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THE



NORTH AMERICAN



RE TIE



VOL. LXXXYII.



Tros Tyriusque mihi nullo discrimine agetur.



BOSTON:
CROSBY, NICHOLS, AND COMPANY,

117 WASHINGTON STREET.
1858.



,! (I ( ,1 {ill c



Entered according to Act of Congress, in the year 1858, by

CROSBY, NICHOLS, AND COMPANY,
in the Clerk's Office of the District Court of the District of Massachusetts.



CAMBRIDGE:
MBTCALF AND COMPANY, PRINTERS TO THE UNIVERSITY.



CONTENTS

OF

No. CLXXXI.



ART. PAGE

I. SIR WALTER SCOTT 293

1. Waverley Novels. Household Edition.

2. The British Poets. SCOTT.

II. GRAY'S BOTANICAL TEXT-BOOKS 321

1. Botany for Young People and Common Schools.
How Plants Grow, a simple Introduction to Structural
Botany. With a Popular Flora, or an Arrangement and
Description of Common Plants, both Wild and Cultivated.
Illustrated by 500 Wood Engravings. By ASA GRAY,
M.D.

2. First Lessons in Botany and Vegetable Physiology,
illustrated by over 360 Wood Engravings, from original
Drawings by ISAAC SPRAGUE. To which is added a
copious Glossary, or Dictionary of Botanical Terms. By
ASA GRAY, M. D.

3. Introduction to Structural and Systematic Botany,
and Vegetable Physiology, being a Fifth and revised Edi-
tion of the Botanical Text-Book. Illustrated with over
thirteen hundred Wood-cuts. By ASA GRAY, M. D.

4. Manual of the Botany of the Northern United States.
* Revised Edition, including Virginia, Kentucky, and all

East of the Mississippi : arranged according to the Natu-
ral System. By ASA GRAY, M. D. (The Mosses and
Liverworts, by WILLIAM S. SULLIVANT.) With four-
teen Plates, illustrating the Genera of the Cryptogamia.

III. THE NEW CRIME OP AUSTRIA 343

History of the Protestant Church in Hungary, from the
Beginning of the Reformation to 1850. With Special
Reference to Transylvania. Translated by REV. J.
CRAIG, D. D., Hamburg. With an Introduction by J. H.
MERLE D'AUBIGNE, D. D.

IV. MICHAEL DE MONTAIGNE 356

La Vie Publique de Montaigne. Etude Biographique.
Par ALPHONSE GRUN.



iv CONTENTS.

V. BUCKLE'S HISTORY OP CIVILIZATION 388

History of Civilization in England. By HENRY
THOMAS BUCKLE.

VI. RECENT FRENCH LITERATURE 423

1. Memoires du COMTE MIOT DE MELITO.

2. Histoire de la Campagne de 1815. Waterloo. Par
Lieut.-Colonel CHARRAS.

3. Memoires pour servir a Y Histoire de mon Temps.
Par M. GUIZOT.

4. Richelieu et la Fronde. Par MICHELET.

VII. THE FIRST STAGES OF THE AMERICAN REVOLUTION 449

1. Collections of the Massachusetts Historical Society.
Volume IV. of the Fourth Series.

2. The American Revolution. By GEORGE BANCROFT.

VIII. THE EARLY DAYS OF HELLAS 481

1. Griechische Geschichte, von ERNST CURTIUS. Ers-
ter Band, bis zur Schlacht bei Lade.

2. Die lonier vor der ionischen Wanderung, von ERNST
CURTIUS.

IX. CLIMATOLOGY 507

Climatology of the United States, and of the Temper-
ate Latitudes of the North American Continent. By
LORIN BLODGET.

X. LIFE AND LABORS OF THOMAS H. GALLAUDET . . 517

The Life and Labors of the REV. T. H. GALLAUDET,
LL. D. By REV. HEMAN HUMPHREY, D. D.

XI. THE OCEANIC TELEGRAPH 532

1. The Story of the Telegraph, and a History of the
Great Atlantic Cable. By CHARLES F. BRIGGS and
AUGUSTUS MAVERICK.

2. The Atlantic Telegraph : a Discourse delivered in
the First Church, Boston, August 8, 1858. By EZRA
S. GANNETT.

XII. CRITICAL NOTICES 544

NEW PUBLICATIONS RECEIVED 573

INDEX 577



CONTENTS

OF

No. CLXXX.



ART. PAGE

I. PEIRCE'S ANALYTIC MECHANICS 1

1. Physical and Celestial Mechanics. By BENJAMIN
PEIRCE, Perkins Professor of Astronomy and Mathe-
matics in Harvard University, &c. Developed in Four
Systems of Analytic Mechanics, Celestial Mechanics,
Potential Physics, and Analytic Morphology. Vol. I.
A System of Analytic Mechanics.

2. Theory of the Motion of the Heavenly Bodies
moving about the Sun in Conic Sections ; a Transla-
tion of GAUSS'S " Theoria Motus." "With an Appendix.
By CHARLES HENRY DAVIS.

n. GEORGE STEPHENSON 21

The Life of George Stephenson, Eailway Engineer.
By SAMUEL SMILES.

HI. THE MISSOURI VALLEY AND THE GREAT PLAINS . 66

1. Exploration of the Country between the Missouri
and Platte Rivers, &c. In a Topographical Survey, by
LIEUT. G. K. WARREN.

2. An Historical Sketch and Business Review of the
City of Leavenworth, Kanzas Territory, &c. By A. G.
HA WES.

IV. CONTEMPORARY FRENCH LITERATURE 94

1. Les Parlements de France. Essai Historique.
Par le VICOMTE DE BASTARD.

2. Robert Emmett.

3. Memoires de 1'Imperatrice Josephine.

4. Etudes sur Pascal. Par VICTOR COUSIN.

5. Fragments et Souvenirs. Par VICTOR COUSIN.

6. La Tribune Moderne. Vie de Chateaubriand. Par

M. VlLLEMAIN.

V. THE PHILLIPS FAMILY AND PHILLIPS EXETER ACAD-
EMY 119

1. A Memoir of His Honor Samuel Phillips, LL. D.
By REV. JOHN L. TAYLOR.



11 CONTENTS.

2. Catalogue of the Officers and Students of the Phil-
lips Exeter Academy for the Academic Year 1857-8.

VI. THE AQUARIUM 143

1. The Aquarium, an Unveiling of the Wonders of the
Deep Sea. By PHILIP HENRY GOSSE.

2. The Book of the Aquarium and Water Cabinet.
By SHIRLEY HIBBERD.

VII. LAWS OF ASSOCIATION IN ORNAMENTAL GARDENING 157

1. Practical Landscape Gardening, with Reference to
the Improvement of Rural Residences, giving the Gen-
eral Principles of the Art ; with full Directions for plant-
ing Shade Trees, Shrubbery, and Flowers, and Laying
out of Grounds. By G. M. KERN.

2. Landscape Gardening ; or Parks and Pleasure-
Grounds. With Practical Notes on Country Residences,
Villas, Public Parks, and Gardens. By CHARLES J.
SMITH.

VIII. OZANAM'S CIVILIZATION OF THE FIFTH CENTURY . . 170

La Civilization an Vieme Siecle. Introduction a une
Histoire de la Civilization aux Temps Barbares, suivie
d'un Essai sur les Ecoles en Italic, du Vieme au XIII.
Siecle. Par A. F. OZANAM.

IX. LORD NORMANBY'S YEAR OF REVOLUTION IN PARIS 184

A Year of Revolution. From a Journal kept at Paris
in 1848. By the MARQUIS OF NORMANBY, K. G.

X. THE BASQUES AND THEIR COUNTRY 211

Le Pays Basque. Sa Population, sa Langue, ses
Mccurs, sa Litterature, et sa Musique. Par FRAN-

CISQUE-MlCHEL.

XI. RECENT COMMENTARIES ON THE NEW TESTAMENT . 235

1. A Commentary on the Original Text of the Acts of
the Apostles. By HORATIO B. HACKETT, D. D.

2. Biblical Commentary on the New Testament. By
DR. HERMANN OLSHAUSEN.

3. Kritisch Exegetischer Kommentar iiber das Neue
Testament. Von DR. HEINR. AUG. WILH. MEYER.

XII. CRITICAL NOTICES 251

NOTES TO ARTICLES II. AND V 286

NEW PUBLICATIONS RECEIVED ... ... 287



NORTH AMERICAN REYIEW,

No. CLXXX.



JULY, 1858.



ART. I. 1. Physical and Celestial Mechanics. By BENJAMIN
PEIRCE, Perkins Professor of Astronomy and Mathematics
in Harvard University, &c. Developed in Four Systems of
Analytic Mechanics, Celestial Mechanics, Potential Physics,
and Analytic Morphology. Vol. I. A System of Analytic
Mechanics. Boston : Little, Brown, & Co. 1855. 4to.
pp. xxxvii., 496.

2. Theory of the Motion of the Heavenly Bodies moving- about
the Sun in Conic Sections ; a Translation of GAUSS'S " The-
oria Motus" With an Appendix. By CHARLES HENRY
DAVIS, Commander U. S. N., Superintendent of the Amer-
ican Ephemeris and Nautical Almanac. Boston : Little,
Brown, & Co. 1857. 4to. pp. xvii., 326, 40.

IN a recent number of this journal we spoke of the work of
the great Irish mathematician as a magnificent effort of the
imagination. The publication of the most valuable original
mathematical treatise as yet written in America, has sug-
gested to us a different train of thought upon the Reason in
Mathematics.

Professor Peirce is distinguished in all his writings, from
his Elements of Geometry to his Analytic Mechanics, by a
peculiarity in his modes of proof. His demonstrations are
always concise, and remarkable for the directness with which
they attain their end. In the present volume is an instance

VOL. LXXXVII. NO. 180. 1



2 PEIRCE'S ANALYTIC MECHANICS. [July,

in which a proposition is established by a few lines of argu-
ment, as clearly and incontrovertibly as by the dozen pages
which the first propounder of the theorem employed in its
proof. Such facts suggest an inquiry into the nature of the
difference between the reasoning of different writers, and into
the effect which the study of different mathematical writers
may have upon the habits of thought in the student. There
is a well-known anecdote of Napoleon's disappointment, when
he took Laplace into his cabinet, and found that this distin-
tinguished mathematician was a wholly unsafe guide on
questions of state policy, seeking to introduce the spirit of
the infinitely small into the government. This anecdote is
frequently used to cast discredit upon the mathematics, as a
means of mental discipline. There are, indeed, upon this, as
upon most other subjects, two entirely opposite views current
among those who have considered the question. Some attrib-
ute to mathematical studies an almost omnipotent power in
strengthening the judgment and giving clearness and vigor to
the logical faculties; others are inclined to ascribe to these
pursuits the invariable effect of rendering a reason er a slave
to the mere forms of logic, and making him forget the supe-
rior value of the dictates of common sense.

In order to decide intelligently upon the merits of this ques-
tion, let us first analyze the process of reasoning. In what
does it consist ? What do we mean by saying that we have
proved a truth? The elements of logic deal with three dis-
tinct things, the conception of ideas, the perception of a
relation between ideas, and the perception of a relation be-
tween those relations ; that is, with terms, propositions, and
inferences. Or, to use grammatical language, logic deals with
subjects and predicates, with propositions, and with the mu-
tual connection of propositions. Different minds are capable
of comprehending these three classes of things with different
degrees of clearness. The power of grasping an idea is essen-
tially different from the power of perceiving a truth ; and the
power of drawing an inference is essentially different from
either of the other two. Now the part of reasoning which is
common to all departments of human thought is simply this
third part, drawing inferences. The ideas or things concern-



1858.] PEIRCE'S ANALYTIC MECHANICS. 3

ing which we reason are different in each different science ;
the truths, that is, the relations between these things or ideas,
must also differ in each department of inquiry ; and the rela-
tion between the relations, being the only abstract thing, is the
only one which is the same in all sciences and all subjects of
thought. But although the process of reasoning is the same,
upon whatever subject we reason, it will not appear so unless
we are capable of perceiving all kinds of truth, and grasping
all sorts of ideas, with equal facility. The same argument
which, in a common matter, seems perfectly convincing, may
on an unfamiliar subject seem wholly irrelevant. An exam-
ple from the Algebra of our author will explain our mean-
ing without obliging us to introduce technical mathematics.
There is a theorem of Arbogast which Peirce has demon-
strated in the space of a single duodecimo page. The stu-
dents of Harvard University are seldom able to master this
demonstration. The whole difficulty of it, however, lies in
about half a dozen lines. Year after year, class after class
of the most intellectual young men of New -England admit
themselves to be unable to comprehend the reasoning of this
short paragraph ; and yet its whole reasoning, if we substi-
tute the names of places for the names of mathematical quan-
tities, amounts to this : If we can go from Boston to New
York, and if we can go from Portland to the City of Notions,
we can go from Portland to New York, since the City of No-
tions is only another name for Boston. No reader will per-
ceive that there is any difficulty in this argument, as it now
stands ; and in the form in which Peirce gives it, the difficulty
is not really, but only apparently greater. From P we can
obtain P, and from Q we can obtain Q, ; but P equals Q, and
therefore from P we can obtain Q,. No reader, except one
who has had an algebraic training, will feel that this argu-
ment upon the letters is as clear as the o le upon the cities,
and yet the argument is precisely the same. The only diffi-
culty is in conceiving, first, what P and Q may stand for,
and consequently what can be the relation between them and
P and Q.

The first great logician, Aristotle, reduced all reasoning
to a syllogistic form, and all syllogisms are equivalent in their



4 PEIRCE'S ANALYTIC MECHANICS. [July,

nature to this inference, that what is true of all members of
a class, is true of each member of it. Thus the most direct
form of the syllogism would be : A certain thing is true of a
certain class of objects ; this object belongs to that class ; and
therefore that thing is true of it. The whole doctrine of syl-
logisms has been beautifully illustrated by three geometrical
figures. Every assertion or denial may be symbolized, for
example, by the assertion or denial that a certain square is
included in a circle, the universal propositions putting the
square wholly within, or wholly without, the circle, and the
particular affirmation or denial leaving a part within, and im-
plying that a part is without. All reasoning may then be
reduced into syllogisms such as the following : The whole
of the square is within the circle, the whole of the triangle is
within the square, and therefore the whole of the triangle is
within the circle ; The square is not within the circle, part of
the triangle is within the square, and therefore part of the tri-
angle is not within the circle.

Later writers upon logic have regarded the syllogism as
simply a test of an argument, and have very clearly shown
that it is not the form in which arguments are consciously
put in the process of thinking, but only the form in which
sound arguments may always be put, for the purpose of test-
ing their soundness. Some have particularly endeavored to
show that inductive reasoning is not readily put into a syllo-
gistic form, and have therefore sought to establish a new
logic for the examination of inductive reasoning. We have,
however, for many years, been in the habit of presenting the
whole matter of logic in what we consider a more simple
and popular form than the syllogistic, and at the same time
no less sound. It has moreover the advantage of embracing
equally those higher forms of reasoning used in modern sci-
ence, both inductive and demonstrative, which are with so
much difficulty brought into a series of syllogisms. Instead
of comparing reasoning to the placing of three figures within
or without one another, we compare it to the laying of a
path from points that are known to points that are un-
known. The known points are self-evident or admitted prop-
ositions. The successive steps of the path are self-evident or



1858.] PEIRCE'S ANALYTIC MECHANICS. 5

admitted relations. The unknown points to which the path
conducts are the propositions to be proved. In geometrical
synthetic demonstration we pass by a series of self-evident
steps from the simplest self-evident truths to the highest de-
ductions of the science ; while in geometrical analysis we pass,
through self-evident steps from the proposition to be proved,
down to the simplest axioms. In either case we show an
actual dependence of the complex proposition upon the axiom.
Now it is true that each step of this process may be thrown
into the syllogistic form, but it is equally true that no man
is, in reasoning, conscious of this reduction; the actual
process of the mind is, to pass directly from proposition to
proposition, without justifying the step by that generaliza-
tion, the result of which is called in the syllogism the sup-
pressed premise. In every process of reasoning there must
be at some point a resting upon first truths. Sound reason-
ing cannot run in a perpetual circle, neither can it be an
infinite series of answers to the question, Why? To such
a series there must at length come the answer which we
are so often forced to give to children, that it is, because
it is. There can be no disputing concerning the primary
conceptions of the mind, or the perception of the primary re-
lation between those conceptions. There are men incapable
of grasping the geometrical conceptions of a point, a line,
and an angle. There are others who seem equally unable
to grasp the ideas of truth, justice, and duty. In neither
case does the inability of a few to form such ideas make
them any less clear and definite to the majority of men. But
some of those who can conceive of points, lines, and angles
do not acknowledge the fact of their existence in space ; they
allow to them only an ideal existence. Those who believe
them to be really entities cannot hold any argument upon
the point with those who deny their existence ; because they
esteem their existence to be a self-evident truth. Nor can
one who believes in the reality of the difference between
right and wrong, enter into any debate with those who deny
that difference. In Jouffroy's Introduction to Ethics, while
he reviews and rejects those systems of philosophy that
destroy the reality of ethical distinctions, he does not enter



6

into an argument to prove their reality ; for the existence of a
distinction between right and wrong is to his mind a self-
evident truth. In the matter of simple conceptions, there
can be only the difference between grasping and not grasp-
ing the idea; and in the matter of self-evident truths, only
the difference between seeing and not seeing them. He who
sees may t>e right, or he who fancies he sees may be wrong ;
but in either case the matter is beyond argument, and can
be reached only by patient meditation or direct observation.
In like manner, in self-evident connections or trains of rea-
soning, there must be steps so simple as to admit of no
further debate. We see their truth or their fallacy in the
particular case before us, and the truth or fallacy is not
usually made more apparent by throwing the proposition
into general terms, and thus converting it into an expressed
premise. The syllogism is of value to detect a fallacy only
when we are reasoning about subjects with which we are
not perfectly familiar, and in which we therefore carry the
cloudiness of our conception of the truths themselves into
our perception of their relations ; as, in the case quoted from
Peirce's Algebra, our cloudiness of conception of the meaning
of P and Q, impairs our ability to understand the perfectly
clear reasoning employed upon them. Now these steps, so
simple as to admit of no debate, are always capable of being
verified by being resolved into the inference of a conclusion
lawfully drawn from the premises of a syllogism ; but it is by
no means necessary thus to resolve them in order to feel their
justness, neither is that resolution strictly a psychological
analysis of the operation of the thought.

The representation of reasoning as the process of connecting
the truth to be proved, by a series of self-evident steps, with
self-evident propositions, has the advantage of including in-
ductive reasoning in natural science, and demonstrative rea-
soning in mathematics, as well as reasoning upon ordinary
subjects. It has the advantage of embracing a connected
series of syllogisms in one simple definition. But its prin-
cipal advantage is, as we have said, that it is more closely
conformed to the actual operation of the mind in reasoning.
Take, for example, the proposition that, if a square is sur-



1858.] PEIRCE'S ANALYTIC MECHANICS. 7

rounded by a rope, and there is also a rope crossing the
square upon each diagonal, there must be at least two pieces
of rope. We first form a clear conception of a square, sur-
rounded by a single line, and crossed by two diagonals, each
of a single line ; and a self-evident connection of ideas shows
us that three lines will proceed from each of the four corners
of the square, that is, a line to each of the other three corners.
Artifice may put this into a syllogistic form, to prove that
three lines will proceed from each corner, but it will surely
not be a natural process. Again, a self-evident connection
of ideas shows us that there must be an end of the line at
each corner of the square; nor do we here naturally say,
Wherever an odd number of lines radiates from a point, one
of the lines must end there. This general proposition may be
framed, but in framing it we should use our perception of its
truth in individual cases ; the perception of its truth in this
case must therefore be independent of, and antecedent to, our
perception of the truth of the general proposition. Again, a
self-evident connection of ideas shows that there must be four
ends to the string about this square under consideration ; nor
do we here use the major premise that every square has four
corners; our thought is confined to the particular square
which is here surrounded by a string and crossed by two
diagonal lines. Finally, a necessary connection of ideas
shows us that these four ends must belong to two pieces
of string ; and that, also, without the mind's necessarily as-
serting that every piece of string has two, and only two ends.
This axiom has probably very seldom been framed as a justi-
fication of any reasoning about ropes.

If, then, the dependence of one proposition upon another is
not usually conceived, in the actual process of reasoning, as the
including of the members of the class under the class, in what
form is it conceived ? We answer, that it is the perception
that those members have the property of the class, without per-
ceiving the fact of their being included in the class. In saying
that C must be A, because it is B, we usually only see that the
B which is in C is A, and do not necessarily see that all B is
A ; which would be the major premise if we attempted to put
our argument into syllogistic form. The dependence of one



8 PEIRCE'S ANALYTIC MECHANICS. [July?

proposition on another is a virtual relation of an included part
to its whole, but this is not the only form which it actually
wears to the eye of the reasoner. The fact that the Eastern
and the Boston and Maine railroads cross in Somerville, and
meet in South Berwick, shows that they cannot both run in
straight lines ; but he who makes this inference, and sees its
truthfulness, does not frame any general proposition by which
he justifies his inference. He simply sees that, if both roads
continued straight after their crossing, they would run half
round the world before they met again. The idea of a straight
line being a great circle of the sphere, and great circles cutting
each other only at the opposite ends of a diameter, does not
enter his mind. He perceives its truth in this particular case ;
but as it is an abstract truth, it cannot be expressed in the par-
ticular and special form in which he sees it, but must in its
expression include all cases of a similar relationship of ideas.
The natural process of thought is simply to conceive of the
two railways as diverging; and it is only in the attempt
to put the thought into language that we say, two straight
lines can cross each other but once.

The acknowledgment that Aristotle's dictum de omni et
nullo is the basis of every inference, shows, of course, that we
conceive only one relation between propositions to be availa-
ble in reasoning ; that is, the relation of a part to a whole.
One proposition can depend inferentially upon another only
if it is virtually included in that other. The doctrine of syllo-
gisms, therefore, necessarily includes the whole doctrine of
logic, in its proper sense. And, conversely, if the subject of
logic be fully and fairly discussed, it must present itself in
the syllogistic form. All that we claim for our mode of pre-
senting reasoning, under the analogy of a road from the
premise to the conclusion, is, that it is a more popular and
natural form, which includes enthymemes and sorites in the
same definition with the regularly expressed syllogism. The
value of this claim is apparent, when we perceive that most
reasoning is enthymematical as it originally presents itself to
the mind of the reasoner, whatever form it may assume in
utterance. No general truth or proposition will be admitted,



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