie.; are all forged. 'The Industry of a nation is misreiire-
sentcd, and the Records of Trade with two ii.itions fabricated. Tor what purpose?
In ('hapter II. the method of obtaining the proof of the faOrications with respei I lo I'rovinies is fiillv outlined.
Kach imported article is stated as given in the Trade Tables. 'The lirst order of Differences shows the visible magnitude
of the deiepiion, and the degree to which eai ii Province has been misre|iresenled in two i lasses of goods only. The
accuracy of the Ki^jures is surprising, and ih.it al< ne is sutiieient lo establish inleientially. a so-called "cooking"
of ai co:int.s. \',\n when attention is given to Cha|)ler III., the buret is exposed to view.
'The title .if this Chapter is:
The Relation between I'.ernoidlis Column No. I\'., and the Details of the DifTjrences between Cotton and Woollen
"Imports " and "Kntries lor Home Consumption '' ligures in the year 1878, and the Mathematii.il I'ormula
showing tneir Origin. . ^ ■
Here let me again cnll atteillion to tin; great Difference between Provincial and Dominion Difl'erer.i es. For the
sake of brevity, the Dominion Differei.ces have .done been presented in an analvtical lorm. On page 17 the
Discriminating Differem es lor llie Dominion are alone given. 'The Discriminating DilVerem es for Provinces are much
greater : for Co'o.ns more *:ian double, ,is may be seen liy re;''.re!i-'e to 'lable \ on page 16.
The |X)sitive .ind negative signs of the Diflerences are ailiniportant. ' 'hange the signs and the lepresentation
of the value uf the Trade < hanges with them. .\ reconl 01 liitics in excess econies a record it duties in defect and
the entire record 01 Traile is reversed.
-Ml of these i|uaiitities represenliiv; Dominion dis rimiii.i
terms of Bernoulli's Column No. 1\'.
Dillerences are represented on p.c-es 17 and 18 in
sur])rising representation of Canadi.iii Tiade in
'The Mailiem.itical I'ormul.i which unites ihein all, foll(nv> thi
Cottons and Woollens with the United States and (ireat Hritain.
This formul.i may be thus indicated ; —
Any term .\ is rei)resented by the expres))ion ,
a(r.+ 0(a+2)(a+3) to... ; a+ (n - j) ;■
1, 2, 3, 4, 5, 6, 7 8, to (D— I)
where a is equal to the number of the column in Hernoullis Table, and n is equal lo the imiulier ol terms in l!ie column
inctudin;^ cyphers. 'The general lormula for die entire series is given in Chapter VI.
The illustration of Dr. Kdward Young's Fish Trade figures, presented on page 20, is merely putting, with their
denominations, a few of the h^ures properly grouped, so as 10 exhibit to the eye the real niiure ol their > haracte: .Ml
of the United .States and Canadian denomin.itional ligures m relation to International 'Trade in the Products of the
Sea, cin be put in similar form for several successive years.
If we attach to the figures in Section No. 11, Table III, the denominations given in Statement No. VI, Table III,
then the entire series oomes out from beginning to end, in the form of the larger (piantitics being sums of the smaller
quantities, the principle on which Iternoulli's Table may be artifically constructed.
In like manner, if we attach the denominations to the figures in Section No. t, Statement No. VIII ; also in
section No. U of the same Statement ; also in Section No. I of Statement No. IX, all in Table IV, we get a clear view
of this sLirprisin,n property of interrhangeahility.
Hut further If the reader will turn to (Miapter VI, he will see that this interchangeable character continues up to
the present lime, and that the Differences in Canadian Records between "Imports" and "Entries for Home Con-
sumption," up to i.S,S5, are nothing more than the sums of Dr. Edward Young's United States Export Fish Trade
figures for 1872 7,^ and these again are interchangeable with the "hire brick and Clay Series," also with the United
States Import I'igures for the next preceding year i87^v74- AH of whi<:h is shown in Table IV.
I'lii' whole may be likened to a knitted .sock — unfasten the knot and the entire fabric can be drawn out into the
one single thread from which it was dexterously constructed. Or they may be likened to a chequered |)atchwork,
whose pieces are fastened together by the cli.iin stitch which is used in sewing machines. Untie the knot which holds
the thread and the whole may be disintregated by simply drawing out the thread.
In subsequent chapters I show that this well-joined adjustment pervades Canadian Trade Returns up to the latest
issue of 1885, all of which, as specified, may be disjointed md resolved into Uernoulli's wonderful scries — and then put
together again -
lOADKM ML'TAIA kliSURUO,
The CoiKiN \vi> Wocji.i.k.'^
'Imports" and "Kniriks kor Homic CoNSUMpnoN'' grouped anu put in the
FORM OF AN E.NDLESS ArIIHMETICAL PROGRESSION.
'This illustration <losesjhc present seiies. It is sufficiently startling. Any school-boy can now b3 taught how to
put Mr. Commissioner Johnson's Rec jrd of Trade with 'he United Slates and (Ireat Hritain in Cottons, Woollens,
Iron, i\:c., in the fi)rm of an endless Arithmetical Progression.
This is the necessary consequence of the artificial manufacture of the figures from a Ready Reckoner.
It is not fr)r me to discuss how it comports with the views of Protectionists or Free traders, or with Inland or Mari-
time Provinces It is sufficient for me to display the fact and show how the imposture is accomplished.
It is thought that the illustrations now presented, which appeal to the uninstructed eye, will suffice to prove tne
interchangeable character of ill th J figures u»ed in the records specified. That this artificial character is very widely
distributed throiigliout Canadian Trade Tables fiom 1867 Iti 1S85, I have satisfied myself by examining the records
purporting 10 represent trade in other branches of Industry —particularly Iron.
I am satisfied that the misrepresentation indicated amounts to many millions of dollars, and changes in a very
marked degree the aspect of Canadian Trade with the United States and (Ireat Britain, besides dis< riminating to a great
extent between the United States and Great Uritain m particular branches of trade, and special articles in each branch.
Then comes in the paramount question of duties, and the secret object of all these fabrications.
In conclusion, ' 'ui justified in saying that the Canadian Records of Trade specifieil, and the United States Records
of Trade specified, are nu;''i:ig more than the ecpuvalents of the sums of selected co-efficients of the expansion of ti'e
Binomial (i+i) to the power of n, where n is equal to 1, j, j, 4, &c., to any desirable quantity.
I look upon ihis matter as one not only of supreme importance in relation to the good neighborhood and welfare of
two contiguous n.itioiis of the same language, origin and blood, hut as betokening the existence of concerted deception,
unparalleled in the history of nations, which lends to destroy that go.xl neighborhood. It threatens to disturb peaceful
inti'rcomnuinicali(jn .ind dealings, which, at any < osl tti intlividuals, ought to be maintained tor the benefit of the millions
who are banelullv infiuenced bv the existence of so alarruing a deviation from equal justice to all before the law, in a
matter which mi deepiv concerns the Industrv of the Peoi'le.
The fre(iuent elTorts I have made in this direction during the pa;
again by fresh disioveries.
Hut the one sustaining inipiiKe wluch has never let', nie, and whiih
cons( lousness tli.u truth, under Providence, must rise above and over all
the supremacy of justice and reverence for law, it must iead to peace and goodwill among men.
eight vi-ars have been stimulated again and
I now fi-el with greater force than ever, is the
barriers. When its aim is directed to secure
HENRY YOULE HINU.
WiNlisoK, Nova SteiiiA, Dec. 16th, 1886.
HI
JS.7J0CtSflnsSttSXIrsir':- r. Mfi^mn,,^^,.
riha
mm^m
^Tl
<i!iif|ii i fi
»,. .rftf«««si»»M*«ifc.^^!SKL
T-A.1^ JE OT.A.3SriDX.
(in, and his 8th Property.
This Table is carried |;luded in the application of liernoiilli's i jih I'ropertv.
1 No.
1
I
1
3 i
1 '
» i
9 i '
.S I
11 of the Horizontal Series.
11
IS
13
•4
9,3
I i
to 4
«5
i6 I
'7
i8
«9
12 I 6
«3
14
«S
•7
19 '7
'3
15
The Squares from
remaining squares from xili
Pkoprrtv.
terms In the Series, including; cyplurs
vertical column.
lorizontal column.
the Series.
Series.
Hernoulli's i2tli property or theorem :-
S.a
S
liCiPKRTV.
5 iion for the sum of the co efficients of (.v + v)"
''//(? Jicticitkris" Hasilix', 17 13, I tom. 4to. The
i
i
TABLE
T-^BLE -FTlOls/L JA^IMIES I3EI^ISrOTJLi:.I'S TK
(Ahiis ('oNjF.i'iAMii, I'ais Sciiinil:i. ( (inlimns I )u( irinani ilc ^^.Tlmlt.ltllillillU^ ot ( 'uniliiii.itinnitnisi, Wii'n
This Table is carried out to twenty terms, ami |);utiriilar .iiuntiuM i> diii'i ted to the relation of the cyphers in solvinj; iinililem-
No. 1
1
2 1
1 i
I
i ' '
I
II I III I IV \
-_L L_„.i__
\i VII vm IX
X I XI Ml XIII XIV
XV x\i
I
3
ti !
lO lO
»5
20 I 15
6 I I
7 ;i .55
35
28 1 56 70 I 56 I 28 8 I I
7i() ^4 1 26
1 26 ' 84 .5'^
I o o
II 1 I
t*
II',
10 45 '. 120 210 I -'5; 2\0 '20 45 j 10 ' I
II
55 ! «6S I 330 i 462! 46i 3301 '65 55 11
'3
I.' 6() 220 , 495 792 92 1 792 495 i 220 (>(> 12
14 1 I i 13
78 286 I 715 12S7 1716 I7'<> '287 I 715 286' 78. 13
14 91 364 1001 2002 300,5 ,5^32 ,5003
2002 1001 364 m
16
17
'5 '05 455 '3'J5 3003 500^ 6435 f)435 ' 5005 3003 1365 455
18
19
14
I
I 16 I 120 560 1 <20 4j68 ; 8oo3 11440 12870^ II440{ 80081 4368 18201 560
___! J ! i i i . > _
105 I '5 I
ISO 16
17 ! 136 ()8o 2380 OiSS 12376 1944S 24310 I 24310 1944.S 12376 6188 2380
48620 I 43758
18
153 I 816 3060 8568 18564 j 31824 43758
19 1 171 969 3876 11628 27132 50388
7558* I 9*378 9*378
31824 I IS364 8568
75582 503881 27132
i 1 I
680 136
3060 1 816
11628 I 3876
The Squares from No. i to xil and i to 12 are taken from ncrnoulli's "Mrs Conjtctandi, opus posthtnnum: acctdunt tra
reinainin« squares from xiii to xx and 13 to 20 are added. Similar relations belong to the Coefficients of (i -1)" where /;=o, 1, 2, 3,
TABLE I.
XJLl:.I'S TREATISE 3DE ^RTE CON-JEOT^Isri:,!.
.. (■on,l,„u„„niln,s,. W „1, .,. Algchrai.: k.,„c..n.:„ion „f IU.,n„„ll,'s ,.,1, lTo,,ortv or Tluor.n,. :,n,l l,i. s.h ITopor.v
^111 XIV I XV XVI I XVII XVIII
XX
•3
9»
455
Powers I
of
Binomials. liKRNori.i.i's i;iii I'roi'Krtv.
( ' + o)" ' , ...
I,ct «= mimlxi <il terms III the Series, indiiJini; cyphers.
I (i + i)' " rt=-iuimliLr of vertiral column.
I
j /, + ,\. ' " /"- numl)er or Imrizontal column,
(i + if
(i + i)' ■
(i+i)» I
i
(I + !)«
" /==last term n!' the .'^^■ries.
j " .S'= Slim of llu" Serie.s.
j Then, ai.cordinj; to Hernoulli's 12th property or theorem :
{^)SJ^\(.),J"
14 I
'OS I >S
820 560
188
564
2380
8568
120
68c
t6
'36, 17
3060 816 I 153
j88 27132
1 1628
3876 ; 969
(l + i)"
{■ + •)"
(i+i)"
, , .V. a I. n
18
17' I 19
HeKNOII-M's Sill I'KOPKRTV.
Let .9 equal the mud of the llori/ontal Series.
I Then:
1 S=i'
*'"'''' ' \Vhi( h is the e\|iris~ion for the sum of the co-effi<:ients of (.v + i')"*
(i + i)" These are e<iiial to j'"
! (i + i)'*
(•+')"
(! + ')"
(l + l)"
(1+1)"
•US posthiimum: anedunt tractatus de Striehus Tnfinitis. et tpistola (Gallia scripta) dt Liido Pihe Reticularis," Basillic, 1713, 1 torn. 4to. The
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The Canadian Trade Tables of 1878 are Fabricated Records.
Il is proposed to prove ihal the Canadian Trade Tallies of 1878. in respect of the Trade between (Janaria and the United States and
Canada and Great Kritain, in Jotlon Goods of all descriptions, and Wixdlen (io'ids of all descriptions, are nothing nvire than a fabricated
record, utterly misleading.
Il will lie shown that they discriminate by means of Fabricated Figures between Oreat Britain and the United States in certain classes
of goods, also that the record of .luties received on |;<«i.ls alleged >■• be importeil is necessarily a false record.
It will also be shown that the Figures in the Despatch of .March igth. l8;o. addressed by the Marrpiis of Lome to Sir Michael Hicki
Beech, are faiiricatcd tigurcs ami wholly unsleading wi'.h regard to the object for which ihoy are siaieil in the Despatch to have been iransinilled,
vii :" A Memorandum of the Fin.ance Miiiisier. shewing how far. romparatively. Kngland is favoured in ihc new Tariff." This Despatch
will be found in Sessional I'aper No 155, anno 1S79. It is dated "Oiiawa, March 19. 1879." The fabricate.l figures recording Trade with
(ireal Hrilain and the United States in the ^oods selected for illustration. \ir , Cottons and Woollens, are types of prevailing misrepresentations
which impugn and render worthless Canadian Trade Tables signed R S. M. !' luchelte. Commissioner ol^ Customs, and J. Johnson, I ommis-
ioner of Customs (or many successive years.
.No attempt is now ma.le to arrive at any conclusion respecting the magnitude of the Fabrications. The item "All other" encloses an
aggregate so disproportionate to the entries in detail as to afford room lor enormous fabrications impossible 10 detect from the properties of
the tigures used Hut it must not he for one moment supposed that the " Final DiKKEkENCi£s" represent the actual Diflerences between
" F^nirics for Home Consumption" anti " Imports."
The Final Differences arc the result of the successive reduction of the Provincial Differences to Ibrm the Dominion Record. The
Provincial Differences are given further on, and greatly ■ -eeil the Dominion Record .\ttenlion is particularly called to the amazing
accuracy of the figures in deiail This accuracy will be a<lverteil 10 presently when the bearing of the Provincial DitTerences is pointed out.
An analysis of the figures proves, -
1st. -Thai when properly grou|)ed they form an arithmetical piogrcssion. (.Vo. I.) On page 2.
2nd.^That when properly grouped they are sums of the terms of the *' F'ire-brick and f lay" Series, aitd conserpiently of Bernoulli's
Column. No. I II. of which ffie " Fir -brick and Clay" Series is the equivalent. (.No. II ) On page 3.
3ttl. — When properly groupe<l they are also sums of Dr. Kdward Voung's United Slates Fish. F'ish Oil, .'shell Fish .md Products of the
Sea KxiKirts to British .\mcnca in 1872-73. (.No. Ill ) On page j.
4lh. — When these DitTerences are grouped according to countries, the aggregates turp out to be etpial to the Differences between Dr.
Kdward Young's F'ish Figures and the Bernoulli l.'olumn, No IV, carried out to 48 terms. t>os. IV. V and VI ) On page 5.
5th ■ -When these last named Differences are grouped and adiled they again produce the Canadian Final Diflerences between Entries for
Home Consumption as compared with luiporis for ('olton and Woollen floods. {.No. VII.) *Jn page 5.
ST.\TEMKNT No. X.
The Dominion Rf.cokd as Distiniiuished from the Record hy I'rovinces hrkkakter given.
TABLE showing the diffcronri.' hotween 1'': alleged values of items "Imported" and "Entered for Home Consump-
tion," in the Trade and Navigation I'ables of ('anada for the Year 1878. The eoltmin showing "Imports ' being
alone found in the "Despatch": the coliMnn showing values "Entered for Home (Consumption," being the basis
of I'arifT Exactions. The arguinent relates solely to the construction of the columns of differences and the mis-
representing artilice this construction develo|>es.
COTTONS <»— YEAR 1878.
tmportad
Entered tor '
\ Home I Differenow.
I t'oniumptlon. I
f /*ai,^f j^j, 7*. ami A'. TaMes. )
Bleached ami Unbleached ....
t treat Britain .. .. I Cottons,
Uniled States „
Great Britain
United Slates
(treat Britain n
United Slates
(ireal Britain ■,
United Slates j >,
Great Britain > •>
United Slates . . . . , I f.
Great Britain ' n
Uniled States | i, ■■ ■ . ■ • . • • .
(ireai Britain ' Cotton Thread, on Spools (3) ....
Uniled Stales | " •■
(ireal Britain . Cotton Warp, not coarser than No. 40
Uniled Slates •<
Great Britain ^ Carfels of any maltrial, txaft IViVllen [^)
Unlteti Slatm 1 n n u » "
Printed. Painted, &c.
Ginghanis and Plaids. .
Jeans, Denims, &c. . .
Clothing, &c.
Another (2) ..
$
$
431.807
430.337
539.7«3
536,357
1,982,444
1,984,044
893.681
89^,633
20,205
20,385
4.463
26,929
4,363
28,528
137.49a
I3S.'65
174.288
177,407
191.441
191,35"
l.75».8oS
1,761,293
729,071
725.366
■75.797
183.221
».'33
2.133
692
692
■4.674
96,000
14,074
96,562
8.058
7.900
$
-1470
-3406
-(- 1600
- 1048
-t- 180
- 100
+ 1599
+ 673
+ 3II9
- 90
+8488
- 3705
+ 7424
o
o
+ 562
■58
(1) N. B. -These items are dilTercnlly grouped In the Despatch. They will he found on pages 353, 352 and 350, ,Vc., of the Trade and
Navigation Tables lor 1878.
(2) In the Despatch this item is made to assume the form of : -
"Manufactures of Cotton, all other" Great Hrilain $3,735,249
,. ,1 United Stales 1,622,752
various details Iwing grou^MJ.! in this item.
(3) Transposed in Trade Tables, page 353, see FCrralt. This item is omitted in the Despatch.
(4) See page 350. This item is introduced into the Despatch as "Carpels of VVo.d and I'oilon," under Woollen CcmmIs,
1 if
I
■■■■IIIMHi
CHARACTER OF C.OOUS.-WOOI.l, ENS, YEAR 1878.
lireal Brilain ■ ■ ■
I'llilert Slates
(irca* Ilfilain ■• -
Uuileii States
Cirea' Uriiain •■ •
L'liitcil Statfs
(Ireat liiilain ■ .
Uniloil Stale!.
Creat Rritain '■•
United Stales
(ireat Hri lin . .
Unileil Slates
Citefri Britain ■ • •
Unitnl Slates
W(K)llens, viz., lUankets
*' ('arpcts ....
" Klannels ....
*' Tweeds ...
" Clothing, .Vc.
•• Wursted aiiii \'arii
Other ..
KriteriHi for
linfMrled.
Horn*
Consumption.
Oifffreiii*-
T'
$
■ $
17J.J94
I9«.'24
+J5.S30
aS.OOK
i.S.Xaa
176
651,49"
64**.W4
2.5^3
M..»5.i
i_t.95i
V.K>
I0i,(>40
'59.35'*
■ 2,287
68,I><)S
67,651
1.043
9J3..1''7
916,684
6,68}
I0.02()
9.507
r^
75O.4.W
77>.245
+ lI,§o6
12X.44<^|
Il8,44*t
+ J
Wl.O^l
65,209
842
5.655
5.655
S,'i".(>ii
5.' .7.773
+ 7.'S0
147.014
t.S,304
+ 750
It will he .ihserve.l iliat the values of the item " Wmillciis, I )ther "■ fireal H.ilain- $5. ! Jo.OiJ ; Unitcil S ate>. $147,614, vastly
exceeds in magnitude the nggri-galc sum of all the other items entered fur (ireat Brilain whose details arc given, ami thus forms a Ilc)»<sil.>ry
or l)ump in which very many oilier " Differences'" may he coniprehciKled and concealed.
It is ini|Hiiiant to note this entry " Other" or " All other," or " .Ml other, N. E. S.," (Not Elsewhere Specified.)
r
I ■
PROOF IHAr AI.I. IHK.SE I KIURKS .\RE EAliRIC.Vl EI).
T.ABI.E prese.-itinx the Kin.1l or Dominion Differences in Statement No, X, arranged in Columns of rositive and
Nct-ativc tcrin.s, showing the excess or defect of the values of (ioods entered .is "Imports" when compared
with the values entered for •' Home Consumption," on which Duty is i)aid.
COTTONS .\ND WOOLLENS.
Po«ltiT« Ternm or RM.flW of Values entarsd for ** Hollis Onnsuruptioll'*
oTcr Values of " Imports."
Total
2
180
673
75"
1.599
1,600
3. "19
7.15"
7.424
8,488
11,806
25.830
. 6q,i8.t
Ncfstlvs Temii or IHtfocI nl TalueM eiit«riHt U>t " Home Consumption"
ss coiupwsd with Imports.
1
1
«
a
3
^ \
4
i
i
I
I
9
9
10
in
II
1 1
la
12
13
'3
14
«5
Negative Tirmt,
Toitl a4t35o
II is ihe characlcr, rnnslruction ami relation* of ihoe I'ositlvc and Negative Terms which develop and prove their artificinl
manufacture, nnd the fahiication of the ijuantitict from which ihey arc derived.
PROPERTIES OK THE KIOURES EMPLOYED,
No, I.
TAHLE sho ing that the "Diffeiences" in Stalcmeni No. X. when properly grouped, form an Arithmetical Progression (roni 1000
to 25.000 and upwards, no single term being repeated in any group of terms.
•si
SUMS
OP
TilK
"DIKFEKENCES"
OUOUPED.
048
ISW
aaSy
a»e7 2*87
7«'4
74»4
I04«
7150
7«'<
66B.,
|*X^
7«»4
74»<
7414
74'4
ai;
74»4
II.Bn«
7'S"
8488
84I8
M83
6M,
s«.
i6a>
«sn
X^ \'^
loo
10,8
,M^
(^70
'470
J"9
7150
6683
IU4B
74>4
7150
71S0
74>4
74«
(6.
^'«
KU
i;6
llo
7S0
1
■ S8
1048
.0,8
i6do
.7*
"04t
1045
104^
H"
370s
3705
3705
7150
«bB7
l^,
.<«
iDo
go
"S' io«3
too
>S«
56»
■7«
750
ts8
7«>'
841
1041
1041
119
I1387
,Mj
.>87
JOO
100
loo 67,
90 )sft
lex.
10
loo
1^
90
3
ICO
7 SO
.s«
'^
^
Ml
158
100
!e
180
176
'is.
loo
90
lun
m8
<>8
loti
3BO
sis
90
loo
90
1,1
100
176
V
>
lor.
100
iOO
JO"
?
too
Ml
V
>5«
100
90
90
IOO
tOQo »aaa toon 4000 yno 6qou 7000 Baoo gooii 10,000 11,000 11,000 i),oao I4<ooo iStOOO t6,ooo 17,000 il,aoo t^iooo aOiOoo fl|Ooo tf,ooo 93,000 14,000 15,000
It will be vhown in another chapter that all the "Innporis" and " Kntriet" ftnr " Home Contumplion" cftn be put in the form of an
Arithmetical I'rngreuitm.
ft
No U.
Tabi.k shiiwing ih«t the "Diffcrfiiccs" ate svicccsiively maile up Imm the tcnin uf the " Kircbrirk ami flay Scries" of 1X67 In l!i7.{.
TMC " DIUKKRNCKh" in TlKM-i OK IIIK " Kl RR-BRICK AM) Cl.AV SURIKS."
ft
10
10
9
9
Q
U8
n8
V1.J
sc^
^6a
il'l
X
84a
»4»
rwi
Ifiuu
a.Br
84a
ajaj
S40«
3406
3705
7ty)
74a4
74'4
Il8o<)
«A
»
33
43
4'
aa
3. XI
171,
Itn
itk)
',5:;
^hi)
,6a
,6a
S6a
lOlJ
■ sa
84a
1,8
3119
3II<>
■ SB
"S3
3715
7434
4>
36
»6
S»
sft
1^
«»
tlio
>,H
HI!
Icx)
3«
»»•
>l>5
180
• as
ifi
Sl»
aa
71
jm
sa
!6a
3119
4'
too
71
n
to
at)
71
,,a
to
i»
(l>
aa
10
4»
4a
50
73
aaS;
■a!
Q
a9
4>
5a
8«
a6
aa
5a
4»
"043
90 ifJo ts« t76 t8o 3rt) «it9 56a 673 750 84i 1043 1048 t47o 159^; tftuo aa87 3533 1119 3406 3705 ()6»3 7t50 7434 8488 tt,Bo6 35,830
fl will lie .ili,eiveil thai liy successive sulisiiiuli.m my i.f the Difleteuces from 90 Id 25.»jo, can \ie reiKlcreil in Icrtus of the nuaniilies 9,
10, 22, 26, 42, 52 anil 50, which form the basis of the "Kire-hrick anil I'lay Series," as shown in Table II., Statement 1\., or ni terms i)f
Herii.iulli's ("olumn III., of which the " Fire-brick and Clay Series" is the ei|iiivaleni.
.No. 111.
Tmk Fi.N/\i. or Domimds Dikkkrh-.m ks I'liK Ciirro.vs in 1(178 in Tkkms oi.- Dr. Kuward Yoi7nc.'s Fish, Fish on, SuKt.i. Fisii
AND Products or tiik Ska, Unitkd Statks Kxi'Oris 10 Hritish Amkrica in 1872-3.
VotlNli's Finn FlUl'RKN
tOl I nx DlKFRRK.NCKS
YotlNO's KlSH FlliURKS
CorrON DlKPERENCES
Yoi'Nii's Fish Fii;"nKs
CoirON DlKKKRKVt KS
51
30
8
90
'i i 1048
••■• ■ "
3
3705
6a
30
8
6530
830
5«
6
7424
62
58
30
8
158
1599
7SQ4
■74
7h
6
S4K8
174
6
i8(«b.
l6<»
90U
1188
989
459
58
108
350
350
SJ
76 ;
loS
280
3"
62 1
62
»5S
8
30 1
5»
'''i 1
6
30
76 1
8
3
258
l(}8
76
62
5»
6
^477
iSS
240
76
62
()
3"9
33*>
2.S0
51
3
673
2830
350
lotl
58
52
S
3406
Jl
Thk Kinai. Dikkkkknoes kok rt'o.ii.i.KNs IS 1878 IN Tkkms ok Dr. f;iiwari) Yoi!n<Vs KlSH, Fish On., SiiF.1.1. Kisii asm) Pro-
ducts OF THE SiA, Unitkd States Extorts to British America in 1872-73.
YouNii's Fisii Kn;i)RKs .
WoOlt.FN l)tFFKREN(.'ES
VouNij's Fish FiiiURKS..
\Vooi.i.F.s Differences
76
6«
30
8
.76
2144
i;S
3
22S7
TUli UIKFKRENCIftj AKKANUKD A(,:C<.>K1>INH TO COVNTKIK.s, VKAR I»f7».
COTTON (lOOM.
qttSAT IRITAIN.
TNITBD &TATKH.
PotUiw Tcnm.
180
S6a
1599
1600
3110
7424
8488
N«(Uin Tmhu.
Po«iUv« T«nni.
Nf^aiivv 1 trma.
3406
1048
too
90
23,972
1470
673
S507
WOOLI.F.N GOODS.
GBKAl HMirArN.
UNITUl MATU.
+ 22972
— 1470
+ 2 1 502
8507
-8507
+ 67J
-7»34
uiiv« Torms.
NrKfUhrvTarau.
Pohitiva Tcnni-
Ncgstiv* I'trma.
25.830
2523
2
176
11,806
2287
750
too
7." 50
6683
84a
1043
44.7S6
"3>335
752
20)8
+ 44,786
— '2,335
+ 32,45'
-2038
_+ ^52
-u86
These numlwrs, (vissesiiing the relatio.is poinle<l luii, are necessatily all rabricaicil numlien. Further analytU herewith subinilieil !>howa
the origin ni their labric.ition, ami discloses other reinarkahlt- relations.
In order tu lieierniine llie ;ip]iarent relative amount of ,Iuty cxacte-l on these differences in excess, or remitted on the tlilferences in defect
according to die entries for Home <'onsum|ition, reference must lie li.,d to the firit or Provincial order of Differences as deduced from the
returns credited to the separate I'rovinces and e>hi!iitcd in detail in sulise<|uent pages.
Then there is to lie considered the Dump or Dcinisittiry -
Manufactures of Cotton— All other- (treat Itritam .. .. .. .. $.1,735,-49
„ ,( I, -United Sia'.es .. .. .. .. 1,612,752
Wotillens -All otber- -Oreal Britain ., 5,150,623
M ,. —United Slates 147,014
4
THE RF.RNOUI.LI TABLE
And the pAnRiCATRD Trade Tables concerning Coiton Goods and Woollen Goods in 1878.
The Differences between the forRcd Imports of Collon (;o<jd. and of Woollen (Jwnis in the Canadian Traile Tables of 1878. and
emiiodied in the I)esp.nch of .March igih, 1S79. are ^^llhin^ more than the groaiied Odferences between Bernoulli's Series, .No IV, to 48 terms,
an,l Dr. l^dward Young's forged Kish Kxports from the Uniteil Stales in 1872-3 to liritish America.
The sum of Dr. Kdward Voung's Fish, Fish Oil, Shell Fish anfl Products of the Sea Exports to Drilish America in 1872-3, amounts to
$195,726, and consists if 49 terms.
The sum of 48 terms, inclmling three cyphers, of the IVth (.'olums of Bernoulli's T.ihle, is 194,581)
•Sinn of Voung's Series to 49 terms 195,726
Sum of Bernoulli's Series, Coluruji IV. to 4.S terms 194,580
Difference 1,146
Hut 1140 is ej'ial I ) 95} (tisc sum .if 20 terms of llernoulli's (Job'^in III), plus 171
arc intercalated for the three cyphers in the Bernoulli Columns
1146-969 t- 171 + 6. Tliese three ipianlities
ide and the differences between Bernoulli's and Voung's Columns recorded, the result is as given below The Negative
Placed tide I
terms of the Differences give the sum of the Positive terms or Kxcess ol Values Entcretl f,)r " Home Consumption" over •' Imports" tor Cottons
and Woollens, in the Canadian Traile Tables of 1878. and emlioilied in the "'Despatch of March 19th, 1879." The Positive terms give the
same ag^jregate. V.'hen these Differences are projierly grouped and adtleil they give in regular sequence Uilh the Positive iind Negative terms,
or Excess and Defect of Values of ''Entries for Home Con«'imption" .is compare*! with "Impirts" The entire relation is sluiwn on the next
page. The mathematical formila is given at the close of C h.ipter II. In Chapter II the distinction lietween Provincial Differences and
Dominion or Final Differences is jKiinted out. The Provincial Differences are tht most ini|iortant antl misleading deceptions.
'I'ABI.IC SHdwiNc TitK Ahitiimkticai. Rklahdnship hriween llEKNoui.i.i's ("oi umn No. IV, I)K. Kdwaru YouN(;'s
KisH 'I'raiik Kigdrfs ok 1X72-73 and thk Canadian Tmadp 'I'aiii.f.s ok 1878.
No. IV sliiiws itic iliffiTtncf lieUrun Ik'iihiijIliV Series, No. IV, (n 48 terms, an I lit. hiU.inl Viiuuk's I'niicl SiiIm Fish Trmlc
Figures of r872 73.
No. V. and VI show llmt these ilifTerinces ire equal 10 Ihf snm.i of Ihc Fosilivo TcrnK or "Final DitTercnccs" lirlwren ihe cntr'e-. for
Home Coniuiiiption .inil Imports for 1872 73.
No. VII shows that the hijiircs are riciproc;illy inierrhan||enl>le, sums one n( ihc other, and apply also to the negative Difl'erence*.
No. IV,
Nn. V.
No. VI.
hlRNUl'I'i-i'a SRHIVS
IV, will) iiAf>, in
Urutlatril, llie ftif-
tircs in ilalirt.
* ■■•
rt
10
30
35
g :;:::::;::
lao
•65
'7' ••■•
220
a86
364
% ;:::::::::
680
816
<A>
969
1140
1330
1540
1771
2024
2J0O
3600
»9»5
3276
3«>54
4060
4495
4960
5456
5984 ■ ■ ■
^545
7140
7770
8436
9"39
9880
10660 52yj
11480 5S94
'2341 6530
'3»44 7894
14190 17929
'5180 17971
16215 29597
o .."^'S
I»K. Yoirvo's KlsH
Tnaiic Kioi-Ki-a
3
6
8 ,
30
52
:.:: &:::::
•••• 76
.... 108
••• 174
240
::;; ^ :.::::.
329 —
■ •• 338
•■•• 350
■••• 353
•■•• 459
700
.... 8.JO .".
• •. 900
933
989
.... 1188
■• '338
>57i
.... 1641
• •■ I7l»
.... 1865
.... 18S4
•■•. 2144
■•■■ 2354
3477
. .. 2598
2614
2«}0
3452
j8oi
4553
4790
5204
DtfrKNRNl Kft.
... — 3
... — a
... - 3
.. — 30
... -- 3»
:= %
. + 8
. + 12
9
.. - 69
38
6
35
"17
210
327
357
269
no
24U
398
583
686
729
958
•213
'413
. 1770
+ 191(1
+ 2141
+ 348.!
+ 2858
+ SW
+ 37'S
+ 3(188
+ J969
+ .)8«3
+ 4349
+ 4(17"
+ 5.5'>7
+ 5';^^'
+ 58"!
+ 5350
- 37. W
- 2791
-13382
-4906S
+
+
+
..+
.+
..+
.+
.+
..+
..+
.+
.+
..+
.+
..+
+
..+
.+
■95.726
195,736 or 138,366
.Sutn of Ncualivc or
IKMitive Diffttrcnces.
3
3
3
6
9
2U
33
32
38
69
3739
3791
■3382
49068
69183
The remaining po..i-
tive Fitial OifTerences,
necessarily amount I'l
69,183, anri the Joint
Cotton an<l Woollen
Scries for 1878. have
their equivalents for
posit ivelfims in either
of the positive or
nepalive Series of
MifTerenres hetween
Herntndli'scolumn IV
and I>r N'oiint; Fish
Figures of i)i72-73,
and their hijnres arc
sums of Ihovc nifTer-
ences.
Tlieipiantity 24.350.
Iteing the suiti of the
defect of values en^
tered for " Home
('onsH in pi ion " as
compared with •' Inu
potts." is easily obtain-
ed l>y the pror(..;ses
illustrated in Xo. VII.
Sum of Difference., without regard to signs . .,
** ** according to signs 69183
.. 138,366
69iS3 = o
I'HK KuukM IN THK DKSCArCH OF .MsRCH I9TH, 1879.
iHk KlNAI. SVRilUI rOM l'oTr"SS .\N|) W<XILI.KSM IN 1878.
KJtlTIVK TKMMaor UtCUS of VALI/M , NICATIVKTaMMR.or DRraiTof VAtru
entered for " llonie Consum)
tion over values of '• Dnports.
lieing Final liitl'ereiiccs.
Vosilivi Tttnis.
2 -..
180 .
562
073 ..
750 ..
1590
Kkw ...
3119 ..
7150
7424 ...
84S8 ...
11.S06 ,.
J58.»o
eniereo for " Monie Consump'
tion," as compared with " Iin'
ports," being Final I >ilTerence.s.
$69183
1 ...
90
3 ...
100
3 .
158
4 ...
176
5 ..
300
6 ...
519
7
7 ...
84J
8
8 ...
1043
1048
9
9 ••■
10
10 ...
1470
II
II ...
2287
13 ,
13
12 ...
13 ...
... 2523
... 3406
14 ...
■ 3705
15 ...
... 6683
$24350
No. VII.
The Final OiflTerences in the Tragic T.iMes of 1872-73 atif! in the
Despatch of March 19th. iSyt), are siim-i of the Differenres, with-
out regani to signs, between Ur, Young'* Fish Trade Figures of
1872-73 and the liernoulli Scries in Column IV.
lioi Vm
9
iTlvi; TmiMS.
20 2 !
IlIK NUOATIVE T«R
MS.
6
23
2 1 6
2
35
2
32
23 1
32
9
35
25
139
551
38
327
JS
20
117
32
583
398
(•9
117
180
563
673
750
90
■00
158
176
117
3
* 1
9 1
2J
2
20
12
269
20
■2
«9 '
,i-'
8
23
35
213
18
95»
240
.15
35
32
38
117
2141
2483
210
117
38
958
210
4349
357
729
.2.3
1599
1600
3119
7150
300
519
842
"043
9
8
8
2
1 n
2
9
2
12
12
(«»
20
y-
20
20
38
1688
. 95S
357
69
35
35
117
2483
3715
2141
.5969
210
958
1413
2141
[5367
3688
240
3715
729
5367
5811
i 104S
1470
2387
352J
1 2858
3370
5811
I
13382
: 398
' 69
i 38
1
327
8
729
117
20
6
-—.—
.■— »■
— _
7424
' 8488
11.806
25.830
3406
3705
6683
1
It follows ai an arithmetical conse<pience of I'le foregoing reLltions, that if ilouhle the sum of the "Kxccss of N'alues" entered for " Home
Consumption" over values of "Imports ' lor Coil.ms an.| Woollens m the Canadian Trade Tallies of 1878, he added in the form of the Column
of DifTerenrcs to Hernoulli's Column No. IV. with 1146 intercalated, the resulting cpiantilies are IV. K Iw.ard Voung's United Stales FiNh
E.spoil Tra.le figures to Hrilish America in 1X72-73. Numerous other relations will appear in succeeiling pages.
Hu! tliis is not all. No. VII shows that the separate terms of ihe Differences when nroperly grouped make up not only each separate
term of the excess of vh "ered in the (-aunilian Tiade Tables for "Home Consumption.' on which duty is paid, but also the defect of values
entered for Home Consi ntion as i.,. .qiared with imports. Hut these separate terms constituting the " defect of values" do not appear in
the aggregates 138,36601 ir.iXj, and et they arc represented figure for figure, when proper adjusiment of Ihe Differences is made. The»e
Differences, then, enclose term lor term two .Series, vij , (he Poiiitivc terms and also the Negative terms of the Final or Dominion Difliiences
for Cottons and WiKilUns in 1878. They make up as shown in No. Vll, not only 69,183 but also 24,350 and the sum of these, via., 93i533.
and ttiey do ihis term for term. ... »..,.„,„. o .
So that the Differeitces Ix-tween Hernoulli's Column No. I\' and Voung's United Sla'.es Fish Trade Figures 1S72-3 made up, term f.x
term, all the Final or Dominion DilTercnces in the olhcial Canadian entries purporting to represent Canadian Trade in Cottons and W.iolK-ns
with Ureal liiitain and the United States in the year 1878. In other words, the ililTerences lietween Bernoulli's Column IV and Voung\ Fi^h
Trade Figures, are Dr. Fdward Voung's and .Mr. Commissioner Johnson's private representation of the ir.-.de ol Canadian merchants with the
United States and the people of (ircat Britain in Cottons and Woollens for the year named. .-Wl this private representation is basest on a
prior private representaticii of trade between the United Slates and Canada in respect of ihe Products of the Sea.
.i{
AN IMI'ORANT I'ROI'KRTY OK RI-RNOUI.t IS TABI.F.,
In Ihr fiircffnihii \Me ihc sum ..f the DifTctcm-M Ixnwcrn ^r\m.i<c liuur.-. .H ilie Hcrrio.iMi Sfiie» «ii.l dr. Kl. \Mi<g\ Unitcil Sl«te*
Ki«h Srii« i» cjual t.'l.mWi- Iho Mini o( the |....ilive lenin ot f^ocs ,.l v.iluo nf the t «n«di»n Lollon Seric, ..t Diligences in If(7»-
ThU ti'l.iliori ill nniitlii-c fiinii nliiaiii* iK'twetn ti'mf nf ilic Ilcinoiilli Serif*.
For iiiMiime : When ihe 1 tilT.renie l.ilwccn Ihc >eiiarttie liKiirc^ of ihc Sctie. iii Cohimn IX anJ XI 1 1 iJ l«rin« is laUn, llic kum ..f
Ihese l>itr.ieiice» «iih,.iil r.-(;.>r.l ii. sini.s is c,|ual n. .hmhle ihc ilifTcinuc lictwecn Ihc lul terms of each, oi with regard to ilgnii, equal to o.
This relation is shown Iwlow: ■■ ^ ■
l.Jumn XI. l)ilftr.iK««.
o O
O
Culiluiil IX.
O ...
o ...
o ...
o ,.
...
..
o ..
..
1 ...
9 ••
o
o
o
o
o
o
, o
o
o
I
II
66
386
3.00J '•<*"
6.435 h°°i
ia,S70 8,oo8
a4,)io I9i44^
43.75» 43.75?
495
1.187
o
o
o
o
o
I
: "i
**\
'54 1
• 419 \^l6,7c;6
1,001
2,oi>a I
t>43>
t.861
4.862 '
o
75,5S3 9J.37* -l6,79<>
167,960 167,960 o or 33, $9a without regard 10 sigiw.
The last term of C i!v,mn XI i» ')2,37>i
The last term ui Co/iiiun IX i» 75.5*1 '
Di«fe ence 16,796
Sum 167,960
or the sum is equal to ten times (he Difference, an.l 33,591 < 5 = 167,960.
Thu properly of -some of the .:oIurans of Bernoulli's Table is introduced here for future reference.
:|;
>
♦ * *
OHA-FTEJR ix.
THE RECORD BY PROVINCES - YEAR 187«.
lan
he
Spci lal attention is din-f led lo the Mlowlnn paKfs. The stibje< t treai.'d relatcn to the Oftu iai Rprord of Canadi,
Trade liy rrovmcts. _, All tin details are Kiven. I'he prixcss of arrivinj; at the results is displayed in full. T
aeniMty of the fl^\lres '\s slrikinn. '"hey are nctcssat'ly all fabricated, hetause they form when |)ro|)erly grouiicd
ist, .All arithiiietiral I'ronteHsinn <«•/• rt«/c;;
jnd, Ihey ran he put in the form of the Kire Urirk ,iiul Clay Se.ies;
,Ud, They are nialheniatii ally related In Kdw.ird NduuK's' United .States Kisli Prade finures in United States
OlVu iai Kerord.s;
4th, They are niatheinati.ally related to llernoulli's t.d)le ;
-th, 'I'hey are inatheinatiealiy e<(»ivaleni to the sums of the Co-efliticnts of the successive expansions of the
Hinoinial (i + i) to the powei of n, where n is successively etiual to i, 2, 3, 4, 5, \c., to any number of terms repre-
sented by »;
6th, They are mathematically subordinate to ihe general formula given at the end of this chapter.
The Record by Provinces, as distinguished from the Dominion Record — Year 1878.
COTTON GOODS.
COTTONS, BLKACHi:i> OR UNBLEACHED, &c*
limnia tuoa
Great Britain
Unileil Sintes
Great Britain
United .Stato
Ureal Britain
Unilcil .Sii\teH
Great Britain
United .Slates
Great Britain
United Stato
Manitoba
ard OHer ol
UlffartncM
lurtlMf
(roupwl.
4lh or Final
omcr ol
G. Britain
+ 3038
-4508
G. Britain
— 1470
- '470
U. Statei.
U. Statei.
- 3406
+ 269
- 3675
- 3406
- "936
•
Tola
11,490
COTTONS, rklNTEl), I'.MNTED, OK COLOURED, Sec.
Great Britain
Ontario
7»5.88j
720.955
- 4928
G. Britain.
+
8630
United Slates
"
326,205
326,309
+ 104
G. Britain.
Great Britain
United States
Great Brii.iin
United States
Quebec
Nova Scuiia
977.243
397.630
76.795
59.421
976,59s
396,924
76,758
59,383
- 648
- 706
- 37
- 38
4928
648
.1309
+ 8630
— 7030
+ 1600
U. States.
G. Britain.
+ 1600
- 7030
Great Britain
United Stales
New llrumwick
159.764
78,447
159.656
78,03:'
- 108
- 409
U. States.
• +
104
- 1153
+ 105
— 1048
U. Stales.
- 1048
Great Britain
Manitoba
13.844
22,474
-4- 863"
105
United Sum
1,
7,220
7,220
706
38
409
Great Britain
British Columbia
(1
4.657
5.393
3,348
5.394
Total
- '309
+ I
+ 2648
United States
- 1153
16,918
* Where a Pruvince is omitted, Ihe Imports and Entries for Home Consumption are the same.
;|
: f
i
ff^^VeAWHtW!-
CilNC.HAMS AN1> IMAIDS. iVc.
IHIMITIO KKoM
(>ie*l Utiltin
United Sum .
<ir»( Britain
Uniied Ntaieii .
Great Diitain
United Stain .
Great Britain
United SlatM..
Great Britain
Uniicil Stales .
Onuriq
Queh«e
M .It H
Nova Scotia ...
iN«w Brunawick
« .1
Manilol>a ... .
I m porta.
i.S5»
8JJ
10,844
5.588
i.3»<)
1.395
>.Si3
436
' Knlertd for j Id Onltr
I Hufii« of
«'imitiini^.i'n. l>lff«rrn<<tw.
M OrtUr :hl iinlvr
ol ol
i>IIT' .'vlit'ti. UlffvrulK^VB.
41I1 C>nl>r
I "I
, l>lltrr«lu-«a.
$
■ .6<4
IO.S44
(i>9
5..S««
i.3«'l
1.390
1.533
510
91
101
■o«
o
U't Britain.
+
lot
_«J
IMS
5
+
+
5
« •
X3
2
' Total ! I j()4
IKAN.S DKNI.MS AN'D URII.I.INCS, &c.
U. Htatea.
+ a
— lOJ
G'l BriMin.
+ 1S5
S
+ 180
V. Statet.
+ »
— loa
(i'l Mrilnin.
+ iSo
U. Slate*.
- too
80
(ireal Hritnin „i,„
Ontario
•.. Ji37»
a.708
+ 336
G't Britain.
United State* ..
Great Hriiain »...
II ...
Quebec
1 35.8»9
... IS.«">5
35.4aa
'5.392
- 407
413
+
3.?6
'.790
li'i Britain.
Unite:! States
Great Ilritain
Nova Scotia
57.6J9
2,048
58.28<.
2.04H
+ 657
2,I2(>
413
+ 2.126
- 537
G'l Uiiiaiii
United Statea
(ireat Britain
n
New Brnniwick
9.005
.. 1..38
9.005
1,138
Q
t>4
- 5*7
U. Stain.
+
657
19
404
+ t.599
V. Stnlen.
+ l.ogo
+ 1.599
United .States „.,.,
Great Britain
Maniiitlia
18.906
J51
18.906
>37
114
~ 407
+ 673
+ fi73
United Sutei
i.59>
1.610
+ 19
1.080
(Jreal Britain
Briliali CniunriMa
5.3"5
7.105
+ 1.790
- 407
United .State? ...
Tiiial ..
j 14.4 '■;
H.»2l
+ 404
+ 9»6
4.140
2,272
nOTlllNi; AND WEAklNi; AlM'AkKI., \c
Great Britain
United Slates..
Great Britain
United Stales..
Great Britain
United State*.
Great Britain
United States .
(jreat Britain
United States.
Great Britain
United States.
» lUliiHfID fKnH
Hi
Onlaiic
Impart*
40,104
Kntfretl for
riinBiim|it'n
$
4o,oir
Ill Onlnr
ol
tHII*r«i«'M.
M Orttr
nl
IHfferAtims.
M Ordn MhOider
.ii or
I>ltrtrf'n<-«a I)|(lBr»iir..«.
OmI Britain
- 87
United States
(1 ...
4«,307
48.149
- 158
G'l Britain.
Great Ilriiain ....
United States
Quehee
44.9>6
*3.5S4
44.773
13.479
143
- 75
-t-
a,443
1.058
G'l Britain,
+ 3.S00
- 381
U'l Britain.
Great Briuin
Nova Scotia
»5.405
a $.405
+ 3.500
87
143
«5'
- 381
U. Statet,
+
334
-♦-3.H9
+ 3.119
United Stales
(;reat Britain
United Stales
Great Britain
New Brunswicic
Maniloh.
31.048
39.860
66.316
«8.a73
30,967
39.709
66,316
»o,7i$
- 8.
- <5'
+ 3,44a
U. States.
+ 334
- 3M
- 90
U. Slates.
- 90
United Slates
Great Britain
Britiib Columbia
3.S7a
4.784
3."9«>
5.843
+ ai4
+ i.osS
>$8
United States
1.
Total
■ 3.013
. •il.'^''..
- 314
44>9
+ 3.039
Al.I. OTHliR, NOT
... I Ontario
■ ■ . ■ Quel«c . • . •
. • • • Nova .Scotia • ■
• ••■ i New llrunswicl<
ELSEWHERE SPECIFIED.
.Vlanilolia .■■■
■ ■ • : British Columlna
Total .
1,001,050
i,or)S,633
+ 3.573
G'l Britain.
367.751
363.57a
- 4. '79
+
S53.4ai
550.084
- 3.337
3.573
59
37a
G'l Britain.
171,306
171,340
+ 34
+ 11.835
G'l Ilriiain
1.037
6,784
- 3.337
105,716
105.775
+ 59
+ 11,815
+ 8.488
+ 8,488
79,003
79.003
3.337
U. Statts.
53.053
53.4a5
A- 37a
U. Slates.
+
+ 1.69^
- 5.401
U. SUtes.
65.997
65.079
- 918
1,663
- 3.70$
- 3.705
7.676
8.713
+ 1.037
1.696
ia.435
14.097
+ 1,661
4.179
918
304
19.564
16.348
+ 6,784
- S.401
31,57a
3i,a68
304
32,359
- 4.783
1,
10
COTTON THRr:Al) ON SPOOLS, &c.
larains Fioit
Great Britain
Uniic<l Slates
Great Britain
United State*
Great Kri'.ain
United Sutes
Great Britain
I'niteil States
Ontario
I Quebec
New Brunswick
Briti>li Columlti.-i
iDiporU.
9,755
473
>"3."43
369
32,. 30
K95
'(.W
KnUfMlfor
UotiHi
Ooniunipt'n.
lit Ordar
o(
IMKaranoM.
IndOnler
of
Piffcrenoea.
9.755
473
"".399
+ 8256
(i. Britain.
+
+ S25f>
369
-693
- 139
it. 446
- f^n
-83a
S95
U. Slate*.
qoo
130
qoM
3nl Onlar
[MITervnoM.
4th Ordar
o(
Dffftranocc
+ 74»4
(1. Britain.
+ 8156
- 832
+ 74»4
G. Britain
+ 74*4
U. State*.
V. Statei.
CARPF.TS OK ANV MATRRIAI,, K.XCKl'l WOOI.. \<.
Great Britain
United Statu
Great Britain
United .states
Great Britain
United Sutea
(Ontario
iQncbec
\iiva Scotia .
• 50.347
I 4.099
...I 16,907
i '.59a
..^ 8,4i8
I J97
50,680
3.941
17,446
1, 59 J
8,118
»97
+ 3.i3 <•• Briiuin.j
- IS*
+ MO
o
310
I 333
539
+ S72
- 310
I'. .Statea.
158
J340_
G. Britain.
+ 87»
- 3'°
0. Biitain.
+ S6a
+ 56a
U. Sutea.
U. Stale*.
- 158
- >58
+ 404
The ligurw of Prince Edward Island from Great Britain and the United Slates are recorded as showing no difference between "Imports
and ** Entered for Home tunsimiption" in respect of C'»tt<tn (itxKis. In case* where the "Import" entries an,! " Kntrie* for Home Con
sumption " aie the same, the items are not here introiluce^l.
THK FIRST ORDER Ol DIllERKNCKS VOR COIlONi (lOODS,
'-S.
Fttilm Ttrms.
Ntgath'i Trrmt.
United Statei
United States
United Stales
Uniic<l Slates
Great Britain
Great Hiiiain
Great Britain
United Slates
United SMtes
United States
Great Britain
Great Britain
(■real Britain
Unii,.-d States
Great Britain
United St.iies
r.leat Britain
Great Britain
<;reat Britain
United Stales
Great Britain
(jieal Britain
Great Britain
'/real Britain
Great Briiuin
Great Britain
(iteat Britain
+
I
3
in
34
f.
toi
104
"4
269
Mi
i}f>
372
404
539
657
'037
105K
1227
1662
1790
1811
244a
3573
6784
8630
8356
41.808
Total UifTerence..
Total Sum ... .
41,808
28,140
69,948
■ 3,tiOH
tireal Brilaiii
(itL-at Britain
United State*
United State*
Unite.1 States
(ireni Britain
I niled Slates
Great Britain
Grt-at Britain
Great Britain
Great Britain
(.real Britain
Unitel States
Initeil Stale*
United Slates
lireat Britain
United Statei
United .States
Uniteil states
Great Britain
(ireat Britain
tireal Britain
United .State*
United States
Great Britain
(item Britain
(ireat Britain
United Stales
(ireat Britain
Unileil Stales
(ireat Britain
United States
Great Britain
5
37
. 5?
87
tot
lOl
114
139
■43
'*!
•s<
■ J'M
. '^
¥V
409
. n
<>iS
laai
'309
• 1391
. iSgS
>9.l6
3337
4"79
' 4^
a8,t4«
11
' Th< Fourth, heint; l/ie Dominion, or Finn! Order oj
T)u Third Order oj Uijfermm Jor Cotfon Goods, 1S78. ; Diffcrenm for Cotton Goods, 1878.
OocntT laroims Pmii.
Po<mvaT«nlK. Ne(>ttv*TarnM.
Cireal Hrilain. . . .
I'nilfil Stales
Gtc.il Britain ....
Unilcd Slates
Grcai Hrilain. . .
Unitcil Slates
Great Britain. . .
United Suies
Great Britain. .
United States
(ireal Britain . . . .
United .Stales
Great Britain. . . .
Great Britain
l.'nitetl States ... .
Total
.Stini! . .
Oifference
3038
369
8630
105
■85
3
2136
1080
334
11825
1696
8256
872
o
Country 1mih)RT«i> Kboh.
4508
.1675
7030
'153
5
loz
527
,07
SU
.14
.'337
5401
«33
3>o
15s
28,140
i(ireat Britain .
iGreat Britain
■United Stales
tircal Britain
iGteni Britain .
'(ireal Biiiaili
Great Britain .
(ireat Britain
Tol.1
PMitlva Teriiu.
Negative Teruw.
180
90
5'J2
too
''73
'5S
1599
■048
1600
1470
3"9
I3406
7424
3705
S48S
33.645
9977
Third Oni,-r
+ 41,808
- 28.140
. . i.i.66K
fi9.'M8
TJierefLrt'.
4 1, Sots
9.977
5".785
is tfjual to
Final Onit
+ 23.645
- 9.977
Suiii . .
. .. 13,668
Difference . .
33.632
18,140
33.645
5'.785
The I )ifferences arranged according to Countries will display other relations. These will be found at the close of the analysis concern-
ing Woollen Goods according to I'rovinccs. The "Country iniporteil from, ' ..-fcrs only to the positive terms.
The entire relation of the figuies in respect of Country is shown on page lb — Table A.
The Record by Provinces, as distinguished from the Dominion Record — Year 1878.
^WOOIL.LB3Sr O-OOIDS.
lnrokTiD rsoii
WOOLLENS — BLANKETS, &c
RiiUred lorT
Great Britain
United Stales
^'.reai Britain
United States....
Great Britain
United Slates....
Great Britain
United States....
Great Britain
United States....
Great Britp.in
United States . . . .
Ontario
t^ludhec
Nova Scotia
New Brunswick
British Columbia
Manitoba
Imports.
4Si3S9
11,106
6»,|^
6,66a
8.M6
Hoam I let Order.
i ODfMmm£jt|n. I
% '■
45.066
10,878
Ol,OJ4
6,66a
7.981
— 393
— ia8
- 153D
o
- 3*5
1.492
'9.917
4.367
".49» j
19.659 ' - »58
4,367 j o
7.985 I 33,986 ' + 25,001
i.»33 '.«33 j o
36 }24 39.699 I + 3»75
537 : 579 I + it_
I 1 1 .003
9nd Order.
Srd Order
G't Britain.
+
+ 25,001
3.375
28,276
+28276
- 2446
393
1,5.!°
363
358
3.446
IT Ui.l..
o
U. Slnlei.
+
4th Order.
+
35.830
I
5»
338
+ 5»
- 338
176
19
, !
CARPETS. \c.
iHmRTVl) Fnau
(ireai Hrilain
United Stales..
CIreal Miiuil.
L'nitcii states..
CtTQM Ilritain
United States..
Great Britain
United Slates ■
Gtent Britain
United States....
Great Hrilain
United Slates.. ..
Great Britain . ..•
United States
Great Britain .••.
United States
Great Britain
United .States
Great Britain •■..
United Slates
Great Britain .••.
United States
Great Britain ....
United States
Great Britain ....
United Miic<
Great Britain ....
United Slatea
Great Hrilain ....
United Sute*
Great Britain • • . .
United Stalei
Iniporta.
KntmJIu
Hau takOMir.
Conaiii«|ii'h.|
I Onlar. Srd Orrtcr. 4th Order.
Ontario . . .
Quei>ec
Nova .Scotia
New Brunswick
British Coltimliia
Maniloita-
JS9.439 I aS4.874
I
7402
^07,143
4S6S
7102 — 300 'Gt Hrilain
308,447 + i<3°* 1,304
753
753
51,602 52,054 I + 452
33' 3i'
116,161 II5,8J2
4920
535'
40s
4920
5966
405
Ontario ....
Quclscc . . . •
Nov* Scotia
FLANNELS, Ac.
i
.... ' 38,858
! 14,048
-... I 148,401
■ • 'S,»33
.... 28,985
! 8,991
t New Hninswicl^
British I i'iiind)ia
Maniuiln . .
3i,''37
»8,5»7
3.294
943
8.9'4
a
Ouelirc
Ontario
Nova Scotia
N«w Brunswick
440,490
'.909
75.'«7
543
88,779
6s>
39.354
'3.«>4
'47,8'7
14,530
26,919
8,991
30,91 3
38,517
4,080
943
8,719
87
TWEEns. &c
.... 321,735 3»'.683
6,916 6,916
'.390
75.439
543
88.156
— 4»
434.640 — 5850
iSlrl&^
o
3'9
+ 615
o
7.565
-t- 496
- 384
-584
— 7'3
— 206(1
— 7J4
o
+ -86
o
- 195
+_M
6003
a.37>
4,565 '
329 j
4.894
U. Statea. + o
+ — 300
o !
300
- 1513
300
G. Britain.
+
496
786
1282
^84
2at>li
714
'95
3569
U. Slates.
+
54
384
7'3
1097
+ 1282
— 3569
- 5'9
— 168
o
-6*3
o
7aoi
+ 54
— 1097
2287
— '043
I G. Britain.
' + 1
I °
1 5*}°
168 I
I 6*3 '
.6683 i
1). State*.
+
o
5«9
+ o
-6683
+ or
— 5>9
6683
— 5'9
\\
i;t
iMPOATRD KBOM
Great Britain
I'nited State**
(iront Mritiiin
Vniteii Strttes
(Jrcat Iliitnin
L'nhcil States
Great Britain
United States
(Jrcat Itritain
Vnilcii Sialfs
Great Dritain
Unileii Slates
Great Itritain
I'nited Stales
Great Mritain
United S'ates
<ireat Hiitnin
I'liileil Slates
Great Ilritain
I'l^iled States
Cl.Oll
UNO, \c
luiporU.
llv
knlerwl for
Hon).. j
lit Ordor.
+ 95«
Ind Order.
G. Hrilain.
Srd Ordir.
4th Order.
Oniariu •••• ....
i 1
178,088 179,046
„
23.590 1 23.030 1
- 560
+
958
(^>iiclter ■.-. •...
102.744 105,665
+2921 '
2921 I
6484
.... 10,855 >".44<)
Nina Sciitin S.mic, Sanu-.
— • 4C6
22j4
12.397
445
346
+ 12.597
79'
ii,So6
+ 11,806
New litun»»ick •. .. 126,0^7 125,^82
445
791
.. i >a,8i3 1 13.368
liiuish (uliinil.i;! . .. 30.479 : .36,963
+ 545
+ 6484
U. Sinle«.
+
„ .. 5>i»50 1 S'.668
P. K. Islan.l .. . 17.947 ! '7.60I
.. i 2,f)62 I 2,C63
i
Manil.ilia .. .. 1 55.625 ' 57.S.S9
-582
346
+ 22J4
545
1005
'550
560
406
582
1548
+ 1550
- 1548
3
+ 2
„
1,898
2.903
+ 1005
' . '
16,486
WOR.STED ANn Y.ARN. &c.
Oiiiaiiii i 19.707
I
— ' 2,267
19,244
2,267
- 463
G. Britain.
+
+
-842
1
!
'. - 842
(,)viel)|.c 23.396
2j.'55
- 241
463
1 i.>i}i
1
2.S33
?i
H^in^h ( ..luniliia ....
1
2.490
61
^.35^
"3
- I3X
84a
S4.
U. Slalcs.
+
.\l,I. OIHKK.
K.it«reil lor
lit Order
id Order
ad Order
4th Order
Nh.HTFn Kr«.m
IK
Iniporta.
l,6o2,7ji
nomd
ul
1,1
ot
ot
OoMUDipfn
l,6il,tloI
DUferencaa.
+ 9070
Dllforuii{.ei.
DIfferenoee.
niRerennja.
Gr»»l Britain
Onlarii)
O't Britain.
riiitcil Stales
.. .•-*..
78,984
80.553
+ 1569
+
9070
(ireni Ilritain
Quelle
2,363.^15
2,364.277
4- 662
662
4160
+ M892
I'niteil State* „., .,. ..
26,014
i5.<-"
293
13«92
I1742
+ 7150
--■
7150
<'.rMt Britain .,.„. „„,
Nova Sriili.i
406,713
*04.359
- 2354
2354.
3652.
7,36
L'nileil States
9,423
8,688
- 735
rireal Britain
New Hrun-«icl<
545.325
541.673
- 3652
674»
I'niteil States
.1
"6.393
16,393
U. Stales.
+
1569
(ireal ilritain
Briliih Columbia
!i8,8ia
32-97»
+ 4160
209
+ 177S
I'niteil Sm«
"
8.737
8.737
1778
- loaS
750
+ 750.
(ireal Miiiain
ManiioLa
48,02
4r.3»
- 736
293
735
I'niteil Slalc»
"
701
910
+ 209
103K
»J.440
•
\
— frtis-: — -
u
KK( AI'ULM.ATKIX.
Wnoi.i.rNs
i>it1uri-fi>-fk IhI ontf r
m.inliCts
$
JI.OOJ
t, ariicls
7.5'>5
(.'lolhing
16,486
Worsu-vl,
ic.
<I4»
Flannels
Sc.
6,0o»
Tweeds,
&i:.
7i>0l
All olhet
JJ.440
$ 02.539
Ti>iai I>ifferenc(^ \ViK)llen (ioods
COTTONS,
I hrtcri'iu-e.'« In 1
t'oUi>n.s, Blearheii, \c
Ci)lt(in», I'lintnl, &c
( im^hanis ,in-l I'laids
$ ll,4<x>
-")4
leans, heninis, At . ,
All oihcr
Cotion Thrciil, ,Vc, .
•t.140
22,151)
.i,o,S8
*'.ir|iels ...
I.J4"
$ 69,94s
$ 9a.539
69.94»
$l')2.4S7
THE SECOND ORPER OK DIFFERENCES FOR WOOLLEN GOODS,
1878.
United Slates
United States
United Slates
Tircal Kntsin
Orcat Britain
United States
Great Britain
Oreat Britain
(treat Brilain
tircat Britain
United Stales
Cirent Britain
United state*
Great Britain
(fre.lt Brilain
Great Brilain
(.treat Britain
Great Britain
Great Britain
(irtat Britain
/>j|/ltv Tentn.
Ti)t»l
nifierenre
Sum • .
— 61, 85^
- 30,687
92.S.W
JI,i6S
61,852
Great Brilain
Great Britain
Great Britain
("treat Britain
I'uiied States
(ircat Bri:ain
(irc.tt Britain
tireat Bntain
Unilcil Stales
I'nited Stales
(treat Brilain
(ireal Brilain
t.ireat Britain
United Slates
U'nited Stales
Great Britain
(treat Britain
Uniie<l States
UnitCil States
United Slates
Great Britain
(treat Britain
Unilcil S^lales
(ireat Xiilain
Ur.ited Slaici
(.•real Britain
(ireal Brilain
(treat Brilain
(ireal Britain
(ireal Britain
Great Britain
(treat Brilain
Ntgalifx Termi.
Tiilal
4a
■38
168
218
241
15S
»93
293
300
J29
346
3S4
41^}
445
463
5'9
560
.S82
584
623
7'3
724
735
736
I. 130
2066
2354
3652
4565
5850
30,687
Hrrtt Britain
United Slates..
(treat Briliiin
United Slale>..
Sum nf (^(itton disciiniinuting Differencen
" Woollen
$ 5K,4lS more air certain clauci ul guud^.
'3.434 '• ;;
25,967 less " "
4.720 '• '•
$ 94.539
Total
$ tK),948
92.539
$163,487
) t
16
THE IIIIKD DRIM'-.R OI I)IFFP;RENCES FOR WOOI-T.ENS IN 1878,
s»
54
1282
1551
1778
J371
ia.597
13,89'
28,276
61,852
Isl or 3rd Order of nifferenccs for Cmtons in 1S78
*' " W.wllens "
300
519
79>
K42
1028
1097
1548
244b
3569
4894
6683
674»
30,687
+ 61,852
,30,687
Difference 92.539
Sura 31.16.S
-(-
—
... 41,808
28,140
61,852
30,687
Sum
.. 103,660
58.827
103,600
58.827
)ifTerences for Cottons and Woollens in 187K
162,487
(nd
103,660
less
58,827
gives 44,833
THE FOURTH liKINC. THE IKniINIO.N' OR FIN.M. ORDER OK DIFFERENCES FOR WOOLLENS
IN 1878.
.; '.~ -"--•- TH
nii/itv Terms.
Nt/^Un Tirm.
United Slates
United Slates
Great Britain
Great firitain ......
Great Britain
7.150
II,8o(J
25.830
45.538
Difference
Sum
176
300
519
842
1,043
2,287
»,5»3
6,6X3
14.373
■t- 45,538
14,373
59,911
•
United Slates
United Stales
United States
Great Britain
United Slates
(ireat Britain
Great Britain
Great Britain
31,165
Sum of I'osiiivt
Terms
of the Final Order
for Woollens in 1
Cottons
J78...
.45,538
2.!.045
Total sum
of I'ositive Term.? for Woo
lens and Cottons
*'
69,183
Sum of Negative Term
of the Final Orrie
for Woollens in
Cottons
878
■ 14.373
9.977
Tntnl sum
of Noea
live Terms for Wo<
jilens and Cottons
in 187
R
■ 24,350
19
THE I'INAl. DIKFERKNCKS FOR l(Vn(i^ (iOOUS AND WOOLLEN OOOHS.
PTrSITIVK TERMS OR EXCESS Or VAU'RS
Fntcre.! for '* Home (.'onsiiiuption/' over values of " Iniports.'
Puithv Trrms - Final Dif<rntiis.
2
iSo
5t.j
673
750
'599
lOOO
3"9
7150
74J4
8488
I1S06 .
25830
$69183
7
8
9
10
II
12
13
SECATIVR Tf.RMS uR llKKEt-T OF VALUES
Khitreii for " Hoiiu- ( "(tn*.uni|ttioii," as roinprtrpd with " Imports."
Final Differentii - fftgttliv/ Ttrnn.
' 90
a 100
3 158
4 176
5 300
6 •• 5'9
7 .. • 841
8 1043
9 1048
10 1470
11 2287
n 2523
'3 3406
'4 3705
15 6683
$»435o
Tiirnitig to nimc 5, the rca.ltr «jll fiml that th(-.i' 11- ihi- I >if1ercncc» ilcrivi-.l from llcrnoiilli'« I'.iliimn IV uvl Dr. Ivlwnnl Nourr's
Kiih Trade (igure» of 1872 73.
^"W'AklSON BETWHEN THE SUMS Ol- rilE I Hh I- KliENl.RS, \VJ I 11 AND WirilOfl KE'.ARt) TO Stl^Ns, VKRAM.F.Ii A(.10RI>ISr, TO
COINTRIES, AS lir.RlVKU FROM IHE I't'OVlMI Al, OR FlKsr ORHER OF IUFKERRM ES AM> 1 HE KiNAt Ok DoMlMON
()R[IER OK DlKKERESrES IN rilE VHAK IS78,
TABLK A. i«7S
Cotton Goods Vear 1S78:-
Oieat Britain
United Sttlei
Woollen Ooo,U -Year 1S78 :
Oreat Britain
United Statei '
First Oriitr.
+ 38.43* -
- 16,930 -
+ 3.376 -
— 11,210 -
69,94«
Ftr^t Ottifr.
+ 58.418 -
■- 15.967 -
+ 3.434 -
- 4.7«> -
9».S39
Final Ortler.
+ 22,972
..470
-f- 673
- 8.507
3J.6M
Final OrJtr.
+ 44.786
- i».335
+ "J
2,038
DifftrcHLii.
4- lf;,46.>\
15,400 1
+ 2.703 1
- 2,703/
36.3^6
30,920 I r o
5,4.^) ot o
27,204 or o
59.91"
riffcitn.C'
+ 13.63JI
— I3.6j» )
2.682 ) = 5-364 "■ o
3J.628
Total Difference lielvsccn isl Order of I)iflerenre» an.l final Order of I)iflerenc» for Cotton .ind W,K.ll.-n 1 imxls in 1878 !
Total Diflfcrcnce
Total Sum Isl or Provincial Onler, Cotton* and Wcmllenk
" Final or Duiniiilun Order "
36,326
32,618
68,954
Sum of Final f\>silivc Term-, wiihoni ri-gard 10 ruuniries
Sum of Final Negative " "
... ^['.'^ T'«^J/69.I'*3 '»> ')«*ii sl>"wn on paRc 5 lo I* the sum ol half the Diflmnres lieiween lirriioulirj Cohimn No. IV and I)r
tdwai-d \ uung > KJi Trade h igurcs for iVja 73. The relaiii»» of the other afxregnies have now 10 Iw shown.
162,487
93.533
DiHerence
. .. 68,954
69,183
24,350
Sum
•• 93.533
: Difference
• 44.833
1?
OH^s^PTBR III.
1"lir. kEIATION tlF.T\VFrN llFRNOIl.ll's ("olI'MN No, IV ANI> TIIF. DKTAIIS OI- TUP. blFFP.KF.NC Ks HF.TWFFN Cni lOS ANtl
\Vo«Ll,r.N "IMMlk^^" AMI " KvTmFS Kok lloMF. IdNSIMITlON" HC.lRF.i- IN 1 HP. YKAR 1878, AM) THE
\l VI HI M \iH Al lokMllA SHKWIM. lilKiK (iKIiilN.
I.
Il has heen shewn "111 [latjc 5 ihat whcrr the ItiRFfcnrcs .Trc inkt'ii tigore for figure, hetween l)r. Krlward N'^irng's Vnileil Slates Kish
Traiic Kigurrs f»tr ilic yrni 1S73 71 arnt Hernttiilli's (otiitnn. N<i. 1\', it> 4S 'erni.s. the rcsiili is the imsiiivc lertns of ihc ('anathaii l-inal Difl'er-
enccs Iiciween •' F'Tiines fitr III.. "onsuniiiiKin" ntxl " lni|>mm" in lelaiitiii to ihe iraiie of (. anada in (^'otions and Woollens with tireat
Britain and the I'nited States in the j ^nr IS7S. It remains to show iltat hke rctatiuns suhsisi l^ctwccn HcrnoulU's Coliinm IV and the other
BKgregnles given in Tnlile .\.
The sum of the Pi>siiive Terms for C'oltoiis an<l Wut>)Ieiis is
I. Negative 1. .,
The sum of 40 tcrnu of the Ilernoulli Column No. IV i.i
Total
69,183
J4,35o
Difference 2,143
Hill 2,I4J IS the sum of the Negative Teim.i lor (."ottons in respect of (ireat Britain, and the Positive Terms for Cottons in respect of
ihe I'niied Stales, vii;., (ireal Hriiain 1,47°
Iniled Stales 673
Ah cxemplihetl in TuIile A where the account stands;---
(treat Hrilain —Charge,) for certain classes of Cotttin Goods ... ,
L'niteil Slates .1
•J43
$ 1,470 less than imported
f>7,l more than imiwrtcJ
II
It follnws thai till- rriiiaininK <ju«muirs shnxvin^; the iivcriHunaling ! tiftprunces between chargtN on In>|iorti from (ircni liritain und the
iJnito'l Slates in respet*( o( tiuiio on (lifiereni tIns!M!> »i ijniKi* are rf|iial in the Mini of 40 lenns <if ihi' licrhoiilli Series N*^- IV, an<I may btf
TJcrivcit ffinn thai source lK*(-au-e ih'' in'iividtinl (|uanttlic^ or tcriiiN iKi^se-'S in rcl:xlion in nne another like jiro|>prties, anil Ixith are mathenia-
tically e<|ni\alent lo />r. Hihiuni YotiHi^'^ huM I tatir /•'tx^u/fi vj iS^J-^J' This scconil relatiiin is shown helow.
1. The jtiini of Curion pi>sitive Terms fepreHeniinn the t*x^.•e*^ (»f chorgCK uvcr Imports on certain claiises uf goods iigainit lireai
Hrilain is $22,972
3. The sum of Worillen !*osiiive Terms repre^^enling the excess ofchaives on certain cla«es of goods against (Ireat Hritain is 44i786
,V The sum of Cotlim Negative Ttrms rrpiesfniing the defect of charges on certain classes of goods in favor of the Unile<l
Stall-'. IS .. .. .. .. .. ■ 8,507
4. The sum of Wmdl-n Ntgnlivc Ternt^ rrprf-rniing ihc delect of charges on certain classes o( goitds in favor of Great Hritain is 12,335
V The "Uhi of WtKiIlen Negative Terms representing the deffcl of charges on certain classes of g4WMls in favor the United Slates is 2,038
h. The sum t»f WiKiIlen I'oMtivc Term* retue^entmg ihc exci-ss of charge;* on cerlnm classes of gitods against the United States is 752
Total excess or delect of charges on Lcriain classes o( ( otion or Woollen giXKls as ilicy appear from the Kinal
Dirterences 9».390
The sum of 4u term*, iniliHiing cyplui- o| Htrnoulli^ ( ohnnn Nu. I\ . is . .. 9I.390
Dilference . .. o
tu.
All of the foregoing si-jiaraie ,niantities are ,i,o»n helow it, be sums of terms in the hrst iorty terms of ( oltiiiin IV ^yi the Hern,)ulli
Table. It is to lie Uirne in n.iml thai this eiiuivn'ency can lie greatly varied, and ihat each Hernoulli term from Column 1\ is the sum of a|l
Ihe terms in Column III msl alnive it, or the sum of all the sh.ping terms to the left. Thus 364 is not only eijual lo 7>'+<)ti+55+45+36-f-
jK+Ji + IS-f-io-fo-fi-Hi but it IS also e<|ual to iX()+ the «lo|)ing terms oti+ii + i, and these may be subsliiuled. These remarks apply 10
each inilividiial membe, given lielow.
The Si MS ni ihf Iinm Iufffhrni r.i for Cottons and Woolle.ns is Taiuk A, in Terms op thk Ukknoulm
COI.l'MN IV.
SKCIION I.
/H< i/uttHiily f.t,v7*-
The 40th Term of Bernoulli's Column IV
" 39ih ■•
" 3"" "
" »«h "
" nth •'
" 51b " «
SECTION IV.
'/lit iiuatililji 7_fv.
9, IJQ The fsth Term of Bernoulli's Column IV
8,436 " I4lh "
4,060 " i)th "
969 " 8th "
364 " 6ih "
4 •' 4th "
^
i»,or»
t
7S«
IF
18
SICTIOS tl.
MCT
Thf •/Mantiiy 44,736.
n, fv
'
The jKih Tfr'.n of llernoulii'^ Column IV
r.770
The 30lh T«rm ..f Heinr IV
J,«J4
" 37th ••
7,140
" 39tll •'
3,176
" 36'h "
6.54S
" lOih " ....
816
" JSth "
" i»ih " ...
680
" .Mth "
" ii'A "
5.4i6
4.O00
" «ih ••
" 7'h '•
56
10
" .IJnd "
4.495
•• 5lh "
4
" J51'' "
),oi4
•• 4lh '•
1
" '4ih " ,
2M>
" 9lh " .....
" glh " ■:
54
JS
8.507
" 7lh '•
10
" 6th "
to
" 5th ••
4
" 4th ••
1
44.7«6
!ii(;riON III.
IBCTION VI.
T^f i/uaHJi/y J,i>^y.
THt </ixmlily ii^sjj-
The ajlh Term ol Httnoulli'i. Column IV
1,094
The iSlh Term .if Hernoulhs Column IV
1,915
" 6lh "
16
" 37ih •• ... ,
1,600
" Sth "
4
" Kith '•
3,300
" 24lh •'
1,771
JO. 38
" Jjrcl "
1.540
" 3151 "
1.14U
" 8lh "
JS
" 7th "
ao
'• 5lh ••
4
U.33J
nacrioN VII.
sri'TioN vm.
r*f fmiHti/)t /^T,).
Thf t/uanti/y 67^^.
The lOth Tetni of Bernoulli s Column IV
" l6lh "
" 8th
" 6ih
969
455
The l6ih Term (if Ilernoulli'* Column IV
•• iiih
43$
IM
35
lO
" lah " " "
" 6th
"4
'■ 4lh " ■■ "
I
" 5ih " " "
4
1470
*7.»
f, , ',','!'-"' ^ ''" »gB'<g«'e'. an<t all ihe -e|jairiic c|uaniiiie.s from which ihe..r .i|>i;'e)!"l'^ Jn lonnpil present ilicniselie. in llernoullis
CoLimn IV, anil aUj, lioni the con>iruciion of the f^ile, in Column III, anil in ilie sloping column*. It noi» remains to supply Ihe Kenertl
mathematical formula liy mean* of which ,ill of ihent quaniilie!. in»y \k obt«in«,l in (q[iiliu nriler.
THK MATHFM.ATIC.M KtRMIM \
^ t
Kach lepanle quantity in the foraKoinii Seciioii, I to VIII, innlu.iTe. c.iii he i^sprowwl liy the Malhematinil Kormula —
.1 (» + 1) (» + 2Ma + J) to la-k-(n-i))^
1, 1. 3, 4, 5, 6, 7, 8 to (n - 1)
Where a i» equal to the iiumlier of the column in IJernoulIi's Tahle, ami n is equal 10 the numhcn.f lerms in the column imtHjiHg 'yf/Kn.
KxtMPi.e : The quantity 5984 in Section II w the 35th term in Column IV, wiih three r)nhers
Iherefore n «= 31 plus three cyphers, and a - 4.
Substituting Ihese valn«.i of n ami a, vi.. 31 ami 4 in the .ihovc formula, ihe expresMoii liecomts-
4. 5. 6, 7, 8. 9. *c., to U + (3a - 3) I^ 4. S. 6, 7, 8, 9, Ac, lu n
I, a, 3. 4. S> ^, &C., «» (.3* i» 1, a, 3. 4. $. *c., to jt
16 » 11 « 34 =, 5p84
»' 33. 34
J. ». 3
All the quantities in .Sections I 1,. VIII ijeing represeme.i lj> ihe general formula A. each separate section conilsis of Ihe «imis of A, A ■ , A«.
" 3 , A 4 , ,\c. I he values of A, A ■ , A " , A i , A » . &c. , lieing determinerf hy the //*/ of the term in the column,
tach aggregate in Sections I to VUI, tuch a« 23.973 i» represented l.y A -I- A ■ + A» + A %+ A<, &c.
Where A i .
A'= .
4, S. 6, 7. &t.. IB U + (37-a) \
I. 3. 3. 4. *f^, ^o (37-1)
4, 5. 6.7. &c, to ^4 + (36-a);
1. a, 3, 4. &c., In (,36- I)
4. 5,6. 7. 4c., to ^ 4 4. (»«-») ^
'.a, 3, 4, &c., tp (a«— I)
9139 (see Table),
= II436
— 4060 ..
ISM^^L'.
\'X-
I»
A>.
A"=..
4. 5, 6,7, *c., to {4 + (i7-»)'
I. 3, 1, 4. *e-. t" il-t)
4. 5. ft. 7. *c,, lo ,'4 +(12 -2);
I, 2, J. 4, .^C, 111 (12-11
i 1«H
4.5.6. r. *c.,io J4 + (a-») !■ ^
I, 2, I, 4, A.C., in (2-1)
»l
Kach Mpsroif iionniiiy in tht fuiegDinu SiTiiuin N... I lo V[|l ini-liiMiT, U ihe sum .if «ll Ibc t«rms ilwvt it iu B«r90ulli'» Colmnn No.
HI, an.I can «Ui. l.c rxprr^iscl t'\ ilu- fiptnuil.T
/. u
V - , — ■
a
which conslitiilcs lh« Alcgelnaic e>|ire>iiiiin nl llermmlli's i 'Ih I'toptrly,
For exampli-: The (|iiaiilily 2925 i; the m lerm in Srclioii VI. Hy rcffrring In erniuini'i rxicn Ifil lahle, thi< number is fininci lo Iw
(he sum (if J25 + ,)oo + 270 + 25.5 + 2)1 -f 210 + 190 + 171 + 15J + 1 ;<> + ijo -f- loj + gi + 7.S + 66 -f 55 -♦- 45 + j6 + 28 +
ai + 15+ 10 + 6 + 1.
Similarly e.irh r|UHniity in the <.'i({ht seciiims can l«. cxprcsseil in a serie.s (iiunil really formed in ihe llernoi'lli Tulilc.
But 2925 is aUii equal In ihe sum iif Ihe lernis in ihe slnpiiii; cnUimn whose base is next above il, or e<pml to 2600+300+244-1 = 2925.
So also joo is equal lo 276+23+1 .mil 2711 - 253 + 22 + 1, an.! 253 =: 2Ji + 21 + 1, and so on Ihrouglioul ih ; enlire series given above,
anri throuKhoui the larRC number of .lifTercnt bui equal scries forme.l out of.'ach. ami all ilie c|uaniilies in the eight .sections.
The« quanliiies can, ibarel ire. li« pui in the subjoined form :
202? =: 3600
JBO
H
I
2925 = 2600
J 276
)0O =
(276
v:
t
2925 =
276 =
2600
( »fi.l
22
I
t
3915
2S? ■
ateo
231
21
[ I
' »■•■
««
fc '
U
I
3925
231
> 2&00
i 210
! aa
1
29aj = itc, *c.
Until thejf Anally resolve themselves into Bernoulli's Columns I and II.
The quantity 2600 can be put in similar (orin, and all the quantittf* '« *seclions I t<:>,VIII po&.sft!i$ like properties. But these are
similar to Ihe pro)>eities [mssessetf by I>r. Kdward Younp's Fish Trade rigurcs for several ycftrs, which folluw the same law
HI.
The Fish Trade Ficukis.
Take, for example, S'oung's Fish Trade figures jiven in TA8t.E III, being Stfttement No. \1, showing the LhwM'ii Slates Exports of
Fish, Shell Fish, Fish Oils and Trmlucts of the Sea to Itnlish America in 1872-73 :
^«("^.,.W^. .T,-
»
the KoifiRn iii-ni fJO.S-i; S«i'line» in Oil e\i>.>rlfil u> (Jiuhi. .
OnlMio, \c , i> nwiir itj. ..( ihr mixed Kluirii iiiid iLmiesUt
iifni*:-
$I7,91I> 'ill nlh«r»' li> (>cl)cc, Oliliiio, \r.
6,530 Honifslic Kxpciti to Novn Siulia nntl N. H.
4,^5i .. I, 111 Ilniish Oiiiina.
1*0 Sotclinr* 111 It, \V. Inilict.
b Iirifil Ki»h to «^utl«r.
SJ9.59r
$17, 919 i« mailr up nf ; —
$i6,(Mi ('. S K»innl« 10 Kirtu Scoiiii tnil N. II.
l.j^S all iiihcr«.
350 Sarilinc.^ 10 N. !^.
240 lietring !o Hritith (iuianii.
$i7,qj9 All ulhen In l,>ucUc, Uniario, \r
$16,001 i> made up of i —
$7,894 I'ish iilher luteil hi Brilish Weil Inilicj.
0,530 . picklcil 111 "
1,571 Ncwrmin'llanil.
6 .. iliicil lo l.'uetifc, ic.
$16,001 K«p<iri» lo Nova sctilia ami New Iliunswick.
$17,071 Kish lined In B. W. Indies, .U , in moiie up i>l :—
$16,001 Fnieign KxporH to N. S. and N. II
1, 338 '.ill iiilieis' 111 Hrilish Columliia.
J5* Kish, Tickleil tn Bri'iih (iuiana.
240 Herrinv m
76 I tried Kish to Nova Scotia and N. II.
jj I'ickled ,. 10 (Quebec, 4tt.
'6 Diied ,. to
$17,971 Ki.h. iltied. 10 H. W, I
$5,^94 Mackerel lo Nova Srotia and N. H. is made up of; —
$4, j53 " Ush, all oihtrs." to Nnva .Scotia and N. B.
',338 M M lu Britioh C'ulumliii.
3 Ki»h, pickled, li>
$5,894.
$5,204 Herrinc in Nnv.i Siotui :ind .Sewlnundl.init 1- made up of' $I<J3V
$2,144 ''ii'ii pitkled, to Nova Scotia and N, H.
2.614 H^h, •innkeil, tn Briti&h (iuiaiia.
338 Ush, nthcr cured. ..
108 Fish, frejh, m i^uehec. tVntarin. iie.
$<.204.
And «i on in regular .etpience Ironi heginning 10 rnl ol ihc Talile foiinin)! pari uf Siatetuent \ I. Inl.lc III.
The reduction of larger lerroi of thU wricn to tinallcr term* ia ahown in ihc Milijointd illustration :
$7,894 ' Msh, nihrr iiirnl, to B. W. Indies' i» ni.ide up off—'
$6,530 Kisli, pickled, to IJniish West Indica,
i>8o AM iiihirs III British liuian.1.
258 Kish, pickled, 111
108 Iresli ti»h 111 Onlariii and i^uiliec.
6 Sniiiked tish .. „
3 I'icklrtl lish to British Coluinlii*.
$7,894
$6,530 'Fish, pickled, t" H. W. Indies' is made up of:-."
$ 7b Smoked tish.
2,144 Fish, pickled.
1,712 Fish, other cured.
2,598 I iy-ler>.
$6,530
$i.;;7t lish. pickkd. to .Ncwlniindl.ind is made upof;— "
$980 Fish, n1) nihers, til British tiuiana.
350 .Sardines lo N, .s, and N, II.
174 Fresh tish tn U. \V, Indiea.
52 I'ickleil tish tn i,lueliec, t)nlario, Ac,
6 Sninked fuh in
$1,571
$1,188 S.irilincs m I 111, IS in.'ide up of 1- -
$280 Sardines ill llr. West Indies.
258 I-'ish, pickled. In Briiisti t iuiana.
240 Ilcrring ii> British iiuiana.
174 Fish. Iiesh. to 111. Wisi Indies.
108 ■• " to I.Uiebec, Ontario, M,iniliiba.
76 II snuikeil, to Nnva Scotia and N. II.
52 II pickled, lo t^uclicc, C ntaiin and Maritolit/
$l.l88
$1,338 'all others <n British (nluniliia is made up ol ; —
$450 Oysters III Newfoiinilland,
338 ( iireil hsh lo British toiiana.
280 Sardines to Bi:lisli Wrsl Indies.
• 58 I'ickled hsh lo British duiana.
3 III British •.!iilumliia
VtAK 1871
Foreigh cxfuiis of iht l.'cited .Stales to Nova
.Scotia and Ncu Hninsiaick
Domestic Flxports tn do ...
Tolul .
Knini I Mr ill lom , * i"'*" '^V"ir'*n°
iii«K«andSa.iga : ^^^ "'"' ''."■i
lion Report.. •'?'f,'\'!'^?,"?'°*
$
l6.c»l
6,530
«.53>
6.5
Foreign F.xporls fioni Talde
2
108
6
I
7f
e.'4A
l,71J
2.59«
9*»
350
174
^1
58 I
/.»94
6.S30 ..
FioRi (I)
Fiohi |2|
74 r
6 1
1,571 ..' ffom (3)
From (4)
IbiOni ;. . 16,001
■ From Ta'ole in Commerce and Navt|{alion
Kcjioits.
( 35°
i I 4553
1 5»4
I —
I . 16,001
F;xpressed in languaee, these qnanlilies in I and 11 and indirectly in tll from the conitruciion of the Talile, are the equivalents of the
auttw of the coefficients of the successive expansions of (I ♦ 1) 10 the [lower of n.
Other formula, which may lie obtained from morlern alRchras iixed in schools and colleges can be rendered applicable. It i» curioua lo
note that in ihe examples eiven in some of these algebras, the series forming the 3td and 4th columns of Bernoulli's Table are employed.
Special reference will 1)« made to ihese fonaulic and examples in a succeeding chapter.
01
aH-A-FTElR IV.
The Canadian Trade Tables of 1883 are Fabricatod Records.
In a i.uWlsh-.l Iclior l,,.-.,inu ,l.,i, VV„„1«,, N.,v,i Sclu. ,\l.,y iMl,, iSS^, rl.o .laiaiU -.f ih» Tf.vlu iu C.n.m (i..o i^ nf.-ill .k.scriptir.n,
hciwcc-h (. ,.na,U ,.vl Ihr I'n.ie.l -iiaic. .m.l Cann.l.. .,n.l (,r«l lltiNiiii, nvcc siil.inillcl lo ibo Kl. II. ,n. Sir fharls. W Dilkc, M. I'., ihfii
rresiilfiii of ihc l,<»:iil (.ovoniiiuMii ll..,ir.l in l,oniliMi.
Ihu v„luniim,u, a,.cinni-ni, ..I uliicii the |."ilil„l:f.l loticr »a» nn nl.Mrafl, waj rolurnf.l Ic, mo. Tho iliwiiMianl ooniaino.l Ihc riifTfri-n-
cts l«l»ecn ihr allcg,.,! ^u|Mrl^ nt i;,,!.,,,, (;,„„|s |,y („„.„!., fruii, (ireai H,ii.,i„ ,ii,.i ilir Ih.iie.l Siaic, ai.-l ih<i all..o,l " Iviirii'* f..r t|..in(i
L,.in»um|.l.. 11 in the l.iriii „( all Ariihiii.-tit,.l l'i..^re«.ii.n ; als , ih<- L.tiii ijf ilic " Kir«-lirick ami Clay .Icrios. ' Ii nl.ci ontaincd
nuim-rmis aii.l Mtikint; iiliiviraii.iii<i .ho«ii,s ihi- tel* i l,i-ncooii Ihosc DilKTc-iiCL.. au.| Ih- Uiiiii-1 Suu, .iii.l Caiijilian I'i.ll Tia'li; fiuircs
vcnrs iSKj .iii<l iKSj
KINAI. OK DOMINION DIIIKKKNCKS AS DI.S riN(;i,MSHi:i) I KOM I'KoviNCiAi. Dil I- KRKNCK^
TAHl h. t^iinftHX the Fmal or /hmution /hf<rfn,«i iti fiojtfn..' ar *»y,i/i>v termi h,'lw:in ihc afhi^.it vjOu^ n/ 'U»i( *^lmport'>
*'EHta«i for liontt Cottyumptum," in thf f'nvie ami Mtj^nuiafi /)tf>ff> of Canoiin fop fhe ymr tSSj.
and
CHARACPKR (W OOODS, COTTONS, -YKAR
(J'offiM III Tnwtu Krnt y&vlfftUun Tal.l«*, flS T^ ^"i tnr)iulv«.)
(^I'HTWf.
1883.
lni(Hn1ctl.
(trcftl Itrilaiu
Cnitcci SlJtes
(iToat Britiiin
I'nited Stales
iWeat Hritain
railed StutrK ■
(ireat Itriiain
Unilc'l Simen ■
iire.1t ItrJlain -
fnitt'd Stale*
(ireal Hiitain {%)
I'nitet! States
(ircat Ittitain
rnited Stalen .
(Ireiii Britain
I'lillctl Stales
*Jieal Hriiain
L'nileil Statos •
(irent Britain
Cnilc'I Stale*
< irent Britain
Unilcd Stales
(ireat Britain
l'nile<{ SlalcB
( Iteal Biilain
llniteii SiiUfs
(ireai ItnUiii)
United Stales
( ireat Britain
United States
( ireat Britain
United States •
(■rent Britain
United States
(ireat Britain
United Stntei
(ircav ttritain
United States
(ireat Britain
United Stales
(ireat Britain
United States
(ireat Britain
United Slates •
(ireat Britain
Unitnl Slaten -
(ireat Britain
Uniletl Stales
(treat Britain
Unitetl Slates -
UotlniiN, (ireynnd Blenchod, iVf,
M (iinghams and I'laidn (dyed)
•• i>(.Miim\, l))dlin|£s, \c. . . . .
M While or I>yed t'oiion Jynns, ike.
II II It II . . -
>• Wiiddjng, ilatling, \Vari»s, \c. (not dyed) ■
. Knitting Vam. i{o«ii ry do., \c. „ • •
.1 Wadding. Batting. W.irps, \e. (dyed) , *
n Knitting Varn, isc. '.dyeil) • ■ , - .
II 11 .' I • • .
>i Sennitess Bag^ ■ • » . .
.1 Shins and 1 )i:iwors, \c. . . ,. ^ ,
.1 Sewing Thread on s|H>»)ls . , , , _
i. Sewing Thread in Hanks, Ac. . ♦ , .
.. Diirk, tor Iwmts, \c. - * •
II Med (.-iiinltirlerw, tVc • . « • , •
.1 Cloihing 111- uihor nialrrial nui .iihcrvvise pniv'd fur, \c
11 RaK'' I'y the Needio .....
t. Netting for HuotJi, dec, ....
It i'runello for Boots, Ac. (a) ■ ■ ■ •
II Parasols and Uipl>retlas .....
Shawl:
, Velveteens, &c. .....
M Winceys, Plain, Sic.
II ......
„ Winceys, Checked, Ac.
„ Winceys, Checked, &c., liver 25 in.
„ At. I OfJIliK MANt.'K.vrURES OF N. K. S. (J) -
J-4,545
i2o,.vyi
H'Uiie
I>iffiireii«i
r<iiii«uiii)>ii<in.
$
V'
48.1,844
(-
7.632
•Ij'i. i93
11,24s
ir.<Hjo
-'
l.Sj
9, Ib6
4i"l, !2>y
.
-0. 205
3^5969
3,i(X)
I..J74.798
t
16,050
iO$,yii
3.636
15.. 58
725
29,505 1 •
'.3.'i6
2
14.748
1
.).046
! ■"
479
31,611
2ci,S89
i +
257
197
l-t.n-^J
4.J78
i(i,oOo
2,246
117.607
+
2,225
.i4.t»S
3.^4°
i-'4.047
,4-
12,612
f.>'.4,i4
qos
511
•)54
930
175.665
11,048
+
930
4.529
2.016
-
86
J't.'.SSl
.
76
225.224
+
218
5.5J0
558
7.364
^
2,297
5.328
-f
239
471
r2,fjo7
+
5.308
866
189,956
2,487
+
668
+
66
16, u8
—
66
880
317.226
+
59
1,823
352.568
+ 3>.o27
365
—
2Q
21,584
—
«47
22 1
28,333
+
782
'65
3.473,878
+
8,561
fiii
421,224
—~«l?*|(Wj>,*-.
mm
}
SUPriRMKNTAUV TAllI.E.
(lint Hrilniii
Unilril Slairn
(irrni llrirnin
Uniicil huiea
N,
Dcgii OHilaining Kinc Soil ' •
Car(>cl», nm clwwhere »|)«iifi«.t
... I 11
S|xin«l attention ia ilirmc^l i" iIim Min'ltMiiriiinry lalile.
B. The thtty i* !n*eil ii|*m the entric* Un 'Mltinu* < '(inHvtniir.lt tn."
Knt«rnl fnr
lln.nt'
CoiMUfitptlOA.
eo,4ir I0.SJ8 ' •- 159
•J yj + <
I69.4J7 I il*).ilV> - l$i
... 01 a o
llf pr<i|iciiin arr >peclli«l fuither on.
Ill UL'Tfrrtu'c In the Trnilc Tnl'Ir*. |>n||f t>7. •.Iu-h'. ihn' Ihtii^h t '•limiliift diil nni imfKnt our ** Knti/inx Jii/f, .V*'.,'' h-imi <»
In i!»>(j. lait ibrre nrr ciiirtril J ititllitr^' wnrih (or " Iltniic Ctrnt. Mptitm" Iroiii (Irrai Hrlmin. II i« nolrwurlhy ihnt witkoiil thi
the " *%me'i for I'ntttin'* IfW iHKj " vttnilil lur tnciiin|tlclr.
IS) $7.a(n *' lin|i*»Tlr<l," 9l2,(J07 •* noiiic t itnsitniptinn."
I Jl The liem "AM r>thcr N. K S.'' it rcin.irkaMr, ln'caiue il is «o mnch ({rcaler ihan (lie %uin til by fat the tar|;er [Nirttoii iif
eniinierjtrd. In ilir |iie*i*uc<' "f ih» " Sttin^ 'A Itlffcience*," il tiiay well lit* .isked ; Ol tthnl arlirlas N. K. S. tn»>t cltawhrre *\
3.4S5,Jt7 lUillari' worth ciinsiM 1
le.il Rrltaln
1 t ilollaiti
Ihc article*
jtacitied) ila
I'kOM.NCl.M. ANlJ DO.MINUN Dll' I Kkl.NCKS.
Comfariim NlWHI Ihi hint or l^nituM Ort/tr oj lliffttinm aHii ikt b'lHal or lifmiMian (>ii/ei of />i/ftrtneft /or Hr Voir iSSj,
COTTON COODS OK ALL IiKSCRM'TIONX.
f
Vttaa t88j. 1
Vpak
1883
1
FinI tr Prtvi.unl On/fr t/ Ihfxtkni.
r
/i«a/ «r Drmitiifm
ihJtf ff IHfftttHitl.
\ »
real Uriiain
Unilttl Klatcn.
real Britain.
Uniieit Staler.
+
•f
^
+
__
+
7S4'?
I2U
45»
'S
7633
r»s
use
11248
'JSK*
25S!(
34S7
i«l
iSS
•il
|iUI>
lobt,
US
•7i
2CU9$
930
36 J6
31"
>4
l«>J
91
1 16050
9J0
Sl«
•«4»
"J37
114
017
1167
1 »
4P9
66
540
■ 827
113
439
T.
'97
'S
86
14102
i6o)l
>57
1225
*&
ttVil
25tl^>
1710
'al?
S9I9
3*41
to
q»2
r>5
<4<S
»39
HI
*'l
Z
479
I
TaS
5308
KM
50
66
ill
liWf
(fill!
35J
■4}
Ufi
.1')
105
908
M 1
J1017
700
930
07 1
7»i
i55»
4741
"99 1
ld|6l
S
J3
*•
»«4
507
37
1.15
$J8
7(1
1»9
90
5i
116
«9
93
a 39
109
$3o»
J47
3(t«
1710
36<>
1
I6(l
50
t»t
3*
10700
'305$
7ii»
193
17810
.1761
137
124
3
'19.234
20,MII
799'
M.9SO
107.0? I
'iSl8
18J7
*ym
Jf"
503
1
159
3
I4»
103
"44
"5
7993
li'
2824
II9,«S8
»I.445
»K.4SO
107,071
8828
n,i*i>
The (|ui\iniiiek lie|„w the first laials are pl.iced in the Cnna.iian Trade Tablen far apart from the otiict items— they will lie found oa
Ijafjes 7 ninl 43 ami nrc the 1 MfTorencea ill the items "Aofi " containing Fine Salt, anil "Carpets ' not elsewhere s|i«cifie'1. The felalioia of
tlle-w r).4.it)ilt.e, nrr very nnlcworlby.
WDOl.lF.N tlOODS ()!■ Al.l, DKSCRimONS.
I'OMI'AtlNnN RCTWR».|I TIIK KIIMT IMU riNAL IIHOM Of UirrCRRNCKN ro* WtKMJJW OOMM. MM
fin! tr PrtvimMl <
>n*r «/ {Hffirmn.
iHmi tr DtmMm Onlir */ Diftrtmu.
VtMi »IW3.
Veak laaj.
YCAK itt}.
Yka* 1883.
(•rem Ilriiiiii.
United SwiWi.
ClrcM Bcitahi.
United Stttet.
■f
+
+ - „
+ -.
alio 4^8
167 50
176 14908
167 ll
114 S*o
IM ISS
! iiii 17369
M4
Tto ■ei84
a79 :
11)11 vmi
^5!
IIM 6ai5
ia6
95S6 776
ihx8 7379
»»9 «7*5
106
«S iirts
17I **i*
IJIO
io«9
1310
1089
114 41.11
27« 49*
tht 3JK
45" '5'
U} ji.a
Jlj 2J5
ill lOIV
91 688
>9e 3179
iuro 1406
:
1139 649
MS 544
Coo >i«
MM 4470
I4S4 4499
Mi 6so
Ml 4>
(71 ifM
*S* 'i*
306 491
«
I4S $03
103
J».dBb
33.118
U.J98
3>M
'7$
17,561
5tt8<M
3070
COMHARIWN llRtWrPK TItF. SlMs OF Tltf, Dlh'FrKRS. f.s WITH AMI. WITHOUT mtCAIln TO Sir.NS ABKANGllt) ACCOkDiNR TO CoUN-
TRIKS AS OeKlVP.I. VROM IMP. I'KOVINrlAl. OR FlRSI Okl.BR OK OiKFKRItNCItS ANU Tllg FiNAl. OR UOMINION 0K')ER OF
DlPFEIIKNCES rOR I 111! VHAR iHSj.
TAllLIi II., 1883. — CotTON (;ooiii,,
Great Htiltin
United StRtn
Great Britain
United Stales
/■'irst or Ptvfimcitl
OrJtr.
.. + M9,b8X
- 21,445
.. -h 7.993
- 28,950
Woollen Goods
178,076
-Year 1883-
Final or PemiHion
Onltr.
+ 107,07 > =
— 8,828 =
+ 3,.S29 =
- M.78O =
I42.5'4
first Qrdir.
+ 33.I.S8
-- 68,398
+ 3.>95
- "75
1 04,92(1
Final Onttr,
+ 17.561
— 52,801
+ 3.070
- 50
73.48«
+ 13,6l>
— 12,617
+ 5. '64
— 5. '64
35.562
+ 15.597
- 15.597
+ 125
— 125
3>>444
45,434 or o
10,318 nr o
31,194 ot O
250 or o
!
Sum of Differences.
/ 3$.S6a
\ 3>.444
67,006
Total sum of l-'irst or I'rnvincial Dnler, Collim? ond Woollens
" Final or Dominion Oriler, "
Sum of Provincial Positive Terms without regard to countries
" " Negative " " "
Difference
Difference
$283,ooi
215.996
67,006
$283,002
The Supplement«ry Cotuin Diflrrences derived from " Iiiii«iil5
«re so remarkttMc a» tu ilcsrrve si>ecial notice.
The Ilfim ill ihc TinJe Tallies arc as follow*; —
Carpeli not elwwhorr tpecifted.
Ureal Hrilain. -Onlario ...
f^uelxrc .... ....
Nnva Soolia. . . ....
Now lirunswick .... ...
Manitolia ....
British Columbia
1', E. Islan<l .,1. .<<
Dags, cwmaininn Fine .S«lt.
Great Britain.— Ontario
Quelicc
British Columbia.
P, E. Ulaml . .
' (if " Bag! containing Kinc Salt, " .iivl "Carpels not eUewheie speoUicd,"
United States.
Ontario ....
(Jiiefiec ....
Manitoba ....
British Colnnihta
Entervd fttf
importeil,
Momf
t .iiituminion
Olffercnct
64,.i»j
6),88i
- 5o»
bIjSq
6.1,104
+ ,lo6
11.9J9
IJ.939
16,835
I6,<)«3
+ 148
t2,oti7
12,0X7
910
81J
- 103
479
479
- in
I.iji
i.ior
- 144
9.02 Jl
9,008
- IS
141
u>
o
a
1
a
39
8
i
41
4
-«»
The Supplementary .Series is,—
» ',,■■'
J
•5
(03
144
14a
151
306
50a
153»
The levcral sums of these quantiiica are respectively equal to the turns of the Difference* between Detnoulli's colimwis— The h ;sh TtaiV»
figures and the Cotton and Woollen Series.
1
«
OH-A.FT.'EJI?, ^V.
The Canadian Trade Tables of 1885 are Fabricated Records.
Th«s« IHffercnres hava not been puMisheii. T.i. / are very remarknltlc. All ihe terms of iha first or Provincial orHcr of Oifler.-
anees for Collons in 1S.S5, in respcci ol (Ircai Hritain, are sinis of eacli other, the larger terms heing siiuis of the smaller terms. It is necessary
to show there relation-i, and also in exhiliit them in the (on.- .)( an .VitHinetical pro^'re"i-«i(in f»»r the p.irp-.ise of illustratin;^ the further reiiiark-
ihlc reIationshi|i hctween ail the Tra-le Tables from 1867 ti> 18S5 "specially portraye. in the following pages.
The Process for olMaininR the Differences is precisely sii.iJIar to those exhibilad in relation to Cotton (»oa U ami Woollen (ioods in 1878
nnil 1883. To introiluce the c!eiait> would unncces;jirily inciimlier this praliminary view of the fabricated nature of our Canadian Trade
KecoriKs. The matter (iiust neces-sarily l)ecome subject to thorough iiivestii»alion with reference 10 (Canadian Trade in many other branches
than those pertaining tc< Cottons and Wooll^n«.
Attention is particularly directed tn the projwrty alxne named viz.—thai lh« larger terms of the [)ifi"erenccs are nr<lbing iDQre than sums
of the small&r terms, and comparison is reqm'sted with [)r. Edward Voung's fish Trade Figures for tbe year 1872-3, as fully illustrated in
XAHLE III, whttrft it U shown that this property of the Heroqutli Series belongs to th*m.
FIRST OHOKR OK rROVINCIAI- niFFERP:NCE6 -COTTONS- 1885.
fire.1l
Briia'm.
I'nilei
.Stalls.
+
_
+
i
>3
1
3
1*
|i
a
16
a
*H
•8
130
d
49
I3«
(0^
90
IW
OS?
iS
lis
<$17
itt
*93
34S
*
2088
55"^
337
39*
170^
St'
401
^
4I«
i*»
539
1*1
X S
STs
m
5i?
9$
1066
•«
:i£
■004
M0$
,
•99?
JJIO
4044
rw»
600a
l»9S3
-37.185
+ 17.U3
f- 13.003
+ 13.005
4- I7.>23
- 37.'«5
— 10,388
Sum
— 14.180
Rum.
+ 6,735
Difference .
. . . 60.190
Piffcrence . .
37-5"
60,190
— 14,180
a7.5>'
■¥ 6.T35
liiim .
87,701
- 7.445
Pifl'erence
3^.679
Jo,9i5
96
lOCl
1246
»49
5*3
1030
(6091
10,388
(•'INAI. 1)11 l-r.Rl.N'CKS~CCTTONS- i«vSs.
13
Ih
a<
106
«39
^\
7»7
910
98r
1791
619}
7051
+18.94J
l»iMt Krilairi.
Unftid St»le«.
-3J.«*»
7 3i.«««
+ 18,945
Sum..
Dift'trcnce
i4,iSo
$1,070
" ' 11,76*
Saw 64,sjs
Difference . 39,30$
+ 975"
+ 9750
— 30'5
+ 6735
ia.765
3
I24(>
341
349
1070
- 301s
fIRST OkDER t)R pfeoVINCIAl, DIFFERKNCES.-VVOOLLKNS, 1885.
4-
112
171
107
1034
1740
3730
144
178
1589
tor
871
4»7
3>9
330
16 1
»334
8280
4*4
•o)
911
J760
i33
'349
190
4'47
4»7
+ 34.144
GtemI Hriltm
bifietence.. 66,412
5«9
I031
193*
«4>
«W
|6oi
415
•sr
no
United Smies.
-3«.»78
"54
^
+ 158
4333
8«B..
ilM
+ J58
4491
- 3971
M
2)
I-'IKAI. OR I)f)MINl<)N DIFFERENCES -WOOLLENS, 1885.
Ortfil Britain.
+
97**
1921
9«19
3683
ijoa
4147
427
J 1, 470
kiS,
«S9
19.6 1 J
+ 21,479
- 19.613
bifTcrencc . .
4i.o6i
Sum
1866
United Slates.
+
'54
+ »5fl
Diflerence .
Hum
4316
>5
- 423'
- 4»3i
+ 358
4487
— 3975
THE ARITkMEttcAL pkOGRESSlON TABLE FOR THE YEAR 1885,
OOTTOISrS.
he First or Prot'm-ial Differences for Cottons in respect of Great Britain for the Year 188$, in the form of aH
Arithmetical Progression, with w as a Common Differenct.
10
I
i
106
110
12
28
170
I
16
»93
3'o
3
6
401
410
I
6
•3
'3
106
3
189
}}0
I
3
16
'3°
170
320
49
37>
430
>3
16
30
3
6
121
'3°
13
189
'3°
28
393
330
•3
16
401
430
12
28
40
I
3
6
'.30
140
106
13
340
49
5d
«3
16
111
l6
16
28
60
38
132
"5°
49
189
350
.2
13
189
337
139
~^o
350
28
3
411
6
441
440
4SO
160
121
•39
360
I
3
6
'3
337
360
■32
•39
189
460
3
12
55
70
3
6
55
>o6
170
12
28
28
201
370
3
i!6
13
337
370
'3
16
441
4JO
12
13
55
80
t
3
6
\^a
180
I
6
13
90
170
280
3
13
28
337
380
3
106
37'
480
I
12
28
49
90
t
6
13
170
190
I
13
16
90
TO
390
t
3
49
337
390
49
441
490
t
16
28
55
100
i
»3
16
170
I
6
»93
300
38
183
189
400
I
3
6
49
441
500
And so on continuously.
^mmammB^ms
With /iX) as a CiDiimcM Difftrtnc/
I
|6
tS
55
6
a8
1066
1 1 00 I
And so on.
53°
403
55
12
<3
16
170
too
I
3
'3°
lo66
I
6
300
3
la
ui
•83
98.
1300
«99)
3
aooQ
28
'83
l8g
400
I
la
a8
»93
1066
140Q
I
3
(1
49
441
300
'.59
645
7»o
1500
I
90
106
403
600
121
<479
i6qq
I
3
90
eo6
700
3
(6
202
'479
1700
With fooo >is a Common Differ in(t.
I
6
90
106
597
HOQ
3
106
710
981
^Soo
2004
981
la
3
3000
1997
1820
i8.?
40.00
4510
441
49
500Q
4044
1820
13»
3
I
600Q
3
6
»93
S97
900
6
12
403
1479
6003
981
16
X
7Q0O
I
55
«44
3
16
55
■ 06
1820
■
2000
710a
777
121
8000
600a
2205
777
:6
9000
600 a
2205
1066
710
16
4044
6002
7102
45>°
45'o
45'°
1066
39»
37>
";
90
6
16
\
3
lOOOO
1 1000
.\n
d
I JOOO
so on.
>»953
28
16
3
1 300Q
"953
981
49
16
I
14000
W9S3
1997
49
I
15000
It is to be noted with regard to these Arithmetical Progressions formed out of the Differences between "Imports"
and "Entries for Home Consumption" in the Canadian Trade Tables for 1875, that the next succeeding Table shows
that the larger terms of the First or I'rovincial Series of 1 )iffercnces are nothing more than si,n\s ot the smaller terms.
Therefore, the preceding progressions can be put in a vast variety of forms by substituting for values of the larger
quantities the equivalent values in terms of the smaller quantities.
EXAMPLft" Let it be required to put the quantity 400 in different forms of terms of the IUffercnces,
, 28
28
t8
28
28
28)
■3 1
'3
13
'3
'3
183 -400-
189)
170 1
t89
- 170
- 3)
6(
._ 3 _
6
3
6
170 V
55 i
106 I
55
'\
400
16
i3\
go 1
I
40Q1
3
'3(
1 2
f. \
3
28
55
49
106 /
55
'3
6
16
90 1
3
6
400
6
55
16
40a
4?)
And so on down to the lowest terms.
40Q
^ *U*i-.-
TJFj1 fTWBaSJ*t ..
39
THE ARITHMETICAL VROGRESSION KOR WOOI.I.ENS. - 1885.
FIRST OR PROVINCIAL ORDER OF DIFFERF.NCES.
(Siwu quantities are introduced in duplicate for special reasons.)
37
161
300
a
37
»i*
649
QOO
«3
161
1316
1500
a
37
i6t
«S7
913
1 03 1
3300
3'9
1031
1740
3100
<3
157
3730
3900
And so on.
>S
141
144
300
t
178
207
400
171
329
500
144
>3 '
161
427
310
415
3»9
677
424
900
000
1000
3 !
161
3
37
190
'5
649
' 349 1
91J
912 1
871
1 600
1700 !
1800
IS
3
17'
>44
37
■57
t4« 1
'7«
329
«S7 1
178
913
913
871
1031
103 1
329
9.2
—
3400
2500
2600
•7'
15
3"°
213
37
330
233
141
3760
3^9
«44
"55
303
3760
1
1 3300
3300
3400
15
•3
3
3985
»57
'5
190
37
»33
178
677
871
3730
912
3985
4000
5000
6000
190
303
307
600
190
»33
677
190
677
1031
1900
212
333
"55
2700
13
37
312
649
3589
35°°
3
«5
102
6881
7000
3>o
212
.78
700
'5
.78
330
677
3
37
178
871
912
2000
2
310
•54
3334
2800
3
'3
37
310
649
2589
3600
3
37
1031
2760
4170
8000
13
213
233
242
700
3
437*
871
1300
3
«3
15
33°
1740
2100
3
37
161
243
203
2255
2900
370°
677
»33
190
373°
4170
9000
161
310
329
800
310
.78
912
1400
>3
37
312
1938
37
203
2760
3000
37
161
203
310
3'9
2760
3800
»
13
«5
33°
1740
3730
4170
1 0000
^imm^
to
THE FIRST OROF.R OR I'ROVINCIAI, niFFF.RENCES. - WOOI.LEKS, 1885.
THK l.AKdEK PRRMS ARE srMS Of TKE SMALLER IKRMS.
1
144
'3
>3
2
2
37
190
;J7
»4i
'44
15
15
141
102
1
"5; 1
144
'54
141
144
154
161
171
178 1
1
190
■3 '
2
212
2 '
2
15
2
a
190
'5
'3
37
141
'S
«3
190
15
203
■54
141
144
»^3
171
171
-3
207
212
m
242
3'o
329
330
37
J03
2
2
13
190
312
«3
'7«
212
'3
>5
207
3^9
330
«S
178
'5
»33
'03
207
207
toa
S19
t6i
■
386
4'5
4J4
4J7
4J7
5'9
542
649
'3
>7>
178
2
'5
2
'3
37
<5
.78
3'o
'5
107
f.
37
161
649
212
424
102
gi2
'5
329
1740
3'o
912
912
141
'44
'034
330
1031
677
871
1031
•034
'349
1740
'938
190
2
13
2
•3
'3
2
2
1031
427
330
207
37
'57
'5
4'5
«034
871
677
1031
161
161
37
373°
1034
«74o
'349
427
»o3
3'°
329
330
3601
»334
2760
360 1
1 2760
"55
3760
2589
3730
3985
4147
'3
i^
1
2
'5
330
«S
15
■57
2760
677
33'^
3985
360 '
3601
242
3985
82S0
8280
4170
6881
8869
On page 32 the "Fire-brick and Clay Series" is put in terms of the Provincial Differences for Cottons for the year
1885. Any well-trained school boy can put the first order of Provincial Differcnics for Woollens in the terms of the
"Fire-brick and (Hay Series." Thus reversing the o|ieration, but using Cotton Differences in one case and Woollen
Differences in the other. I do not introduce thi.s form of the Differences for Woollens for the year 1885, because it can
be so easily effected by any one who choMs to take that trouble.
THE FIRST ORDER OR PROVINCIAL DIFFERENCES. -- COTTCNS, 1885,
Af.I. THE
TtRMs OF THi First or Trovincial Differencis for Cottons in 1885. in respect of Great Britain,
Sums of each other, tnk Larger Terms being Si>m^ of the Smaller Terms.
i
3
i
1
12 !
' !
1
6
,
3
3
i
3
16 ;
13
49
It
6
i
6
12
'A
1
28
49
•._
*■ — '•■
6
11
u
16
a
49
SS
90
16
i
3
1
1
3
«3 U
13
90
12
b
i '■
6 !
6
170 170 1
.189
106
121
i
1
6 1
16 !
106
'3» ,
.^
N
106
111
I. 10
1
132
139
iro
183 i«9
am
I
16
i
1
3 :
3
16
i
>3
28
4<)
3
6
16
^n
«93
193
16
12
371
39»
37 «
40J
j
345
•93
J.?7
345
371
392
401
403
41*
I
6
1
3
12
3
3
i
18
12
i
16
S30
6
6
4"
49
441
t>
12
5. .8
5o«
53°
49
539
S97
*<;i
S08
530
527
S4«
539
597
«o6
1
1
'J'
'30
I
I
12
1
1
3
6
64s
777
130
7'7
d
«3
49
\l
!l
55
•^5
16
908
907
,1?
606
.
6*5
710
777
907
908
944
98.
1066
,
>
I
1
6
6
12
16
i
i
SI
16
12
'3
13
371
ar
■•I
508
<83
1820
441
2205
,m
1479
l8«3
1479
2004
2205
4044
45 lo
1479
1820
1997
2004
2205
4044
45 '0
7i<n
•3
6
1479
12
4510
ss
202
1066
4510
7102
60M
1*953
It would needlessly encumber this Exposition to put the terms of the First Order of Provincial Differences for
Cottons in 1885, in the form of equ.valenls to Dr. Edw.i "oung's United States Fish Trade Figures for the year 1874.
These are tabulated in Table IV, and any school boy c - put the above First Order of Differences for Cottons for
the year 1885 in the equivalent form cf the column of United States Fish Figures given in Sutement Na IX, Section
I, Table IV.
'i
«•
Thi "Fiia-BiicR AND Cl«v SRmn" m Tp.rms kk ihk Iikvi ok CRnviNciAi Dippkikncu rO' Cottons in 1885.
I I
J
6
I
3
6
lA
a6
16
16
42
38
26
56
6
II
55
73
16
16
I
3
16
106
'»S
3
6
la
Ml
14a
I
I
<)
>3
139
16a
6
la
aS
■39
185
I
I
1
i«>
1 1
IJ
1
3
1
6
3
6
16
as
aS
3
6
a8
la
la
6
16
38
' 55
170
U
55
.^
37 <
1W
54a
54*
530
710
1066
16
aoa
1066
1
aoa
1066
1066
3S«
55a
565
;qo
7<M
ia7fi
i;}oi
'33a
M3a
U5S
1
a8
,
6
'3
lb
la
,
1
■ 89
3
la
M
41a
• 3
16
6
11
1479
6
.55
aaos
55
a8
• 3
106
49
i8ao
aao5
508
•479
55
U79
l8ao
aaos
aaos
aoa
'479
aaos
1602
1696
1879
iKoi
2462
163?
a793
3719
3961
3
la
S5
4114
12
28
aoa
4044
4*87
106
530
aaos
710a
9943
3
6
28
4044
710a
11.184
3
38
■S3
441
4044
710a
ll,8ol
16
412
4044
ia953
■7.435
I
3
6
■ a
■ 31
710a
■a953
30,198
These interchangeable figures am thus be represented in many equivalent forms, one of these being a prior series
twelve years old, and purporting to represent the Fish Ex|Kirts of the United States in 1874 to British America.
COMI'ARISON BKTWP.t.S rHF. Sl'MS nt THE I HKKKKKSCEs WITH AND WTTHOl'T KKiAKH TO SIGNS ARllAN(iKI) ACtTlRniNG TO COUN-
TRIES AS IIERIVEI) PROM THE PROVINCIAL OK KiKST ORDER uF UlfFERKNCES AND THE FiNAI. OR IX>MIMON OROKK Of
Differences for the Year 188^-
Great Biiiain
United Slates
C.reat nritain
United Slates
TABLK C., 1885 — Conris Goons, Year 1885.
firsl Ordtr.
+ 33,005
- 37.^liS
+ I7.ia3
.... — 10,388
♦ 87,701
Woollen (;o<ii>s, Year 18S5.
Fit si Ordii.
+ 34.'44
— 33,378
+ 2J8
— 4.aj3
Total sum Firjt or Provincial Order— Coltims and WoolleiH,
It Final or Dominion Order, ....
Sum of Provincial Positive Termt without refard lo countrin.
Negative .,
70,913
r>iH'eren>:e,
DilTMenre,
Final Ottitr,
+ ■8.945
— 33. 'as
+ 9.750
— 3.o'S
64.835
Finai Ordet .
+ 31,479
— 19,613
+ 256
— 4,23'
45>579
Differtmti.
— + 40601
8, lao or
4060/
- 7373 / *''*
33,866
Differeiuis.
4- 12,665
— 13,665
+ 2
— 2
35.334
a5.33oor
4 or o
$ 158,614
110,414
48.»oo
+ 74.530
- 84.084
i5«.6m
CHA-FTER 'VI.
THE INTKRCHANOKAHI.E OFFItJIAl. FIGURES OF IWO NATIONS.
In this (.'lia|itcr some illustrations arc (jivcn of tlio interrhjiin,'ealilc diaracter of the i|iiantities cmiiloyed under the
siipcrvision of Dr. Edward \ oun)^ and Mr. ('(jmnii.'.sioner lohnson, in the Manufacture of ( anadia- and United States
Records of irade. 'I'hcse illustrations cover the years froiii 1872 to 18K6, intlusive.
Any person who (hooses to take the troulile ran put all the Canadian Entries for Cotton Coods and \V'oollen
Cioods in the form of an indelinite Arillimetical Progression, bv ])ursuinf; the process mdi( ated in the followin({ pages,
for the years iK;,^, i88j and 1885, and, 1 have reason to helieve, for many other years and many other classes of goods.
Any [lerson can also take the differences between the "Imports" and "Entries for Home Consumption," and put
them in terms of the Denominational Figures used by Dr. Edward Young to represent United States Trade in Fish,
Fish Oils, Shell Fish and I'nulucls of the Sea. These again can be put in terms of the "Firebrick and Clay Series,"
and they can all be rediued down to the Bernoulli Columns III. and II. In other words, they are all the equiva-
lents of the sums of selected Co cffi( ients of the F.xpansions of ( i + i ) or ( 1 - i ) lo the [lOwer of n, where n is succ^jssively
e(|ual to 1, 1, 3, 4, 5, \-(., as far as it is found convenient to go. The work is done by means of a "Ready Reckoner."
These Trade Tables are, in fact, practical illustrations in figures, of Bernoulli's famous words engraven on his tomb:
EaDEM .MITAIA RliStJROO.
To these illustrations I have added one of the etpiivalem forms of the "Fire brick and Clay Series," in terms of
Bernoulli's Column No. III.
.'\lso, First .\ mathematical formula for obtaining any desirable ratio between two (juantities, and the corres-
ponding series in Hernoulli's I'ahle.
Second — A general mathematical expression for the terms of any one of the vertical columns in Bernoulli's Table.
Third — The mathematical process for converting Hernoulli's Formula into the "Differential Method" of expressing
the sum of a Series, as given in modern algebra.s.
I'ttK WONDERFUL ACCURACV OF THE FIGURES.
It is time now to direct attention once again to the surprising .icruracy of the Figures employed. Nothing short of
a joint ready-reckoner coulo have produced this .accuracy, (^istom House figures in 1S78, 1883, and 1885, referring to
certain cLisses of goods, are found to be interchangeable with Custom House records relating to other classes of goods
in prior years, 1872 3 or 1873 4, tor instance -and also interchangeable with the dutiable Custom House Records of
a neighboring people, numbering til'ty-six millions, the greater portion of whom are more or less engaged in commercial
transactions who.sc alleged records pos.se.s.s these properties. The illustrations given below are types only of a vast
system
THE AI.I.EC.ED CUSTO.MS HOUSE ENTRIES FOR THE
FORM OF AN ARITHMETICAI.
YEARS 1878, 1883 AND 1885, IN THE
I'ROCRESSION.
The following tables show how the .alleged Custom House entries themselves, for the years 187S, 1883 and 1885,
may be grouped in the form of an .\rithii>etical Progression, with looo as a common difference.
Vinr /SyS.
Ecjiiivalcnl Differences,
Cotlnns only.
+ 5<"
-)- iSo
- 158
THE yUANriTV lOOO, WITHOUT KEOARD TO .SIGNS.
Yrai iSSj.
E(|uivalent I^ifTerences.
Col tons only.
+ 78»
+ 218
— 100
1000 Ioe»
Yttir iSyS. --The corrc ponding entries with (heir negative signs changed :
I'lrent Bril»in— Carpets of any intterial, except W.xilien,
(jreat Hritain —Ginghams and Plaids, ... .... ...
United Elates- Carpels uf any material, except Woollen,
1,'nited St*Ie< — Ginghama and Hiaids, .... ...
$I294WS
128468
Ytar iSSs.
Kquivaleni Olffercnces.
Cotton.s only.
+ 403
+ 54a
- ss
$96562
20385
8058
446J
129468
$96000
20205
7900
4363
1 2846*
i .
Ytar /SSj.—Tht roc rwpom ling cniiin with ncgmive iigns ch.iiigtrf.
Cir.il Itiilain Wincryi, I lirikecl, .tc, Mvi-t J'i inclifs, ^...
Unit«l SUIM.— Clothing, ot uihet m»lefUl n»i othi-rwis* (inviikil fm,
$25.1557
»5a557
looo
Ynr tSil.—Tht: CDtresimmlinu cninc* »ilh negative iignu ch»nntil:
litMt Brilain. All other, ,.>. '" t "" ""
(iteiil Britain. --Par«»i>l», ■ • • ■ •••• •■••
Grnt Btitun.— ColtoD», I'rinlcd oi Dyed, ... ....
li842H
$ JX.M.l
153557
$J7,'!5«
»5».S57
4050-1
4U101
6l(iai
60946
37913
- 37J81
liUM
U84»8
rtar isri.
/^uivalenl I )ifreit
nccb
Cottons & \V\iu)lcn».
— 100
+ ito
THE QUAS iirv JOOO.
Yiar iSij.
Kiguivalent Piffrrences.
Cottons only.
-90«
-613
— 479
1000
Viar iHyS.
Unitcil Slalen. - llin.fhams aiiil I'laiU.s, . ..
United Sia:e». -Carpets,
Oreat Britain.— Coltom, Primed, Pointed, 4c.,
$2,002,760
*,ooo,76o
Yiar riSj.
RquivalenI 1 >ifrerence».
Cottons only.
+ "W7
1
4.4''.>
"4.25J
1,984,044
1,00a, 7te
$
4..163
1J,95.'
i,<)8a,444
a,ooo,76c.'
Ytar iSSj.
Great Britain. -Sewing ThnaO, in ILinksSc,
United States. All other Maniilnciuri-i N. E. S.,
Cleat Hfiuin.— Wadding, Batting, \Var|», &c..
s,ooo
$577,704
575.704
$
I52..?4i
411.837
3.5»5
577.704
i
1 5 '.434
421,224
3.046
575.704
Cleat Britain.
Great Uritaio.
Year /SSs.
- Cottons. Bleached, Sc,
-Winceys, itc.
$44.6I«
42,6lK
20,429
IS.'89
44,618
$
42.Cl!i
!!
Y,ar 1S7S.
Bquivalent Differences.
- 1048
- 842
-t* 561
- 158
- joo
- 90
3000
THE IJirANniY jooa
Ytar /,Wf.
Kquivalent Uifferencea.
+ 1356
■¥ 78J
- 558
+ 21K
— 86
3000
Yta
iSXj.
■jjuivttlen
1 lifTcrcnccs
+
i0O4
981
JOOO
United States. —Cottons, Printed and Painted, —
Great Britain. — Worsted ami Yarn, .... ■-..
Great Britain.— CarpeU of any material, except Woollen,
t'uiled States.— „ .. 11 n
United Slates. -Carpets, ....
United States.— Clothing, &c.,
$ 1,270,046
1,267,046
$
893,681
66,0s I
8.058
■4.353
191,441
1,270,046 -.- 1,267,046
JOOO
\'-\
■i-w Kr'»lnSii'mmM/:VMiJ\ '
•M
Vtar iMj.
United Stii!««, — W.id.ling, Hailing, W.-\tp», &c., (not dyed) ..
(iteal lltitnin. - Winceys, ('liccked. Sic, nut over 25 in.,
flreftt Hriloin. -Ha^;'* by the Needle,
United Stiles. -(Nuliinu nr olhcr material, &c
United Staien. - Iteil CnnifuiKrs
$291,243
28)i,242
3COO
Vtar iSSj.
Great Hritain. - VVIvcteeni, ......
(ircal Mritiiin.— Ik-d (lomfnrier.^,
Great Hrilain.— Jcins and C'uulillei,
C'ireal llrilain. —All other,
$285,671
282,67 ■
]ooo
291,242
2S5,67i
188,241
$
$
06,178
3.476
2,229
73,788 -
304,174
3,495
1,217
73.785
282,671
Vtar iSfi.
Equivalent I )ilk'rcncc!.
+ "599
+ 1600
519
+ 180
-.. 100
+ 3
40cx>
Vtar IS78,
(Ireat llritain. - Jeans, Penims, &c.,
(ireal llrilain. -rotions, I'rinled, I'-unted, &c.,
1,'nited Stales. - Tweeds,
(Ircal Hrilain. Ciughams anil Plaids,
I'liiicd Siale.s.— .. ■.
United Stales,— Clotliing, &c.,
THE
cJUANTirV
Vtar tSSj.
4000.
IV|U
valent Diftercnces,
+ 1356
- 908
- 558
- 613
= *??
4cx»
$2,175,894
1,171,894
4000
Year 188^
United Stales.— Wadding, Batting, .%c
(Jteat Britain.— Sewing Thread in Hanks, &c.,
(ireal Hrilain.- Hags l)y Ihc Needle,
V'niteil States.- Alliilhcr manufactures N. K. S.,
(ircal Hrilain. • Wadding, Hatting, Warpk, ic,
United btales.- Bed Cunifoticrs
Year I8)i5.
(Ireal Britain. —(;, .lions, Ble.iched,
(ircal Britain.— All iilher
(ireal Hrit.ain. -Shirts,
$615,380
611,389
4(XI0
$691,479
687,479
4IXXD
And so on, continuously, up t^) 10,000, or 30,000, o. 50,000, &c., &c
Vtar iSSs.
Kiiaivaltnt liitTerenccs
+ 1907
"f lita
- 183
4000
$
$
28,528
—
16,939
1,984,044
—
1,982,444
10,026
—
9.507
20,385
—
20,205
4.41^3
—
4,363
128,448
—
128,446
3.I7S.S9-1 — 3,171,894
$
$
39,505
28, 149
I53.i42
- IS'434
6,07s
5.520
421.837
- 431.224
3.535
3,046
Z,102
— 2,016
615.389
611,389
1
$
39,439
564,379
97.<'7l
37,433
- 502,559
- 97,48s
6»1.479 — 687.479
In a similar manner all the Custom House entries answering to ihe Difierenccs on pages I and 2, 21, 22, 33, 25 »nd 16, can be Jiul
' - - Where ihe reduced Uominion differences form
rences furnish the details for a common differ-
in the form of an Arithmetical Progression with a common difference of 1000, or 100 9' 'o.
only an Arithmetical Progression with toco as a common difference, then the Provincial diffe:
ence of 100 or 10, as shown on pages 27 and 28, for the year 1885.
rms o( every -Vrilhmetical Progression are subject to certain malhematical relalioni, and the grouped Custom House entries
, of an Arithmetical Progression arc subject to the same relations. This is a point which need not be illustrated, for it reqmtiB
1 it is a mathematical certainty. It remains to show that the Equivalent Differences can all be put in terms of Dr. Edward
Now, the terms c
being in the form (
Y'oung'°"FiIh Tr"adc 'Figu"e5,"an'd"liuw con'nec'i'the deceptions going on now, with the deception* which have been succesjful, but Mill temaiu
to be used again, as these Trade Tables fur 1885 foreshadow.
Thi CquiVAi.iNT Cotton or Wooi.lin DivriRtNCU rot 1878, i88j anm 1885 in Tr.«M« nr DR. Kow^tn VnrNO'i FllH
TiADi FiouRU TAKIN nii'M Hilt Uniikii Htatm C'ommircc AND Naviuation KuroRT, roR 18717.1.
(Sm nti't III., SmitmiMl N; yt.,/tr DtHomimUtmal dtlails.}
1'
S6a
180.
158
Sr\* 1878.
F^luivaknl I)«nnmiii4tioit«l Fiiuin i.f Ynnng', V. 8.
Kiih, I'ickleil, lo lltiliih (JuiaiM.
.. Fresh, to Qurtx'i*.
.. Siniikol, III Niiv» Scoun,
n \Vh»le Oil 1.1 N.iva .scntia \ N«w Drumwick.
I) Tickled. In (^'uelwc.
n Iirieil, til ..
I, Kre«ti. to liondura.«.
.. Drieil, 1,1 (,iiirl)ec.
Whule Oil 10 Nova Scolm ami New Uiuii'iwick.
Spermaceti lo Quebec, &c.
Sperm, 10 ..
WhaletKinc lo Britinh Cnlumliia.
VVlLile Oil to Nova Scoti:i nnd New llninowick.
S|ierm to » •,
WhalcUme to Hritiih Columbia
I
1
78J
ai8.
YlAR IMJ.
K<iuiva]ani T)«n*Mnin«itotut Fittiru ni Vouiig'a U. S,
► l.h lr«il« kuKil II, i«;i.7|.
Kith, Drieil. 10 llrilUh ColumM*.
,r Ciireil, til llritinh duiana.
.. Tii^kleil, 111 (.iiietiec.
Siierm to i^uclier, i^c.
Kuh, Sinokril, to i^liicliec.
., I'iikleil, to llritinh Columliia.
.. Kresh, lo llrituli Went Inilict.
Sperm lo f^iuetier.
WhaleUme to Hrilith Cnltitntiia.
Fish, Smokeil, lo (^ueliec.
Yrak 1885.
Rqutvalent r>l(fcr«nce«.
Colton* only.
403
$4*
$5
340
108
Herring to British lUiiana.
Fiih, Fresh lo (^ueliec.
52 „ I'ickleil, to .,
3 !• .. lu Hritith Columliia.
340 Herring to British Cuian.i.
174 Fish, ■ -'■ - "- ■
76
YrAR 1878.
F.quivRl«nt T1iff«rcncei
(ottonft k Wolilten*.
5a
3
Fresh, to British West Indies.
Smoked, to Nova Scoiia and New Bninswick.
I'ickled 10 t.)uel)ec.
lo British Columliia.
300
l6no
Whale and Fish Oils lo N. S. and N, H.
Spcrni, to l^ueliec, &c.
Whalelxine to British Columbia.
Fiih, Fresh, to Quebec.
,. Smoked to N. S. and N II.
Spermaceti to Queliec.
Fish, Tickled, 10 British rolunibU.
>i I>ried, III Quebec.
Oysters to Newfoundland.
.Sardines 10 Nova Scotia and New Brunswick.
,. to British West Indies,
Fish, I'irkled, to British (•ui.ina.
.. Kre»h, to Bntisli West Indies.
,1 Dried, to Nova Scolia and New Brunswick.
•• Pickled, III British Columbia.
Veak i^i.
KquivBlcnt Tliffercnre.1
Vkak 1K85
KquivsUtil Differences.
C'Hions only,
240
258
908
6t3
479
I
P.
/'353
I 108
; 61
('(itliKi^ f>nly.
Sanlinct, Ac, to Nov« ScntU and New Bi"nswick
Herring lo Hriuith (tuiana,
Ki^h, Pickled, to {British (fuiana.
•• •• to Quel>ec, Onlariu.
Whalebune tu Hrituh I'alumUia.
Fish, Wricd, to Hritish (.Columbia.
Fresh, lu <^ucUrc.
Whale Oil to Ni>va Scotia and New Hrunxwick.
Fish, Pickled, lo *)iiel>ec.
.Sperm lo do.
Whalebone to Hritith Columbia.
Herring to British (iuiana.
Fish, Fresh, lo i^ucbec.
Dried, to Nova .Scotia.
I'ickled, (o Quel>ec.
H to brituh Columbia.
1997
1K84 Mackerel tu Prili<ih West Indies.
58 Si>ermareti to <,>ucbec.
5a Fi»h, Pickled, tn Qucl)ec.
) .. .. to britiah ('olumbia.
3 Fiih, PickSed, m Britiah Columbia.
3:
Ykar 187K
Sanivmltnt
iHffiirvnrt*.
84J
562
*».
90
3000
I. *J
I 45')
I .15"
I ^
/ «.«
I hi
!"
6
!
( 340
I N
I ''
I S
r.guivftlfnl (Icniintrtali'iriiil Funrci of VtHlill 4 U. H.
Kl.h IriJa lta<:<>n)* ill ll;a )}.
VVhtlelMinc 10 (judivr. Ike,
Spernuirrii iii „
Kiih, I'icklcil lu ..
.. Driril, In ..
OyMrra III NrwfniinilUiul.
Snriliiifi III N.ivfl Scniin.
>>|i«rni 111 i^iurlirf.
hull, I'icklcil III llniuli I'liltimliit.
Ki»h, Until, HI lliiii.h I'nlijinliia.
Kresh, m i,>ueli«c.
Whale Oil III Niivn Scniin >ni| New Rruniiirick.
Sjicini III i^luflifc.
Kul), Dried, In i^'iicIh*!-
11 I'ii'kk'il, In MiMi'll ('iilumlNa.
Merrill); in ltriii»li liiiiann.
lull, rii'kicil, lu i,liltln:r.
Whalflnilu' In llrillili rnlilinliit.
Kmh I'irkleil, in l,turlirr.
Sjieriti 111 i^hu'liec
'VhaliiUiiic lu llrili>li (.nluiuliit.
\'nr iSg],
KilUlviite
IJiirirc
IvRtem
wt*.
KiiaivalMN
JOOO
115ft
7»i.
558
JtH
86
J003
I
FigiHt* III Viiunf'ii V. |.
ItrifiU uf i>7i • 7]-
(' 700 While Oil In HtltUh (Aimnii.
Jjo Surilintk 111 111! m N. S an<l N.
' 141/ lliTiliig In llriIKh (luiiria.
I SH Whalrlwiie In l^iirlil-c.
\ H . Ilriiiali Ciiluinliiii.
[ 700 VVhtIr Oil III llrilinh Cnliinibi*.
! 5a V\\\i, I'irklcil, In l,)llaliec.
\ JO Sperm In (^urlicc.
ifi Kitli. Other C'liiril, In llriliah (iuiaiiii.
loS „ I'lc^h, In l,>uelier.
76 > Orieil. Ill Nuvn Sciiiia ami Ncy Qruniwkk.
JO S(«nii In i^iiielwc.
6 Smnki'tl |''ii.h In l^uelirt-.
iu8
S»
5i
61
8
6
»9W
Ki>h, Kre^li In (,>iii'lirc.
Sjieriii.n:rli In tin,
I'li'Ui'il Ki'h 111 Owlier.
Vkau iSHj.
Killll*alriit
niffircMi e*.
K |iiiv. ill-lit lltii'>i«iiuii-)iiNl Kigurtt of Vimiiir't
Ki<h iablt.
*XV|
9«l.
I lH6j llrrring in llrii«h W'eil lndie».
] IC18 Kl.h, Fresh, in ijuelicc.
I 30 Siwrni In (Juchec.
I 3 Kith, I'leklcil. in Hritiih Cnlumliit.
f7oo Wlialu I lil In Rriiinh Cuiana.
240 Herring In „
.Jo >lH'rni In i^luclier.
IH Whalelinilc U> Uriti\h ('nlutifl^i^.
3 K11I1, I'lcklcd, to I. ,.
1|
b ]c\»\\, Drieil, In i^iirli«c.
J II I'ickleti, In Dritinh (.'uluinhia.
6 II Drieil, in (iiieliec.
JOOO JOOO
And to un fgr luccceilmi; it>nii«.
The tlHive illuMraiiiw for ihe year lUj is itiir«ihioeil lo niiuw thM
these Equivalent Uifrcrencrs, nlthmt^h they ^rnduce ihe re(|tlired iiiiin*
lier JOOO for cotlnnii, yet cannui be pu( in teritis uf l>r, Kdward Vuung'f
lish Traile Fifuren for 1872-73, the qiianlity 86 nnt lieing iiitei-
chaneealile with thein. Ttwrefore uther K<)ii>valent Differences mux
be la\;n, — Micb aj> ihe fullowiiiK, which aiunxr nil (he cuudi/iuoi :
782 =
318
908 =
350
280
6a
53
30
8
loS
I 108
= 58
I 5»
909
8
f 12
6.3= I
( 280
I tun
JOOO
jam
On pa^e 29 11 is staled that "some i|uaniilics aie intru>Uiced in d«pU<|iU for »p*:ial reasons." The reasuna arc ikal anieu regard l> hod
10 the duplicate nr triplicair fnrms 111 which the dilTi.'reni leriiiH nf the Arithini^lical I'rugressinn luay 1>C put, eKurii to ulilain ihc ojiiivalent
diflerenccs in leriii
r triplica
siif^ln.
Kdward \'inini;'s Ki^h Trade Figures may fail.
The reader wilj Ijeaf in mind that fhe foregoing "Denominationai Figures of Young's United States Fish Trade
Records of 1872-73," can t)e imt in terms of an Arithmetical I'rogression, as in Se<;tion III, Statement VII, Table
III; also, that the larger tcrnii are sums of the smaller terms ; also, that these ie denominational figures can be
put in terms of the United .Slates Imports from British America, as in Section I, Statement VIII, Table IV; also,
that they can be put in terms of the "Fire-brick and Clay" Scries, as in Section I, Statement VII, Table III; and if
the reader will turn to the suceeding page, he will find the "Fire-brick and Clay Series" in i'irnts of Bernoulli's
Column No. III. The relationship Is thus carried back from 1885 '" i'^^?! ^"'^ 'l'^" '^^<^'' '° ''^^ Bernoulli Table,
first published in 1713, or 173 years ago.
S^rtwi*5:^^ l'fMS(M^9WWHIMIp^».»-.-J
f
I.
81
THK "FlRK-BRtCIv .\NU CLAV SKRIKS IS \'Hh 1:ijLIV.\LP:NT UK BKRNOUI.MS COLUMN No. III.
(It will Ih.' reiiu'iiilH.-l'i.'d that the name "Kirehriik ami Cl.iy" Scries is derived from the substitution of 11,184
dollars' worth of "Fire-bricks and Clay " for "F'.h," in the rcndeniig of the Canadian Trade Tables cif 1867.)
.V T.AHt.E II, SlATEMKNT I, for the Orixin 0/ this Kcmarknblt Sfries.
It I-. slidwn Ml Tabic II, Statement IV, that the "l-irebriik and (^lay Series" ronsists of the sinus of the (iiianlities
9, 10, 2.>, 26, 4." .iiid jt), lieihu Its >ix l(]«e^t terms. I'hesc quantities are the ecjuivalents of the grou|)e<i sums of the
first icn terms of lieriioulh s Column No. III. The terms are o, o, 1, ,?, 6, 10, 15, 21, 28 and ,5(1, whic h are themselves
the successive sums of the natural niimUrs 1. j, ^ 4. 5, 6, 7, ^c, as may be seen by examining litmoulli's Table.
1
i
1
1
()
iO-
1 "
1 '°
42-
1 "
1 '5
},(,■
1 '
1 '°
II
1
1 .^
1 I.S
( :i
I45
Hy substituting l!iese Values or their equivalents in Statement IV, Table II, the "Fire-brick and Clay Series" can 1)6
put in terms of the quantities i, 3, 6, 10, 15, 21, 2S, 36, \t., Jv<; , or column III of KernoulliV Table.
Hut this form wouKI be |iur|>oseless. The ])rni)ertv of the Hernoulli Series is th;it c.v h term of any series is the
sum of two preiedinij terms of the s.ime and iie\t adjoinin;^ i ohinin to the lel't. 'The " Fire brick and Clav Series" can
therefore be put in small groups of Column III and IV, of which the following is one of a vast number of eipiivalent
forms. 'The endless variety of these forms of the lnr>;er terms is a notable feature.
Thk "Fire Brick and Ci.av Seriks" in ihe Terms ok Bernoulli's Con mns III ani> IV.
1 '
; 3
« t
6 !
1
10
1 ' 6
»5 1
'5
10
88
I.
28
S6l
I90
1696
6
28
9'
4
10
78
794
2^
78
•42
I
'27.')
1276
26
3
6
162
6
20
'27.^
1301
4i
10
■85
1326
'.13^
6
10
i(>
5»
I
6
.?5'
358
3
6
45
•378
• 43-
I
10
45
56
3
31
528
■
10
66
'378
'455
aS
45
73
I
3
561
56s
4
310
'378
1 60a
4
703
2*
6
1 20
3
1128
i t
66
1176
3 J 5
55
loSi
iqo
'3 75
i 6
300
'54°
1 176
'43^
2600
1326
300
ijafi
1225
3654
1879
'893
J462
2l»33
»793
3729
3961
3
I 1
3
2S
3 1
3
3
' 3<'
'5
496
3^5
6
595
45
190
45
10660
1 1 480
1 20
1 9600
4060
4060
9SK0
17296
4114
41R7
9943
'7.4JS
20,198
11,184 ii,.So8
It must be borne in mind that ir\ order to api)re< iate the full value of the artificial construction of the "Fire-brick
and ("lay Series " this remarkable series is not only the equivalent of the sums of groups of its first si.t terms, but it is
also the equivalent of the fore);oing sums of the terms of the Bernoulli's Columns III and IV, each term of which is
itself the sum of a prior series either vertical or sloping in Bernoulli's Table.
l-urtlier, the "Firebrick and (lay Series" has been shown in Table II to jxirsess certain pro|)erties ; in 'Table III
it rqiresenis the terms of \ouiig's United Stales Kxport Fish Trade figures, in Table IV, Young's United States
Imimrt Fish Trade h.<ures; j\lso, in Table 1\', Young's United Slates Fish Trade Kxi«)rt figures for 1874, jointly with
the Canadian Fish 'Trade InqMjrt figures' for 1S74; also, it embrai es the Cotton and Woollen Series of Differences for
the years 1S78, 1883 and 18X5; and it assumes the form of an indefinite .Arithmetiial Progression. All these figures
specified are interchangeable, and have ln-en proved to be so, togeher with eiiuivalem v to Bernoulli's ("olMnins III or
III ami IV.
ilence the fijjures or quantities s|je< ified are nothing more than the Cipiivalenls of the sums of the selected Co-
efficients of the F^xiKinsion of the Binomial (i -f- 1) to the power of n.
Now let the reader lixik at the origin, and subse(]iient use to which this scries has been applied, and then consider
the object ol its presence m United Slates and Canadian Records of (lovernment, and dwell for .1 tew minutes on its
a|Jii«arance and applic.it ion in the Canadian Trade Tables for 18.S5, as shown on p.ige 32 Let the render then ask
himself, whether it is not time for those who (are for the privileges of freedom, anrl are conscious of having duties as
freemen to fiilfil, to be stir themselves in a matter which threatens to strike at the root of fr< ednm, and to destroy ths
equality of ;il! men before the law.
80
CRRI.MN I'kOl'KRIIKS OK ItKKNOUI.l 1 S lAHI.KS.
I.
to (iHTAiN Any- ratio betwkkn two series.
Any dfsirahlc ratio Ivtweun the- sums of llic terms of flifr,.Tent series framed arcording lo Hcrnoulli's Table can be
secured hy means ol ilie lollowmg deduction from ilie i;th property.
Let .S" == the sum of « terms in any <(ilumii (( of llic fl)le.
" / - the last of « terms in column a
Then
S: M. / =-- I : ,1
or 5. (( - n. I
A dediu tion from I'ormula No. ( i) ^iven in Hernoulli's 'lablc.
KXA-MfLE. The sum of 19 terms in Column XI is 75,582
The last or 19th term in i;ol»inn XI is 43.758
',•1^'" 75.5*^2 is'" 19 '< 43.758 a.i I : I I
'"■ "X 75.5*^^ - >9X4.?,7S**
75.SXJ
75.S«-'
831,407
43.758
'9
,?93.«''2
4.V75«
831,401
Ilernoulli expresses this remarkable relati^m in tlu- followint; (|iiaiiit languagf, as ijiven in the translation published
by I'kANcis .Masirks, Cursiior Hamn of Ihi- Court of K\ehe<|uer in 1705: "The sum ol any number of terms in any
of the vertiral eolumns 1 ontained in the forcijoinH table of combinations is t.. uie sum of the same number of terms all
e<iual to the la^t of ihem, in the |)roportion of i to the exponent of the said column, or to the number which denotes
or expresses its place m the saiil lahlc."
Then
II.
(JKNKRAl. KXl'KKStilllN R)K THh. llK.Ms OK A.\^ UNK Of lllh. \KRIIC'A1 lOI.UMNS IN HKRNOtll.Lrs TAUl^E.
I.et S - the sum of the .Series in any Column ii to n terms, including cy))hers, according to Bernoulli's Table*
a(a + i| <i{,i + i)(n + 21 a ja + i) (j + i) (« + j) n (u + iMi + J) (•< + 31 ItJ + 4)
.V- 1+ i4- + — + + — +&c.,&c.
i »• 3 I, J, 4 ». 3. 4. 5
KxAMi'i.K. l.el 1/ 12, and h the mnnber of termsca2i ; equal to lo -f 1 1 = 21, including cyphers, Ijeing 10 quantities
and 1 1 cyphers.
The Series is
.S :-.. , -(. 13 4. 7S -f. j(,4 4. 1JO5 4- 4,0s 4- 12,376 4- Ji,S24 + 75.5S2 + I<i7,900
And according to Uernuulli's formula,
167,9«)>< 21
29j,9jo
/x ff
S =
S -
In detail, the calculation is as follows:
a ' \l\ H - 10 quantities, then,
13, 13 12, IJ, 14 12, 13, 14, 15 12, 13, 14, 15, 16 12, 13, 14. 15, '6. '7 , '». '3. '4. '5. '6, 17. '8
a. 3. 4 2. 3, 4, 5 2, 3, 4, 5. 6
12, 13, U, 'S. t(>< I?. iX, 19 12, 13, 14, 15, 16, 17, iS, 19, 20
S
I + 12 + + ■
* *,3
2, 3. 4. 5. 6. 7
2. 3. 4. 5. 6. 7. Ii 2, 3, 4, 5, 6, 7, «, 9
:^ I + 12 + 78 + j(.4+ i.j(.5 + 43!i6+ 12,375 + 31,824 + 75,582 + 167,960, which is the Xllth Column in Bernoulli's
Table to 2 1 terms, and each of the quantities in the series is etpial to the sum of the series in the column next precedilig
if to the left and beginning with the quantity one square above it. Thus, 75,582 is the sum of all the quantities in
Column XI from 43,758 u|)wards, and there are 19 terms in that t olumn, including cyphers; or 75,582 is the sum of the
Vlllth column, beginning with 31,824 and thence upwards. 3i,82.( is the sum of the VTIth column, beginning with
12,376 and thence upwards ; or ol the .\lth column, t)«ginning with 19,448 and thence upwards, and so on for all the
(|uuntilies in the series.
It IS to be noticed thai the sloping column to the left of 75,582 up lo No. 1 1, consists of the same figures 83 the
vertical column No. XII over 75,582. ThiS rule holds good throughout, together with numerous i>thcr relations bct(»tfcn
columns and |>arts of columns, which it is not necessary now tu puiiu out
V^
!
i
40
^
III.
THK KFrECT OK POSH ION IN IJSlNd RKRNOULI.l S TAIILI;.
The effect of position in Bernoiilli's Tabic is rfniarkablc, niui must always be attended to. The value of n varying
with each column.
When using any of the formulas given in school or college algebras for determining the sum of a series by the Differ-
ential Method, such as that given on iKige 5,^7, of Hind's Klements of Algebra, 5th Kd., and applying it to Bernoulli's
Table, the value of ;; must bo made e<|ual u> { h - a t- i ) on account of the cyphers which Bernoulli's formula alone
includes.
The etjuation then becomes
(I) V:
1. J. i. 4
/am
(1) .V
A.
Ex.\.MPi.F- I.ct ii be re()uircd to fmd from "ither formula the sum ol 40 terms of tin- series
I -H 4 + 10 -t- 20 + 15 + 56 + 84 + \c., 10 91 j9,
which is the 40th term in the Bernoulli Column IV'. including cyphers,
(40 i) (40-2) (40- 1) (40-0) J7 X jg X 39 X 40
Th*i> from ID .V =
Kn.ni (2) V
I. J, ,), 4
0139 X 40
I. 2. .1. 4-
91J90
01300.
Many other striking features and projierties of Bernoulli's reniarkab! table are pointed out in the Ars Con/ti-
tandt, or in the M.aseres translation, or .ue easily deduced by any one familiar with the elements of Algebra.
Thk M.\(;NiTi;nK of thk iMceisruRF..
It will be understood why no attempt is made in this Ex|X)sition to arrive at an approxim.ition to the extent to
which the use of the artifice |)ortrayed affects the visible record of Canadi.m Trade since 1878, when it i'. stated that
the combined Pkovinciai, 1)ifh-:kkncks in rhe year 1883, for Cotton Coods and Iron (ioods in relation to tr.ade with
Great Britain and the United .States, amount to no less than $377,000. If the si^ns onlv of these Differences be
changed, the resulting sum would represent a difference in the record of the Tratle, tVom what it now is, of $754,000
for these two articles alone in one year.
But besides Iron Cioods and Cotton (ii>ods and VVix)llen (joods there are numerous other commodities in which
the recorded " Different es" between "Imports " and " Kntries for HonR- (Consumption " are verv large TI.ese figures
have no relaiion to the "Valuator's" estimate, or to "Bonded (foods." or to " Drawlncks,'' or any other Custom
House contingency. They are the grou|it-d terms of a (ontinuous .Vruhmetical Progression, interchangeable with
United State-' prior Custom House entries, an<i mierc hangcable with a prior (\tnadian series, already successfully
utilized, and interchangeable with Bernoulli's wonderful grouped figures, 170 years old. (Conse(iuently, they are fabri-
t-ated figures from year to year.and mathematically related to the Custom House details of a neighbouring nation.
F.ADFM MtTMA RlSVRC.O.
A .SIATKMKNI AND CONCl.L.SION.
In what I have now portrayed there lies an instruction and a warning not to \k disregarded.
We arc brought face to face with the mo.st far-reaching 1 onspiracy -for il deserves no belter name — history disrlosex
Thi« ronspiracy has had for its object the systematic joint falsification, by a secret mathematical process, of the-
Annual Tradf Records o( two inde|)endent nations, during a time of profound ()eace, and in the midst ol laudable
commercial rivair)'.
This secret procew has already tx-en jointly and successfully used in relatively distorting the 'I'rade Records 06
these neig oriijg nations, so as to give prejionderancc to one of them during an international arbitratioK in a matter
governed by irealiea, and of the highest moment to the interests of the maritin>c i»ortion of both natio is.
As a conaequence of the succe.ssful practice and continued maintenance of this conspiracy, we have bow to con-
front and diacuss serious international complications, to the detriment of good neighborhood and the psoatotion uf ilU
wilL Therefore, it is necessary to present the fai ts fairly before the public, in order to lessen these evils; not to du so,
would encourage multiplying troubles.
The necessary Annual Official Statistics of the United States in relation to the Fish I'rade, during the period when
.lh«e records were under the supervision and control ol I )r. Edward Young, were fabricated throughout, and made
41
siihordinatL- to reii()rociiI Canadian stalistics by a mathematical |)rocess pursued in rominon at Washington and at
Ottawa. The method and its results are sulTiriently described in this hook, but suscepiible of much more ample
demonstration.
This secret process has subsecjuently lieen continued by Canadian officials up to the preSL-nt lime, and in
such a (jross form that the figures of the National Records of the Trade of ("anada in their latest issue, are interchange-
able with those of the earlier Trade Records of her powerful and independent neighbor, and mathematically related to
them. They can all be put in the form of an endless .\rithinctical Progression, with subordinate consequences.
In glaring contradiction to the solemn averments made in the Canadian Parliament (i), and re-echoed it the
Imperial Parliament (2), some \ears since, this unexampled abuse of trust is mathem,">ticallv proved in the pages of this
book to have been going on then, as stated, and also to be going on now, but with tenfold greater ( ontingcnt burdens.
The responsibility resting on those who favored this subterfuge, and permitted the secret scheming to continue, has yet
to be measured.
If pa|)ers are railed for in the House of Representatives, it w ill be found that I have not been remiss in comnuini-
eating the grave delinquencies of Dr. Kdward Young to the Ciovernment of the United States, even so far back as
i88j (3).
'These printed communications point out the artificial construction of Dr. Kdward Young's Trade liguresin the
United States Commerce and Navigation Reports for six years. 'They notice also his misrepresentations of ('anadian
OtTicial Returns in the "Monthly Reports."
I now find that the special features then enlarged upon are nothing more than the subordinate consequences of the
continued use of selected co efiii ients of the successive expansions of the Uinomial (1 . i) lo the power of 11, in order
to represent United States Trade in the Products of the Sea.
The absence 01' mathematical proof of the fraud may account for the absence of notice being taken of the state-
ments made.
But the permitted i ontinuame of these practices in Canada derives special force from the fact '' with the
exception of the formul.1, the whole was described by me in a communication to the Rt. Hon. Sir Charic? \V. Dilke,
(4), when that statesman occupied the |)osition of President of the Local CiOvernment Hoard, in May, 1.SS4, and a
synopsis was previously published by nic and circulated in Kngland. and sufficiently so in Canada (5).
The title of the voluminous paper addressed to Sir ("harles Dilke and ret,urned to me, was .is follows :
"TlIK C.\»ADIAN OfFICIAI, FRAl:nS CONTINliOlM.V PRACTICKt) IN RKI.ATION TO THE CANADIAN ProI KCIIVK.
'Tahikk and Canadian Trade with the United Kinc.dom."
'This v.ast fraud, as continued since 1877, unequally afTects the international 'Trade Rel.ations of m.iny millions of
people on this continent alone. It has favoured the industries of cme class and abused the privileges and rights of
another class. It has unecpially and inequitably represented, by means of forged figures, the several industries of these
cl.asses, and their commercial rclation.s. Page j of this book embodies an indictment no one can dispute ; Chapter
VT further confirms it.
'The hidden influence this fraud exercises may at any moment be called into action. Unless exposed to public
view, it may .again suddenly become an unsuspected controlling power in legislation, in the adjustment ol trealies. in
arbitration, and in the administration of the law.
'The conspiracy has already become a rooted and a growing evil, which must be extirpated at any < ost, or it will
lead to grave international bickerings, and internal unrest, if not disaffection.
It IS not very long since that men wondered at the saying imputed to a distinguished personage, ex, Ited in rank
and high in public estimation, that "Representative institutions are now on their tri.il." It looks as if this saying had a
great deal of truth in it.
'The irony cast by the process 1 have outlined, on solemn arguments based on the interchangeable figures which are
its outcome, is uns|Kakable.
(1.1 8m oIIIi'IoI r<;|>t>r« ■>( the Dlmiaiiion li the (an ili«n St'iiatc »ml th« IVnvllan Hotiie n( Cmiimuim. In .l«nimr.\ nnd Fehnmrv, \»*\. rpii|Hic'llni| the <'hi>n;F>
Dwcid 1.) tnt ; >l»>. Mr ('<illiliiliwi.>lmr Whiti'hrr » »hlt«wuhili|| lueiiKiraiKlllin (<ir Kir J A. M«iiloii«lil. •»! 111} reiJ) to His KMiillciiry llro ll<iver,i..r (IcinTa) .if tho
llniiitrtloii, uonrflrtilti4[ thl« outrage AKKlnit tnith ami honour.
(t.) Mr Charlw W Dllka, IMI.
(S.) Tin liiltixl HUtM Siiiirioii. SI,Atlrtl<-. »mt th» «in»pl'»'"'r "t'lf'' iroatml thoni, hulmf lottcn- nWlTiMrt to the Hon. t'rwIfrloV T. l-'r»llii«huvwn. ((wn-tarj-
ot SUU. lUtml lit. WInilmr, Xo»« N.'OtU, Oi-«. 111. ISii. 'iml Wln.l«ir. Nova 8c.tl«, Nov. I, l.wi. :lr.l. Wiii.lii..r. Novo St-otla. Nov :!o, ISK-.'.
4 ) NoTTMOIIill, Jul.v nth. ism.
To Iha Rl(llt HonourablK Sir Cn>U.M W Ihi.na, M I* . I>re«i<lant of the txxsl llovoniMuiit llo*nl.
Hlr. I hava tha honour to traiiauiit a prlnUjil wpy of tho " Corranpoiiilenov wilti tli« lato l.iml t-'rwlcrlck C*>endl«h." publUIio-i »Uii tin- coiia.-nt of Uiv Uaniuiii
I'lhoiiWiioa b« very jratalul If >oo aoiil.l aulhorlle oie Ui |.olili«li my lottar of May loth to youraoll. arlth the aililaiiUa, oiiilMliiu «uih |««»«K«ii, if any , yoo
miifht <lm*tn uniieoaaaary.
Vhare .'ould only Ita thraa piirpoaea aervf><l liy aueb an act, namely
The Hop|troMlon of r<i>ntlno«i1 atmrloua erlmna.
Ju«tJo« to iiilllliHta of tha iinluatrlal olaaaoa of our oountryinjn ; an<l
An Imnatua iflven lo the |irlnol|ilM olJiitt Uavaminant.
I havf the honour to Ik' vonr nlie<llanl aurvant. . _.
HKSHV VOIT.K. IIIMl. M A.
I.n'al (Oiverniiii'ot lUanl. Whitehall. .Inly ITth. ls>4.
Wr, In rauly to your latter, 1 ain illreotaii liy Sir Charloa IHlkt to mo thai he never under any olreuioalMieaa iMn«ant» to the |.unll.atlon ol o,.rre-i».ii.leiH ■ «llh
I am vonr olia'llant aarvant,
II. Y. HOD, R.I I"'!"""" •' ' « " •'■•^
Ooiiuaminit a letter lo the Ht Hon Nir Chailee W IMIlio, M. I'., I'roaldenl of the lo-al (l.rterninanl lloanl. rvlatlnir lo the farf* Ttwia Tat-toa at Itf
hUn.
Don
(t.) Oon
I 'nlon o(
(luuuia for the ) earn l«7H and twts, with an llliBilrallon o( one oietho.1 o( fmnd. May I'Hl
,*f»i.-
I
■♦a
Consiik-ring that I have rercived the consent of the Rt. Hon. the Marquis of Hartington (i) to the publication of
correspondence with the late Lord Frederick Cavendish, ri-iating to the first discovery of the conspiracy, now more
(ully developal, I am not stepping lieyond the hmits of respectful bearing if I |x>int to certain conditions urtd siiggest a
(luery.
The highest human function is the administration ot justice. To this end vv- are governed by direct or delegated
authority. Can it be the function of the .Minister of (Customs, or of the Covernor-Cieneral, to receive manufactured
Records of Ciovernment which display their own one-sided falseness, and turnish an unanswerable indictment against
their compiler and his evil methods?
It now remains for those who seek to mould publit ojiinion. or profess to guide and protect public morality, to
take the matter in hand, and aid in sustaining the principle on which our liberties rest, -that all men are equal before
the law.
The independent press of both coimtries can do infinite good by persistently calling attention to this matter,
inquiring into its insidious partiality, and denouncing a practice which can only lead to discontent and destroy the
blessings of good neighl)ourhood.
HENRV VOUL.K MINI).
(I J KmihlulcTit Offlfii.1 KcM-onN ot Uuvvminent (\>rrii(iioiKl«iict' with the l«te Ijonl Krodorlck r^vendiiili, H V. {*ubtt(thetl with the eonsoiit of the HI. H«i
Th*" HaniuUol HMtiuykMl, M. )'., Bvrratary ol HU(«. War l>u|Mu-tiui;iit, Jul;. 1864.
u43i[£kL. i
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