tine
the
United
States
ciation for
refer-
THE
340
—
outclassed the
a note
and without
to
the
Uni-
1878,
and
vastly more advantageous.
revised.
page
of
John
Bolyai's
and
the
geometric
criterion
of
of
a
perfectly
general
case,
and
thought
of
Anglo-Saxons have not the
or
as
superior
to
all
others
nor
wrong,
but
much
understanding of
they would never
scientific
made
incapable. It
English-
appreciat-
baffle them.
But that
has
based
on
the
principles
of
the
a
thing.
also?
thought in mathe-
knowing
the
world
just
there
begins
the
difference
render
the
analogies
they
think
they
discover
to
they sometimes
eye,
the
unknown
the
shown
by
our
resembling it
laws
by
in England
it the laws
student,
since
the
which many
disciples of
rest, were
Theories
of
sense of
ers
and
can
recall
to
mind
some
highly
the
author
was
more
any
notable
scientific
to reduce what happens
orthodoxy was
as
completely
settled,
devices
for
unorthodoxy
but because
in
conflict
tations. Certain
great obscurity
 
you
may
dignify
hypotheses by the
terms of which
of
quently
very
doctrine of
constructive use
nature,
be
constantly
edge
to
be
in
the
manifold
teachings
which
this
the
probabilities,
in
still
other
find
him, or even if he differs
from
the
admit
the
work
tinct
positions
occupied
of
course,
is
something
determinate;
to
lines of interpretation
will prove most
Three special instances
or classes of
type
of the
of
each
of
purpose
applies M. Poincare
as
point
out,
geology, and
past.
The
origin
the laboratory
doubt
the
im-
namely,
in
a
science
at
the same time an organic science, I have been led in
the course
notice
the
origin
of
a
vast
number
of
diseased
conditions
the
touched
consequences
belonged
to
the
diseased
entity,
but
is
the
contrary,
a
esses are
reached
indispensable
to
the
submitted to
the
authority
and
the
to
enter
here.
of
our
the fact
a
bodies,
of
mathematics
and
ting their first notions
a
the
world
On
a
place
fashion is
still to
of the
at the
we
find
it
in
measure
and
a recreation
so
strongly
the physicist
to
by
everything should
A
the
see
in
them
could be
a
powerless.
II
purely analytic.
But ask
sterile because
of numbers,
them as
matical
rigor
tleties
but
without
skipping
logical
definition;
—
we
confine
our-
selves
to
chess-player is able to
a
able
to
a
the
infinite.
This
allowing
always
arrive
language.
"We
order of
of a
property of
always
endeavor
to
enter
into
these
found
by
studying
efforts.
more intermediary
be the
still necessary to
them-
tional numbers without using any material
other
be, in
this view,
to
them
square of
to suppose
Creation of
the Mathematical
would
imagine
some
image
magnified
be,
will
and
a
point.
two lines
so called.
has
constructed
the
mathe-
matical
continuum,
which
is
only
a
particular
large measure. It is not
completely so, however. It is subjected
to
certain
conditions
chosen satisfies these
and it
great
and
if
I
shall
continuum of the
be
distinguished
11
grams.
the
that
would remain
true if
becomes
space,
and
geometry
is
are equal
upon
1°
or
a
great
liegen. This
works
and
among
which
it
is
proper
to
cite
deduce Euclid's
evident
we
should
be
led
play
for
some
contradiction?
This
difficulty
fact, as we
over a sphere.
of
Lobachevski.
right angles.
of
a ques-
require
to
be
enlarged
capable
of
applications
I
have
The
possibility
properties
besides.
possible
to
trans-
port
a
figure
in
a
certain
because
when
with
are
geometry
are like
of that question :
of
to
Geometric
Space
and
Perceptual
Space.—
It
space,
thus as
reduces itself
to the
two
dimensions.
The
as a
physical continuum
of four
add, a
correspond
to
move-
ments
in
associations
of
numerous
experiences;
without
any
to
different
space
object
from
the
totality
A
A mind already familiar with geometry would reason as
fol-
lows:
the
various
must
be
in
as a consequence
smaller elements,
'deformations' from other changes of state;
in
these
deforma-
different
movements;
but
'correcting'
a
modification
come
into
we could change
portion
as
its
inhabitants.
only
according
of solids
by
that
of
longer in the same relative position,
nevertheless
we
shall
see
the same.
In fact,
the
eyeball,
dimensions.
The
ous
taken from
different points
of view.
At the
by muscular sensations.
perspective A
transition
are
associated
with
the
same
from and better adapted
habits.
lax
of
it
will
my
would
directly
six
feet ?
Examine
space the straight
without
the
mutual
distances of these
of these
bodies and
that
distances
absolute
translation
and
rotation
of
the
this
same
instant,
varied at
to one
of
bodies
different
many
equations,
but
successively
space. They in no
of
as
solid
bodies
in
to a group
aggregate of
so
as
to
met could
Observe,
how-
attitudes A
and B
series?
because,
the
(which my muscular
touches at
other criteria
sight. But the
enunci-
ating
say
shall we
Ex-
perience
has
guided
us
are
naturally
obtrude
themselves,
and
is
sub-
jected
from all
distant
constella-
the
"when
it
is
gone,
order
will
of
and
dem-
of the
of one
whether,
starting
from
this
be
some
bodies
of invisible
for
But how
measure force, or mass ? We do not even know what
they are.
by
the
the
action
A
;
the
two
definition, action
of
these
A and B
;
components,
and
other
words,
the
motion
of
the
center
of
gravity
of
this
system
;
in general only
gravity,
principle
of
areas).
Only
be
less
simple.
Let
alter the
masses by
he
took
ducible,
indefinable;
we
mental verification of
But, after all, what have
we
further
assumed
to this
on
this
thread
has
rather
crude
experiment
the composition
is
of
nished
The
principle
of
highly inter-
esting and
'tion
uniform?
It
an
we
there
it was a
why
should
be taken; we
law requiring
a law
have supposed
solar system. Our universe is
more extended than theirs, as we have fixed stars, but still it
too
is
limited,
as
the
also
upon
this may
else
the rapidity
solution
for
geom-
etry
easily,
of
remain constant.
velocities
the
This
resolution
a
electric
energy
constant.
Under
its
turn
out
will
be
quantities
experiment, could no longer be invalidated
by
it.
mathematical physics.
we no
longer confess
as is
necessity from which the human
mind
upon
the
point.
but it is im-
But
has
even
this
I
shall
the
quan-
parameters
under
the
for
simplicity,
from
all
as
rigorously
true.
If
these
postulates
it because certain
would
be
could
make
of
geometry,
as
for
instance
Euclid's
postulate,
as
unreasonable
to
inquire
whether
they
fact,
who
what
shall
be
isolated
will
be
only
way
be
com-
It
with such an aid, one which
seems useless and perhaps even
dangerous ?
And
yet
on
a
reality
of
while the fact that
might
It is because from
us
be,
It
be
it make
of the
so
easily
only
of
Only
these
are
unconscious
;
called
the
us to
or
those
of
the
minor
numbers
gravitation is not
needlessly
complicated.
We
To sum up,
merely apparent, and
lytical rule
some
complicated
mechanism,
to
the
impact
of
some
cases,
we
and
it
would
resist
service than
a true
natural and from
mathe-
or, on the
has demonstrated,
Whether
ful
if
they
of
a
phenomenon,
the
the
the
the
forces
that
at
at a distance, or
as the
be
submitted
to
veri-
fication.
approximately,
successive
approximations.
whatever
hjrpothesis
may
be
the same.
and in that of
that
the
medium
is
symmetrical,
and
we
only
apparent,
concealed
to
our
because we
of
a
/
like with like.
chapter
to
see
of
and
hence
they
con-
idle.
Maxwell's
is
instance) is really due to the vibration of some atom
which,
act-
ing
like
a
pendulum, really moves in this or that sense, is neither
certain
exists a
bother
of
an
embarrassed
laity
give
them.
In
be
sought
explained
by
there
are
more
naively
have
a
hypotheses
extension
which
more exacting
be made
In
a
geometric
locus
of
and not
by
the changes
the
the theater
state of the
differential equations.
not believe
soo say
why, and
if the theory of Lorentz, of which I shall speak
in
ciple
the
difference
would
not
be
been made on
de-
day
new
phenomena
sometimes,
to
make
one
be demolished.
that of Lorentz, which,
nates
traces
he
According
to
him,
the
have
the
magnitude
let us
of
mechanics.
Irreversible
phenomena
; the
light
its
to
a
whole
No one can
yet foresee the
place they will
Take,
for
example,
the
estab-
seemed
to
the
memoir
Finally
the
fifty years ago, we have not
always
taken
the
induction, he requires more
obliged
to
introduce
a
parenthesis,
and
the physical sciences
in order to
we
wish
to
make
the
slightest
application
able to
calculate the
From this point
the forefront of these
knowing
a
hit or miss, and
the
a prac-
tical value.
Unfortunately the
advice.
its
In
mathematics
probability
is
1/10;
rithm without recourse
wish
to
give
given instant
initial
state,
and
the
law
entific
applications.
I
play
ecarte
ten
the
king
of
the
experi-
mental
corres-
that
the
of stifling
Academicians, they would have
"We have compared the probability that an unknown
savant should have found out what has been vainly sought for so
long, with
of
the
15,
1899.
The
property is
because I
had often
a
be
escaped.
so different in
of
the
the
6. All
apply
of
all
the choice of the
the
This
be represented
value is
practically very
of
that
a
black.
subdivisions.
The
that this
give
law; but it
are
playing
a
calculate it,
me
probability for
up
a
I
sary was not honest.
played
me
to
an
liminary
be
represented
points, and
are the
that
the
observations
have
been
this
or
which I am
I
seek
to
trace
a
The law of errors
we may, however,
a
great
number
of
demonstrations
farther
and
be better
that the
the
other,
and
very
der
which
we
the
would
be
provided only
that
is
the
affair
that this hypothesis
variations.
has changed
revealed
to
us
some
Why are the
desire to
he
noth-
ing
but
mathematical
dynamics
to
renounce.
Thus,
optics
informing him
immediately of
what he
and
what
he
contradictory theories,
provided one
the basis of things, may both be
useful instruments
paths.
a
little
ber of
the principle
of the
the
1°
m,
and
2°
the coordi-
U
which
molecules,
nor
the
expression
of
will
TJ
to deduce from this
same
system.
There
parameters
g?
tives
of
these
parameters?
This
choice in
choice
V,
periment
shows
if we regard the
It is easy
great
fugitive
shadow
not
to
be
grasped.
hypothesis,
hand, perceived
They
to
BNA,
the
electricity
is
carried
by
a
as
altogether
AMB,
which
is
open.
a
positions,
the
In
and
depending
variation
of
3°
The
that pole and
ing
at
p
the
circuit.
Ampere
made
it
necessary, since
in Faraday's experiment.
draw
a
distinction.
or inversely, may
take place either
by simple contact
the
tends
to
take
a
part of
the
experiments
on
closed
currents,
suffice
to
in
the
spoken
3°
Finally
an
B,
the
that not
the usual
senses of
conse-
propos of closed currents, is an immediate consequence of the
existence of an electrodynamic potential.
In
that if the
contacts of the
to
run
of
force
met
by
of renouncing inveterate habits of language
and
of
thought.
There
is
dis-
tance,
electrodynamic
phenomena
in
producing
sys-
properties
made
Maxwell's fundamental idea, the
the induction
an
analysis
of
which
I
must
not
think
there
the
to
convection,
the same manner
VI. Theory of Lorentz.
tive
the
and of
Helmholtz, made
almost
forgotten.
award
speaking
characterized him
as the
the
exhaustless
fountain
working
this
inspira-
marvelous
fact,
geometric
illusions have,
of
move-
ment
is
created
by
what
intellect, in
to serve in some
to
seek
truth
it
is
necessary
to
be
independent,
wholly
independent.
If,
on
the
them.
If
we
meet.
There
can
no
there
can
the
it
them upon
chance
still
lished principles, those even
;
modified.
prior
we
can
attain
we
should
attach
to
the
by
The method is
others
the one sort
their mind which
Nor
is
sub-
truth that we
M.
Meray
by
a
poles
of
distribu-
the
enunciation.
Doubtless
has
given
here
only
Riemann,
on
the
his
aid;
caught
its
meaning.
differences
are equally
necessary for
vast
construction,
of
which
each
piece
It
is
not
hard
to
find.
even
certainty
Nothing is
upon
to
say
point
? It
is
form of
to
can always picture these
care
happened.
cians were
long iU
image of them and
the
to
Pure
logic
could
never
to a
yet
the
first
the second is a
to
senses
; the
chiliagon, and
and renouncing all
it
some object whose
approximate proofs
an
irreproachable
manner.
reality
composed
a naturalist
by reproducing
to
confidence;
we
are
assured
of
intuition is this
it will
not suffice,
appeared from
guide.
This
ment
of
;
role
of
are
capable
of
inventing
said
above that there are many kinds of intuition. I have said how
much the intuition of pure number, whence comes rigorous mathe-
matical induction, differs from sensible intuition
to
This is the
kinds of intuition
play two different faculties
search-lights directed
have called
analysts. This
it is
without
the
senses
appearing
with
formal
logic ?
of it
of
classifica-
remained
present.
we
flowers in
On
arrange
our
there
people
space
and
measure them b
ing?
We
know
perhaps
that
some
fact
Therefore two difficulties:
different
worlds?
Ill
ject of long discussions
to
time,
and
the
corrections
are
made
by
same duration.
nition.
Many
of
them
think
that
the
of the
going
more
rapidly
will say;
the
the
postulate.
physical reality
down.
the
principle
of the
moon, cal-
which shows
more
true
us
which
new
star.
An
,immense
body
before
thetical
intelligence,
impene-
trable.
It
is
therefore
necessary
to
are
than the
present of
by-
simultaneity
or
antecedence,
for
their
turn
know
directly
the
physical
phenomena
B
and
G.
What
we
know
are
very natural,
stellar
phenomenon,
plicated.
So
may
be
as
simple
as
problem we are
chronometer
set
for
Paris.
pend upon the
difficulties
relative
to
emphasized
them
at
length.
Or
else
they
observe
an
astronomic
be
which is that of
such
we
think
it by the
the
measurable,
or the
have
by
it, we shall see
one can satisfy
this
transportation
for
worthy natural
to this question we
the
bodies
in
the
universe
a sense
properties
in
relation
to
the
will
I
straights
of
these
men
will
not
be
at
science
abstrac-
if we
between
the
points
A
and
C,
shall not
or
geom-
etry
dis-
tinguished
analysis situs.
Are they
were
impossible
to
not
have
dimensions,
four,
a
half
mathe-
It happens that
can
read-
become
and
C
new
elements
D
E,
E
number
of
dimensions.
"What
continuum C,
also find
the
to
B
continuum
of
two
dimensions;
if
tinua of two dimensions
pieces
of
space,
lines
points as the
boundaries of lines,
called
are
points are necessary; we
continuum. Then
of two
mathematical
con-
tinuum
of
several
dimensions
same magnitude.
suffice
to
to represent
that
be
distinguished.
It
is
necessary
cases
different
tempted
to
relative
position.
It
remains
to
decide
the
same.
objects
not
directly
is
the
has
of the
make upon
it is
necessary to
common.
reach
it.
(2)
the
external
by
us
very
different
the sphere to place myself
opposite the
the
blue,
now
the
green
succeeds
to
reestablish
the
made
the
therefore, to know
geometry in advance
me
they
are
connected
by
the
on the
only has
for
instance,
are
serve
blue,
half
red,
and
us
the
passing
of
blue
into
red
^
likewise
corrects
pi
Experiment
alone
can
would
be
no
space,
because
experience
in
all
this.
It
how
space
geometry
is
possible
geometry
an altogether
blue
geometric, so
sensations,
whatever
may
be
have
dreamt
of
by the
the same
tions
of
different
color.
myself an artificial limitation
whole
side
of
the
Imagine
a
surface ;
and
set
cut
itself a continuum
be
indistinguishable
and
may
be
regarded
as
identical.
Therefore
C"
will
not
from
an
them has given
can say is that
that
element of
C,
and
suppose
in
a
we
can
represent
to
know
how
to
dis-
if
they
in
the
initial
attitude).
that a
Two of
change
natu-
will
be,
space may
these
different
sensa-
the
hypothesis
and
some way that there is
something
in
to
If
being fulfilled
not
be
It
so we
should conclude
operate
at
a
distance.
only
of
my
 
time
to
the
was
I
At the end of
two
only
the
retinal
sensa-
tions,
of
This tactile
consider
further
dimensions.
Why
has
space
dimensions
same
relation
between
red at
the point
often
the two instants
tribute to space. I
Co
be
the
aggregate
of
all
series
2.
of all the series
Co,
that
Cj
will
of
Cj
for
both,
is
found
at
M
ments.
Experience
alone
tells
they preserve
distin-
our im-
I
muscular sensations
the series o- do
with this
the initial
from
aU
the
other
continua
both
have
C,
or,
if
of the
Moreover,
the
same
in
the
ob-
A. Finally
I make
the movements
corresponding to
the series
two
points
sensations,
it
is
clear
are
asso-
;
identical with
identical
experi-
mental
truths,
space
has
three
dimensions
objective
experimental
proof,
an
invincible
force.
it
has
served as occasion. But this role was none the less very impor-
tant;
and
I
have
thought
was space
this form exist, or, if you choose, can we represent
to
our-
what
does
this question mean? In the true sense of the word, it is clear
that
we
either in
three,
dimensions:
(1)
§2,
our sensations
with
to
is
useful
prairies,
since
it
is
usually
represented
armed
with
a
scythe.
That
one
can
not
represent
I have
straight
sion
space
always
the
other
In consequence
of nu-
of muscular sensations
are classed in
series
of
my muscular
other three.
sary first
of
sations play in its genesis. These are series which may
repeat
tion which
has given
many
of
them
would not
rightly
understood
the
for one to understand
pairs
of
canals
spin
believe that
their manifesta-
S
at the same
good
Among
those
a
distinc-
tion
the
sacrifice all reasons
an
immediate
result,
the
intermediary
links
are
food,
progress
would
mobility of old
And above
others.
and
sci-
ence
and
too
vague,
to
at
a
purely
mediately.
correcting
necessary to make
would
ever
those
compli-
belief
others before
him had
that
vented
imaginaries
hardly
suspected
the
in
the
above
changed.
so
to
speak,
will
constant and
has
largely
paid
us
in
advance
for
the
should
forget
have
neglected,
and
beautiful and
are
tempted
forget
it
; it
whole
and
to render
do
so
we
must
it
is
a
problem
see at
are not
ments converge
properties of
choose
from
a
continuous
function.
The
physicist
may,
therefore,
at
will
suppose
derivative
functions which
tion which analysis
sciences
should
above ourselves
body,
how
great
his
mind,
since
immensity,
where
and
dear, since this
I
repeat
light
which
strikes
our
on
the
earth
some
the
universe
anything
but
caprice
to
those
employed
to
gain
the
also is regular, it also obeys
immutable
had
or in
describe
conies;
carries, it
of
its
hoped that
the com-
are
the
general
us
vibrates
four
appeared to
obliges us to
showing
vented
from
it? What science
speaking
is
not
mine
material cares,
do
not
say:
Science
to
antag-
onism,
founder
of
they could
everything
as
no
chemist
the
mysterious origin, even
to the
some day teach
would
a
mad
dream
we
any prophecy.
anxious:
this crisis
attraction
is
the
of
the
bodies
which
the
disclosed
would
scarcely
dimensions,
and
infinitesimal
but
it
of
exponent
that
arises
all
as-
tonished
theory must
stations;
an
a
in
a
has acclimated this form
by
copying
as
far
as
possible
bring out in Chapter
cient,
and
this
is
the
first
the mechanism
verse is also
from
most
remarkable
example
the equations of
their very generality
yet
emerged
ing fifty
its
hypothetical
character.
The
are elastic
as
an
;
a
certain
movements of
seems that all
the
in nature, and
heat can
less
different
temperatures
of water;
whatever may
liquid, we shall soon
water
separating. Here
Maxwell
the
one
eyes are
too gross
force them to
that is
believe?
To
in
the
conservation
of
energy,
but
the
principle
so
in relation
new unknown fluid
in relation
physics has
spared
it;
but
precision
to
to
em-
through
it,
it
is
Imagine
two
the
station
A,
from B, whereas
All
the
shrunk by
one two-hundred-miUionth
while the other diameter retains its
normal length.
Thus the
hypothesis about
bodies;
these
bodies
carried along
preceding,
and
other.
Thus
we
must
we
call
ether.
The
movements
even with
the most
sensitive radiometers;
but it
be
simul-
taneous
space
which
from
the
is
even in
it,
and
recoils
that
is
able
to
experiments on the
the
now certain per-
sons think that
only
because
in
mechanics
merely
would
cease
to
be
longer
the
is
understood
; but
the
positive electrons, from the little we know of them, seem much
greater. Perhaps
electrons,
the
of the
And it is
not merely a
these results,
This is
From
of light,^
along himself in
a
ra-
quantity
of
heat
store of energy
survive
Brownian movement;
electrons are
another
them
ourselves with
to
get
principles
only
hypotheses,
the
others;
but
all
hope
of
we
make
crudely
the
thousandth of
relative veloc-
ity with
respect to
300
kilo-
meters
vibrations of an
of
Fourier
we
tion; according
satisfactory;
will,
what
experiment
reconcile it with the
one
this
is
not
the
been conjectured
energy
and
If
ephemeral
structures,
which
we
pace
and
makes
itself
a
way we are
about to expand
merely
resultants
a
an entirely new
 
would
out
and
even
mathematical invention. Let
rise
to
true
of
its
I think
myself only
the more
accusation
is
him?
Nominalist
in
doc-
trine,
but
realist
The
intransmissible
internal, or,
scepticism?
strives
to
remain
faithful
to
itself,
also
their
brevity,
is not
wish
to
doubt; by so to
a
rule
tric-trac
that its
that
science
never
be
contradicted.
that
science
was
are
they
that
we
the
industrial development,
furnishes
a
facile
argument
faith
he clashes
ground,
seduced
by
would
not
in
the
rough
This distinction
either
exactly
pose that the
and
the
third,
fourth.
Allow
me
galvanometer
by
on
a
divided
:
accidental
and
fact
in
the
rough,
while
the
scientific
fact
is
a
sense
Now
is no
the
shades, in number infinite,
an
eclipse;
but
it
growing
dark?
bright,
would
importance is that?
In the same
a theorem
senses that I
verifica-
the question to
shall
interrogate
my
senses
spoken
? It is because
per-
anything
but
the
shall say:
this
convention
hour ? it
yes or no.
appearances without
ever agreeing
on interpretation.
a
fact:
we
facts
there
the
first
is
only
the
translation
had
only
to
advance
his
this
understand
it
And that is not
we
take
as
the
hour
y
at
the
moment
are
three
dis-
tinct
conclusion
is
and
the
scientific
fact
free
activity
of
"When I
a law;
in reality
it is
just the
the properties of phosphorus,
true.
Just
so
give the
nothing,
ful
to
not know
other
to the
globe. This
is possible,
but, if
name
of
free
fall
to
from experiment, we may adopt two attitudes: either we may
leave this
law in
incessant
that
relation
between
A
and
C
convenient.
body
A
and
was
com-
;
as
optical,
etc.
have
principles,
make
this
is
only
the recti-
branch
among
it desired that
to
construct
invariant which
and
inversely.
have been made.
the
you
think
there
little
human-
ness
for instance, in
the
experiment
be stated :
forgotten
may,
in
fact,
that
action
from all time
wholly
improbable,
may
be
replaced
by
only
theory
all
great
devia-
that they
But this com-
most
ultra
of
mechanists.
Their
a
fraction
of
a
second
it
they
are
is
by
means
of
us
stars
he
constructs
in
the
past.
Still,
in
to
con-
tradictory
that
supposed
that
the
actual
well
tions and for
natural laws.
evolution
iastanee,
different
consequents
evoluted,
but
the
circumstances
which
have
changed.
Here,
tingence.
that
will
be
found
that
this
word contingence will not
For one
sary
be
impossible.
Yet
to come
back by
fication
we
under-
at
the
so
much
distrust
red.
that, on
and
on
him
the
sensation
shall never know anything
the
second
red.
In
com-
qualities
themselves
of
we
other end of the thread
and which corresponds
the
scientific
point
of
we
an
identity
if
a
comparison
to
another.
except
the question. An absolutely dis-
ordered
aggregate
could
not
a
well-ordered
assemblage
sensations really
condition, and I should
not have dreamed of
maintained that
physics is
not an
experimental science.
losophers, it is well
Two conditions are
reality^
from
the
dream,
considered
as
bond,
and
this
bond
in
itself,
Therefore, when we ask what is the objective value of
science,
true
relations
of
things
to us, and
not
find
words
to
we really
durable
and
a
priori
reason
enough
for
they are
the
superannuated, and
theories
a
in the other theories which
will
light is
intimate
the
other.
And
the
since they embrace
a classification and
But it is
it is
may
go
round' are,
other.
To
for
parallax
In
not be explained by the action of central forces, belestial
mechanics
to
deny
remains, therefore,
pro-
found
and
more
rich.
other
facts.
this hierarchy of
facts that they
for example, I
they
are
capable
that
and
yet
own
sake,
fore,
ciples, foretell
errors
definition as precise as possible of this concept, so indis-
pensable
one
says
efforts
their doctrines,
for
ex-
have
procured
for
pains it
costs to
own
sake'
is
in
all
facts,
infinite.
on
our
moral
needs;
have
we
nothing
sense men of
Little cares he for industrial
applications, for the
ideal ; I want neither that
plutoc-
dwell
them, and, in
again. Now most
guides
them
and,
as
they
are
will
be
is.
there were 60
like
so intimately
mix,
it
knows
not
how
to
distinguishable, it
must be
made expressly.
facts,
and
aim
at
is
less
the
ascertainment
of
resem-
recognition
of
likenesses
hidden
in general
"When
how-
to
capricious
variations.
little
it
is
beautiful.
If
nature
the
Greeks,
made
light now
of
the
stars,
now
to
ex-
beautiful
is, according
at the same time
ediflees
that
we
known
how
to
pro-
portion
the
means
to
the
savages loved loud colors
beneath
sen-
and
it were
soon
become
encumbering
a medley
limit
ourselves
to
to
day the
we should have been
century
neither
telegraphy,
nor
of
a certainty
that avoids
new result
I have
alge-
a type
of nimieric
the
letters
by
numbers.
Thanks
to
it,
a
single
analogies inex-
one to
reigned.
merely
precious
the
more
see
that
chance
is
seems,
all
we
wished
to
is
nothing.
A
demonstration
which
is
not
rigorous
if
it
excessive;
the
geometers
did
not
see
it
at
all
too
at,
after
us
example
the
importance
lieve
a
certain
A
well-chosen
negative quantities, imaginaries, points
are pernicious because
are
those
which
allow
of
these
happy
science.
ticians
advancing
the
more
least
from
what
the
There
we
almost like this: aaaaabbbeeeeii,
who have
tempted
delusions. He
to
in
a
word,
to
specialize.
If
would
by
unexpected
union
between
them
with
our
own,
to
model
of the two
gruences,
where
found
a
parallelism
to
the
theory
algebraic
And
relating
strueted language, not
themselves by the
to set ourselves new
help find the
of
its
really to see in hyperspace
and
gested
themselves
if
analytic
language
mathematical
in-
in
certain
minds,
for
instance
certain
appar-
delighted Zeno
the Bleatie
axioms
and
postulates,
more
or
less
hidden,
some-
thing
to
essential
the
journal
called
and methods
main
to
it.
are
proposition
as
conclusion
of
one
syllogism,
several links
by a
we
attribute
to
it
a
in his
ing,
danger
call
them
player; I
and then finally
be insufficient
gisms placed in a
perceive
at
a
developed in
so
made
would
be
infinite
in
number
he
functions.
I
day
I
seated
myself
at
contrary
to
my
crowds; I felt them collide until pairs interlocked, so to
speak,
making
a
sus-
at
the
sea-
and then
all of
presents itself
to the
mind. It
has been
rest has
mind its force and freshness. But it is more prob-
able that
independently
of
this
work
on the one hand preceded and on the other hand
followed
this)
never
the demonstra-
say,
is considered
it.
Keexamine
the
facts
many others which were
lacking in interest and
at
it,
all
the
domain
of
consciousness.
And
What is
threshold,
while
others
remain
below ?
privilege 1
stimuli of our senses,
I
mean
mathe-
maticians
know,
but
ignorant
as
often
to
of
combina-
mind, these atoms are
to the
put
the room)
you prefer
What is
to
freely
these inspirations,
fruits of
unconscious work,
such calcu-
lations
In the subliminal self,
and to the
combinations.
shall
consequently
it
for
to
for
ours to-day.
of chance ;
we should
always lose.
the stars, they
obtain
draw
our
happen.
If,
unluckily,
I
than
the
name
will
provision-
ally
give
information,
from
those
which
given us
or
the
other,
of
air
us,
determines
of
to
fore-
see
we have
we had
chance.
to the ob-
distribution of
different
past by the
be produced by several
to the conse-
temperature come
colder;
so
we
may
other,
and
unstable
of gases. How
should we picture
us here is
yet
the
former
ele-
in
a
at random ?
atmosphere.
For
a
long
so
to
their
of these
it is
To how many
! He
should
avoiding
them.
Whenever two
reaction must be
been
man
or
the
tiler
to
Does the fact that the causes are
slight
in
probability of this
which
the
needle
What
same
franc
(pi
equitable.
any
the
they conserve something,
because we do
Let us
to
all
appearance,
not admitted there would no longer be any way of
repre-
senting
produce
small
effects
? This
is
the
case
though this
filled
up
the
valleys.
However
capricious
he
impossible
to
All
these
points
already been said. A
of
this
interval
accentuated.
up
the
reentrants,
and
this
is
why
our
probability
another
step
will
have
mean
curvature
satisfy
us
to
gaze
from
afar,
before
And
yet
if
we
accept
microscope
is because all men
to
facts
of
the
physical
sci-
ences
the
birth
of
a
great
man.
It
is
only
by
chance
that
meeting
to
would
shield
us
a
slight
difference
of
argument
will
give
a
this result will
where this
must
to
check
a
take
too
much
back here
run
over
these
precisely in
seek
space
were
relative,
nothing
at
proportion.
We
I say: I
parallel
to
the
movement
the
it
exists
the
deformation
will
be
100;
10,000
times
more.
exactly
smaller
in
the
one
than
particularly simple, we
could imagine any
deformed according
bodies
without
exception
were
deformed
according
to
be indistinguishable
A,
we
will have con-
be
the
same.
into
is no direct
to
therefore
not
have
well,
this
instrument
to
is in relation to
our
we
are
able
to
the
other.
sensations and
can
I mean nothing more.
I
represent
ment
the left arm,
have reached the
With
a
cen-
and things
ills,
and
that
a
centripetal
the same iU
or
the
conquests of the individual,
the
them
the
than
There are points which
not
seem
to
parry, but a parry
menace
us
just
I
to a
conscious
contrary,
our
another
position,
B,
A,
we
have
previously
same
point,
since
not
know
geometry
find
warnings
with the
belonging to the same
of being entirely
a
certain
measure,
so
that
space
these
we refer
less
than
and
dimensions
; to
attempt
this
pains
ran-
dom.
internal
VI
A
few
remarks
to
this rough space whose
these
habits
seems
retains a
if
you
not work.
re-
main
blind
when
we
show
them
derstand.
lean one
their
is
not
example,
the
intuitives
like
'by
analysis'
that
there
a pity to
straight,
or
synonymous
and
stopping
short
conceptions.
us for instance
to say that every con-
tinuous function
as we
sought certainty,
been
slow
not
only
a
rough
image
and
not
of incongruous elements, some
is
this
and
if
we
could
not
prove
it,
our
do
it,
the
logicians
however
;
and these atoms then all the reality of the human
body?
of
the
a
reality
the elephant
will
not comprehend the plan of
the architect? Now
pure logic can
of
the
total
effect
seems
in
the
mass of
sophists.
this long
and
see
them
quickly;
hands can take hold. How could he do it if
we should
numerous,
at it except
is
by
logic
versed
in
grammar
ymetry of grade and
reigned the very first
of
necessary
;
more
right
to
some familiar
a satis-
examples.
not
All that
these
ex-
routine
and
out
thing else.
line.
verifi-
necessary,
the
other
yet
retain
three
degrees
Perhaps
first
of
a
group.
And
what
group?
con-
upon
the
dynamic
notions
of
force
to
the
it
in a nook
one makes
shown
forces
it
is
necessary
to
learn
the force
with
to compare
same
point
of
application
to
from
time
to
on
the
be attained is
definition should
for
light
to prove
which
perhaps
not
unprofitable
to
examine
it
was
a
variable
quan-
tity
Cantor
capable
of
passing
regarded as
there
more
points
in
space
proceeded in con-
think,
of
very numer-
logic by
up
the
those of
pending
between
logic
and
that
intuition
this he
like
design
arithmetic
of
play-
the
pieces.
Among
all
the
constructs
instinct,
or
by
some
vague
consciousness
all.
But
it
is
not
at
wish to
of logic
question
n,
it
I'Enseignement
mathe-
matique,
a
M.
Couturat,
"applies,
Mathematics
is
material
strate that, it must be
admitted
definition under
definition.
Usually,
to
show
proceed
definition,
an
A
is
anything
to perceive it
if the gate by
a
longer
a
question
of
this
pure
admitted
new one would
this
I
the writings
at work in
del circolo matematico
and my
portant of all those
initiated
given
the
first
of
mathematicians.
The
efforts
it
I understand
member
and
Un
in
letters
in
the
second.
is
a
number.
definitions of
To define
number
of
But as never means in no case I do not
see
that
the
progress
it
It
We
have
seen
as if
Russell
attributes
to
subject
classes and took
to
carry
back
declared
have been introduced,
are the
point all seem
seems
to
me
doubtful,
is
that
after
new
logic
is
altogether
in-
dependent
usual exposition
Hilbert
says
combination belongs
a
certain
combination
super-addi-
tion
and
making
that of
new
point of extension.
of
Hilbert
that
every
results.
mathematics
has
to
their
meaning.
So
postulates
wherein
the
we see the principle
uncontested, is
of Hilbert and
principle
line
other
two.
First, we have seen that
a
contradiction.
this mean
that the
?
mathe-
the distinction
I made
us
of
assumptions
with
it
the
absence
number
priori;
happens with
definition
would
yonder flask.
at
44°."
And
it
fusion,
there
is
some
other
to say. I
in number
phosphorus stated
the
case
the
line
whUe
finally
it
is
doubtless
subject
to
change,
so
that
such
a
line
which
to be
melt
at
44°,
but
at
43.9°.
Shall
we
the
one
modified on certain
the
debate,
two questions
invention
'stilts
and
Peano published
curve,' a
gone
wingless
mathematicians,
and
would
On
a
bond
does
not
can
one
have
a
blind
You have no right
are
infallible,
and
yet
we
where they went
all the case ;
the logicians have
M.
Couturat
con-
tests.
"Logical
existence,"
says
he,
"is
quite
another
thing
null.
And
or touch
an a
without being
meaning
be
established,
in
order
that
it is
prouder
case, the onus probandi
to
jump
I
have
found
it
will
and
to
stop
paying
oneself
haps
will
deductions whatever,
contradictory.
This
is
a
truth
admitted
by
most
he opened, but they
say
aggregate
E,
see that this aggregate is countable,
that
is
to
1
whole numier which can not
he defined by a
finite
in
capable
'
difficulty
is
not
of logistic would look
survivors in
how Russell hesitates
a defini-
tion is
too complex
clear
that which
storms which
above,
Bevw
tion
the
again
Now
principle
to
be
proved.
for
instance
shall
we
have?
"Will
the
therein
by
their
actually proving new
applicable
of
the
reasoning.
If
we
have
the
appearance
of
a
classification
to
be
modified,
and
antinomies.
There
that Cantor-
then we
he
years.
the
novelties as
finally established,
it
neces-
the same
these
two
actions
are
two
equal
of
reaction.
Astronomic
physical phe-
a century
;
relation
we
double
at
will
second;
as
may
compare
decreases, the
electromotive force
variation
of
in motion
inertia:
firgt
their
the apparent inertia,
will
there-
fore
that
the
force
of
inertia
deviated;
total
is
upon
the one
hand
the
ratio
that
called,
it
could
not
ity, the
may be
will enable
mass.
Such
is
entering
upon
with
nega-
tive
canal rays spread
back
of
the
cathode, in the direction opposite to that of the cathode rays,
and
them. It is
cathode
rays,
is
less,
as well as the ratio e; the positive corpuscles are less
charged
than
the
negative
the ether. The ether
oscil-
lations
upon the
ether. So
any
cause
an
for
example,
we
should
have
fixed
electrons,
between
which
would
going
out
from
the
metallic
which separates
on, becomes the source of a luminous wave, and this
is
why
hot
oscillate
about
their
I confine
the
known
facts,
as
;
the
ating upon the
would
bring the
Thence
toward
the
The
velocity
we
know
parts:
the
that
body in motion.
along
by
the
motion
is founded
to this theory
at
the
electrons are in motion; in the void, where it is only
a question
almost the case,
the undulations are partially carried
along.
These experi-
not
carried
along
by
the
motion
ratus
same,
whatever
reference
to
the
astronomic
aberration
happens,
it
is
translation
wiU
not
to explain
day
came
fringes
of
interference
permitting
the
along
in
a
this translation,
measuring
contraction
the
not
cease
orientation, and that although
will seem elongated ellipsoids, and
all these
tricity of all these
which
explains
to feel
at
things
begins
to
move;
it
produces
be
to move only after
measured, or are
we have
Sup-
pose
push
forward
the
when
the
wave
counterpart
ever be
this matter
medium is less
Hertz, who regards matter
the
to
second.
of
flattened
ellipsoids.
ical properties. In fact I have said that the displacement
of
self-induction of
synthesis;
stop
a
the
constancy
of
mass,
must
therefore
be
as
their mass
should
be
their
electric
we come
be
carried
out
suc-
cessfully
only
by
a
not
here
expound
submerged in a
our
fluids
are
viscous;
in
the perturbation
around it, the ether would be stirred up, but this
perturbation
would
accompany
the
the
electric
would
as its velocity
but may approach
the
same
concerning
form
of
luminous
the
motions
We
may
then
product of
acceleration
gases
radiate
light
electrons
are
put
in
swing
discharge,
an
exercises
applicable.
Now,
conclude that the
of deciding.
which
mutu-
this
coefficient
make hypotheses,
be
null.
;
tion to
the electrostatic
attractions, that
something additional;
the action
elec-
field
of
electrostatics
for
elec-
tricity
slight, so that the effects of the wave
of acceleration
the
straight
distances,
conse-
certain analogy
secular
poiat
purely
with that
of Newton.
definition ;
be secular
motion,
great, because
dynamics, since it
the
earth
this,
travers-
ing
in
the earth
sun
for
the
moon,
and
thence
would
theory of
Lesage, that
time
; I
am
it
Lesage with an
elasticity imperfect without being null. In truth, the vis viva of
these
count that,
if our
eyes were
sensible of
the sun
not
suffice
X-rays. Moreover a
to be
lead
to
an
difference
of
is
ether
impels
the
electron;
the
electron
must
therefore
be
slower
motion is analogous
would
ground
to
be
frightened
by
are
not
yet
demonstrated
the
right
New
may
be
undertaken
to
a great
had
its
is only
;
contact,
it
suffices
that
other for their mutual
the
molecules
are
this
law,
the
to
explain
in
this
gases; for example
dust
and
yet,
to be
Jupiter.
atoms, the milky way would seem only bubble of gas.
Such
was
Lord
drawn
?
advantageously
the ideas
tell us, so to
the
same
for
sphere
would
be
by
so
much
layers.
We
may
the stars,
the following
a
homogeneous
manner
; thence
the
mass
of
sun
corre-
sponding
what is called the free path; of course this length
is
molecules; but
we may
take a
density
of
receptacle wherein
the gas
do
we
mean
by
sufficiently
near?
That
is
perforce
a
little
arbitrary;
take
it
;
radius.
Are
the
times the
celestial sphere
all
But
there
is
form
of
equilibrium
gregate
have
just
enough
energy
back
and
the other hand,
the run
way and
a
common
rotation,
and
for
that
flattening
is
considerable,
the
word
is
used.
it
would,
therefore,
be
the
a
velocity
10^^
times
second
of
are
in
a
rapid
for
are other
radius is for example
of the
of the
drain
away
pro-
gressively.
But
the
composite
centrifugal
force
be
so
that
with
a
already
it
tends
 
upon
other
considerations,
an
ephemeral
ex-
;
only
a
feeble
minority
compared
with
those
extinguished
to pointing
this
a
useless
luxury?
as
well
as
those
kilometers
thick-
ness,
by Jules
measurements, has reached
New
observations
search
and
what
the
The
'Discourse
on
in
Then, only those
discoveries were esteemed
that
aim
of
science.
Is
nature
governed
by
would
be
nonsense.
Iso-
traversed
there
mysterious
and
against
me!"
more
of
and
was
nothing,
the
all
these
Mechain
antisepsis
of
successfully completed, and Biot had
returned to
took up arms
of
a
thousand
safeguarded under his
his instruments had traversed unhurt these terrible adventures.
Up to
this point,
not
late ourselves upon it. For success in geodesy, scientific apti-
tudes
are
; the
shoulder
the
innu-
the
natural
to
make
have explained
I
the
questions
I
had
studied
;
once,
but
are
not
facts of
great yield
devote
himself.
Doubtless
circumstances may
I
should
rather
say
that
these
of the
mathematical
them,
and
then
we
of facts with more
but among
Saint
they
its
unexpected.
And
his
great
the
hump
would
be
518,
525
principle,
505