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iceberg was floating. These cold currents exist in the main Arctic current whether
ice is present or not, but the presence of the ice is to slightly elevate the temperature,
To assist in illustration of my meaning please refer to the microthermogram taken on
the Allan Line R. M.S. Victorian last June (fig. 11). This record, which isa direct trace
from the chart on the instrument, is through the ice track at a depth of 18 feet, by the
Cape Race route. After passing the ‘‘Cold wall” the Arctic current drops in tempera-
ture regularly as the ship proceeds westward. The small variations up and down are
partly due to icebergs passed at distances of 6 to 8 miles, and partly due to colder
Smithsonian Report, 1912.—Barnes. PLATE 2.
ICEBERG USED TO OBTAIN THE ISOTHERMAL LINES.
ICEBERG SHOWING THE EFFECT OF WARM WATER MELTING. OBSERVE THE OVERHANG-
ING RIDGE OF ICE.
This berg is grounded and prevented from turning over,
Smithsonian Report, 1912.—Barnes PUATERS:
ICEBERG SHOWING THE SLEEPING WOLF.
ICEBERGS IN NAVIGATION—BARNES. 739
currents. The lowest temperature recorded here was reached nearest the Newfound-
land coast, but the effect of ice can be seen well marked by thesharp peak of temper-
ature, which I have shaded. Just here we passed most of the ice close to and were
obliged to proceed slowly in heavy fog at times. This colder and swifter Arctic
current carried with it the greater proportion of the ice, but it is well known that this
colder current exists whether accompanied by ice or not.
The great drop in temperature just before coming abeam of our largest berg was not
due to the iceberg itself, but to the influence of the cold current. The effect of the
ice is to hold the temperature abnormally high. The dotted line on the diagram
represents how the temperature would probably have gone had no ice been present.
It would depend which way we approached this berg whether a drop in tempera-
ture would result. The temperature rises rapidly, whichever way we approach it.
I have many other traces illustrating the same thing, and for this reason I was forced
to abandon the idea that an iceberg sensibly cools the water in which it is floating.
I was also unable to find by calculation that an iceberg could appreciably influence the
sea water on account of its slow rate of melting.
It is very illusive to depend on laboratory tank experiments to illustrate sea water
circulation. The conditions at sea are so very different. I was very much surprised
not to find during my experiments last summer more conclusive evidence of sea-
water dilution due to the melting icebergs. A large number of conductivity tests
were made of sea water, and these are described in my Canadian Government report.
The following may be of interest; the readings were made at 26° C.:
‘ Table of conductivities of sea water taken in July (1912).
Close to grounded berg, Cape Bauld, Newfoundland ....................... 0. 05007
Siinlinciebatlersio. CAsterMend 22 nce sce 5 cca ee eet os oe CMO! . 04827
aiputles ens Or pele uses e252 Shel. ode. Tee AN SILL ee Sa . 04850
Clone ocamaylarge bergen 2. We es been ee colin Uke oe ee Jw cee . 04787
Peete ipta EL EOk SLM CLA) PA a IS o wi Sater orm ancl 8S eie sews ao calayd af bia = Salem ete . 04806
Close abeam same berg..............--.-- Satta oh eo ees Nhe oa) oe ai aase . 04827
DOME AUBATES) DOLE Da) seemless a shas = eee oh ac cb en een eo Aste cies Beas . 04768
DUVETS bO LCOWALC OF a DERE: sa cece aces ose 2S aiees Soe be S ee ened ee ee ee . 04787
AO -yatasto windward of same bere. 05001 i. Ye: eas. potad 2k Bee . 04787
ihaecs tonlea ward Ofie Derr. aoe. oid). os thie da naan oem zee . 04806
The numbers may, perhaps, indicate a slight effect, but nothing like what I
expected. My conductivity tests of the sea water brought back from Hudsons Strait
in 1910 gave a value of 0.0480 at 25° C. Correcting for temperature this observation
serves to connect the sea water entering the Strait of Belle Isle with that in Hudsons
Strait. Eastward from Belle Isle Strait the conductivity rises rapidly for 180 miles,
after which it becomes uniform up to 450 miles. The greatest Arctic current sweeps
down close to the Labrador shore, and in through the Strait of Belle Isle where the
resultant flow is westward. The following measurements of the conductivity through
the ice track by the Belle Isle route were obtained last October on the Empress of
Britain. The values were all measured at a uniform temperature of 25° C.
NDCATMSOLDOu eG TSlOsaracs ee eee. oe ee het RE ey) OT Be re wnt at ay 0. 04865
AURMCM CHSOL OMS THC... ..f anaes Nea ks vie Mend) SF el eg aie bla 04986
BUPA CARU OL CUO Aik eee kee i eee kk a hae 05047
151 eC A A Root re “Ae ed SO aed Fe: Rs PN RI a I oe 05150
RELIED Sh Bate pcr oi SEY Aho ce 3 cy eels ato Sn ha Be del ops oes ne hia ee a | . 05235
RP EBIOR re ei Se eames, eee SE ERE RAE. Gre EON ors SSNS... he sek Ae 05257
POM ENREERNRSS I oe anc RC ea) Sian Ueno J. cor aay ae ee ath yy Ault etl: eshte 05211
740 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1912.
It is evident that the great Arctic current is of a. lower order of salinity, and that its
course may be traced along our eastern coast.
In the early spring when the water is cold the Newfoundland fishermen will find the
cod in the vicinity of the icebergs, and will always obtain their catch there. Per-
haps this is an indication of the warming influence of the bergs, for the cod will not
live in very cold water.
Next summer I shall continue my observations more particularly with reference to
the influence of land on the temperature of the sea. I hope before long to be able
to publish here some typical microthermograms howing this effect.
H. T. BARNES.
McGint University, January 27, 1913.
(From Prof. H. T. Barnes, F. R. 8.)
——— ee
HENRI POINCARE: HIS SCIENTIFIC WORK; HIS
PHILOSPHY.'
By CHARLES NORDMANN.
With the sudden death of Henri Poincaré a great sadness came
to all lovers of idealism and of science. Among all classes it was
felt that a great light had been extinguished in the firmament of
thought. But that feeling was nowhere so poignant or so lasting as
among those who, in their silent arsenals, slowly forge their weapons
for the struggle against the unknown, in the workshop of the physi-
cist, beneath the dome of the astronomer, or in the bare room which
the philosopher so richly furnishes with his meditations.
Henri Poincaré was not only the uncontested master of natural
philosopy, the intellectual beacon whose penetrating rays could
pierce all the regions of science. It was not for such qualities alone
that we admire him, for he had also those characteristics which made
us love him. That is why for a century he, more than any other
philosopher, has had “that personal influence which he alone can
exercise whose heart has not ceded to his brain.” ?
And now, when death takes from us this master whose task is
done, it is the man alone for whom we mourn. In the work which
he left was the best part of himself. When a man passes from us
while yet young, yet full of creative activity, of mental vigor, of
moral force, the weignt of whose authority was constantly renewed,
then our regrets are beyond bounds. In our sadness we are angry at
fate, for what we lose is the unknown, the hopes without limit, the
discoveries of to-morrow which those of yesterday promised.
Other nations regret the loss of Henri Poincaré no less than we.
He was received with unbounded admiration in Germany where,
on the invitation from their universities, he several times lectured
so brilliantly on his work. Such intellectual crusades were among
his greatest joys, for he felt that he was not only carrying conviction
but friendship as well. Philosophers, mathematicians, astronomers,
all spoke of him as the greatest authority of our time (‘Die erste
1 Translated by permission from Revue des Deux Mondes, Paris, Sept. 15, 1912, pp. 331-368.
2 All the phrases included within quotation marks were expressed by Henri Poincaré himself unless
otherwise stated.
85860°—sm 1912——48 741
742 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1912.
Autoritit von dieser Zeit”). And just recently one of the most
eminent of American astronomers, Prof. Moulton, a member of the
National Academy of Sciences of the United States, wrote of him
that ‘‘although France had the honor of giving birth to this admir-
able man yet he may be regarded as a genius of the whole world.
On his tomb should be engraved those words which the English have
put on that of Newton, ‘Mortals, congratulate yourselves that so
great a man has lived for the honor of the human race.’”’
When, contrary to all precedent, he won such honor among men
of judgment the world over before the lapse of a century or two, we
may be sure that the work of Poincaré was truly great and remarka-
ble. But before glancing at that work as with the look of some
beetle at a majestic oak, let us dwell for a few moments upon the
thoughtful and captivating personality of this loved master.
I. THE MAN AND THE SCHOLAR.
With his ruddy face, his beard turning a little gray, and not always
geometrically arranged, his shoulders bent as if under the ever
present weight of his thoughts, the first impression of Henri Poincaré
was one of singular spirituality and imperious gentleness. But two
traits were particularly characteristic in him: His voice, deep and
musical and remarkably animated when speaking of problems which
sreatly moved him, and his eyes, rather small, often agitated by
rapid movements, under irregular eyebrows. In his eyes could be
read the profound interior life which unceasingly animated his pow-
erful brain. His glance was absent and kind, full of thought and
penetration, his glasses scarcely veiling its depth and acuteness.
His short sightedness, poorly corrected by his glasses, added to his
absent look and made one say of him, ‘‘ He is in the moon.” Indeed,
he was often very far away.
Legend began to form about him long before his death and attri-
buted to him numerous traits, many of which for half a century
have been attributed to Ampére, some erroneous, some indeed true.
It has been said that he was absent-minded; absorbed in thought
would be more exact. Great thinkers, as well as all who are intense,
are slaves of the interior tyrant which usurps their souls. When
thought assumes control of a man it holds him under its claws as
the vulture of Prometheus. The profound visions which possessed
the soul of Poincaré left him no rest. Often he lost sight of the
near at hand objects and the petty things of daily life, for his vision
was closely focused on the infinite. It was when he was troubled
with the immediate and ordinary things of life, and his judgment
was then as sound as in regard to weightier matters, that he was
ever really distracted, if we use the word in its true etymological
sense.
NORDMANN. 743
HENRI POINCARE
In the discourse in which he was honored at the Académie fran-
¢aise, M. Frédéric Masson wittily narrated several anecdotes of this
absent-mindedness. Especially amusing was the carrying off one day
unconsciously by Poincaré of a willow cage from the front of the shop
of a basket maker. The incident was true, but upon inquiry we find
that Poincaré was only 4 years old when it happened. How many
men. of genius, indeed, how many men of no genius, are there at whom
no one has ever been astonished that at that age they did not show
the prudence of Nestor in their conduct on some stroll? Nor is this
at all for the purpose of weakening our skepticism at that “little
science of conjecture”? which we call history. Poincaré was himself
amused at all such anecdotes. ‘‘They say,” he conceded with a pleas-
ant smile, “‘that creates a legend.’’ Moreover, he has very well
explained that ‘‘if we meet so many geometricians and naturalists who
in the ordinary doings of everyday life show a conduct at times aston-
ishing, it is because, made inattentive by their meditations to the
ordinary things which surround them, they do not see what is about
them; it is not because their eyes are not good that they do not see;
it is because they are not seeing with them. That in no way hinders
them from being capable of using keen discernment toward those
objects which are of interest to them.”
. The psychological characteristics of Poincaré were made the object
of an interesting and very full study by Dr. Toulouse,' of which cer-
tain conclusions should be noted. This study was made especially
as an experimental test of the celebrated statement of Moreau of
Tours that ‘‘genius is a nervous disease.”? We know how Lombroso
took up and amplified that idea and that he thought that he could
conclude from his researches that genius is inseparably connected
with nervous troubles, especially with epilepsy. Yet, despite all
those researches and from whatever side they conducted their attack,
Dr. Toulouse and his collaborators were unable to find in Poincaré
the least trace of neuropathy. All their measures, all their tests,
showed them aman perfectly normal psycho-physiologically, possessing
in every way the most harmonious and perfect equilibrium. Thus
he demonstrated at its proper value one of the most brilliant, one of
the most sensational errors of Prof. Lombroso.
Because, physiologically Poincaré was, despite his genius, in no
way different from the average of ordinary men, I would not fail, were
I a spiritualist, to use this as an argument in favor of a soul apart from
the body.
The instability of attention in Poincaré was one of the characteris-
tics which most struck Dr. Toulouse. Indeed, Poincaré had a habit
1 A medico-psychological inquiry into intellectual superiority, vol. 2 (Enquéte médico-psycologique sur
la supériorité intellectuelle).
744 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1912.
of jumping from one subject to another entirely unconnected, of
jumping, if I may employ a slang phrase, ‘‘from a cock to a donkey.”
In keeping with this was his habit, which often astonished strangers,
of rising brusquely in the middle of a conversation, walking briskly
for a moment, and then reseating himself. ‘‘Those are ideas,” he
would say, ‘‘which come and go.” Perhaps we might thus compre-
hend the ‘‘demon”’ of a Socrates or the “‘voice” of a Joan of Arc.
‘‘Poincaré is not an emotional man,’ Dr. Toulouse also wrote; ‘‘he
is neither affable nor confidential.’ Perhaps that might have been
inferred, but Dr. Toulouse was certainly deceived. Poincaré, retired
within the ivory towers of his thoughts, was insensible to all that dis-
turbs the hearts of ordinary men. He himself used a somewhat lofty
phrase full of a sad stoicism which would confirm that impression,
when he said: ‘‘The sole end which is worthy of our labor is the search
for truth. There is no doubt that first we must set ourselves to ease
human suffering, but why? Not to suffer is a negative ideal and one
which would be most certainly attained by the annihilation of the
world.’”’ If in the eyes of the world he thus seemed to resist his own
feelings, we ought not to believe them the less sensitive. But to good-
ness no less than to beauty belongs the quality of modesty. Poin-
caré was adverse to the familiarity of special friendships, because,
with Renan, he felt that they made one unjust and were unfavorable
to larger interests. Nevertheless, his kindness was perfect, even with
those who importuned him for advice or praise. Within those two
concentric circles, the family and the fatherland, modern society has
accustomed us to limit our altruistic affections. He loved them
dearly. He was too good a son of Lorraine not to feel hurt when he
thought of mutilated France; in what sad and troubled accents he
knew how to speak of that great grief which has left us twice inconsola-
ble, even though our sons seem to forget. But it was especially in
his family, that confidential fatherland, that he showed without con-
straint his charming tenderness of heart. He himself taught his four
children to read, and I have known aspects of his romps with them
which would recall Henry IV, but it would be imprudent to describe
them here. How far removed he seems in these from that abstract
mind in which they would have us see him, retired like some monstrous
snail within the inaccessible convolutions of his thoughts. Moreover,
he had the good fortune to live in surroundings the most favorable to
creative work, in an atmosphere of silent affection and discreet quiet
which the gentle hands of the women of his household knew how to
create around him.
Poincaré was attracted by beauty in all its forms provided only
it was noble. Music, painting, poetry, were his preferred relaxations.
Even as to his science we will see that he loved it above all for the
esthetic pleasure it brought to him. An anecdote is told of him by
HENRI POINCARE—-NORDMANN. 745
M. Sageret which shows well the disdain with which he neglected
what was not science for science, or, if I may dare to use a new
phrase, Science for Art. The director of the Ecole supériore des
télégraphes had asked him to discuss in a lecture a somewhat diffi-
cult problem relative to the propagation of electric currents in cables.
Poincaré accepted and solved the problem “at first sight”? without
having had the time to discuss it. Congratulations came from the
director. “Yes,” replied Poincaré, “I have found the value of L,
but is it measured in kilograms or kilometers?”’ It is useless to add
that he knew very well what he was talking about.
We should also recall his briluant school days, his wonderful
faculty for assimilation; he followed all the mathematical courses of
the Ecole polytechnique without taking a single note, not because
he remembered the demonstrations but because he could reason
them out at will. We should recall that he was very skilled in rea-
soning, but what does that prove? The greater portion of the
teachers: of mathematics have left no trace of themselves in the
world. For it is one thing to assimilate, another to invent, and we
know of scientists of renown who have not succeeded in making
themselves accepted as fellows in our colleges.
To be complete we should conclude by speaking of his career, his
rise to the very highest rank, to the greatest honors given by society.
But that matters little. There is no common measure between
Poincaré and the many other men whose ranks and titles in this
social ant hill are equal to his and of whom some one—I have forgotten
who—said, “their conceit ill concealed their incompetence.” Poin-
caré, on the contrary, never attached much weight to such honors.
He was deeply and sincerely modest, hesitating always to announce
definite conclusions and his intellectual attitude was constantly one
of doubt. It is perhaps for that reason that among a dozen great
scientists who have lived during the last century, he accomplished
the miracle of never having made a single enemy, a single one hostile
to him in science.
In his scientific work, Poincaré touched all the great mathematical
questions. He did not merely touch them as, from the multiplicity
of problems examined, one might suppose—just skimming over them.
This Michelangelo of thought could not, would not, stop at the little
details—for the small harvests to be reaped from the beaten paths.
It was in the most obscure corners, the most inaccessible of matter,
that he knew how by first onslaught, with great cuts with his chisel,
to open paths full of light and unknown flowers.
Mathematician above all and before all, he could clear fields for
himself in those studies which transcend reality and where the pure
geometrician, lost completely among his harmonious abstractions
and pure deductions, constructs at his will, immaterial, impeccable
746 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1912.
beings of strange beauty. The pure mathematician has at his beck
intimate delights of such esthetic quality that it often comes to pass
that he no longer finds interest in the exterior world, lost in a kind
of grand mysticism. Poincaré, however, was not of that kind,
although his researches in geometry and analysis made him the
greatest mathematician of our times. ‘‘ Experience,” he said, “is the
sole source of all truth.’”’ And those words acquired a singular force
coming from the mouth of the greatest theorist of our epoch. That
was why among mathematical problems Poincaré attacked especially
those which physics brought before him. That was why he passed
so readily from pure analysis to mathematical physics and then to
celestial mechanics. And, finally, that was why he came to reflect
upon the very foundations of our knowledge, upon the past and the
future of our world, upon the value of our thoughts as we pass to
the limits of what we can know to the borders of that abyss which
separates physics and metaphysics and into which abyss most of us
can not glance except with dizziness. It tore from Pascal many
superb sighs of grief, yet Poincaré could look at such matters as he
looked at all other things, not with a useless despair, but without
prejudice and foolish illusions, with simple, clear, and profound good
sense; he knew how to look at them and after a glance with his eagle
eye to sum up all in a word.
II. POINCARE, THE MATHEMATICIAN.
“My daily mathematical studies,” said Poincaré— ‘how shall T ex-
press myself ?—are esoteric and many of my hearers would revere
them more from afar than close to.” That is what he said one day
to excuse himself for speaking on a mathematical subject. When-
ever he commenced one of his profound lectures, in which he charmed
his listeners, he felt the need of thus excusing himself. Thus by his
modesty he knew how to make us pardon his genius. However that
may be, you will permit me to appropriate that remark for the pres-
ent occasion that I may not beyond measure speak of the purely
mathematical researches of Poincaré. It would require a dozen years
of preliminary mathematical study for the curious reader to be able
to know them, and if he were familiar with the elements such as he
would get in the ordinary college course he might take a glance at
them.
Were I to characterize in a few words what Poincaré brought new
into the divers processes of calculus and which won for him the title
“Princeps Mathematicorum,” which unanimous consent has given to
no other man since Gauss, I would proceed thus: In algebra and in
arithmetic, where he introduced the new and fertile idea of arith-
metical invariants and in the general theory of functions, his dis-
HENRI POINCARE—NORDMANN. 747
coveries were numerous and would have sufficed for the glory of
several mathematicians.
It was especially in the theory of differential equations that the
genius of Poincaré showed itself. If he spent on them the greater
part of his intellectual resources it was without doubt because most
of the problems offered in the physical study of the universe led to
just such equations. Newton was the first to show that the state of
a moving system, or, more generally, that of the universe, depends
only on its immediately preceding state, and that all the changes in
nature take place in a continuous manner. True, the ancients in
their adage, ‘‘ Natura non fecit saltus,’’ had an inkling of it. But
Newton was the first, with the great philosophers of the seventeenth
century, to free the idea from the scholastic errors which perverted
it and then to assure its development. A law, then, is only the neces-
sary relation between the present state of the world and that imme-
diately preceding. It is a consequence of this that in place of study-
ing directly a succession of events we may limit ourselves to consid-
ering the manner in which two successive phenomena occur; in other
words, we may express our succession by a differential equation.
All natural laws which have been discovered are only differential
equations. Looking at it slightly differently, such equations have
been possible in physics because the greater part of physical phe-
nomena may be analyzed as the succession of a great number of ele-
mentary events, ‘‘infinitesimals,’’ all similar.
The knowledge of this elementary fact allows us to construct the
differential equation and we have then to use only a method of summa-
tion in order to deduce an observable and verifiable complex phe-
nomenon. This mathematical operation of summation is called the
“integration” of the differential equation. In the greater number
of cases this integration is impossible, and perhaps all progress in
physics depends on perfecting the process of integration. That was
the principal work of Poincaré in mathematics. And in that line
his work was amazing, especially in the development of those now
famous functions, the simplest of which are known as the Fuchsian
functions (named after the German mathematician Fuchs, whose
work had been of aid to Poincaré). We may represent by these new
transcendental functions, which are also called automorphic, curves
of any degree and solve all linear differential equations with algebraic
coefficients. Poincaré thus gave us, using the apt expression of his
colleague, M. Humbert, of the Académie des sciences, ‘‘the keys of
the algebraic world.” Poincaré himself used these algebraic tools
in his researches in celestial mechanics.
To tell the truth, the Newtonian idea as to the continuity of phys-
ical phenomena has of late been somewhat battered down in several
748 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1912.
places by the new and odd theory of ‘‘quanta,” to the construction
of which several physical discoveries have led. This supposes a cer-
tain physical discontinuity in the atomic phenomena which produce
radiation.t. Not wishing to go too much into detail on this subject,
T am going to make a somewhat bold comparison, but one which is
perhaps not wholly void of meaning: The hypothesis of quanta has
grown up side by side with that of continuity, just as in biology the
Larmarkian and Darwinian theories of slow and imperceptible evolu-
tion have come recently face to face with those of sudden and dis-
continuous mutation of the Dutch naturalist, De Vries. The latter,
by the new evidence which he has brought forward, has not destroyed
the older theory; he has merely enlarged it, shown its limitations, and
left it intact in its greater significations. Similarly, the theory of
quanta, it is probable, will not prevent the greater part, if not all, of
physical phenomena from being capable of representation by differ-
ential equations. The progress which the latter have brought, the
physical discoveries to which they have led, notably in optics, in
electricity, and in astronomy, are their guaranty. Accordingly, the
new functions discovered by Poincaré will always remain one of the
most brilliant contributions which he brought through pure theory
to the study of external phenomena.
If we study the characteristics of the method of Poincaré and of his
mathematical genius, we find especially a wonderful faculty for gen-
eralization. Instead of starting, as do most students, with a study of
the minor details, he jumped to the very heart of his problem, neglect-
ing the intermediate details, like an audacious conqueror, who, with-
out preliminary skirmishing, makes his first onslaught upon the
master difficulty, the most impregnable fortress, inventing on the
spot the instruments for subduing it and then forcing its surrender
without striking a blow. Then we would leave to others the investi-
gation and organization of the new province which he had just won
and pass immediately to other conquests. In that sense we may
speak of him as being ‘‘more a conqueror than a colonizer.’’? There
resulted that peculiar method of thought so noticeable in his philo-
sophical writings, so disconcerting at times to the novice and which
brought upon him the reproach of being disconnected. True, Poin-
caré’s process of reasoning was not smooth and continuous; he pro-
ceeded by successive bounds which had more the effect of a broken
line. But the profile of a diamond is likewise made of broken lines,
from the very virtue of which its brilliancy results. Such a logical
method is not common, but, borrowing the words of M. Painlevé,
1 Poincaré summarized excellently in the following words shortly before his death the conclusions to
which the theory of quanta led him: ‘‘A physical system can exist only ina finite number of distinct states;
it leaps from one of these states to another without passing through a continuous series of intermediate
states.””
2 Borel: Revue du Mois, vol. 7, p. 362.
HENRI POINCARE—-NORDMANN., 749
“Should we be surprised if a lion does not run with the steps of a
mouse 2”
Upon the very structure of his thoughts, upea the mechanism of
his marvelous cerebral workshop, Poincairé has left us strange and
suggestive confidences. Since what we know of the universe comes
only from its image as reflected to us through our brain, that knowl-
edge is affected by all the properties and deformations of that inner
mirror, and psychology will without doubt one day be the master
science. Accordingly the psychological aspects of a brain like that:
of Poinearé, which he has shown us naked with such touching sin-
cerity, are of unequaled interest. In studying the genesis of mathe-
matical invention, ‘‘which without doubt is the purest and most
exclusively rational process of our brain because it seems the least
conditioned by the exterior world,” we find the most essential char-
acteristics of the human mind which we may ever hope to get. La-
place has said, ‘‘A knowledge of the methods of a man of science are no
less useful to the progress of science or toward his own glory than the
discoveries themselves.”
Contrary to our expectations, conscious work, voluntary and logical,
did not with Pomearé play the most important part. Nothing is
more amusing in that respect than the manner in which he has told
us of his discovery of the Fuchsian function. This idea which strug-
gled vaguely in his brain one evening after he had taken, contrary to
habit, a cup of coffee so that he could not sleep, took shape little by
little under the strangest of circumstances. Everyone has read the
pages where he has told how he saw in due proportion all the chief
difficulties but did not consider them further, and then how, long
afterwards, in a flash, the solutions he wished appeared to him when
he was putting his foct on the step of an omnibus; at another time
when crossing a street, and yet again on a geological stroll in the midst
of a triflmg conversation.
The ‘‘subconscious self,” or, as some have put it, ‘‘the subliminal
self,” plays in mathematical invention a supreme part. There where
we believe reason and will ruled alone we find something appearing
analogous to the inspiration which custom attributes to poets and
composers. And it is a troublesome circumstance that this subcon-
scious self succeeds in solving problems and overcoming difficulties
which the conscious self could not. Is then the subconscious not
superior to the conscious self? Have we not here something within,
which is greater than ourselves, a sort of divine essence superior to
our will and reason whichmakes us capable of tasks greater than our-
selves? We can understand the importance of such a question and
the spiritual significance of a positive relpy. The positive mind of
Poincaré, however, would not admit supernatural explanations unless
absolutely necessary and in a penetrating and accurate investigation
)
750 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1912.
he has shown a way to escape such a conclusion. He makes us see
how the automatism of the subliminal self works only upon material
which the conscious self prepares for it and then explains how,
among the great number of combinations which the subliminal self
forms, only those come into our consciousness which are apt and
elegant and consequently affect our senses and attract our attention.
The simple and most harmonious construction turns out to be pre-
cisely the most useful as experience and reason repeatedly teaches.
The esthetic sentiment for the harmony of form and number and geo-
metrical elegance dominates the thought of the mathematician. His
soul is first of all that of an artist and a poet.
These views, so deep and true, are somewhat at variance with the
classic idea of a mathematician, respectable, exact, but rather ludi-
crous with his mechanical brain and an eye which the traditional
glasses have rendered blind to all beauty and in whose heart nature
has placed, instead of feeling, a table of seven-decimal-place loga-
rithms.
Tn unveiling to us in a man of science worthy of the name, a sensi-
tive and esthetic being, Poincaré has again yielded to his innate
modesty. The limitations of our brain have made us exalt its merits
in our modern society where the ‘‘cult of intelligence” rules; we have
had and perhaps still have a tendency to exalt the virtues of the will
at the expense of those which come from the heart. We hold as
superior to all else the attributes of the thmking man and so our
justice has a deep disdain for those who are irresponsible; though
indeed we do not judge that they merit punishment. In thus show-
ing us that his so logical a development for science was due largely to
his subconscious and involuntary and only partly to his conscious
faculties, Poincaré doubtless somewhat lowered his own glory, per-
haps that of all scientists in the eyes of some; as to that I imagine
that he would be easily consoled. This marvelous autopsychological
study has explaimed one thing which seemed at first very surprising,
how working only four hours, or rather consciously working only
four hours a day, Poincaré was able to produce a scientific contribu-
tion perhaps greater than that ever made by any other mathemati-
cian. Uncontrolled by his will, his cerebral machine worked by itself
night and day, without stopping. Perhaps otherwise he might not
have died so young. That interior flame which without rest, shone
so brightly, burned up too soon the lamp which held it.
III. POINCARE THE ASTRONOMER.
In astronomy the work of Poincaré was gigantic. That science
could not have failed to attract him from the very first because of all
the exterior world it offered to his power as a generalizer, disdainful
of conditions, the greatest and most lasting problems. There is no
HENRI POINCARE—NORDMANN. 751
other branch of natural philosophy which provides to the meditation
or to esthetic revery such grandeur. Astronomy is the mother of all
the sciences and it is still today the most advanced, that in which we
can best predict the future.
The study of the stability of our universe has been for two centuries
the fundamental problem of celestial mechanics for the solution of
which the genius of mathematicians has striven. This portion of
space wherein we are placed, the solar system, is it stable? Will
those planets which we have observed from time immemorial con-
tinue to describe invariably the same immense orbits with only a few
periodic oscillations from their mean positions, will they continue
thus indefinitely in the future? Or will this machine so harmo-
niously contrived, and wherein we at present see no apparent sign of
possible destruction, never become unstable and disappear some day ?
That is the problem.
When Newton demonstrated that gravity acted not only between
the sun and the planets but also between the planets themselves, it
was seen that there must result irregularities in the harmony of the
solar system, that the reciprocal attraction of the planets must
slightly deform the perfect ellipses which the attraction of the sun
alone would have made them describe. Truly these deformations are
small because of the smallness of the masses of the planets compared
with the central sum (Jupiter’s mass is 300 times that of the earth but
only one one-thousandth that of the sun). But might not these
planetary perturbations, accumulating through centuries the effects
already observable in the time of Newton, finally destroy the Kepler
ellipses? At any rate, the simple harmony of the world of Kepler no
longer is real. Newton, strongly embarrassed by the foresight of the
impending catastrophe, has made, in his optics, this allusion to the
planetary inequalities, ‘‘which probably,” he says, ‘will become so
great in the long course of time that finally the system will have to be
put in order by its Creator.”
In 1772 Laplace believed he was able to demonstrate that these
fears were groundless. He showed that the secular inequalities of
the planetary elements compensated themselves periodically at the
end of a sufficiently long period and the terms of the first order of the
perturbations would disappear in the calculations. That implies a
stability of our system at least for a very long time, thousands of
secular periods. Consequently, Laplace criticized the deus ex
machina invoked by Newton and somewhat haughtily believed he
could affirm, arguing from his results, that the machinery of our
world had had no need of the initial fillip and that it would go ahead
indefinitely without the need of outside assistance. Is it necessary to
note that there must be some fault in logic on the part of one who
could suppose that when the solar system had so beautifully evolved
152 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1912.
from a nebula the process of evolution would stop and become fixed
in eternal immobility or perhaps better in invariable mobility? But
even great men sometimes make slips in their logic. There were
never men who made none.!
Later, two celebrated mathematicians, Lagrange and Poisson,
considerably extended the system of Laplace. The indefinite sta-
bility of the planetary elements seemed assured forever. The
address delivered by an astronomer, and he not one of the least,
M. de Pontécoulant, before the Académie des Sciences, when the
statue of Poisson was dedicated, shows well the state of belief of the
world upon this matter then, and it was scarcely altered at the end of
the nineteenth century.
“For his masterpiece,” he said, “ Poisson had the honor of solving
that most important problem, the stability of the solar system, of
which, after the works of Laplace and Lagrange, doubts still existed
in the most judicial minds. In the future the harmony of the celestial
spheres is assured. Their orbits will never depart from the almost
circular form which they have to-day and their respective positions
will make only slight departures from a mean position in which the
succession of centuries will finally see them revolving. The physical
universe was therefore built upon indestructible foundations, and
God, in order to conserve the human race, will not be obliged, as
Newton wrongly believed, to retouch his work.”
So matters stood when Poincaré attacked the problem. Soon dis-
coveries succeeded discoveries. The problem set is this: Being given
several bodies of known masses in given places and with given
velocities at some known moment, to determine what these places
and velocities will be at any future time, ¢. For a single planet and
the sun the problem is completely solved by the laws of Kepler. But
when two planets and the sun are considered the reciprocal attraction
of the planets upon each other must be considered. Then we have
the celebrated problem of three bodies. The difficulties of this latter
problem are such that it can be solved only by the method of succes-
sive approximations. In the equations which led Laplace and his
successors to their conclusions as to the stability, the coordinates of
the planets were developed in a series whose terms were arranged in
powers of the masses. Poincaré first showed that we could not thus
obtain an indefinite approximation and that the convergence of the
ton, some place had been left to the Creator in the maintenance of order in the world. Laplace replied:
‘Citizen, premier consul, I have had no need of such an hypothesis.” If that was the response really made,
I do not see at all the ground for the irreverential or atheistical attitude often attributed to Laplace. There
may indeed be a very deeply religious sentiment in the belief of a universe so harmoniously constituted
that there would be no need of continual retouching for it to preserve its course. ‘Men,’ Poincaré has
written, “demand that God continually prove his existence by miracles; but the eternal marvel is that
there are not miracles continuously. It is for that very reason that the world is divine because it does
work so harmoniously. If it were ruled by caprice, how could we then prove that chance did not reign
supreme?”
HENRI POINCARE—NORDMANN. fae
series had been assumed without proof by those who employed them,
and that it is probable that in the terms of higher order, t, the time,
enters not only with the sine and cosine, which would lead to periodic
compensations of the irregularities, but also outside of the trigono-
metric functions, so that certain of the terms, at first negligible, may
possibly increase indefinitely with the time. Here with one blow he
reduced to naught the conclusions of Laplace and his successors.
Poincaré found later that certain new methods would allow him
to express in every case the coordinates of the planets in a purely
trigonometric series, avoiding the inconveniences of the former
methods, and he proved for the purpose a brilliant series of new
theorems of great generality. The rigorous proof of the stability
now depended only on knowing whether the new series would be
convergent. This was the knot of the problem, for before Poincaré
all astronomers had supposed a trigonometric series to be absolutely
convergent. Poincaré showed that that opinion, despite the fact
that it was classic, was erroneous, and indeed that, when we have
represented the coordinates of the planets by a convergent series
which is not very different from that employed by Laplace, we will
not have demonstrated the stability of the solar system. Because
of these great results, which are like the crowning of three centuries
of incessant research, posterity will certainly place this new treatise
on celestial mechanics (Les méthodes nouvelles de la mécanique
céleste) by the side of the immortal Principia of Newton. All future
researches on this subject must be built upon the solid foundations
laid by Poincaré.
Celestial mechanics in general considers the planets only as if all
their matter were concentrated in mathematical points. It leaves
out of consideration the other properties of these objects, evidently
generally negligible in comparison with the Newtonian attraction,
but whose effects with time may become of importance relative to
the stability of the systems. Attacking the question from a new
side, Poincaré showed that there are three preponderant forces tend-
ing to modify the orbits: The resistance, weak though it may be, of
the interplanetary medium; the tides which the planets and the sun
produce upon each other; and the magnetism of the planets. The
accumulated effects of these will finally precipitate the planets into
the sun. That will be the end of our system of planets. Will that
be the end of the human race? Certainly not, for it is very probable
that other changes will have ended terrestrial life long before the day
of that final catastrophe; the day? no, I should not say day, for there
will no longer be day and night, for our earth will then forever present
the same side toward the sun! Many reasons lead us to believe that
in the future as well as in the past the duration of human life upon
this globe will be infinitely small compared to the time our earth has
754 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1912.
its being. So those who fear that their end will be hastened by that
of the solar system may be reassured. The retinue of the sun once
disappeared, does that mean that other analogous and distant sys-
tems, scattered here and there like a living dust, will not exist in-
definitely? That is a question much discussed at present, but which
we can not answer.
The problem of the shape of a star resolves itself into that of a
fluid mass rotating and subject to various forces. Next to the
problem of three bodies it is the most important one of celestial
mechanics. Here, too, Poincaré made remarkable discoveries. They
mark an epoch in the study of the subject, as Sir George Darwin
remarked the day he presented to Poincaré the gold medal of the
Royal Society of London. Formerly but two figures of equilibrium
were known for rotating fluids, the elipsoid of revolution and that of
Jacobi with three unequal axes. Poincaré found through his calcula-
tions an infinite number of others which are stable and shaped like
pears, whence the name apiodes given to this class of bodies. The
pear-shaped bodies discovered by Poincaré appear to have an im-
portant place in nature, as proved by the evidence from certain nebule
and close double stars. They enable us to get some idea of the mech-
anism of that bipartition, somewhat analogous to that of organic
cells, which may have given birth to a great number of binary sys-
tems and which successively separated the earth from the sun and
then the moon from the earth.
Finally Poincaré showed that no form of equilibrium is stable
when the velocity of rotation exceeds a certain limit. He at once
applied this fact to that enigmatic marvel, the ring system of Saturn.
Maxwell showed that the rings could not be solid and if fluid that
their density could not exceed three one-hundredths that of Saturn.
Poincaré proved that if the rings are fluid they could not be stable
unless their density is greater than one-sixtieth that of Saturn. He
concluded that the only alternative is to suppose that they are formed
of a multitude of small satellites, gravitating independently. We
know how spectrum analysis subsequently proved this marvelous
deduction of this mathematical genius.
A small portion only of Poincaré’s scientific work is included in that
just described. Even a superficial description of all would require
volumes, it isso vast. Before turning to another branch of his work,
that which will reveal his philosophy, I feel almost a kind of remorse
as I find myself obliged, by the limitations of this tribute, to pass
over in silence all those great*discoveries which he has so generously,
almost indifferently, if I may use that word, worked out, always
with the same mastery, in such different branches of science, in
optics, in thermodynamics, in electricity, or in astronomy; some-
times with daring strokes he treated of the relations between the
HENRI POINCARE—NORDMANN. 155
matter and the ether; again he compared the thousands of suns of
the Milky Way to the molecules of a bubble of gas, applying to them
the kinetic theory and opening in the stellar universe such astonishing
aspects; then from a ray of light sent from one of the planets he
teaches us to learn at the same time the motion of the sun which
sends the ray, of the planet which reflects it, and of the earth which
receives it. But we must stop; when we are passing through a beau-
tiful and vast forest full of varied aspects, we must not stop only in the
first pleasing shade we reach, for yet farther on there will be found
others where new rhythms will arouse our emotions and enchant our
eyes.
IV. POINCARE THE PHILOSOPHER.
From science to philosophy there is but a step to take, they
so bound and penetrate each other. The Greeks had but one word
to express each. Even to-day the English call the physical study of
the universe natural philosophy. Poincaré could not escape that
attraction which has forced all the great workers in the exact sciences
from Democritus to d’Alembert, toward the end of their lives, to
reflect upon the primordial mysteries of the strange universe wherein
our ephemeral thoughts live and die. When, upon the front of the
Parthenon some rival of Phidias had cut that exquisite equestrian
frieze, he must have stepped back a moment so as to judge his work
the better as a whole, and then later, forgetful of his own efforts, have
become absorbed in the vast harmony of the whole great temple.
And so all the great wise men worthy of the name feel toward the
universe.
The philosophical ideas of Poincaré have deeply impressed all
those who think. They have helped through their tendencies to give
the intellectual attributes of our generation its so definite profile. By
singular chance they have stirred the most adverse camps. Each one
has wished to use them for their weapons; vain desires, for these
ideas soar far above them, and, indeed, such ideas sometimes seem
to unchain and reanimate quarrels of other ages. Whence does this
man get this strange power of moving thus, despite himself, by his
thoughts alone, in this abstract domain, in a realistic epoch where the
conflicts of every-day life press harder than ever upon the world of
ideals? This power is due to Poincaré’s intellectual superiority and
especially to his thorough sincerity. In what way are these new points
of view which this great man has developed so suggestive, so useful,
so convincing? Let us try to find out.
If we exclude the bitter, ever-present struggle for better living,
which does not gain in dignity as we pass from animal to man, it
seems as if all man’s striving came solely because he thirsts both for
truth and for justice. And we always find, save with Dr. Pangloss,
756 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1912.
who was a mythological bemg dead without descendants, that in
reality justice is not always the rule. The two words, truth and jus-
tice, which we are accustomed to couple, correspond in a certain way
to states which the very nature of things render mutually exclusive.
Some men, whom truth, the desire for knowledge above all else,
attracts, follow to their last consequences the dictates of reason even
though they drown in the bitterness of their dearest illusions. The
others, ever protected by that magic potion called justice, and which
some intuition, whence I know not, assures them must exist, deliber-
ately turn their eyes from exterior reality which at every step spoils
their dream. ‘To them it is enough that a thing be just in order that
it be the truth. Their inner ideals are a superior guide to outside
reality.
The first mode serves as a mantle for diverse forms of materialisms,
rationalisms, positivism, scientism; the second rules as mistress to
various spiritual doctrines of which the most recent and suggestive
is pragmatism in its various forms. Contrary to its various prede-
cessors, pragmatism pretends not to ignore science. With varied
shades and pretenses, often modified by circumstances, these two
tendencies have separated men as far back as we go in history. Nor
can it be otherwise in the future. As long as our nature is what it is
are we condemned to toss between these two extremes, which are
called intelligence and sentiment, reasoning and dreaming, the reality
and the ideal. We may sum up all history of the torments of human
thought by that name which Goethe gave to one of his most beautiful
books, “Wahrheit und Dichtung”’ (truth and fiction).
The conflict becomes especially bitter and irritating when it no
longer takes place between schools of thought but between individuals.
Sometimes one sect seems to be supreme. Oftentimes both lose.
The love for the ideal and the taste for the real, lost in the bitter con-
test, leave the soul empty and lifeless. Poincaré’s philosophy shows
how we may challenge both of these dogmatic extremes. Nor does he
do this with arms rusted and stacked in idle repose. He has nothing
in common with a vague eclecticism, which, like the costume of
Harlequin, made of pieces and bits, tries in vain to conceal with words
the wounds received and which no longer survives except in our col-
lege educations, those museums of antiquities. He attacks the
problem at its very foundation, assigning to each step its definite
limitations. He gives us reasons for doubt, but at the same time
reasons for action, for loving the beautiful and the true, even though
they may not be accessible. May we not love the stars even though
we can not touch them?
To a superficial observer scientific truth is beyond the pale of doubt; scientific
logic is infallible; if sometimes a scientist is deceived it is because he has overlooked
some conditions.
HENRI POINCARE—NORDMANN. 157
Mathematical truths are derived from a few self-evident axioms by an unimpeach-
able chain of reasoning. They rule not only over us but over nature herself. They
limit in a way even the Creator. He can choose only between a few possible solu-
tions. We need, then, only a few trials to know what choice he made. From every
experiment many consequences may follow through a series of mathematical deduc-
tions, each one leading into knowledge of some new corner of the universe.
Note the significance of these facts for the good of the people; the importance to
those colleges which first discover the physical basis of some scientific truth. But
note how they have misunderstood the relation of experiments and mathematics; for
hundreds of years philosophers have made worlds of dreams based as little as possible
upon facts.
Poincaré first undertook to show the weakness of that creed which
refers all phenomena to time, number, and space, and which was left
to us by the traditions of the seventeenth and eighteenth centuries.
The ‘‘mathematical universe,” that dream sketched by Descartes and
elaborated by the great encyclopedists, expressed the very essence
of everything in an absolute, definite geometrical form. According
to the Cartesian conception, all the properties of matter are reducible
to extension and movement; matter hid nothing further. This
ambitious dream was indulged in not only by the people and the
colleges, as Poincaré has stated, but even in our days by scientists of
considerable repute, notably in the work of the celebrated German
naturalist Haeckel, who developed such a system and with naive
arrogance believed he had solved the ‘‘riddle of the universe.”’
There has been quite a little doubt since Kant whether these no-
tions of time and space upon which this metaphysical structure is
based, this absolute pragmatism, if I may use that term, are not a’
little subjective. That at once renders the very foundations of their
structure insecure. But it was Poincaré’s task to show in a not easily
refutable, scientific manner what was to be thought of these funda-
mental ideas. For that he examined in turn the various sciences
based upon geometrical form; first, geometry itself, then mechanics,
and finally physics.
Mathematics was first tried. Complete rationalism after having
first pursued dogma and the absolute into their ancient fortress, by
a strange and somewhat paradoxical turn restored them to mathe-
matics. He believed that mathematics could not be what it seemed.
There seemed to be something of fatality, necessity, which could
not be got away from about it. When all our ideas melted away it
alone remained solid like a rock in the ocean, under cover of the con-
tingencies and the relative.
Now, if with Pioncaré we examine the sciences of number and exten-
sion, especially the first principles, which are the most frail parts just
because of their apparent and undemonstrable truths, we find this:
The postulate of Euclid, upon which all geometry is based, states
that ‘‘through a point we can pass but one line parallel to a given
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758 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1912.
right line.’ For centuries the greatest efforts have been made to
demonstrate that postulate, and then during the last century the
Russian Lobatschefski and the Hungarian Bolyai almost simulta-
neously showed that such a demonstration is impossible. Yet the
Académie des Sciences each year receives a dozen or so pseudo-
demonstrations of that postulate.
Lobatschefski did even better: Supposing that several parallel
lines can be drawn through a point parallel to a given right line,
retaining the other axioms of geometry, he proved a succession of
strange theorems, between which it was impossible to find any incon-
sistency, and built a new geometry, no more unimpeachable logically
than the ordinary Euclidean geometry. Then Riemann and yet
others came who showed that we could construct as many more geom-
etries as we wished, each perfectly logical and coherent. The theo-
rems of these new geometries are sometimes very odd. For instance,
the following one, imagined by Poincaré himself, has been demon-
strated: A real right Jine can be perpendicular to itself.
I imagine that architects and engineers would scarcely admit such
deductions, although they are in no way logically contradictory.
That brings us to the kernel of our discussion. If, as results from
what has preceded, the axioms of geometry are only conventions, or,
as Poincaré has expressed them, ‘‘definitions in disguise,’’ and if the
Euclidean geometry is no more absolutely true than any other, why
have men chosen and used it? Because it is better adapted to our
needs, to our daily life, to the exterior world in which we live; because
in this world its theorems reduce to the simplest possible form the
relationships between things. A measurer could express just as
accurately by means of a Lobatschefskian geometry the relation
between the volume and the sides of a cube of wood. But it happens
from the nature of a cube of wood, or rather from the way our senses
comprehend it, that those relations would be more complex than with
the ordinary Euclidean geometry. It is possible to imagine a world
so constructed physically that men having our brains—that is, our
kind of logic—would not find Euclidean geometry the simplest.
Geometry, then, is no longer the inner temple of the absolute. It
is an arbitrary creation of our intellect. It can inform us only rela-
tively to the corresponding logical developments. However, in a
certain sense geometry depends also on experience, since, as we have
just seen, the exterior world appears simplest in the Euclidean
aspect. That does not mean that geometrical truths can be proved
or invalidated by experiment. Our instruments and our senses are
imperfect, whereas a geometrical theorem which is not exactly true
is false. If we measure with our instruments the sum of the angles
of a triangle drawn upon paper, we shall never find them exactly
equal to two right angles. Sometimes we will find the sum smaller, by
ea
HENRI POINCARE—NORDMANN. 759
perhaps a millionth, as much smaller as you please, but nevertheless
smaller, which would verify a theorem of the Lobatschefskian geom-
etry, sometimes a little greater but sufficient to conform to a Riemann
geometry. Experiment, then, does not show the exclusive truth of
Euclidean geometry, which, like the others, is at the bottom an edifice
formed by logic. If the Euclidean method is innate to us, it is doubt-
less because of ancestral experiences, because the brain of man has
little by little been adapted to the exterior world by natural selection
and because Euclidean geometry has proved to be ‘‘the most advan-
tageous to mankind; in other words, the most fit.”’
If in mathematics deduction is almost all, fact almost nothing, we
find the reverse in the observational sciences. Pure deduction can
teach us very little about nature except in an indirect way, and then
only because our brain has little by little become harmonized to the
exterior world with the fewest clashes possible. In that sense, cer-
tainly, the study of our intellect teaches us indirectly of the universe
itself just as the appearance of a mortal wound indicates to the
medical expert the instrument employed and the gesture of the
assassin. But that evidence is not only indirect, but it is incom-
plete, for it tells us nothing of those external conditions not involved
in the adaptation of the species. These latter are the more numerous.
Accordingly, the discoveries due to the experimental sciences are
unlimited, whereas those from pure deduction are doubtless limited.
It is better to observe than to reason, and doubtless in that sense
Poincaré is to be understood when he wrote in regard to the methods
of the physical sciences: “Experience is the sole source of all truth.
It alone can teach us new things. It alone can give us certainty.”
But, then, should not the theorems of mathematical physics,
which are but the synthesis and expression of physical experiences,
furnish us with a definitive, although in a way dogmatic, image of
the universe such as certain philosophies have promised? We once
believed so; but having observed how precarious was the fortune of
such theories and how rapidly and repeatedly the most brilliant gave
way to others, some have been pleased to call science futile and only
a source of error. But Poincaré has shown that physical theories
deserve neither such excesses of honor nor of indignity and has
brought their blind adorers as well as their systematic detractors to
a more sane view.
Observation and experience furnish the physical facts to the
physicist. Should he be content merely to accumulate them? No,
for “he must coordinate them. Science is built with facts as houses
are with stones; but an accumulation of facts is no more a science
than a heap of stones a house;” and, further, a physicist must
“predict” phenomena. So he generalizes what he has observed,
interpolating, connecting by a line the isolated facts; then he pro-
760 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1912.
longs that line, extending it into a region not yet observed where the co-
ordinates of his curve indicate to him new phenomena. Then by further
experiments he may test these predicted phenomena to see whether or
not he has truly predicted. If truly, then his extrapolation was justi-
fied and expresses real relationships; if not, then he must try again.
Unless I have been deceived, the picture just sketched indicates
just exactly the purpose of mathematical physics and the part it
plays both in synthesis and in prediction. The mathematical
expressions of physical theory are algebraic translations of the
curves such as I have just described and which the physicist mentally
draws. The better a physical theory expresses the real relationships
between the phenomena, the better will it predict hidden relations veri-
fiable by trial and the more useful it will be, the more fit, the more true.
But the truth of a theory must not be misunderstood. No theory
could be more useful than Fresnel’s in attributing ight to move-
ments of the ether. To-day we prefer that of Maxwell, which sup-
poses light is due to oscillating electric currents. Does that mean
that the theory of Fresnel was erroneous? No, for the object of
Fresnel was not to prove the existence of the ether or whether or not
it is formed of atoms, whether these atoms move this or that way;
his object was to predict optical phenomena. For that the theory of
Fresnel serves to-day as well as it did before Maxwell. What
changes is only the picture by which we represent the objects between
which the physicist has discovered and proved relationships. Various
reasons make us from time to time change these pictures which other-
wise are unimportant. But it is these pictures alone which change;
the relationships always remain true provided they rest upon well-
observed facts.
It is because of this common foundation upon truth that the most
ephemeral theories do not die in every part; but like the torch which
the couriers of ancient times passed on from hand to hand, each
theory transmits to its successor that which is the only accessible
reality, namely, the group of laws which expresses the relationships
existing between things. These conclusions reached by Poincaré
relative to physics hold as well for the other branches of science,
chemistry, the biological sciences, even for those sciences which are
yet young and classed as moral or social, since they all branch out
from physics, and according to their nature, have for their final
object the foundation of their more or less complex laws upon those
of physics; accordingly, upon the latter will be based all of our
knowledge of the world.
It is clear that the conclusions of Poincaré reduce to its proper value,
which is a minumum, a certain common materialism which dreams of
attaining the absolute and inclosing it in several differential equations.
There is not, there can not, be a metaphysical conception of science.
HENRI POINCARE—NORDMANN. 761
Those who, in the name of Poincaré, have proclaimed anew the
failure of science have not understood him. Otherwise they would
have seen that he battered down only a certain interpretation of
science made by men who did not know it at all. The attitude of
Poincaré has nothing in common with that of the men of the rank
and file whose agnosticism ill conceals their ignorance and upon
whom he sometimes liked to use his indulgent irony. ‘It is not
enough to doubt indiscriminately; we must know why we doubt.”
The fragile nature of scientific theories proves nothing against
science; they are only show cases, shop windows, frames wherein we
arrange more or less conveniently our treasures. It is just the same
as when for our world’s fairs we gather together all the most marvel-
ous products of our industries in ephemeral palaces built of mill]
boards but of the most brilliant designs; and then because the wind
and the rain demolish these structures of boards, if we try to keep
them too long, or because we demolish them ourselves to build again
others yet differently to expose anew our products, who would dare
to say that our human industries had failed? But that is just the
way these men reason, who, may I so call them, are the perpetual
assignees of the failure of science. Is it not just as a blind man
would reason if it occurred to him to disparage the light of the stars ?
But, side by side of these simple and ingenuous detractors, there
has recently arisen a new class which criticizes and diminishes the
value of science; they uphold a body of doctrine due to a very intel-
ligent, educated, subtle set of men who belong more or less to the
new school of pragmatic philosophy. They pretend to draw argu-
ments from the ideas of Poincaré. What would he think of them?
What gives pragmatism its absorbing interest is that while not
ignoring science, arguing indeed from its results, it appeals to other
criteria than reason. But this is not the time to examine these
doctrines. In order to know what Poincaré himself thought of
them let us ask him. There at once arises an essential antinomy.
The aim of pragmatism, whence its name, is action, practical service,
and if science has a value it is as a means of action and because it
furnishes us with practical and useful rules. To Poincaré, on the
other hand, it is knowledge which is the end of action. If he was
glad of industrial development, it was not only because it furnished a
ready argument to the defenders of science, but also because, by
freeing men more and more from material cares, it would some day
give to all the leisure to work for science.
This point of view is not only full of nobleness and beauty, it is
indeed richer in useful consequences than utilitarian pragmatism
itself. For a century and a half the pragmatists as well as the posi-
tivists (how can we refrain from wondering at the strange bond
which unites two such different schools?) looked upon the discoveries
762 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1912.
which Galvanus and Volta made upon the frogs as perfectly idle and
useless. ‘These men of science with a wholly disinterested curiosity
ardently pursued their researches. It is from these little experiments,
more or less then a plaything for the idle hours, that all our electrical
industries with their innumerable practical consequences have sprung.
To many pragmatists science is only a nominal thing; the scientist
creates the fact through experiment; then he denatures the rough
facts, transforming them into “scientific facts.’ Poincaré replies,
showing that “all a scientist creates in the fact is the language by
which he expresses it.”” If some day we find that the statement of a
physical law is incomplete or ambiguous, we have merely to change
the language by which it was expressed. Because the language by
which each one expresses the deeds of daily life is not free from ambi-
guity, should we conclude that these happenings of daily life are
only the work of grammarians ?
Finally, and this is the culminating point, the pragmatists con-
sider science an artificial creation, contingent, uncertain, and teach-
ing us nothing of objective reality. Has not Poincaré shown, indeed,
that the mathematical sciences are contingent and that physical
theories express only the relations between things and not the objects
themselves? But here Poinaré calls, ‘Halt, there!’ He shows that
the only objective reality is precisely these relations between things.
The first condition of the objectivity to us of exterior objects is
that they are common to other thinking beings, which fact we may
know by comparing their impressions with our own. Perhaps, in my
opinion, Poincaré goes a little too far when he affirms that this
guarantees the existence of the exterior world, that this suffices to
distinguish the real from a dream. We could, indeed, imagine our
whole life a dream, with beings similar to ourselves telling us of sen-
sations analogous to our own in regard to objects, so that the fiction
of our dream seemed outside of ourselves. But this is not the place
to discuss the reality of the exterior world, since its existence is pos-
tulated both in the scientific and in the opposing theories. The
existence of what we call the external world being placed beyond
doubt both by the scientists and by the pragmatists, it results clearly
from what has just been said that since it is through “discourse,”
language, that men exchange sensations, there is no objectivity with-
out “discourse.”’? Discourse which, according to certain nominalists
creates nonexistent facts and is a veil before objectivity, becomes,
on the contrary, its necessary condition. But, on the other hand,
“the sensations of others are for us an eternally closed world.” I
shall never know whether the color sensation produced upon me by a
bluet and by the first and third stripes of the French flag are the
same as yours. All that I know is that, with you as with me, the
bluet and these stripes produce a similar sensation which we call
HENRI POINCARE—NORDMANN. 763
blue, or otherwise, and that the third stripe, with you as with me,
produces a different sensation from the first. Thus what is “pure
quality’ in sensations is nontransmissible and impenetrable. Only
the relations between the sensations are transmissible, and conse-
quently may have an objective value. And that is why science, which
furnishes us with the relations existing between phenomena, tells us
of all that is purely objective.
The profound and subtle criticism which Poincairé has made of
scientific theories leads us in no way to agnostic conclusions. Those
who have tried to use it to contest the value of science have reasoned
wrongly.
[Here follows in the original French, Section V, discussing Poin-
cairé and the moral problem, which is necessarily omitted from the
present translation on account of the length of the entire paper.]
VI. CONCLUSION.
A great inventor, a great philosopher, Poincaré was also a great
writer. If it were for literary merit alone he would deserve study.
His language was vigorous and vivid, with a consciseness and clear-
ness peculiarly French. He did not disdain to clothe any profound
thought in the garb of a pretty phrase wherein he grouped himself
with the encyclopedists who, like d’Alembert, believed a precious
liquor yet finer when served in a finely cut glass.
The last century has produced experimenters of genius like Pasteur—
men of astonishing intuition like Maxwell. It has not produced men
who have done as much as Poincaré for the progress of the purely
deductive sciences and for mathematical discipline, or who like him
could ‘think science” and place it exactly. The picture which he
has left us is at the same time sad and encouraging. Science has its
limits. It can know only the relative, but in that it is supreme. As
to wishing to penetrate into what is called the absolute—the “things
in themselves’—these questions are not only insoluble but illusory
and void of sense. Science is an asymptote to the total truth as is the
hyperbola an asymptote to its directrices, and futher, like the hyper-
bola, it extends without end.
In the somber forest of mystery, learning is like a glade. Men
enlarge continuously the circle which borders the clearing. But at
the same time it continuously touches the shades of the unknown
at a greater number of points. No one on the borders of this glade
has known how to gather newer and more magnificent flowers than
has Henri Poincaré. So, as long as there are men who think that it
is noble to live at the summit where harsh truth is enthroned, his
Loraine name will tremble on their lips.
If I may paraphrase a famous saying, he was one of the essential
elements of human thought.
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Page.
sssl BTEC Cie Stee Ae te Rea eae Nn Zeke et ccm i xii, 12, 17, 105, 128, 138
on’ Astrophysical Observatory. ...- 2.25. ..-5- -<.06-% fee Hse aed ae 82-88
ie TACHA HOMO BNE SUM tae e teas Se cea eek Coe) aes ke eee 153
JS ISO LD sees ANU Breet pe lane ae i tear RSE NN A ER A Re RR Be 105125
Em EAOCp UO OF Tadiation Dy Walter VAPOP.. 22222222042 2.0 ae soe one aN 86
/aJDD 7S SITE es: ahs plas Ace aa Ae ry RS Pa Se PETES 8,9
ACECSMIONA CO BUreal American HthnoOlogy.- .- 2552-62-52 sa dujgee enone 56
RADARS oe ra nono sere cet ce cites ENE: a Ne Fe aed Ah ER BS a 98
DSO DEMISE lee cces cc ekecneinn melee cic see e soe a 8. 9. LO Ade 2a
A Dan BAYS | EAN asa: 2 ey Al a Ae NEE a 71, 76, 77
Adams, Wi. L.(accountant and disbursine agent)... .--.- <5 <2. - coe ie Rone ns 5 ined
Adaptation and inheritance in the light of modern experimental investigation
(CEST UDT STEVE 2a a a at A an a ee aa i SN A ef RR ea la eS 421
NOvAIpOry, coInmittes on printing and. publication <6 cot. mcrae - «sais «55h 109
PrErialbroakerse tess e sce nec nc = puts Be AN hy ea RII TOE ts 266
CES SCTE CS)S es Bas cS Co acs any Sha mM RET ENS Pane ah ieee ne SR 261
COURIC US Bite eter tate ere rs haved age re a yayN SNP tats Ta anid nhere % cteeeS sm ees 260
pCO Sa yi WR Pa et i a ai mr a ee PO eae Ye ee 258
OTEOMUS ar ei arate sie Se a Safe tayo cya au oye, Sea es Net ong Nas oat aia oe Sea ae 265
15 2TRG) AGT UV LON aa UES UTES PY 1 ee ta am ira MI Oa Ge er NE = ES
Pee EOGUVIRINC Ree is reat et ac in a etic sic Seas Sait cies ciae nite Nt ee ae 278
PREECE CCUM OMS sense cea. 5 Oss sieleme ssl, spel pegge eet mas e ce 8,9) .33, 121, 122° 9245 125
J Wag U esa Shed D Sy oberg h Fes) 1 Cy Cea aR a ae Pa eR PIE 9, 27, 125
Secretary of (member of the Institution).......................- pa el fA |
RTRCMEROM DA PO OLUZOM UGE 6 = oo aac. Ae cree ace nine a ayers ses Sted claperaeie aloes 267, 268
SUE LUC o Mees Ras tals rats tI Ree a rn Bea saa! cs Ao ern 267
TIGSIE' SE alee tl pee A CR eG gr A RN eee ya ere eet ee 257
Ji1 FUE) Dice bes 3 ae Ae nba ale ne gl 0 ec a en pA ON OPS 82, 126, 164
Algeria, Smithsonian astrophysical observations in..........---- 12, 86, 126, 153, 164
ATER VENUE CAMA a 3 ei oah ie oem aia ie cide Sim hors cio ee eg ee one 11
AGAIN OUMELALDS, (OX PeCIbOl, tO oo. = a a8 eee acid oie eee ais ty a 10, 125
JoX\ eC aT Ed REN TE YS) bese ye alt» Mg 5 a a Peres eae ee aoe lO9
Js RS COTaa Ne ha nN) Sale ete al ea, Ln Tele ee eA Pen eae ane eee | Ue aaa aia ga 109
PME MC AP ATCRSCOLOOY SCHOO! Oho. socal ogee ence Se Sen ka eae 37, 39
PINE MCHM AMANO LOR Ye PUTOD OLS e \arcrcie cits (cS ocine v siclare see feel pie ae yi UY RS 7 fa
PUMNCATONS OL... a2 ase ase een ee eee et 14, 17,18
IPEICAE EL ISTOFICHI A SBOCLAUULOM a 4 4 oe ole 2 Shs ethene Soncye aiets eels ete ae wis = 17, 18, 108
American Historical exhibits and accessions. .... .\2222-.4 5 fsebusb de dee cca 33
PiMienicine Nn Gians and, SLOCTIAN NAGVES= <5 =. 265 6 case aoe yes ae Sy cietes a2
American Revolution, Daughters of the..........-....-.-.-- woes MRS oe! 17, 109
UNE TLC ANITA, CODOTESS OF Saws code ac sas Made, | SON IS PISS = 52 5 ce ss 21
Amundsen, Roald (expedition to the South Pole).............-..-. ren. P. 701
766 INDEX.
Page.
Angell, James): (Repent). =< leis eee oe ee ie ee ee 2 le
Anestrom, Anders Kimutson <0 0 see, ae ee 12, 86, 87, 164
‘Animals: Huroepeanidomesties 2.2 22222555. 2565 sees see eee eee eee 483
in ’National' Zoolopical Parkt..2 52) 42a. s- seo ceee oe eee eee A a
Aattarcticse xX PlORAbIONS. = seo nse ere eee eee vein doe ameter 701
Antarctic: Ocean, lands and life of the. sr e474 4-822 Se ee eee 443
Antarctic: Peneuwins: ones ees eer oe erm ees meat ta tel eaaieiete tele ete 475
Acrtaretical, paleopeopraphiy ol. \c\-rea teers ain Fo cipleye ae ei atte le 443
Anthropological researches in Siberia and Mongolia...........--.------+----- 1
Anthropology, antiquity of man in Europe.........-.-----+------------+----- Iz
blond: Brrropeansin'e les see se ees ee oe acetal ere 609
évolution Of Mans. 6 hoes aes seca eee eine ee arte 553
Hohokaimy the acc soe oikois tie Se as ate hee er 383
music Of primitive peoples... 2. 2--....22.22.-5-- sp ee ae 679
PIOMIStOLNIGs 2 5c2 seme ee oie sg eer cae ee ee erie 22
slaves obancient Greece... oa. o22 522 45. tei om mete ee ere 597
Anitsiand their guests (Wasmann) — 22-2 ee a el re 455
Mpplied Chemistry. 222. 2.5.08. sc0c24-2 2s ee -e eee eee ee eae as.
geology (Brooks) (2.052055. S232 - sce orien ae ne a = ane 329
MeChANIGH. 20-232 eset cee oe seen ee aes Rae eee eee 269
Appropriations, Congressional ......-.------------+.-,---------------2----- 114
Areheological Congress... 22. ==. 2 os nee wae ee enw om wine on 21
Armstrong, H. E. (The origin of life: a chemist’s fantasy).......-.----------- 527
erhoentus, ‘the My POthesis Of 26226 2 oemes ap ae pee oe ee eee eee 543
Art and industry exhibits in National Museum.....:.-.--.------------------ Sica
Netional Gallery Gis... soes22- 6 eee ene ata isle ea ees 34, 35
TOOHM SIGLNSOMISN SG sess. ook = sos eso ee eee ener eee 94
TEXCM ES oe eee ooo ee es eon ene emcee © Seen naman eee 35
Wrrvati bty pOLneSsIss.c2 onsen ee ae a Se iene nein 609
Aesistatit Secretaries of the LnisitUlMOl 22.826 ere eee eee xi
Astronomy, life of worlds..../..--.----.2---2-22-¢----F 3-2-2 += = - ce men ae 543
Spiral mebullse. 02. oes tare eee ete ee 143
the year’s progress in) (Puisewx). _.- 2-2-7) seo e fe ee 135
Actrophysical Observatory, - 22-2 ee ee a xii, 1, 6, 18, 28, 114, 153
OX PCOIONS Ol. Mois eye ieee ere ete erie 12, 86, 127, 164
personnel (Of. 22 eke arco attest ate eee eee ree ee 87
Publica Ons Oss... 2 aie ete eee eee 14, 18, 108
TEPONt OD. oe. sia ia = eee ila aye oe ee ee 82-88
Astrophysics, standards of pyrheliometry. .--.-.-----.-----------+++++++-+-- 86
FAIA tions Of the BUN... cc. see ee aA ee ee oe eee 153
Variability ot the sun s..22 000202 o2 0 eae er ee 82
Attorney General (member of the Institution)..........-.--.--------------- xi
Audubon, John James: 1. A). 2 i-le ee ans sa em awe oie in ein ola = lee 106
Avery, Robert S. (bequest of). ......-..---------------++--+-+-+-+- 6, LUT, 112, 113
Aviation, dangerous currents and winds in........-.---------------------- 257, 267.
B.
Bacon, Senator Agustus O. (Regent).......-.-------+------+- xi, 2, 114, 115, 116, 122
Baker, A. Bu. -- a ccbecec qs ceeges a7 as ao~- NL DE SERMOOs oe Eee eee ae xii, 104
Baker, Dr. Frank. /.... MB.-222256---+-- 2-H OE ES. SEG ee xii, 17
report on Zoological Park......-.-.-----------------+--+-++-- 71-81
Baker,.T. Thorne... ..2..-<0mcc0<-stik UES Bt OE-CRE DOS ER Sa Ose sii 105
INDEX. 767
Page.
Balfour, Henry. - 2.8... 22. Sota eps eR SNS Le RS inte He ay OBR ety ace oee Aie una Rte an I 106
Betou Prom Howard Me) ess hk5 ge diac Jak eee ee Ra ei ak 53
Barnes, Prof. Howard T. (icebergs and their location in navigation).......... 717
Peery ay ee a YS Se see Sy oe NG er ed ee La Ld pan eA ae xii, 107
Bassour, Algeria sobservationsiat: 2/.:...:..4 90 deus).co eae we 82-87, 126, 164
Bee querel ySenns. pet 30 eee! Rbk ace te tiaed paso, oe ene ee 105
“8 2.2102), AE EVAL LET rr RS a lel Ree Se SRM RSE 1 eee Spee OMS wy Newey OO 105
BectimmtaDontley.< 12525 oo ease ce cere tine tee A ROE 106
E Bikey NS IS 5 eb mtr Ce eo Oe foe Py EY | 106
Bell, Dr. Mexander Graham (Regent), i scecok eens xi, 2, 114, 115, 122, 123
Benjamin, ID Eg MEY cent Pepa eke ee eels ee eR MA eRe Set cee ATCT ESB Ba a xi, 107
RIP ON ie sec een bowen onese come sneer seek wal fe lh, 103
Berpet, Alphonse (the appearance of life on worlds and the hypothesis of Arrhé-
PSUS) i gE oe, Spee 2 de) £2 Sh aaa ae eee tS eerie Ay SO RNNNIe ALELAZ LS Lad pa 8 543
Bery ls indMadagascans| .2e ssvusieus fuse Stetuneves cos Aad oot), Sects De 371
BTS CE MDA VG oS epee pare miss aterm arciayan it eronener roeslcra ions Sah sae yy, La ee TD eed 105
ab aetlurcopra phy, ASI I:) hoe hac ORE a Cee Gites AF RO 669
15) SGLUS TE 1/8 EON Santa 1a ae nee anon tery UREN Peis sapere LEVEES Le 2, Vc at. 493, 527
Isiperaphy: Oni omeares 00) tien) aj)t jo nediions woke, beLUE toe)! to So 741
Buolegiedlta hibits and accessions. - 2. 2.5 saci Se ote tice ne oe oie niecie Sew aeeaioess 33
Biological Survey of Department of Agriculture........5..0. 20.00.0000 02000. 27
oi the Canadian Rockiese:s<2s2-0. = SOs) 3 TL SI 11
ofthe Panama Canal Zonewoo. cee. cone cen den ote 9-10, 16, 121, 124
EIS TA Va MC aS Sa Se mre eee er ee iy eoih eye een oor eS MN RENE? (22) od 493, 527
Bards: i National Zoological Parkin « 2ssjearrtaeta nes = etre PRIS AE Se 73-75, 77
Of THOLATITANCIIC TEPIONG soo oy ona trsnayanaschtssvalcberc roramalcnars nome sedhcyoOURMa SERA PEM Re Me 475
Bloch, Dr. Adolphe (origin and evolution of the blond Europeans)...........-... 609
ERR A AM UTO Pea D Sere, sorcrctorotarereter ora tercrahatcnarste nna sdieinse PEO. ALAS, A 609
MSU RIDA E ERD cia ara a ar 5 oi crrich ate xj cpatarsiarer ot arabaatatavaieraictotarstatan be td SEL) Se xii, 51, 52
Boerschmann.,, Ernst. ... 2... 2 Jones BAT, SED SHOES ooo ts Sos) 2a)g Se cae we 107
NOMIC TORS oe cadre icoties RIE R I rk IS GR eR Moh e hmisak IOC A erro NS eI ae 154, 156
Borel, Emile (molecular theoriesand mathematics)................----------- 167
Berney CX Ped OM Js. SUES SUES SRO EE SSS AETEIE YO woe a LOP126
Bblers Jie sore satcisiarais © io SSUES EL 2k OA, SII . ae OS
Beara SACO IN 6 aera rete ano clay apcporstayatotecnarainjaparckr eee w RR irenemicion 2 ucte dS 109
Boys, C. Vv. (experiments with:soap, bubbles)... jcccb 6 aieeeis os ee A 211
PACK OLL etOr ARCATA 3 ecw os cinchoy Aol case ote poy teh yoney rate Ryerss 3 ok SINS 82, 87, 126, 164
BRON LAD ae cis naires cialerer ore eiataiotoia. aims Cronin = St SSSI OANA Mie Bee 5
Brain, effect of experiences onthe: ().b2 08s 22205. JU SU Ache Sosa 558
PEAMN GRA IO csoccmia c's ome nae morntt area 101-2 SEIU SILOS = PEA See LR Boek 106
Breer TieutColy Ts, Misc ce sa sos tates Saye 3 oat cite arctan aed BAREIS Mes Sed 71
SEMELOW Sy MON tROSG sae oA a nisieicinre ws a5 anal arniermcanicinin.n! aiciaia xis Reet LL as eu)) OB
ira a PU a eae apse page aS war cles hemi ding wate mo PE SR = 103
"EELS (2) LA UBT BRE 3a” Oe ree erie. ely yy 53
768 INDEX.
C.
Page
Cambrian geology and:paleontology...-.- .--c.sc2 <5 soc wee cairn. IRR ee 7,16
Campbell), Prof. (Wisi Webescc 2b eel toe Sd Da. Be SE eT SO 105, 137
Gangdian Rockies; biological survey. 0f2.2.-2. ceo oe det ace eee eee Gee 8,11
Canal Zone. (See Panama Canal Zone. )
@apillarity ofsoapibubblesi--.3) see oe pec d eae bee beck eee 211
@arrel Drs Alexie ® ono eee cepeeee Me R Ar Celad cnR Ee ee eee een 105, 413
@elestial bodies, studyiofiec2d.2 eo. eee coos s- okt cee cee eek Bee 135, 143
Wetlss life! ofiesa tsa ten atehiei Eiko Oe ac A ERE ks Oc oe ene ae 413
Cell atoid) imanufdeture.of2 7.22). 2ccdaee tue. uc SSE REE 253
Ghamiperlin. Thomas Chrowder:<..--<-4.2.255 -boo4242 sac> pct eee eee een 105
Chancellor of theanstititlonie: .. joc. eink aces ciegi onesies eeeee xi, 162,112
Chanute;/Octavedcuiteie st oes Joes abiseer a. eR! io aeneeeres a eee. 105
@hircot expeditions. »/ estat at meee ee en cee rere eee ee Peeree 475
Chemical industry, the latest achievements and problems of the (Duisberg)... 231
@hemistry, Congress of Applied eve 20. 5-2 cei e asec a sj mele inne ae eee eee ge
Chemistry of lifes. sparse delescicnebaeecne sek ede rens aoe pee aes 493, 527
Gheriint SivdewnOr les. 4500 ee Gece o eect cu bees ceeermerete eres eee 527
Chief Justice of the United States (member of the Institution and Regent).... x1,
1, 2, 115, 122
China; fincer-print system)in:........ wurtuoieA. bs dansieeceek ta eee ee 634
Choate} ‘Charles .h.,jr:, (Regent). -5-.-....:. + RMA eS Get te xa, 2,115,106, 147
Ghristhi Dr! He.if 2 Woes ees cies ee 3 ea ee ei ee owen Sere 102
Giivesyianciont (cei Aes eee ee eres eecreréecessceemee reba seaeee eee 653
mineéteenth: century... 22-o2836~ ee eels oi os oe a HER eee, Beer eee 659
Or Middle Apes! so... -0-ecendmekes ener sk neoko Meet eeeeties Bere 656
study, 0f.essictacgacoew eh banld.od? te aitilers-bes stints ogee Sek 653
Gigilazetion in. North America... 2-25-55 - > lm ecb REN CS a A TPN 54, 108
RMON UME ere tseeser teat ee Ve hee ele was ee Meio he ie aces nema e 105
Duisberg, Prof. Dr. Carl (the latest achievements and problems of the chemical
TEES STA) ECR sae m5 A 8 Sa a ae a me eR. 231
Sh tin LP Capa SF SPASM Bs (Yo) Psy 10 pes pe rae ea Wea AS aE le 5
iMuscoldormmechanical congress: 2ohe 25.1. casei c «2 2 5 an writ cowie ene 280
E.
BIBER RISLEY OL LMOe. scene oe ws oad fo eee pies Ba eieeereoseeee 359
nocturnal radiations: of thes.: )-ctasenooh-saeorseseack te sotecbencek. 2 12
DMO ITOERTG. SOOO DY ead eet ae es esa says ee a Se a a he a a al 329
mumeralogys on hese oases aap se oes eee igel- Soba deer 371
Bie anne Ese CrP G ATTIRE sen ge ta ee ere a cna Stet ake eee 653
BIEL GAMOL HAO oAELL SOTA 22122 io lod se chic le eties cine etese eee ensyoe iss de xi, xii, 17, 109
TeporhOl the: al eee ce ee Se eee 102-110
Mlectrical precipitation of dust, smoke, ete.........-.52.2-.-25--2+ 45s SUG 5123
Pe earrow Lnaerintlonue Ochs ts mS. en nig. aoe Suc spin ae = beta ii ee 38
Bi rres eras and Petroleum. 2 cece nme nace amie nicl nine eee SORE 272
HETUETSR. (OB TT| ea 28 ee aS 7 OPE ee eRe oe PRR II rei) <2 109
Entomology. ante and. their guests... .-.---.-----.-.----.4- 28s aq - Ree -Beeeee 455
Bieiabhsbment, tae nomi nsonian . je nd on Soe en, See Bae xi
Ether and matter, the connection between the (Poincaré)................-..-- 199
Mibnestaphy Grecian slaviess eq isis acl. 2 Peis a nalts Hestents oS Saeje «oh eis «os ae 597
Bensolory. ured of American.) 2/0). oot sae enon og xii, 1, 6, 25, 33, 54, 56, 108, 114
COMECMONS ionic isc ae nae ae ae eee 56
brary eee ee ee 19, 97
publications. 75.2 0s 4s oars es cap ce 14,17
TO PONG Ole ec aw cro ae oy ere eva te eee 37-57
Bremer rrersea iad CU Vac AE AIDS ...5<.2- 2. 5.0. o- aao tee eRe ee aeee 257
Huntington, Ellsworth (the fluctuating climate of North America)............ 383
Hygiene and Demography, Congress of....-..--..---.------------ je MeaRy 22
i.
Icebergs and their location in navigation (Barnes)......-....----.--+.-----+--- rau)
Indian memorial buildings.) {decline te atiide cb bs cee oe baeeces: 127, 128
Indians, American (see also Ethnology).
researches MMODG.. 2 cols. tcc sche sarees a Pe Cate eee 37-57
and Siberian Natives. ...-cee-sse2ee eee oe Sase et eee 1 02
Infection and recovery from infection:.:.:t) 2: .. is... 5... 5-2 5 .s eee eae ee 20
Infinitesimal quantities of substances, measurements of (Ramsay). ..-.-..---.- 219
inheritance, sdaptablomiand . 2. soc. ose a «sce eee ee ee ee eae 421
Inorganic chemical substances.....-----.------ +--+ 2 --- 2022-22 = oe eee ono 238
Institiiion, members of the omithsomian: = 2° 2.5. 03-6. e 2 cease else <1
Institutions and individuals, consignees of exchanges .........--------..---- 69-70
Interior, Secretary of the (member of the Institution)............-.-.-.-- x, 127, 128
International Archeological Congress at Rome..2.4- - 5. sce e-bay eee ae 21
International Catalogue of Scientific Literature..............---- xii, 1, 6, 18, 28, 114
PEPOLUOU Ns be eee cata eects 99-101
Commission on Zoological Nomenclature ...........-.----.--.-- 16
Congress of Applied Chemistry, New York.......-------------- 231
congresses and celebrations. ..-....-.--.------++:2-----r-sess 21, 22
ADP. Cel YN Toss ae ed ee Ee eT Pi eae ee ee xii, 1, 6, 18, 25, 114
FEport OW. i. 5222s 262 ase aseass sds Sep coe ae eee cee 58-70
Seismological Association .- .:....8222 By 6 a r= i 16
HITE Ot MG MARCH er sees ae et ee ee Dee e tee Melee camer tee ee aie es 5
Knowlton, Dr. F. H. (the relations of paleobotany to geology)................ 353
mio Enmanaen ©. secretary Ol StatGs-<- oof oto e soe lose ira seseae xi
LST SLi 40] 025 eae A og a a PNAS RN AN el aes av hte. teens 106
i:
Labor. (See Commerce and Labor.)
PACCAMNNE UNA IOH Al MUSCUTO Cm ot. o5 tet ant Senioe een ele oie nis bare tis lee ee 35
Lacroix, A. (a trip to Madagascar, the country of Beis) Lies SPR SE Ce We Ss Pact Bal
MerminIenGlO METANCIN 6 fhe fee arte so oon c ae On aa x1i, 49, 51, 54, 56, 108
Sabesaarerts Claclaland POStrIACIal <5: .fss..c- scenes ae =e = 2m sce cies = qaintgerces 291
LL EGE BETO o hs EPCS rE Sa le eh da ae 0 2 al Ci aR eRe a TR 291
LS CUNO TIS 8 He oleate esata eat eae FS pe DE 70 SR LC a UP fit 291
JAF To TS es ORAS Fh peace tes 6 Res alr ei hat T Te eee a che 291
LCDI ETT ta a ee 0 Ne ln x gee be les oi. lle AR Oe ane Ma neta e aS Pa 291
HPCRION. facets ees < is BSA ms Bi) ae ea ES mea re 8 291
LL EIST TVEY SOY aa cel at A Eel SA RE ye See i io ee en anal 106
Langley, Samuel LE alah g 00} Wages oa TA es amor aie e A lhe Na 2S ee en 19, 102, 153, 154
JST 05 se ne Bap ace at ay el ee ea Re ta SSSR, RS, li RRO Ce RAD 14
fe Me ToC er Lk 2) of 12) mAs ae aA a A Aes mE Rm pen 19,119
NlPapatrirersret hel OYE a 11 le SA Mpeg MS ok at eae ol at eo al Gea na aOR FED 118
Laufer, Berthold (history of the finger-print system)............--.---------.- 631
PBPERC RULE UNO KEn #OTCR Leen ee see ene. ois aioe oo ce a ota teen nana s 291
GOST Gaga EXE EN CETUED, 8 ete ele ee eat eR A a Re pan Ba 5
LSS, EDIE ee ag Pitas aes es lle a i ig RAS AAD Dye POR Ties A eR RE 55
Eecorm. D..(review of appied mechanics)... 2.22.2. eeee nae nes pete pia 269
IRC eESEE GES ae CR CE ae re Ee re SS sale ols nickel el 8 tae a sins eee reco 107
UE EEEE De ESL ES AS Sa oe As eg Oa ae A BRT aR a Py “eps, SOU
Legendre, R. (the survival of organs and the ‘‘culture” of living tissues)... .. 413
Galery lai elon Greener tae on Ce te or Cir -( ny samme Ne ie eis notice eee 109
LSHiES Tea (HS A ie ei ec oe ae a Pe RN CES Oe Raped Lp. 8
Eabrary of Compress: -.2.2--).2.- SRI 2 A IRE ES Ca ORB NRO. Zip ihest 19
Sires ivaG ar MCSE ONG se. oe cae <2 ac esp snp eee eect eas 19, 89-98, 112
libraries immder che) Smithsonian... 5. oe2- 5.5. ss cols seciete eee case 36, 55-56, 95, 97, 98
ine. its mapere, ori. and maintenance (Schafer). . (20025). 1. 22 od pees ec 493
the origin of, a chemist’s fantasy (Armstrong) ........------.-...------ 527
on worlds and the hypothesis of Arrhénius, the appearance of (Berget).. 548
eeO MENLO THOTIA TAOUEIB! = 3.225 52 anes Hee ne ce Looks, oe plasbie bool ee ate atare ates State mi 24, 32
Sr ELEMP EEG NOUNG San aes cstina > oe oe seme a 2S 5 eee eevee a ars eee 8
VATEETE Ie GAS gh, SR a Pa pg ca clang pm Pe PO REN BIR Sdn 107
DLTURELS, solu BERTI Dy Sani Renee lit aeh S608 a lll as I Pa aaa MA raga ees h Mian apy 5
Temenos, “CULLUTC OL (UOROUOIC) or. 2 fate on ew iae eciewla ns se nigen qewn nine 413
Lodge, Senator Henry Cabot)(Regent).-...-. 2.02 xi, 2, 115, 119
edon Enonprial Meares COUGIG. 1. ci. fee cere, 2a rice ae we dns aes nletes isan ool 13
Papaatinen tart COGOLC ts. fee er oe rn ta iene a hep eater athe aemdula ste mien 10, 125, 126
TOCOSTELS AIS 0 Aa cece pl snd Ree ol i Balle 2a aon lash Aen an Raat beer ae hae aot 118
85360°—sm 1912——50
174 INDEX.
M.
Page.
MacCurdy, Dr; George Granty i ob oats Bien ers ae ee a 21, 22
MoDermott: PY AMlex. 2.50. ae csi eee ce eee eect ate re eRe et ace 106
Macnamara, NC lec =" pcmcaate auc Pe ee ts ak eeesae eee eee ee 106
MacVeagh, Franklin, Secretary of the Tesery RA Ce aspen t= ans WS Xi
Macie; James Lewis. 2.202820 25> jones ya. bly to Bete Ag ee ae eee ae 130
Madagascar, the:country of beryls, a trip'to (Lacroix). 2-22. - 2: = ae ee ee 371
Matloch(S'.. Bi. s..) ose: Heestice ae ce ee dat tite ed ees aes 104
MEMOCK Ab 2 bie eee a ee eras ch Net oy ole Losey Sep eee eee es na 106
Maninials’ differemtation ofc; 2202.2 iat fe 02 teal tae ae 559
in: National Zoological Parkes .(2).205.... i). eer eet eee 72-73, 77
Man. evolution ‘of: 28 252 tote nse e a et ieee er 553
OBI QUI OLS . Ob
erative Peoples, MUSIC OL. ..2 <2. .4-5-5-.4s5esee 2455? ore So-eeTeeee Some 679
Punting, allotments for.....2.-..--~++-+/+2 0.5555 12955 SR egee RH) eee 17,18
Printing and publication, advisory committee on.......-.-.-...--------ess:- 17, 109
PYOGHELO, (FOOLES We ocecc Sane ws isinrepmnisioe sie a! 3 Maj hic pat ate SE Seale a2 eC eee 109
Public Printer Sadan ols.d oles Sn nlm a cin’ Suis a he Se Risjs it eee el ee ee oe 18
Publications, American Huctoac al Acecintion. 2.3 ac ena PS aE AES 108
Daughters of the American Revolution .-....-.. 2.2 .------- scene 109
Publications of the Institution ‘and its, branches: =>. 022 50.--5--2-- nee anaes 14-18,
25, 54-55, 99, 101, 102-110, 112, 118, 129
Piiseux, P:) (the spiral webule)*. 5... 2 2 a26* w--cp nee ee eee 143
(thie “year's progress im astronomy). 2s... esc en ae eee ee 135
Fumpelly expedition: 2220.2 SSeS See aoe ee ee eee 383
INDEX. TT
Page
PRAMAS WRENS =. Sa ccc eee then aS Se wie os ta miele cemnete ns DOM oS ee 109
yr MOLINE ORT < oo tos os oss SAREE SO Ee Sok oa Ys 12, 86, 88, 157, 158
Pyrheliometric standards. ..... Boies ek lel. Lede as Lu eee ee ee 86
R.
RaingomGr cio sun. COG (CAD DOb)s =. a Sateen enn -onS oe eeiec ages Safe eas 153
lava briny: Dyas, Jeb ell ts, eee 5 ake aa Spd tee eee ae Sp eI Ne ashe ee 51
RAT ELCHAS wlOCOMOLVES ean aoe an SEE ie ce ee oe aie ee a tec eva mee 275
PEER C Vane MM ine. Senor ea ane ase ese Gees wa tinesec cause $3.9; oo, lol dee aes
LETes ae Src AG TU DN ee a Mae Ee ee Sth, tae ee ee Gea sa pe eee 5 106
(measurements of infinitesimal quantities of substances)... 219
LE 7D] OLED af ns bei a7 [eA a SN AD. es Ol ate Rel aR A ee aie a Sls 104
Rathbun, Richard (Assistant Secretary in charge of National Museum). ....xi, xii, 2, 21
report of .. 30-36
Lid Zoi 1 Saag ah OI aes oa ta th it et Ot ie Ae aot aR a 125
iavenoL ow. doc, .(admininurati ve assistant). --20-- es .< 2 sees ee et p oe eee xii
iecaenten- olthe United states, -Order Ols. J22 sees sos0es ee een t ee e See 127
Pee AS mOArd Oleue site rn eee ee ee eR EL ROe tee cee tetra: kal Xi 1263
PROC CECIN DH Of eet ee en see een es aia, sain c/s eR 115
report of executive committee of the...........-...-....-. 111
POLUFALEA Ole sos se ee IS ee nee ets Cuetec e reco css Lae ces we Sate 130
| AEE S CILIA 0) a i i 2 CRS ea ea SE 130
rcpules ine Aoolgetealsrarksne ene nee >< eee tate env alctiala cates (srl)
TRIES Ea ige! STE Scare en 202) 18) @ eRe eR op oe ee SA 124
COT POra OMe ee ae eee creates Sloe eon rte eelacs ona ccrrare te ts oe 3,4
esbarches amonovAmenican ndlanse...-cscc lees soe eee ey see sees ls cee 37-57
GX DIOFAHOUS ANG sess ae os taie ete ee aoe eile inte bate teeta fice 6, 16
ia MeNICAaN! CEANOLORY) 2 o-oo oie oes aisle wes 2 was Ships Wine eyepiece 3)
Rice Institute, address at the inauguration of the................-.-.--....-- 167
Renate oe OSM AW bee iser ee PR are se oes aeite mes bale sas 9 Seedy eure 106
Echands Eheod ore, Wwilltamisace Sena cancers 2b: Dae SLES ee 106
Fripeomanon OMAnen TG Ward. qh: os) 2 Ga. fle leeseines oe snes sass keene t eee 104
LCi asTa very le LOO eer tes a oT le i RRC ett Saint a AME tea BP re 4 97
Ly Sie ENS 16] SS a a Oe 5 BES Va 2 2k fe xii, 97, 107
pL NGS Ce TSC ALI 1 2) ey aL Bay 57
latosicy IDeA le IN tac sees ster a Se, els OA ae Rg Snes AINE Ss SRS gt eg loa xii, 108
OREM EIU HOO | TNEOOONCe2c ce-ch matras eno a coace anes be 8, 9, 121, 122, 124
Le Qype eres lel eas = eat i a a. ee as PI GUEST ee cee ee ere ee 105
PeOMCE Meee tae ae frends Se Soo a le,. S Make aime AE eae One ce eree 104
Peer Minn ACt UNAM: een ee ee ects Lo). oss scm scien one ee ae ee ee 253
S.
eons WwtiiammeP lw. o oA goes los... 5-5-5556 sn aes = RRS Ree 105
Sapir, Dr. Edward (the history and varieties of human speech).......--.-.---- 573
poe PEG IMBIVION Saeco: Hoss gee an as'<= sss ave vies 359 Lee ee ee ee ll
Meni wrireir ay Wietrot at ER oon eee ye pecs ane ewido aoe sete 21
Schiifer, E. A. (life: its nature, origin, and maintenance) ........-.---------- 493
Scientific Literature, International Catalogue of........--- xii, 1, 6, 18, 28, 99-101, 114
2 En ied Gy GN (St Sl ES Se ARTE tet. sts gem ae Sieh 5
Secretary of the Smithsonian Institution.........-...... Xi, xii, 5, 7, 21, 102, 118, 153
Keportofs es 354s. eee xii, 1-130
SeePTOTU VRIES 2 dk eo oon als oete/as a sles ai sin'g oe yin 95-4 PORRIE OSE 109
778 INDEX.
Page
be ppard Hon AMOrris 2 40) ce wins de ates ee cee atten wie eo ela, 128
Sherman, James S., Vice President of the United States............. xi, 15/2, 115122
Shoemaker, Co Won costes vice scte occle dues cee eee ees Hee ee Ree a eee xii
PiberianExpediON . ees. 9 ee ees 553
ISRO OSH C8 ie, eee a i ee OS 2 tne ok 2. ee a Re 130, 153
eQUPRT Obs ao] tc eisai c5. 6 te oop k «CE ee mie ease ae Ha
SSAA LGOM PON CH aecpcl aed caps Sloe sits eat Sra) any aad sagt ey SO eA 130
Smithsonian African; ex Ped lone. ccs 4 cei ce se tes ee 8,9, 33, 121, 122, 124125
Wiperian Ox peditlon. 525. cats es ee one ete 12, 86, 126, 153, 164
ALU TOOMM AS jaro late sia leiclere re nis iaiw eins a Sia Sie na see e ee oe ny ee ce 94
establishment: < ioc6 6c «2 0's x srcieig ne eee a eee 1
Tunds.o€ thes ..<:. 2) pegs ro ops Sa gS ep eee ee aes ee 111
Tibrary, ACCCSBIONB ws: -) (5 Siac asics « Shao. mick Ss ae ere 19, 93, 96, 97
exchangesess J22 bocce ce earns oe er rat Rea ae 93
hishory Os. si 6.c2cias denotes sy + auto pe Reena 89-92
read inp TOOMBS S23. Mise be aed eis a ee ee 94
Mublicationsu: em een eee 14-18, 54, 99, 101, 102, 110, 112, 118, 129
research .associateships 0.85 bso seco Se eae ss ae ee ieee ee 124
Feport.of Seeretany: j= Les: s.s~ sess esse eee poe eee eee xii, 1-130
SIbeHan SxXpediIony 2 .sse asses Stee eee eee cee CoE vc eae 10, 11, 125
tale et; Naples. ici. ois bd ciel ii fe ta ale Uh ga 13
aap bubbles, experiments with, (Boys)... 20.0. vo. eee ei incl ine ee 211
Raleir COMSAT: CN ox. = ope! vo: Se oso hos a Site e: omtate Shee Sey Seer ee oer dee 28, 82-84, 87
FACIAGION erie BS sic in's ae Sole arse’ sate SS State eel ee eee ee 153, 154
Sanlth Pole; expedition :to.the (Amundsen)... .-02 5 << 222-26. see ne ae eee 701
lands ‘of THO.) 2 o5.2..655 26s <=