SCIENTIFIC BOOKS. so by steps of the highest degree of certitude.

POIKCAR&'S ' SCIENCE AND I-IYPOTHESIS.' I n this process he sees the creative force of
La Scierace e t I'Hypothhse. P a r H. POINCAR$ mathematics, which leads to real proofs and
Xembre de 1'Institut. Paris, 1903. Pp. not mere sterile verifications. The illustra-
284. tions used to malie the thought clear are
Wissenschaft und Hypotltese. H . POINCAR& taken from the begiqnings of arithmetic,
Autorisierte deutsche Ausgabe, mit erlauter- where mathematical thought has remained
enden Anmerkungen, von F. und L. I,INDE- least elaborated and uncomplicated by the
~ZIANN. Leipzig, 1904. Pp. xvl +
342; the difficult questions related to ,the notion of
nates, pp. 245-333. space. I n successwe instances i t is shown
A work from the pen of one of the dis- how more general results are obtained from
tinguished savants who have so recently been fundamental definitions and from previous
the guests of the American scientific public results by means of mathematical induction.
is 'doubly interesting at the present time. In each case the advance is made by virtue
Among the several domains of pure and ap- of that " power of the mind which knows that
plied mathematics which &f. Poincar6 has it can conceive of the indefinite repetition of
enrich2d by his researches, not the least im- the same act as soon as this act is at all pos-
portant is that of the fundamental concepts sible. The mind has a direct intuition of
and logical developmeht of various branches this power and experience gives oilly the op-
of science. Like its predecessors, the work portunity to use it and to become conscious
under consideration here is remarkable f o ~ of i t " (pp. 23-4).
the clear, incisive and succinct fashion in The conviction that the method of mathe-
which it deals with the dificult and elusive matical induction is valid our author regards
problems lying at the foundation of mathe- as truly an d priori synthetic judgment; the
matical knowledge. mind can not tolerate nor conceive its contra-
The work is divided into four parts, pre- dictory and could not even draw any theoretic
ceded by a short introduction, viz.: First consequences from the assumption of the con-
P a r t : 'Number and Magnitude,' 1,;. 9 4 8 . tradictory. No arithmetic could be built up,
Second P a r t : ' Space,' pp. 49-109. Third rejecting the axiom of mathematical induc-
P a r t : 'Force,' pp. 110-166. Fourth P a r t : tion, as the non-Euclidean geometries have
' Nature,' pp. 167-281. been built up, rejecting the postulate of
The first chapter is entitled, ' O n the Euclid.
Nature of the Reasoning of Mathematics.' The second chapter terminates the first part
A t the very outset, even the existence of and is entitled, ' Ifathematical Uagnitude and
the science of mathematics seems to present Experience.' It deals with irrational num-
an irreconciIab1e contradiction. If mathe- bers and the creation of the lnathernatical
matics is deductive, drawing all its conclu- continuum, concluding that 'this notion has
sions strictly from their antecedent premises, been created by the mind, but that experience
how can it be more than a huge tautology? furnished the occasion' (p. 35), " The mind
Row are all the ponderous tomes of mathe- has the power of creating symbols, and by
matical theory aught else than devious ways this means i t has constructed the mathemat-
of saying A is A ? If, on the other hand, the ical continuum which is merely a particular
conclusions of mathematics say more than system of symbols. This power is limited
their antecedent premises, how is the unques- only by the necessity of avoiding contradic-
tioned perfect rigor of mathematics main- tion, but the mind makes use of it only when
tained ? experience furnishes the warrant" (p. 40).
M. Poincari. finds the answer to these ques- The second part, devoted to ' Space,' con-
tions in the so-called ' mathematical induc- sists of chapters on ' The non-E~~clidean
tion' which proceeds from the particular to Geometries,' ' Space and Geometry ' and ' Ex-
the more general, but at the same time does perience and Geometry.'
 SCIENCE. [N. S. VOL.XX. NO. 520.

I n this part t h e fundamental question is: impossible, negative parallaxes were found, or if
W h a t is t h e n a t u r e of t h e axioms of geom- i t were denlonstrated t h a t all parallaxes a r e
e t r y ? O u r author's views m a y b e seen in superior t o a certain limit, two courses would
be open; either we could renounce Euclidean
t h e follomiiig q u o t a t i o n s :
geometry, or we could modify the l a n s of optics
l'ltr cr~iori~sof geoinetly a l e neithrl- synthetic and admit t h a t light does not travel rigorously
judginents h piiori, no? c q e ~ c ~ n e n t facts.
ul They in a straight line. I t is useless to add, t h a t every
are coi~cclltions: our choice aillong all possible oiic 11-ould regard the latter as t h e more ad-
conventions i s gz~trledby experimental facts, but vantageous, Euclidean geometry has nothing t o
it remains p e e ancl is liinited only by tlie neces- fear from new experiments ( p . 9 3 ) . " No ex-
sity of avoiding all contradiction. Hence the perience ill ever contradict the postulate of
postnlates can renicin ~ ~ i g o ~ o utsr luye even though Euclid, nor nil1 any ,ever contradict t h a t of
t h e experin~ental 1a~r.s rvhicli hat-e determined Lobatscheffsky " ( p. 9 5 ) .
their adoption a l e o ~ ~ approxiinatire.
ly
T h e t h i r d p a r t , d e r o t e d t o force, consists of
I n other nords. thc Grtoncs of gronzc2t?y ( I am
not s p e a k ~ n gof tliooc of aiithilwtic) a t e ?11~1ely chapters d e a l i n g w l t h ' Classic mechanics,'
desgz~iseddefiiztlions. Consequently the question: ' R e l a t i r e n ~ o r e i ~ e na n t d absolute movement '
' I s Euclidean geometry t r u e ? ' 11:~s no mean- a n d ' E n e r g y a n d therniodynamics.'
ing. As well ask whether t h e metric sgsteni is IIere, a s i n geometry, o u r a u t h o r finds tliat
t r u e and the old nleasures false, whether Cartesian t h e fundalliental principles a r e n e i t h e r ci p ~ i o r i
coordinates are t r u e and polar coordinates false. t r u t h s n o r cxperilnental f a c t s b u t convenient
One geometry can not be more t r u e than another, definitions o r conrentions.
i t can only be ino1.e colioe~~ient. I f t h e principle of i n e r t i a , f o r example,
Euclidean geometry is and will remain the
were a n ci priorz, t r u t h , how could t h e Greeks
most convenient :
b e l i e l e t h a t n l o r e m e n t ceases a s soon a s t h e
1. Because i t is the simplest; and i t is so
not only in consequence of our mental habits, or cause which o r i g i n a t e d it ceases t o a c t ? H o w
of I k n o ~ rnot what diiect intuition we may h a ~ e could t h e y beliere t h a t every body f r e e f r o m
of Euclidean space, but i t is the sinlplest in itself, c o n s t r a i n t would m o \ e in a circle, t h e noblest
just a s a polynomial of the first degree is simpler of a l l m o t i o n s ?
than one of tlie second. I s there a n y more warrant to say t h a t t h e
2. Because i t accords x e l l with the properties velocity of a body c a n n o t c h a n g e w i t h o u t
of natural solids. cause f o r t h e change, t h a n t h a t it c a n n o t
Beings with minds and senses lilie ours, but c h a n g e i t s position o r t h e c u r v a t u r e of i t s
wlio had received no prelious education, might
p a t h except u n d e r t h e influence of a n exterior
receive, froin a n external ~ v o r l dsuitably chosen,
cause ?
impressions such t h a t they ~r.ouldbe led to con-
struct a geometry other than tliat of Euclid and H a v e a n y e x p e r i m e n t s ever been m a d e o n a
to localize the phenoinena of t h a t external world body s u b j e c t t o n o force, a n d i f so how w a s
in a non-Euclidean space, or even in a space of it k n o w n t h a t n o force was a c t i n g ? A sphere
four dimensions. rolling o n a rnarble t a b l e f o r a v e r y l o n g t i m e
If, on the other hand, we wl~ose education is a u s u a l example, b u t h a s the force of
has been received i n o11r actual world weie sud- g r a v i t y ceaqed t o a c t ?
denly transported into this new world, n e should C a n t h e l a w t h a t t h e uccelerntion of u body
have no difficulty in relating i t s pl~enonlenat o our r.qcials i l ~ eforce a c t i n g o n it divtded 7 1 ~i t s
Euclidean space ( pp. 66-8) .
?nctss b e verified experiinentally? T o d o so
If the geometry of ~obatscheffskyis true, the

t h e acceleration, the force a n d t h e niass n i u s t

parallax of a very distant s t a r would be finite;

if t h a t of IZiemann is true, i t ~ r o u l dbe negative.

be measured. I f we orerlook t h e difficulties
These are results wliicl~seem ~ r i t l ~ itlie n
reach of connected w i t h t h e m e a s u r e m e n t of time, it
experiment, and there have been hopes t h a t m a y b e g r a n t e d t h a t t h e acceleration c a n b e
astronomical observations might enable us to cle- measured, b u t t h e r e a r e inextricable d i E c u l t i e s
cide between the three geometries. i n t h e definition of muss a n d force. U s e f u l
But in astronomy 'straight line' iueans sinl- definitions m u s t t e a c h h o w t o m e a s u r e m a s s
ply ' p a t h of a lun~inousray.' If, t o suppo.ie the a n d force, a n d r e q u i r e definition of t h e
 SCIENCE.

eyunlitq of two forces, and this implies the tist must foresee. A good experiment teaches
principle of the equality of action and reac- more than an isolated fact; it permits us to
tion. " Hence, this principle should no foresee, i. e., i t permits us to generalize. In-
longer be regarded as an experimental law, terpolation is necessary. Experiments gire us
but as a definition" (p. 122). The result only a certain number of isolated points; gen-
reached is that the ' law of Newton' as to eralization traces a curre. This curre does
acceleration must be regarded as a definition, not pass exactly through all the points giren
in which mass is still undefined. " W e are by experiment. We not merely generalize
driven to the following definition, which is experience, but correct it. Experimental
simply an avowal of impotence: Masses are physics furnishes the facts; mathematical
coelgicients which it i s convenient to introduce physics orders them, makes the generalizations
inio calculations" (p. 127). and points out the needs. I n this generaliza-
tion the unity of nature and the simplicity of
While the principles of dynamics are defini-
its laws is presupposed. The curre does not
tions, they can be approximately verified by
follow all the zigzags indicated by the points
experiment. A more precise experiment would
given by experiment. Nevertheless, i t is not
show simply that the law mas only approxi-
certain' that nature is simple, but generaliza-
mately true in that case; which we knew
tion, and with i t science, could not exist if
already. Thus weasee how experience has the hypothesis of simplicity were entirely
served as basis for the principles of mechanics abandoned.
and still can never contradict it. Generalization requires hypotheses. There
The analogy between geometry and me- are three categories of hypothesis: (1) Those
chanics would a t first glance seem complete. which are natural and which can hardly be
I n each the fundamental principles are merely avoided, as that the influence of very distant
cor~ventionswhich experience has led us to bodies is negligible; (2) those that are indif-
set up as convenient. But there is a dif- ferent, as that matter is continuous or that i t
ference. The laws of geometry are set up is composed of atoms., These indifferent hy-
in consequence of experiments in mechanics, potheses are never dangerous, provided their
in optics, in physiology; they are in no sense true character is recognized. The hypotheses
experiments in geometry; they do not relate of the third category are true generalizations
to space (which geometry studies), but to ma- which experience should either confirm or in-
terial objects. On the other hand, the funda- validate.
mental conventions of mechanics and the ex- The hypotheses of physics lead to physical
periences which show that they are convenient, theories which, though apparently well estab-
relate to the very same objects or to analogous lished, are in turn displaced by others. Vari-
objects. This is not an artificial barrier be- ous examples are discussed.
tween sciences but a real distinction. The "No theory seemed more solid than that of
teaching of mechanics should, therefore, re- Fresnel which attributed light to movements of
main objective, experimental. ether. Rut now that of Maxwell is preferred.
The fourth part, devoted to 'Force,' con- Does this mean that the work of Fresnel was in
tains chapters on : ' Hypotheses in physics '; vain? No, because the real aim of Fresnel was
' The theories of modern physics '; ' The theory not to find oat whether there really is ether,
of probabilities, optics and electricity,' and whether i t is or is not formed of atoms, whether
' Thermodynamics.' I n this part the relation these atoms really move in this or that sense;
of observation to hypotheses and generaliza- his object was to foresee optical phenomena.
Now the theory of Fresnel always permits this,
tion is taken up. Experience is the sole
to-day as well as before Maxwell. The differ-
source of truth, but one must use his observa- ential equations are always true; they can always
tions; he must generalize. A mere accnmu- be integrated by the same procedure and the
lation of facts is no more a science than a results always retain their value.
pile of stones is a house. Above all, the scien- Let no one say that thus we reduce physical
836 SCIENCE. [s.S. VOL.X X. s o . 3.20.

theories to the rble of mere practical recipes; rich mass of niaterial has necessarily re-
these equations eapiess relations, and if the equa- mained untouched.
tioils remain true it is because these relations T h e work is characterized throughout by
preserve their reality. They teach us, now as masterly clearness and by the skill with which
then, that there is such a relation between such the overgrowth of unessentials and conse-
a thing and such another thing; only this some- quences is stripped off and the fundamental
thing which formerly x e called movevzent we now idea presented i n a few phrases. I n its tone,
call elect?ec cu~rent. Rut these appellations were the work addresses the non-scientist. Little
only images substituted for the real objects which
technical knowledge is requisite to read it,
nature will eternally hide from us. The veritable
but still it will hardly prove inviting to those
relations between these real objects are the only
reality that we can attain, and the only condition who have not i n some way attained a certain
is that the same relations exist between the ob- facility i n following strict reasoning. T o
jects as between the images by which we are these it mill furnish a n excellent and stimu-
forced to replace them. If these relations are lating discussion of some fundamental prin-
known to us, what matter if we deem it con- ciples of modern science apart from the
venient to replace one image by another. technicalities, while the scientist will welcome
That some periodic phenomena (an electric this presentation i n connected form of care-
oscillation, for example) is really dne to the fully thought out views which have already
vibration of some atom which, acting like a aroused much interest i n their earlier publica-
pendulum really moves in this or that sense, is tion i n various journals.
neither certain nor interesting. Rut that be- The work is also remarkable f o r the ease
tween electric oscillation, the inovement of the and directness of its style and f o r the genial
pendulum and all periodic phenomena there ex-
manner i n which t h e illustrative examples are
ists a close relationship which corresponds t o a
pi of ound i eality ; that this relationsliip, this chosen and treated. M. Poincari. is a past
similitude or rather this parallelism extends into master of t h a t most difficult a r t of giving the
details; that it is a consequence of more general central thought of a large theory i n a few
principles, that of energy and that of least ac- ~vordswithout sacrificing lucidity.
tion, this is what v e can affirm; this is the I t is t o be hoped t h a t the work will receive
truth which will always remain the same uncler i n America t h a t wide a n d thoughtful reading
all the garbs in which we may deem it useful to which i t deserves equally on account of the
deck it out " (pp. 189-191). subjects treated and the stimulating orig-
O u r author has thus discussed t h e question inality of the treatment. A n English transla-
of the degree of reality i n various branches of tion of the book and of the notes of Lindemann
science from four points of view. I n arith- is a desideratum.
metic we have necessary t r u t h developed Of the German translation little need be
ci priori i n the mind; i n geometry me have to said. I t is faithful and quite close, and
do with conventions, conveniently related to acquits itself remarkably well of the difficult
t h e material world, but not themselves amen- task of conveying the delicate and precise
able to direct experimental treatment; i n thoughts of t h e author into the German
mechanics we have likewise to do with con- tongue. The task was of course much
ventions, but they a r e amenable to direct ex- facilitated by the remarkable clearness of t h e
periments; while i n physical sciences we seek original, i n which there is seldom opportunity
under various images to express relations to questioii just what is meant, though the
which are profound realities. domain is one where few can avoid involved
I t is impossible to give a summary of a ideas and entangling phraseology. The im-
work which is itself so summary. W h a t pre- perative requirement that every shade of
cedes is a n inadequate attempt to present a meaning be faithfully reproduced effectually
few characteristic views which may serve to restrains the translator from any of those para-
indicate the general spirit of the work and the phrases which must be permitted if the trans-
style of treatment. The larger part of the lation is to conforrn itself, unhampered, to
 SCIENCE.

the genius of the language. I n view of these tude, and the records related chiefly to de-
restrictions, the translation seems good, but structive effects. The earliest philosophy of
of course, other things being equal, preference the subject r e g a r d d the tremor chiefly as a
will be given to the original. cause, ascribing to it various geologlc results,
A few points of detail may be mentioned: such as the uplifting of coasts and the erup-
Page 9, lines 3 and 4 should read : ' ... 'tion of volcanoes; and only by slow degrees
dass
er auch fur a-=a + 1 gilt, wenn er fur did it come to be recognized as a n effect, the
a = a richtig ist.' Lines 8 and 9 analogously. jar communicated by subterranean rending.
Page 91, the essential phrase, 'ce qui est The new seismology employs instruments of
expGrience, ce qui est raisonnement math& the most delicate and sensitive character, and
matique' (p. 111 of original) has not been by their aid not only detects tremors far too
translated. faint for direct perceptioh, but undertakes to
Page 92, line 2, read ' ist ' instead of ' ware.'
measure in absolute terms the amplitude,
The original, pp. 31 et seq., ascribes to period and speed of the waves and the in-
Xronecker that definition of number (as a tensity of the shocks. I t s analysis discrim-
partition of all rational number into two sets) inates earth waves of four different kinds,
which is commonly known as Dedekind's. The classifies shocks according to origin as vol-
translation renders all these passages imper- canic or tectonic, and by means of its data
sonally, and a note calls the presentation of discusses the physical condition oi the earth's
the text Dedekind's, as modified by Tannery. interior. I n a volume recently issued Dutton
The notes added to the translation have de- sets forth the present condition of the science,
cided value of their own, and make i t desirablesketching its history in outline, describing its
either to own both editions or on their account instruments and characterizing its progress
to give the translation the preference. They toward the solution of its more important prob-
are to a considerable extent bibliographic, giv-lems. The treatise is well balanced, compact
and as comprehensive as consists with adapta-
ing excellent lists of references to other works,
many of them classic, on the numerous topics tion to the needs of the general reader. Tech-
which come up. I n this respect alone, the nicalities are avoided so far as practicable,
notes constitute a welcome and useful supple- and details are introduced only for the pur-
ment to the original work, which makes cita- pose of illustrating principles. While i t does
tions only in the most general way with not neglect that aspect of the subject which
almost no specific references. B u t they also falls within the domain of mechanics, and
develop in many instances mathematical properly gives a major share of space to the
treatment of points touched on in the original, treatment of tremors as elastic waves, i t is
which contains practically no such matter. especially strong in its discussion of the bear-
Frequently the notes state briefly the views of ing of seismology on geophysics. Fortunately
others on the topic in hand, or sketch its his- for the geologic as well as the general reader,
torical development, usually with detailed the author brought to his task not only the
references. experience acquired in monographing the
A good index and a fuller table of contents Charleston earthquake, but the mental equip-
have been added in the German edition. ment resulting from prolonged study of vol-
J. W. A. YOUNG. canism and the greater problems of the inner
THEUNIVERSITY OF
CIIICACO, earth.
October 17, 1904.
The discovered blemishes of the book consist
of occasional lapses, either of statement or of
THE NEW SEISZVIOLOGY.*
correlation between text and illustration. For
INthe o;d seismology the only earthquake example, the symbol a (page 175), which
trenlors studied were those of sensible magni- stande for the intensity of a shock a t unit
"'Earthquakes in the Light of the New Seis- S. A. [No. 14 of The Science Series.J New York,
mology,' by Clarence Edward Dutton, Major U. G. P. Putman's Sons; London, John Murray, 1904.