Download The Fixed Idea of Astronomical Theory

C O P Y R I GH T
R E S E R VE D
N O T
.
THE FIXED ID EA
OF
A S T R O N O MI C A L T H E O R Y
.
t hought pursue a train of hypo
th eses and supp ositions but they do not th ereby
ac qu ire reality ; st ill in a n o rma l co nd itio n of
th e h uma n i nt e ll ect
it is imp ossib le to concei ve
that any th ing can exist a nd not exist a t th e
sa me t im e
We ma y
in
,
,
,
.
BY
A U GU S T
S C H N ER
L E I P %I G
GU S T A V
1 885
F O C K
.
.
A
C O P Y R I GH T
N O T
R E S E R VE D
.
5
OF
J
AS T R O N O M I C A L
%
)
J
EO R Y
.
th ought p u rsue a train f hypo
th eses d supp osit ion s bu t th ey d n t th ereby
a cqui e r ea lit y ; s t ill i a n o rm a l co nd itio n f
th
hum an i tellec t it is imp ossible to n i
th a t y th i g n exist nd t xi t a t th e
sam e t im e
We
m ay
TH
J
in
o
an
o
,
r
,
n
e
an
n
n
o
co c e i e
'
,
ca
a
.
BY
A U GU S T
T I S C H N ER
l
L E I P %I G
GU S T A V
1885
F O C K
.
o
.
no
e
s
N ic o l a us C
T erra e motor,
o pe
r n ic us ;
so/is
sta tor
.
J
d on t d oubt th a t y ou l oo/e in
b ut tr uth
a nd
,
ad
mit ,
th a t th e ory is b ut
p l a in ine xp l ora bl e gre a t N
ex
,
b ut
se r ve
r th e r
u
f
is
f
or
p oin t
re n de r e d
,
imp ossib l e
must b e
oth ers
t
u
i
e
q
I t was
th a t
th e
unive rse
a nd
sc ie nc e
sta te d
pa c e
s
b ut
,
f
o
motion
.
In
r s uc c e ss
u
r
t
h
e
f
a nd
is
i
t
m
e
y
a t e ver
th e c ourse
f
o
p l ac e d by
e ve n
re
.
a
fixe d
;
th is
in th e
e arth
w as
th e ory
move me nt of th e
th e
b a se d itse lf
th a t
,
can
p l a na tion of th e ph enome na of h ea ve n
sta te d
a l so
to
to d og ma ,
ra ise d
wh ic h in
a l te re d
b ut tra nsp oses h imse lf in
at ,
mpt
th a t th e ory
too, th a t
,
on
wa r ds it wa s disc ove re d , th a t
a r riv e d
a tte
an
ex
as a n
now th e ory
f
i
a ny
p roves
to th e m
pp ose d
wa s
a nd
th e ories
v a riously
o
wh e n
te n a bl e,
f
th eory
f
.
o
b ee n
h a ve
n oth ing
or
point of dep a rture for
a
,
sc ie n c e ,
th a t
sta ndstil l ,
a
T h e h istory
time
a nd
p l ora tions
ex
a nd
a ture ,
re sting -
a
b ro ugh t to
th e re
sc ie n c e
’
not
onl
th a t th e
sh or t ,
pace
s
y
fi
.
xe d
sun
th e
sun
T he
sun
too,
wa s
f
o
th e
to be nu
ound
f
ear th
e ve n
th e
sta rs,
a
c e n tre
,
i
n
z e d,
g
rec o
But
.
is
not
c on vic tion,
t
e
r
f
a
fixe d
too,
,
wa s
moves in mund a ne
a re
n ot
in th e unive rse th e re is
fixe d
no
,
b ut in
immova ble
th ing
ne ith e r a
stars
N
.
ba se d
o
fixe d
ea r th , n or
w , inste a d
th e
up on
f
sta tin
o
fixe d
f
or
wa rd in
g
or d e r
o
th e
e ve n
d a re d to
f
w h e t h er
f
or
at
a str ono
re st
D
to
th e
rm
fi
f
s un
me rs
th a t it is q uite
,
is
c onsid e re d
say ,
“
we may
me th e ory
as
so
h e a ve nly
moure d of th e ide a of
c o urage
p re se n t
l onge r te na bl e
no
fixe d
me
to
co
p
c on c e
T h ey h a ve
.
irre le va nt to th e ory ,
fixe d
c onsid e r
as
or
th e
in motion ;
sun
as
be ing
”
.
ear
l ea d
S ir , I d on t doubt, th a t you
’
scie nc e
t
u
e
s
i
o
n
t
h
u
s
q
'
to tr uth
ra ise d
to
o
r
u
y
L
e na
f
me r h as th e
is
nor
th e
all
o
to d e monstra te th a t th e
a
.
so
sun,
se e h z ng
a str ono
nnive rse
tion
or
move me n t
e nera l
th a t n o
sun,
fixe d
’
g
b odie s, ma nhind h a s be c ome
a
a
e
ip z i g
.
,
a nd
se riously
I
m S ir
,
obe d ie n t
0
g
I h op e , y ou will
be
a
e n de a v ourin
a re
disc usse d
c a use
.
,
se r va nt
u
9524
fl
soh n e r
th e
T o t h e R e ad e r
.
remove misunderstanding
To
,
we must remark
that
,
.
in
our
whi ch ,
p amphlets we do not attack practical astronomy
with the e xcellent instruments at its command h a s
,
attained a high p erfection
astronomical vi ew
hypothesis
the
sun
.
is
of
.
We d o but rej ect the present
the world along with the Copernican
According to the hyp othesis
,
,
we know that the
,
him
as
of
Copernicus
,
fi xed in the centre of the universe ; observations
prove h owever that he is not fixed
“
,
”
at rest %
sun
On
,
b ut
moves
.
N ow if
,
moves why are we always to tre a t
,
this account astronomers are b oun d
to give a ratio n al e xpla n ation
.
14
t
Gali
s aid to have e xclaimed : A nd yet it ( the
t :
e arth )
9in
B ut b e caus e the earth is in motion it
ril y follow
n e ce s
that
the
sun
is
at
rest
If
s
a f
g
”
both move that is the sun as well
as the earth Laplace would have b een sp are d the p ains
”
“
of arg uing
analytically that the sun must b e fi xed What
”
“
analysis is that which argues that the sun is fixed while
observations prove that he moves '
All astronomers know very well that the sun changes
his p osition in sp ace and other)who C opy their words in
their b ooks know very well that the sun is in motion
How then are we to e xplain this frivolous trick of so
lightly overlooking the fact of the sun s motion %
Herschel was the first to make determination ab out
the dire ction and course of the sun N ow a day nobody
doubts the truth of this fact ; it being the general
Opinion that not only the sun mov e s its elf but that
nothing at all in the univers e is at rest Y et they teach
by writing and speaking and in school that the sun moves
in the Sp ace and is at the same time motio nless or may
b e considered at rest There e xists thus for astronomers
”
“
a motion at rest
If the sun is not fixed the system of Copernicus is
fa ll en if the system is a truth astronomers must prove
that the sun does not move M otion round the centre as
well as the closed circles or ellips es in which the planets
a re said to mo ve are conceivable only with a fixed sun
N ow to obtain their closed ellipses and the planes to
them astronomers must absolutely determine that the sun
does not move Either the sun mov e s or it does n ot ; a
moving sun which is at rest is an imp ossibility a nonen
tity If the sun moves th ere is n o fi xed centre there are
no clo sed or re current curves and no planes of orbits ; if
a
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these must to b e obtained at any cost the sun must b e
made to b e ab sol utety at rest b ut he cannot b e made to
b e at one and the s ame time in moti on and not in motion
Circulation round the fix ed centre or in close d curves
is after the establis h ment of the theory of attraction by
attracting centre proved to b e i mpossible for if an at
tracting centre is moving the b odies attracte d by it cannot
move round it in closed curves
The sun eternally moving in the universe carries with
him his system the planets etc ; none of the appertai ning
b odies can remain behin d all must follow the sun with
the same velocity without re g
ar d to their circulation
without regard to their own movement Wh ile the plan
they make curves of revolution
e ts are following th e sun
The sun advancing no planet can pre cede or move in
front of him in his p ath or orbit If the sun is moving
there are no closed orbits reentering into themselves nor
planes of orbits
The moving sun changes the orbits ( curves of revo
l ution )
of the planets following him into
s p i r a l s ; the
ring of the spiral is therefore the true c urve of revolution
of the celes tial b ody
which it describes by its own velo
city ; the curve centrally seen is a circ l e the consecutive
rings will therefore exhibit a series of revol utions as a
c y l i n d r i c a l s p i r a l I f the diameter of the ring is
known there results thence the proper velo city of the
celestial b ody The longitudinal e xtension of the spira l
depends on the sp ace the sun p asses through during the
time of revolution of the planet ; this sp ace indicates the
le ading or con ducting velocity of the p l anet The total
or absolute velo city o f the planet c onsists therefore of its
o wn velocity an d that of the sun
if
the
latter
is
kno
w
n
;
the elongatio nof the curve of revolution is likewis e known
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It
is evident that the leading velo city of all planets is
the same independent of their distance from the sun
B ut the spiral in itself a line of do uble curvature
by the cours e of the sun its third curvature for a
motion in a straight line b eing impossible in sp ace
the sun makes a curve himself If we imagine the mo on
as she follows the earth we see that her orbit is com
p osed of at least four di fferent curvatures ; if we consider
the rotation of the earth as it influences the phenomena
of the motion of the moo n and the geographi cal situation
of the observer who s ees the phenomena changed according
his very po sition : we have formed an idea of the com
plications of the motion and situation of the moon in
s pace and we comprehend that in cons e quence of these
uninterrupted variations in motion and position the various
phenomena shown by her must change at every moment
If therefore the mode of this motion comes to o ur know
ledge the ine q ualities anomalies perturb ations etc will
e xplain themselves
The notion
the connexion and coherence of the
system is only to explained by the moving sun : that what
follows him and does not remain b ehind b elongs to him
The sun draws h is system with and after him ; if there
fore the whole system moves each b ody b elonging toit
must undoubtedly move with it in the same manner ; it
is for the sa me reason evident to o that the direction of
the sun is the dire ction of the system and all its p arts
Whatever is incomprehensible on the hyp othesis of a
sun at rest or fi xed
b e comes p erspicuous an d intelligible
if the sun is in motion
Whi l e they worked ou/ confirming a nd as they suppo
se d perfecting the system of Cop ernicus
they must surely
have felt that moving sun was capable of overthrowing
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17
their theoretica l conceptions ; nevertheless the y continue d
to work until our time
Whi l e Laplace continued his work with ex emplary
perseverance the sun protested loudly enough agains t his
immobi lity ; he clearly dem on state d that he will not b e a
fixe d p oint for the fi xed planes ; but it was in vain : the
great mathematicians despise d his remonstrances and so
he had to act fixed nolens volens accor ding their high wi ll
“
Lap l ace says als o in his Considerations on the system
”
o f the world
pp 3 96 397 : The moon makes a nearly
circular orbit round the e arth but seen from the sun
sh e seems to form a series of e
i
d
e s
l
the
centres
i
c
c
o
p
y
of which are on the circuit of the e arth s orbit The
earth likewise makes a series of e p i c y c l o i d e s the
centres o f which are on the curve which the sun de
scribes round the centre ( p oin t of grav ity)of the group
of stars to which he b elo s Final ly the sun himself
makes a series of e p i c y c l
th e centres of which are on
the curve which the point of gravity of that group of
”
“
stars describes round that of the universe
Astronomy
h as already taken a great step by m aking us ac q uainte d
with the motion of the earth an d those e p i c y c l o i d e s
whi ch the mo on an d the sat ellites des crib e on the orbits
of their resp ective planets But if it wanted centuries for
the understan ding of the motion of the p l anetary system
what immense Space of li me is re q uire d to determine the
motion of the sun and stars %Already observati ons are show
ing us these motions : they seem up on the whole to indi
cate a general movement of all b odies b elonging to the
solar system towar ds the constellation of Hercules ; but
they seem to demonstrate too that the apparent motion
of the stars is a combination of their own movement with
“
that of the sun Laplace says also that the proper velo
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18
city of the
”
its orbit
sun
is at least e qual to that of the earth
in
.
And yet it is the very same Laplace who says rep ea
te dly in his work that the sun in tr uth i s m o t i o n 1 e s s
and supports all his conclusions and demonstrations b y
t h i s i m m o b i li t y
,
,
,
.
It is the same Laplace who sets forth here the e p i
o i d e s rolling on in infinity without end
but
in
his
c
c
l
y
work strictly demonstrates the e l l i p t i c a l movement of
celestial b odies
ex cept comets
by means of
al l
analysis which re q uires invari able plan es
,
,
.
For Laplace therefore the motion of th e sun is so me
thing acci dental a secondary thing a curiosity which has
nothing in common with theory and which is without in
fluen c e of no conse q uence to him and his work
,
,
,
,
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.
The fact is that the planets do not revolve round
the sun b ut follow him It is evident that the revolution
is related to the sun and his centre ; but in truth they
proceed round the orbit of the sun The moo n for ex ample
moves with the earth in the same dire ction The velo
city ofthe earth surp asses the prop er velo city ofits satellite
even according to theory more than thirtyfol d : their
distance remains the same But now how can any on e
say as Laplace says himself that the moon revolves round
the earth in a c l o s e d n e a r l y c i r c u l a r c u r v e % It
is p ossible that this circle round the earth is in agreement
wi th the laws of highest mechanics but it is surely in
But how do astronomers render
c ontradiction to N ature
p ossible what is imp ossible % By considering the earth
”
“
wi th reference to the moon as at rest ; for they think
”
“
at rest it will n ot
t hat if they consider the earth as
If the plan e ts follow the sun and the satellites
m ove
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fol l ow the planets h o w are we to get a revolution aroun d
the centre %
While the planets describ e the ir original curve they
are drawn for ward by the sun ; the conse quence of which
is the i n evitab l e necessity for the s p i r a l as the definitive
curve of orbit or moving line of do uble c urvature wh ich
results from the combination of two velo cities ( forces)
b eing their originally
o n e of which b elongs to the planets
received velo city which the themselves cannot change
%
the o ther b elongs to the sun It is this movement of th e
wh ich is communicat ed to the planets by attraction
sun
their own velo city receives by it an increment which may
The sum
b f ca l led l e a d i n g or c o n d u c t i n g velo city
o f b oth movements is the absolute velocity of the planet
in sp ace Wh at is understood of the sun an d planets may
b e said likewise of the plane ts and their s ate llites
It is therefore the original circular motion of the
planets modified by the motion of the sun which may
be taken to b e the path of their orbit an d the figure of
which we have considered as a ring changed into an
e n d l e s s S p i r a l An isolated piece or p art of the uninter
i
ru te dl
continuing
orbit
which
may
b
e
s
gnified
by
a
p
y
p eriodically re turning coincidence we may call the curve
This curve proj ected on the
of revolution of the planet
celestial Sphere on the apparent hollo w Sphere of the sky
and seen centrally app ears at fi rst sight as closed ; a
continue d more accurate consideration shows however
that even th e proj e ction is not a closed figure but is
sel f continuous A pro of of this is given b y the pheno
menon of p r e c e s s i o n
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E s sa y
.
Q uae ren do
fi
n on af rm a n d o
.
The first conse q uence of the mov e ment of the sun
delivers astronomical theory from a great burden : it n o
lo nger nee ds c entrifugul force Vide appendi x VI
.
.
attractio n
thanks to the sun
has delivered
its elf from its mortal enemy the centrifugal force it to o
can act unhi ndered and wi l l produce the invariable di
s tance of the planets from the sun
We may n o w sketch as an appro ximation the
following image of the solar system
After the sun who is like the nucleus of a comet
preceding it there come ranged one after ano ther the
planets the curves of revolution of which enlarge more
an d more accor ding to t h e ir distance as if they represented
ugal p en dula the threads of which pro ceed
so many centri f
from the centre of the sun
If al l these are in revolution and the sun is for a
moment considere d as immovable the threads ( radii vectores )
form regular cones the b ase of which is p erpendicular to
their axis The circumference of this base of the cone is
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the sun is greater compared with the proper velo city of
the planet ; these curves of double curvature are no longer
p erpendicular to the ax e of the cone or to the orbit of
the sun but they have s uch an inclination to it as 1 8 i ii
dic ate d by the a n gle of the cone
I f we supp ose that the sun moves in a straight line
the rings of the sp irals describe d by the planets form a
cylinder the diameter of which is e q ual to the diame ter
of the original curve of revolution or Spiral ring ; in that
case one might call the Spiral cylindrical the consecutive
rings of the same diameter having likewise the same
situation ; but it is clear in itself that the sun moves in
a curve too therefore the cylin der we have imagined
plane will ac quire a curvature which to the curvatur e
of the spiral
double by itself
adds a third one I t
is a matter of course that the diameter of the spiral rings
is not altered by this third curvature but the proj ection
modified According to this view the cone
of them is
the figure of the system will ac q uire a slight curvature
and give an image which reminds us the figure of the
horn of plenty The central se ction
in the length of
N ow
the axe
of this curved cone is a Spheri cal triangle
seen centrally the sun will n o longer b e in the centre of
all the orbits ( spiral rings ) but there are produce d the
as the apparent inclinations of the
e c c entrities as well
orbits towards another
The earth is little distant from the top of the cone
the sun
and moves on its surface ; it sees the ever
changin g position of the planets in perspective ; at every
moment of the motion there appears another proj ection
If we suppose that all plan ets are in the same lin e
that is just as if we were to
o f th e surface of th e cone
that the interio r
say according to the system of Copernicus
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planets are in co njunction at the same time as the e x
This position of all plane ts
terior ones are in opposition
was taken into consideration alrea dy by th e ancients atwl
its re currence called the Great P erio d That this Great
P erio d has b een very much enlarged b y the two newl y
discovered planets U ranus and N e ptunus is clearly apparent
E ach planet has its orig inally re ceive d ve l o city an d
its p erio d of revolution seems if not to depend directly upo n
All perio ds of revo
to b e in proportion to its aphelion
l a tion renew themselves regularly as we l l as the relative
p ositions of the planets with resp ect to each other It is
therefore comprehensible that the planets duri n g th e ir
revolution assume those various positions which they have
marked with the name s of conjunction Opposition q uadra
ture etc but whi ch nee d a corre ction even if the appa
rent angular di stance in reference to the sun is preserve d
as is re quired by observation
A S to the p eriods and positions of the b odies wh ich
form the movi n g system their change is inconsiderable th e
whole re maini n g together and conse quently the figure of
the system b eing unchanged
The resp ective distances
are chained to the regulated motion : if therefore ob ser
vation of the b odies b elon ging to the system was sufficient
for astronomy the phenomena might b e reduced to their
v er the starry heaven a n d
greatest simplicity ; as it is h
its content which serve as b asis of comparison an d
proj ection there follows hence a complication according to
which the heaven seems to transpose itself in the space
I f we co n sider the c o n i c a l figure of th e system on
the hypothesis that the sun is immoveable the p l anets will
describ e closed curves that is they revolve in the same
p l ane curve which we have called the S p i r a l r i n g or
the original curve of revolution of the planet and which
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24
of course does not change its place in sp ace for which
reason its plane according to present notions is to b e
considere d as invariable But that presumes another in
admissible condition according to which the attraction of
the sun e xercis es no other effect on the planets than that
which is necessary to preserve the e q ui librium of the
system and the invariable distance of its b odies fro m the
sun in such a manner
that none can approach to and
none remove from him This condition remains unchanged
with the moving system and the e ffect of the attraction
of the sun is reduced to
th e communication o f his own
velo city in conse q uence of wh ich the original curves of
revolution change themsel ves into spirals But now it
b ecomes intel ligible from this effe ct of the attraction that
the plan ets must necessarily remain at the same distance
from the sun That the elongation of the spiral dep ends
up on the relation of the two respective velo cities (that of
the sun and a planet or of a planet and its mo on )is a
matter of course This longitudinal exte n smn of the curve
o f revolution is at the same time the inclination
whether
(
declination or inclination do es not matter)of the spiral
orbit towar ds the axe ofthe cone of th e system ( sun s orbit or
f
e q uator)
the
angle
o
inclination
is
therefore
obtained
;
from the proper velocity of the pl anet and that of the
sun
That the conducting or leadin gvelocity therefore
is the same for all b odies of the system we have al
rea dy men tioned
I t is evi dent that if there is observed in th e heaven
a perceptible transposition which appears to b e inde
on e may
e n den t 0 f th e double movement of the earth
p
conclude with certainty that this is the conse q uence of
the sun s motion and the transp osition of h is syste m
in space
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The foregoing diverse considerations will enable us to
bring clearness into the q uestion of revo l utions or times
The continual transposition of the solar
o f revolution
unintermitte d trans position
system in space re q uires the
and their revolution ; there is therefore
o f the planets
and
a n uninterrupted continuation of the same movement
neither a true revolution n or a time of revol ution A
p erio d of revolution is therefore the return of the same
phenomenon or the s ame a p p a r e n t position ; it is there
fore relative it is a coinci dence That these coincidences
return perio di cally results from the nature of general
m ovement ; that they return regularly is
as it seems
the work of the universal attraction
The question now is which coincidence the return of
which phenomenon is to b e considered as an accomplished
revolution a p erio d of revolution or time of revol ution
and to w h a t does this perio d relate %
Theory has founded its choice or d e c i s i o n not on
that rational view which proceeds from the study of the
phenomena and has proved this by referring even the time
o f rotation of the e arth to the Stars
thus p ostulating a
s i d e r a l r e v o l u t i o n whereas it is evident enough that
we can only refer this movement of the earth to itself
I fthe system of Cop ernicus w a s founded o n reality
if the planets did indeed revolve round the sun ever move
i n t h e s a m e s p a c e i n c l o s e d c u r v e s it is evi dent
that after having passed 3 6 0 degrees they would return
to th e same place in their orbit an d that in this case
their p osition in reference to some comparative stars after
e ach revolution accomplished on this manner wo h ld b e
the same
But as coincidenc e with the st ars takes
place in increasing p eriods the conse quence is that the
m ovement of the planets cannot take place a ccording to
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26
the syst em of Cop ern icus an d that therefore their p eriod s
refer to the Stars If the system
o f revolution cannot
tra nsp oses itself in sp ace and remains everywhere the same
without change the coincidences that is the periods of
revolution of the b odies forming the system can only refer
to their guide t h e s u n and we may conclude with
certainty that the coincidences of the resp ective p ositions
fall at the same p eriods as the planets keeping their
aphelion move with e qual velocity
I t is a matter of course that in conse q uence of the
gen eral movement as well as of the uninterrupted serp entine
on war d movement of the orbits there arise different c oin ci
den c e s that thus there appear peri odically different phe
circumstance that
n om en a; it was on account of this
theory ascrib ed to the moon five di fferent times of re
”
”
“
“
volution
R evolution or time of revolution employed
in this manner has no longer any Significance any sens e
as according to the nature of the malt er we have to b e
contente d with but O n e p erio d of revolution
If we call orbits th e sp ace passed through by the
planets and Satellites and the endless spirals described by
them in this Space we emb o dy in our thought the p ath
of the celestial b odies which van l sh e s and le aves no track
in order to facilitate figuratively o ur conception of their
movement ; if this running through on e extende d Spiral
ring is termed describ ing 3 6 0 degrees and an accomplished
revolution it is s o te rm ed with reference t o t h e s u n and
assumes that the two e xtremities (b eginning and end)of
the Spiral ring thus imagined are in th e s ame line that
is if the p oint of a Spiral for instance in the e q uino xes
of spring coincides with the sun its p oint of ending in
this very same position
after an accom plished revolution
coincides likewise with the sun
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27
Having comprehen de d th e imp ortance of the solar move
men t we may perceive why so few phenome n a of heaven
are understood and wh y so often we do not know what
it is that we are observi n g That is the Spel l which has
and can b e
l ain up on science for four thousan d years
remove d o n l y by the sun
This solar system moving on without e nd an d b oun
dary fl
ying through infinite space ; this c o n e a p oint
vanishing as resp e cts its Size in the u n iverse transp osing
itself in a l ine of double curvature contains by the way
which man may distinctly perceive an d success
al l that
fully observe in the heaven ; the phenomena apparently
different the motions and p osi tions ch a n ging without e n d
the periodical and s ecular variations etc all these e xist
it is the un ity of sc ien c e th e b asis of its theory C om
prehending the movement we do n ot need to take refuge
in hid den p owers ; each explication becomes superfl
uous
even use l ess ; nature e xplains itself assuming that man is
cap able of Studying it
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Th s idea
i
xity of the sun has taken root in
the fi
such a degree that to pull it up there e xists n o natural
ower
which
would
b
e
strong
enough
Howsoever
the
p
sun may move while astronomers e xplore dili gently whither
he goes how swiftly he goes they seem to think of his
”
“
fixity and continue their investigations and explorations
witho ut drawing from them the least deduction As so on
as they feel in themselves an impuls e to make some deter
mination theory or law they fix the sun solidly on
the ether The s cholars faithfully repeating what they
have learned from the professor astronomical writers b elieve
themselves to have done enough if they respe ctfully mention
the motion of th e sun ; but all their deductions conclus ions
theorems e xplanations proofs arguments laws etc are
founded on his fixity according to the system of C op er
ni ons
It is very striking that the astronomers of the last
century could and those of the present can yet believe that
such men as Cop ernicus K epler and N ewton had they
b een conscious of the movi ng sun would have state d th e
same system the same laws and th e orie s wh ich they founde d
e xclusively on his fixity his immoveableness %T hat in this
circums tance there is somethi ng to b e a shamed of cannot
b e denied cannot es cap e thinking men
With great satisfaction astronomers ro ck themselves
in the idea which h as graduelly b ecome a comfortable
of
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30
still to come they wil l continue to teach in books and
“
s cho ols the true things and unchangeable laws o f thi s
day as the mysteries of heaven till now reveale d %
We cannot bring ourselves to b elieve that those
astronomers wh o teach that the sun has a pr op er motion
that the sun must b e regarded as
are re ally of Opinion
”
“
at rest for theory What can b e the reason of their
Stubb orn perseverance in upholding the C op ernican system
at any price untouche d for eternity % A y how c an it b e
e xpected that the queen of science praised as the most
pure and irrefutable truth astronomy which ai ded b y
analysis p enetrates into the deepest recesses of heaven dis
covers all its mysteries shall now at once fall down
miserably b ecause h er theory does not agree with re ality %
That re q uires from our mo dern astronomers and from
learned men in general a s elf denial whi ch at present is
not to b e hop ed for But in time they will no doubt b e
forced to avow that they are wrong and will p enitently
confess : p ater p eccavi %
We Shall ever rep eat that a b asis for a theory of
tfl
s olar system can b e got only by rightly p erceiving the
original type of the celestial phenomena and this
i
n
l
a
typ
e
is
to
b
e
fo
nd
only
by
observations
o
n
the
u
g
e q uator
Will the necessary works and studies for this purpose
b e so on undertaken on the e quator % We do not b elieve
it for learned men as we see from history have ever
resisted by all the means at their command the rise of
new ideas if these a re contradictory to those already
e xisting and rooted by cente nnial prop agation and they
h ave persecuted the upholders of them with contumely
and fanaticism V ain endeavour % Truth op ens its path
altho ugh sometim e s very Slowly The Ptolemean intuition
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31
the world endured undispute d through fifteen centuries
th e Copern ican intuition of th e world is but in its fourth
it was rej ecte d by thinking men at its very b irth
c entury
a n d sti l l now is attacke d repeatedly ; even genu ine astro
The proper movement
n omers a dmit it but as a h ypoth e sis
o f the sun having b een discovered however the Copernican
intuition of the worl d has b ecome a c urios ity a folly of
t h e spirits of the age for after the general movement of
a l l heavenly bo dies without any e xception has b een acknow
le dged there is re q uired an e xaggerated dose of imagination
”
t o conceive the sun as immoveable or at rest
of
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“
.
I nfinite Space
its content as the celestial mecha
nism are b eyond the i ntellectual faculties of man to under
stan d an d it is a matter ofcourse that knowledge is replaced by
imaginatio n Theoretical astronomy or what they have agreed
to call e xplanatory s cience it but th e fruit of imagination
In order to comprehend the observable phenomena
they have resolved to search after their causes and to
produce these they have imagined theories which are
often devoi d of sens e and n ot without contradictio ns
It is very indifferent what ideas one feigns ab out the
mechanism of the heaven if they are but more or less
rational ; but one will never attain so far as to b e able to
affirm that they are the only true e xplanation of reality
The ide as e xhibited in our pamphlet must contradict
those which are taught now a day that is inevitable Are
they nearer to the truth % The future wil l decide
The ob servable phenomena lo ok to day as in ol d
times but the intelligence of man is mo difie d it may
enlarge a nd s cience will b e p erfected What they don t
t o day they will comprehen d perhaps to
c omprehend
m orrow an d we are p ersuaded that the numb er of thos e
who will occupy themselves e arnestly an d attentively with
the study of the celestial phenome n a will increase an d
then the m ost sublime obj ect o f n ature heav e n and its
phenomena wi ll find better commentators than we can
e xhibit now
an d
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O n e who d oubted the p ossibility of the Cop ernic a n
ystem des ired to b e enlightened ab out it a nd went to
Ale xander v Humb oldt wh o was indeed ever the first
seeking information and was to o so
r efuge of those
that he sent nob ody away that he even con
c omplaisant
The visitor was friendly
s c ientiousl y answered each letter
received by Ale xander v Humb oldt and whe n he laid
b efore him his doubt ab out th e Copernican syste m got
n to o for
f0r answer the memorable words : I have kno w
a long time that we have no arg uments for the Coper
nic an system b ut % Shall never dare to b e the first to
attack it D on t rush into the wasps n e st Y ou will but
bring upon yo urself th e scorn of the thoughtless multi
tude If once a famous astronomer a rises against the present
conception I will communicate too my observations but
to come forth as the first against Opinions which the world
”
has b ecome fond of I don t feel the courage
From Humb oldt our doubter went to Encke Here
indeed he was n ot fri endly received In a surly m anner
Encke declare d that astronomers h a d something b etter
t o do th an to meddle with hypothes e s ; he had no time
to teach every one who had any doubts ; ther e were b ooks
enough ab out astronomy thes e he should re a d The doubter
replie d that h e had already read th e b ooks written for
the general public by Littrow a nd M adler but he had
found i n th em no reliable in formation Encke r e marked
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34
th a t that if these b ooks did not s atisfy him he too
c ould not give him further advice
In 1 8 5 4 our doubter visited Carl v Baumer at E r
la n gen wh o avowe d to him Openly th a t he too was not
fond of the Copernican h yp othesis but h ad never dare d
do more than utter vagu e obj e ctions ag a inst it
Thus in
”
his Croisades p 1 1 9 where he writes : N ow indeed each
schoolmaster accordi n g to hear say teaches that the earth
m oves round the sun without thinking in the least ab ou t
e xertin g hi mself and h is scholars to perceive the planetary
”
movement
When the doubter left B aumer the latte r
co ngratulate d him on h is purp os e of helping truth to h er
rights h e was however doubtful whether it would in a
Short time b e p ossible to van q uish th e fanatic rsm of th e
world
A t M unich our doubter visited Lamont
director of
the observatory L a mont said to him : Y ou and the world
in general are in error : never yet has any real astronome r
Spoken of a Copernican system we only know a C opernican
hyp othesis Whether this may b e true or erroneo us does
”
n ot matter a t all f
The doubte r
or each genuine astronomer
re plied that he very wil l knew that but then s urely on e
Should not abandon lay people to the pres umption tha t
astronomy t a kes the Copernican hypothesis for a truth
”
I h ave never meddled with l ay a stronomy s aid Lamont
if Littrow and M adler instill superstition into the p eopl e
”
by selli ng hyp oth e sis for truth that is their a ffair
At t tingen our doubt e r made th e ac q uaintance ofth e
astronomer G auss who met him in the most friendly manner
aided him with b ooks and allowe d him to apply to him
at each time when h e thought himself to have need
of his
counsel The doubter communicated to G a uss
th e course of h is investigations made hitherto ; he told
on
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35
him of h is havi n g found that all great think e rs such
as S chelling or H e gel
had criticis e d th e tran sc endentaf
s uppositions of the Cop ernicans while only little spirits a nd
uneducated folk claimed the right of n ot only scorning a s a
fo o l but even persecuti n g with wild fanaticism him wh o did
Gauss avowed
n ot agre e with the choru s ofg e neral opinion
to the doubter that every new discovery in astronomy
filled him with new doubts ab out the dominant system
When our doubter communic a ted to him that Ale x ander
v Humb oldt had de cl a red that he would lik e wise arise
i mme di a tely against th e pres e nt conception if s om e famous
astronomer would declare himself against the domin a nt
system Ga uss an swere d : A y if I were twenty y ears
”
younger %
The astronomers of our days ( 18 85 )
say: Every b ody
will understand that an a stronomer of the present tim e
cannot take up any other system that th at of Copernicus
though it were but by the way of trial Th e y assert th a t
th e system of Copern icus is th e only possible on e
th e
eternal foundation of all further progress of a stronomy
that with the system of Copernicus the whole of astronomy
stands or falls and that without it we must renounce all
e xplanation all scientifically founded prediction
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*
It is strange : even sound intelle cts yield to that
mighty incubus the spirit of the age %
Is there no renowned astronomer who has the courage
to arise against the untenable present theory of the sun
”
b eing thought as at res t and to establish an astronomy
which agree with the prO per
on more rational principles
movement of the sun %
How long yet shall the great genii disfigure this
magnificent sublime science by their transcendental ideas
and scorn the s ound human understanding %
The modern astronomical the ory that is th e expl a
i
n ator
astronomical
sc
ence
still
to
day
b
e
called
m
a
y
y
rightly
do c t a i g n o r a n ti a
,
,
“
,
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,
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,
-
,
,
as astronomy was called more th a n
C a rdin al Cuza
.
4 00
y e a rs ago by
A ppe n dix
.
I
.
The heaven or firmament as it is calle d app ears al
most as a hollo w hemisphe re in the centre of which we
stand on the surface of the earth and on the concavity
of which that magnificent legion of stars seems to b e fi xed
I n spite of the astonishing distance of the Stars among
themselves in spite of the endless depth of h e aven th is
latte r a ppears to us as a sphere a hollow sphere of one
pie ce of crystal
The Opinion has been
of ol d style
pronounce d that this phenomenon is e ffected by the atmo
sphere one of the q ualities of whi ch would b e of course
f the heaven
to round o f
We know indeed that what
ever spreads around an d ab ove us assumes a Spherical
figure The heaven when partly covered by clouds Still
re mains for our vision a Sphere If we are enveloped by
mist the b oundary of o ur sight narrows very much and
yet we see continually a hollow Sphere which is changed
or b ack
an d renewed with every step we make forward
ward but in doing so always preserves the same
dimension wh ich is too prop ortional to the density of th e
mist The same phenomenon appears to us in the celestial
regions : wherever the earth m ay b e in the universe
everywhere the same Sphere is presented to us If we
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42
wander in thought through the wi de celestial regions
there Opens ev erywhere another Sphere a new one and
all these Spheres of endless number have the same dimen
sion ; th e app arent size and e xtension of the vault of heaven
rema ins therefore ever the same to our vision A philo
s 0 pher once said that the heaven or the infinite sp ace it
o ccupies might b e regarded as a Sphere the centre of which
is everywhere but the circuit nowhere ; as there i s
however no centre without circuit he might have said
immediately : The heaven is eve rywhere a Sphere cous e
q uently its centre a nd circumference are everywhere to o
From these remarks we may conclude that the heaven
i s not rounded off by the atmosphere
which is b esid e s
rounded off by itself
but that it is our vi sion which
effects this work : for it is b ounded e q ually to all dire ctions
w/
and as our eye re a che s necessarily in all dire ctions to
the S a me dist ance it meets everywhere with its b oundary
the co n se quence of which is then that our eye
like
us ourselves
must b e in the centre of the visible
sphere
Whatever of th e heaven is visible to the earth is in
p erspective N o ab solute direction n o orientation in space
The g e n e r a l m o v e m e n t allows at mo st but a mo
mentary hold Whatever abides a nd move s in space
b ecome s visible by proj e ction on a sphere which always
remains the product of our vision E ach visible obj ect
therefore b e it a heavenly b ody as a p oint of light or b e
it movement is a p ersp ective proj ection on the surface of
an apparently hollow glob e or Spher e the geometrical
q ualities of which are kn own and wh ich is the b asis of th e
a stronomical observations
The heavenly Sphere in itself is however our vision
w
b oun de d all directions
and considered thus the Sphere
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43
is b ounded by our vision its app a rent e xtension
dep ends on the p ower of our vision
greatness
if
determinate it accurately
o n e could measure this p ower
by numb ers the dimension of th e visible heavenly
S phere would b e known
The stronger th e p ower of vision
or our eye
the more the S pace of heaven e xtends itself
a n d the telescope
strengthening the ability of our Sight
at once the sphere and increases its content
e nlarges
W ith each e x tension of the Sphere there Opens a greater
d epth of heaven and the angles of vision are e x tended
in prop ortion to the enlargement
T o each distance from the earth there corresp onds
a nother circle
another Sphere The sun moves apparently
in a circle 4 10 times greater than the mo on and if on e
o f the stars nearest to us is 2 00 000 times more dista n t
than the sun the circle describe d by it will e x ceed that
o f the moon 8 2 mill ion times
It is prob ably this circum
stance which led the ancients to the ide a that the many
c onsecutive heavenly Spheres wer e
so to
speak encas e d
o n e into another
The same succession of ideas has induced
m odern astronomers to imagine the various circular orbits
o f the planets inclined to on e another in the same manner
a s if they had planes which cut on e another in di f
ferent
p oints transpose themselves on e on another have their p oles
a n d describ e with them geometrical figures on the heave n
It must b e remarked that as the h eavenly b odies
a n d the phenomena connect e d with their movement are in
the same manner proj ected on this Sphere what e ver may
b e their distance from the earth the moon n ear us in
j ust the s ame way as the smallest or apparently most
remote star the study of this Sphere totally neglected
till our days must give imp ortant disclosures ab out many
c elestial phenomena
itself
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44
Each visible obj ect or phenomenon is with relation
t o its apparent p osition more or less a ffected by the motion
”
“
This more or less depends on the distanc e
of the e arth
relative situation to the
o f the obj ect as well as on its
direction of the moving earth ; each translocation line a r
and angular is conse quently proj e cted on the heavenly
Sphere and is there seen p erspectively
,
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.
The solar system itself appearing but as a p oint in
the midst of th e heavenly hollow Sphere it is very prob able
that the heavenly sphere offers the same aspect to all
b odies forming the system ; each planet sees therefore th e
same constellations and stars the prop er motion and tran s
location of which will b e too the same for each planet
with regard to time It is not the same with in th e
system itself each planet s ees the other b odies of th e
system in other places in other proj e ctions and p erspe ctives
Thus for e x ample for that b ody which is nearest the sun
are no inner planets no conj unctions and no solar e clipses ;
for the most remote on e in the contrary there are only
inner planets and nothing but conj unctions for it all other
planets and their mo ons may p ossibly app ear on the disk
of the sun
But it is very probable that M ercury as far
as N eptune is invisible as this little planet seen from
that other never de viates more than 4 6 to 5 0 seconds of
an arc from the sun
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All heavenly b o dies transp ose themselves with relation
to another e x actly in conse q uence of their own move
ment The translocation therefore as well as th e move
ment is a general one
.
.
T o these real or proper translo cations there must
b e added the a p p a r e n t ones in conse q uence of the
earth s motion as well as of the tr a nslocation of the solar
,
’
is absol utely impossible that two or more observers b ein g
w
p erceptibly remote fron ain oth er can see accurately in
the same manner a phenomenon observe d by them at th e
same time : each one of them will perceive in the pheno
menon something di fferent This circumstance is a uni
versal on e and without e xception and in the strict se ns e
of two
observ e r s
o f the word even a very little distance
produc e s a di fferent result : the matter is ther e fore with
wha t accuracy and delic a cy have the observations b ee n
p erformed
ferent
O f such observations as have b een made in di f
”
countries or p arts of the world there often arises the
q uestion which of them has b etter and more a ccurately
indicated one or th e other p
henomenon From the differenc e
they o ften infer a greate r
of the results they have got
ection
or less precision in the observati ons ; with a little re fl
we shall find the true cause of most :of the di fferences
even if we lay no great stress on the correctness of
the watches employed which cannot in a ny case agre e with
e ach other or on the accuracy of the time as determine d
by calculation
It is very remarkable and of high importance tha t
the heavenly Sphere is a tr ue copy of the geometrical
surface of the earth All points lines circles of the e arth
are to b e found on the sphere of stars ; the c o
is
perf
ct
e
py
and e xtends to the minutest details Thus e g the visible
heavenly Sphere is flattened a Spheroid a magnified form
of the little e arth ;
thus the surface of the earth is to %
tally proj e cted on the heaven as well a s its movem e nt
without e xception A s the e arth thus as it were graphi
cally transfers all its geometrical and me chanical qualiti e s
to the heaven its image is by this means p erfe ctly re fle cted
The velocity of its rotation for ex ample different for e a ch
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p oint of its surface b etween the e q uator and pole is found
in the parallel circles of the heav e nly sphere which corre
in
such
p
erfe
ction
that
b
y
s on d to those of the earth
p
accurate observations made in this sense on e might find
how the heaven i tself indicates the flattening of the earth
and this only by the difference of the velo cities which
belong to the e quatorial p art s of the earth b y the
rotation
This sublime remarkable phenomenon that the sur
face and movemen t of the earth are accurately copied by
the he a ven has never b een the obj ect of study simply
b ecause e x pl anatory science seems to know nothing ab ou t
its e xistence That the e quator eclipti c parallel circles
a x is of the world and the p oles of the world correspond
to thos e of the e arth is ab out all that theory knows
B ut it is just this magnificent phenomenon which e x
plains many other gre a t and small phenomena ; it e xplains
b eside other things the variable velocities of the sun
in the e cliptic it e x plains p artly the v a riable diameters
o f the sun and moon ; nay
it discloses why some astro
n omic al instruments
the p arallactical
or e x ample
as f
ones among them especially the e quatorial will not do
good service an d will not indicate the caus e of their
doing so
This true wonderful reproduction of the Spheroi d of
th e earth and its surface o ffers us a view of the most
delicate mechanism of the he a vens ; it informs us ab o ut
such phenomena as the im a gination is not enabled to
compreh e nd W hatever may b e the p osition of th e earth
in Sp ace the repro duction is always a nd everywhere a
p er fe ct on e If the a x is of the earth or its p ole is di
re c te d to S irius
S irius is the pol a r star ; if the ear th is
0
inclined to it at 90 S irius is in the e quator and so
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48
The least displacement of th e earth is therefore indi
but the earth transpos e s
c ate d by the heavenly Sphere
itself in space incessantly and its situation changes in
conse q uence of the motion o f the sun Whatever to the
the ori cian seems to b e disorder irregularity ine q u al ity
anomaly disturbance etc is the m ost p erfect harmony ;
but the g e n e r a l m o v e m e n t is not to b e e x plained by
the l a w s o f a t t r a c t i o n
on
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II
.
The earth thrown into universal Sp ace with its double
movement communicates so to say to the heaven its
geometrical qualities ; its poles lines and circles are a dopte d
C opied by the heavenly Sphere
The ax is p oles and e quator of the earth transform
themselves into the a xis p oles and e quator of the universe
I ts p arallel and horal circles are drawn on the fi
rmament
on the
apparent heavenly h O IIO W S ph ere ; its longitudes
and latitudes b ecome right ascension and declination for
the shining ahd light giving p oints of the heaven the
heavenly b odies But as to the e c l i p t i c and its poles
the earth does n ot know them : these arise from the
a p p a r e n t p osition of the sun
The horizon and z enith like the horal circles (meri
dian)are the prop erty of th e observer that is to each
p oint on the surface of the earth there answers its own
horizon zenith and meridian which transpose thems elves
together with the observer in conse q uence of the motion
of the earth
The celestial m a ps and glob es a kind of topography
s erve for nothing but to represent the
of the heaven
a p p a r e n t and relative positions of the stars among
th e mselves ; they Show us the distribution and arrangement
and in general the firmament as it
of the constellations
a p p e a r s seen from the earth ; if we should ex pect any
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4
50
thing else from them we should lose ourselves in the
infinite
A terrestrial glob e is a tr ue im a g e of this planet for
the matter is here p artic ularly the s urface of the sphere
and whatever may b e the size of such a glob e it always
remains in a calculable ratio to the Size of the e arth
while a celestial glob e of p aste b oard is mere nonsense
as infinity cannot b e re duced and in all its
ideal
parts ever remains infinite
Let us for e x ample assume that to construct a cele
b eginning from its centre
the place of the
stial glob e
earth
we give the distance of the sun the value of a
millimeter The diameter of some si x ty millimeters for
a glob e which includes the known s olar system w ill s urely
surpris e nob ody on account of its siz e ; but if we wi sh to
find room for that fixed star deemed to b e the nearest to
the earth the diameter of the glob e increases instantly
to as much as 1 2 00 metres ; if we wish to include b y
d
th
th
t h magnitude
the
degrees the stars of
3
4
5
6
glob e of paste b oard will forthwith surp ass the dimension
an d thus
with the distances of the follo wing
of the earth
stars exten d into infinity
In general cel estial maps an d glob es repres ent the
stars with their constellations as they a p p e a r to us
proj ected on the surface of a hemisphere ; the marked
distances are a n g u l a r distances for astro nomy itself
cannot bring into account the diverse directions in Space
But now as the starry heaven is neither a p l ane nor th e
surface of a glob e the real positions and planes like the
relative distances of the stars from another cannot b e recog
n ise d
The 6 or 7 Stars for e xample which represent the
Great B ear appear to us in the same plane of the firmame n t
they are e qually proj ected on the a p p a r e n t s p h e r e on the
,
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51
apparent heavenly h oll owsph ere and yet each of these
stars may belong to another pla ne or as the ancients
imagined the heaven to b e comp osed of many spheres e u
~
cased one in another to another sphere or concentric
globular surface ; whi ch surfaces are also at enormous
distances from e a ch other and may be independent Of the
apparent angul ar distan ces
As to the distance of the stars we have only ide a s
about it but n o kn owledge According to these ideas the
distance of the stars is very great : the star nearest to th e
earth is said to b e represented by the number O f 7 billions
O f miles ( a 4 000 meters )
Although we cannot think th at there are two stars
the dista n ce of which is the same still we may assume
that the linear space between two stars
on thi s hyp othesis
which are diametrally Opp osite on the heaven a mounts
to at least 1 4 billions of miles ; transferring thi s line to
n d deeming it to b e its di a
th e celestial h oll owsph ere a
meter we may conceive that the sun with his system is
a lways in the centre Of the celestial h oll owsph ere as it
appears to us the cons e q uence of which is that either his
translocation in space with reference to the Starry heaven
and the stars is imperceptible or that there is taking
place an e q uable general translo cation Of all heavenly
b o dies
For a star whi ch is nearest to the earth even the
star ; the plan ets his
sun appears as a little Sp arkling
retinue wi l l b e hidden by h is refulgence (irradiation)
an d
b e invisible ; the movement of the sun wil l for the ob ser
ving star Show almost the same angu
lar velo city which
from the earth is observable for this star
For the earth however this sp ace occupied by the
solar system is important ; according to the notions Of
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4%
52
our day it e x tends from the sun as far as N eptune a
distance which represents by the way 1 1 8 4 mil lions of
miles the
p art of the distance of the two stars
wh ich are nearest to the earth T o pass through this
distance which separates us from one of these two Stars
imagine to b e the semi diameter of the
an d which we
heavenly h oll O W S ph ere the sun would with a velo city Of
millennia
4 miles in a second have to sp end ab out
“
N ow if the student asks : Pray where is the fix ed
sun to b e found on the celestial glob e b e it of paper
”
or real % how and what will the professor answer % Will
he say that the sun is not fixed but moves round the
celestial glob e in the ecliptic
which is very well de li
n e ate d on the glob e and that his positions during the time
of his revoluti on are noted accurately for each day that
he crosses the e quator twice in a year etc or will he say
that th e sun is fastened inside in the centre O f the glob e
which centre is at once the focus of all ell ipses p arab olas
and hyperb olas in which the planets moons and comets
move round the sun that therefore the movement Of th e
sun is but a semblance %
It is very prob able that the professor to avoid c om
mitting any mistake s ays b oth the one and the other
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54
this insufficient c ompreh e nsion we prefer the cate
according
oric al declaration given by some astronomers
g
to which astronomers do n ot meddle with absolute move
”
“
ment in sp a ce but consider o nl y relative movement as
for e x ample the movement Of the planets relative to
the sun
To
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.
”
”
A b s o l u t e and r e l a t i v e are intend e d here to
”
”
“
“
The word
b y synonymous with t r u e and a p p a r e n t
”
a p p a r e n t signifies that we c a nnot see and obse rve the
phenomena of the heaven otherwise than they repres e nt
themselves to our vision app e a r to our eye In astronomy
th is word has no other meaning but it does n ot the le ss
indi cate , that the phenomena may well b e of other kind
than they Show themselves to us
“
“
.
“
.
,
,
.
.
N ow comes the question : does theory b elieve that
the absolute movement of the pl a nets in Space is n ot
relative to the sun or does it b elieve that the movement
of the planets b eing relative to the sun does not o ccur
absolutely in space % B y establishing the s i d e r a l times
of revolution the astronomers prove that they don t view
such a movement of the planets as is relative to the sun
,
,
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’
,
.
The practical astronomer is b ound to consider only
the relative a p p a r e n t movements and to take these for
the b asis of his calculations If he removes but in the
least degree from th e a p p a r e n t h is calculations
es pecially if they are to b e a prediction
have no longer
any value ; for only the s a m e a p p a r e n t will appe a r
another time
.
,
.
The practical astronomer h a s nothing to do with the
th eory which looks for the W h y of the phen omena ; it
is of n o matt e r to him whether the on e or the oth e r
system has b een a dopted th e s e or those l aws have been
,
,
Of no matter therefore whether there are Sy
stem
and laws or n ot : he abid es directl y by the heaven its e lf
and he does well
But now even the practical astronomer may b e seduced
to derive conclusions from Observations and their nume
which are defe ctive in that very
ric al determinations
point he does not st udy and that is the absolute movement
The reali ty of the celestial phenomena can b e inferred
only from a p p a r e n t things as th e true movement does
not p ermit any dire ct Observ a tion But by supp osing
that the reality is represented by the system or by the
laws we enter on the converse method and get no useful
res ult we Shall ev e n rece de from our aim S O it b ecomes
e vident that astronomers in Opp osition to the ab ove
categorical declaration don t take into consideration thos e
movements of the planets which refer to the sun as they
make their observations in the sense of the post ulated
system and refer to the stars not only the time of revo
l ution but also the rotation O f the earth
N ow if the sun and the stars are e q ually fi x ed the
movement of the planets must b e e q ually relative to b oth
and no difference can take place b etween the s i d e r a l
”
“
and ot h er revolutions but as for e x ample s i d e r a l and
”
t r o p i c a l are two different thi ngs and astronomers
grant the preference to the stars they just prove that
they don t compreh e nd the movement of the sun and his
system that they have not perceived the manner of the
transition from a p p a r e n t to r e a l things N ow if astro
n omers content with the pl a nes and surfaces
will not
meddle w i t h s t u d y i n g a b s o l u t e m o v e m e n t i n
s p a c e they may also Sp are themselves the trouble of
ex pl a ining and demonstrating the phenomena propounding
the ories and enunciating laws
decreed ,
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56
Th e observations of the stars continued since Bradley
with z eal and ability have proved clearly that their right
ascension and declination are subj ect to annual changes
they have proved that these variations continue without
interruption A n esp ecial case of the continually increasing
right ascension of the stars is that phenomenon which we
have known for two thousand years by the name of
precessio n of the e quino x es
This uninterrupted transp osition of the stars on the
firmament and their coordinates in right ascension and
declination teaches us that in tr uth there e x ists neither a
precession or advance n or
as it is found in the b ooks
a retrogression ; but there e x ists
if on e will call it
thus
a precession not generally e qual b ut common in
which the whole starry heaven seems to remove or trans
p ose itself change its place in space in conse quence of
the solar system b eing dislocated in space The general
precession is therefore called
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“
S
olar mo vem ent
”
.
The phenomenon is indeed simple : even as we are
varying chang i ng our situation or p osition ( place )
in space
the vault of heaven o ffers us another asp ect a changed
view and the ques tion ab out the dire ction of the move
ment of the sun is reduced to the question ab out his
orbit ; to the di s covery of this orbit we shall b e led by
the study of h i s movement which has been already made
observable partly by obser ving the stars partly by what
even now is unknown t h e m o t i o n o f t h e e a r t h
The system of C op ernicus the laws of K epler and
N ewton s theory of gravitation or laws of attraction are
the basis of the astronomical theory and it is admitted ,
that these three doctrines supp orting and proving one
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57
another reciprocally make up on e and the same whole
A fter thes e three immort als their followers had nothing
more to do than to produce their arguments in such a
ma nner as th e system of C opernicus and the laws of K epler
and N ewton re q uire that is to say h e a v e n a n d n a t u r e
m u s t c o m p l y w i t h h u m a n i m a g i n a t i o n N ow in
this manner L aplace could say that the system of C oper
n ic us and
each
its correctness with each new theory
analytical in quiry became firmer and fir mer until at last
it attained the highest degree of certainty
“
N ow if an astronomer should say that the system
”
of C opernicus is the
only on e possible he means that
the solar movement is an imp ossibility ; if h e says to o
that with the system of C op ernicus the W hole of astronomy
stands and falls he means that before C opernicus astro
n omy did not e x ist and after the fall of his
system will
once more not e x ist ; he means further that the true
astronomy is what they have imagined ab out the heaven
and the causes of the phenomena
If astronomers had merely presented their ideas and
’
opin i ons to the world as su c h and no more no on e
y
opi
l e
could rais e any obj e ction ; b yjfi
lay
down
their
y
n i ons in words and on pap er as a p o s i t i v e s c i e n c e
they give their views as i n c o n t r o v e r t i b l e t r u t h s
and this fact alters the situa tion fore we cannot admit
that science is a mere barge to be taken in tow by the
imagination
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IV
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The position taken by the sun in space cannot seen
from the earth surp ass his ap ogee ; if therefore they eu
l arge d the a p p a r e n t ecliptic to a great heavenly circle ,
th ey did so in conse quence of a false application of
geometrical relations to the heaven We know that a
circle being in space from that of the rotating earth up
to th at of N eptune produces th e same effect on the starry
heaven : they a p p e a r all as g r e a t h e a v e n l y c i r c l e s
which don t e xist in reality
N either the sun nor the earth are moving in the
e cliptic none of them describes a great circle The solar
system takes a very diminutive place in that space which
the apparent heavenly sphere the apparent heavenly holl ow
sphere includes it is however i nevitable that whatever
is visible in Space proj ects itself on the sphere on the
apparent heavenly h oll owsph ere the conse quence of which
is now that the a p p a r e n t e c l i p t i c cannot bfi
anyth ing
else than the t r a c e o f t h e s u c c e s s i v e p r o j e c t i o n s
o f th e
s u n o n t h e f i r m a m e n t on the apparent
heavenly h oll owsph ere
A s the greatest celestial circle the e cliptic has nothing
to do at all it accompanies the system wherever it goes
its proj ection is always a new on e its place is therefore
changing every year even every day every moment it
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59
changes even its inclination to the e quator
,
its
obl i
i
t
u
y
q
.
The orbit of the earth derived from the declination
a p p a r e n t s olar move
of the sun
or rather from the
ment theory h as made the ecliptic or solar orbit and has
raised this to a great celestial circle which is e qualled
by only one other great celestial circle the celestial
e quator and even surpasses it in imp ortance The notions
given by theory about the e cliptic are unintelligible and
confused as theory itself does n ot know what the e cliptic
is
N ow it is the solar orbit the circle in whi ch the
sun moves which he never leaves ; then it is the orbit
of the earth ; again it is a great circle inclined towards
the celestial e quator The two great circles
e quator
c ut o n e through the other in two opp osite
and ecliptic
p oints The ecliptic has its plane a x es p oles standing
0
f the poles of the world 2 3 5 and des cribi n g ge o
of
metrical figures
A s long as the ecliptic represents
the orbit of the sun or alternately the or b it of the
earth it must b e an ellipse and h as of course two foci
two a x es and four poles but after having b ecome a
celestial circle it loses on e of its a x es and on e focus
being thus enabled to rival the e quator even as system
of coordinates
The obli quity of the ecliptic decreases p eriodically
and is subj ect to secul ar changes
It makes therefore
variable co ordinat es ; nor h as it latitude as the sun is
ever in the e cliptic for in the system of coordinates the
latitudes are relative to the ecliptic In this case the
ecliptic is therefore at th e same time e l l i p s e and c i r c l e
at the same time o r b i t and g r e a t c e l e s t i a l c i r c l e
If the ecliptic becomes e x clusively the orbit of the earth
it has triple character : it remains s olar orbit and great
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celestial circle too the conse quence of which is that the
earth an d sun are mo ving in the same circle of ellipses
and in th e same direction F rom this definition we can
neither draw c on c lusiom respecting the orbit of the sun
nor that of the earth
The confusion respecting the eclipti c ap pears most
distinctly in the conception they have formed of the
periodical movement of the earth as well as of the ax es
N amely the a x is of the earth describes a circle
of the world
round the pole of the ecliptic C onnected with the pre
cession the pole of the world describes a circle around
the p ole of the e cliptic in 2 6 000 years in conse q uence
of
of which diverse stars arrive by degrees at the place
the present p olar star N ow as the imagined p ole of the
°
ecliptic is distant 2 3 5 from the pole of the world this
O
describes a circle the diameter of which has 4 7 ; the
conse quence of it is that the present polar star after
°
1 3 000 years will have a declination diminished by 4 7
as it inclines by this arc to the south But as the celestial
e quator is ever p erp endicular to the celestial axis it to o
0
must in question ab ly incline by 4 7 farther to the south
But n ow the wonder emerges : the ecl i ptic remains on the
same place with its planes and p oles it does not move
at all its a xis and p oles continue to be parall el to them
selves The stars the declination of which has changed
0
by 4 7 retain their old latitude unchanged ; but th e still
greater wonder is that while the celestial e quator transposes
0
itself by 4 7 the celestial ecliptic has always the same
inclination to it % If the inclination between the a xis
e quator and e cliptic did really take place the inevitable
conse quence of it would b e that the de clination of the
stars would chan ge in the very same manner as that of
th e sun
It is known that this is not th e case The
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V
.
Kepler
must have known that the observable orbits
are p e r s p e c t i v e p r o j e c t i o n s and that an inclined
circle may present all possible ellipses up to the straight
line just as the inclined ellipse may proj ect a circle
but only on e H e must have known that all the more
since he says that if men could see the orbit of M ars
th is too would then pres ent itself as an ellipse
c entrally
N ow as it is hard to transplace one s self in such a
manner as to view the centre of th e orbit of M ars an e
must take K epler s word for it that thi s planet does
describ e an ellipse
C l o s e d o r b i t s and their p l a n e s were the basis
on which K epler grounded his opinion ; he could n ot sever
himself from th e system of C op ern icus for it belongs
still to th e dogmas of astronomy
h is Opinion that is
K epler could n ot therefore suppose that all p r 0 j e o t i o n s
rmament can have but two dime n
on the surface o f th e fi
sions A s a sphere proj ects itself as a c i rcular disk so
lines of double or manifold curvature will proj e ct them
selves as sim ple curves Thus for ex ample a cylindric
spiral will in its central proj ection app ear as a circle
but proj ected lengthwise it will show itself as a s erpentine
F rom the proj ected movement alone no conclusion can be
drawn as to the figure really described by the b ody The
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63
celestial b odies cannot move in space in simple curves
b ut the figure they describe always proj ects itself in two
dimensions
With his ellips e Kepler h as led theory into a laby
rinth
from which it can never escap e : the important
question of the difference between the a n g u l a r and
v i r t u a l (linear or spat i al)
velocity clearly gets into con
fusion as well as the question ab out unifor m or variable
movement
A ccording to the principles of me chanics
a body
moving in free space can advance only with uniform of
course th e same velocity ; if it does not there are either
retarding or accelerating forces which in fl uence it A stro
n omic al theory acknowledges on the on e hand a u ni form
motion of the celestial b odies but p ostulates on the other
hand a variable velo city
If a body moves uniformly in a curved line its angular
velo city is prop ortional to the c urvature The greater the
curvature the greater is the angular velo city The ellipse
is an une quall y curved figure in which the curvatures of
thos e parts which are diametrally opposite are e qual
the apsides
A t the two endpoints of the maj or a xis
the b o dy will therefore have the greatest
but e qually
great
angular velo city and the least velo city on those
p oints of the curve answering to the minor ax1 s
If for ex ample th e sun were to describ e an ellipse
with uniform movement he must have in his ap ogee the
same angul ar velo city he has in hi s perigee b ut must
move the most slowly in the e quino x es O bservations say
that the sun
earth substituted for him moves
or the
quickest in winter and slowest in summer that his angul ar
velocity attains its ma ximum in the p erigee ( the p erihelion
of the earth )and thence dim inishes gradually until the
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G4
apogee ( or aphelion)
to increase again in the other half
orbit The immediate conse q uence is that the
of the
question is no longer ab out the angular but the linear
velocity which must b e variable
A planet cannot
according to the preceding
move u niformly in its orbit it cannot of course in e qual
times pass through e qual spaces but through spaces pro
p ortional to its variable velocity That the angular move
ment is proportional to the curvature is understood of itself
The ellips e b eing elevated to a law they were oh
lige d to attain their end to place the sun in the plane of
a planetary orbit and they chose with much c irc umspec
lt on to lo cate it in one fo cus of their favorite curve as
j {
from this sp ot the planes are des cribed by th e radi us vector
N ow we must clearly imagine the radius vector to b e the
u
n
stre tched thread (fi
l tendu)
m
ln
the
centre
of
the
s
o
j
g
with that of the planet for e x ample the earth This
thread must in order to do its duty properly first lengthen
and then contract again It is indeed hardly to be under
stood h ow a force the attraction the quantity or greatness
of which is g iven by the invariable mass
for
e
x
ample
(
of the sun and earth
can
increase
and
decrease
alternately
)
But if we add too that the swiftness of this force is
infinit e and its permanent action conse quently momentary
which L aplace de monstrates by analysis we get into
confusion
What is the reason what is the cause of a force
b eing diminished the greatness and action of which is
constant and mo mentary the swiftness of whi ch is infinite %
This is on e of those questions to which natural philosophy
i
phys
cs
gives
answer
n
o
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VI
.
C entrifugal
force
as a force
does not e x ist in
n ature
it is an imagin ary force
The s cience of me chanics teaches that centrifugal force
generates itself together with the revolution and that if
there is neither rotation nor circulation there is no centri
fugal force ; it only remains for mechanics to teach us
that the movement is not produced by the force but
inversely that the force is generated by the movemen t
even the nature of the
an d that the movement changes
force A ccordin g to the view of mechanics the impulsive
force which has produced the rotation or circulatio n changes
into centrifugal force wh ich disapp ears as so on as th e
rotation ceases The centrifugal force ofterrestrial mechanics
was by the great scientists transfered to the heaven
I f the material parts of a sphere which is in rotation
are not hurled in to universal space it is on account of th e
cohesion the compactness of matter the heaviness or at
traction but principally because the rotation does not pro ceed
q uickly enough A celestial b ody circulating in free space
which describes its re vol utive curves may of co urse lose
itself in infinity if it is not restrained by somethin g they
are therefore obliged to call to their aid the sling th e
s tretched thread in on e word c e n t r i f u g a l f o r c e in
order to check the annihilati n g centripetal force The
higher geometry has tried to metamorphos e these two
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5
66
forces by taking the tangential velo city and central attrac
tio n for their e quivalent ; according to new de termina tion
both forces infl uence each celestial b ody together e qually
and in the same measure they are Opp osite they abolish
themselves mutually they annihilate on e another
m
T o po stulate forces acting against an oth er contrary
ones is to annihilate directly each movement ; one has
therefore no need of their permanent action But wh y
contradict fundamental notions why deny them if they
are proved by fact and don t change %
”
The resultant of forces having b een propounded as
law there is but one action one force It is by the
action of mutual attraction of p erturbations that theory
has simply abolished the first and capital law of mechanics
about the action of forces
With reference to centrifugal force the rotation is
often chan ged with the c i r c u l a t i o n It is a matter of
cours e that both movements are made round the centre ;
as to the circulation this circumstance is e xplain ed by
the sling for by this the circulation around the centre
is obtained by force the body h as b een forced to describe
a circle
says mechanics But is not a slinging motion
rather a r o t a t i o n than a c i r c u l a t i o n % Translation
alone is generated only when the impulsive force hits
the centre of gravity of the sphere in which case all its
molecules move with e q u a l velo city ; if the force produces
a rotation the molecules get d i f f e r e n t velocities the
centre of gravity has however in this case been in fl uenced
but partially indirectly by the force which is aiming at
a p oint of the axis The farth er this point is distant from
the centre the greater becomes the velocity of ro tation
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%
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But
an e
llips e c ann o t
be
p roduc e d with
th e
sli n g
.
67
which attains of course its m aximum when the force in
fluen c es the end point of the a xis
N ow if the mechanics calls circulation the movement
it has forgotten the
o f the stone which is in the sling
essential di fference b etween r o t a t i o n and c i r c u l a t i o n
for it c an hardly fail to b e understoo d that every p oint
which attains
o f the stretched thread has another velo city
its maximum at the end of the thread
of course at the
stone The movement in the sling is therefore a r o t a
t i o n it is that of a flying wheel : it is from the centre
where it is the least
that the velo city of the a xis
stretched
thread
increases
up
to
the
surface
or
circum
(
)
ference of the w h eel ( stone in the sling)where it attains
its ma ximum
It is evident that thos e p arts of th e rotating sphere
which are provided with a greater swiftness endeavour to
part from those th e swiftness of wh ich is less
for they
will advan ce
that therefore the elevation of the e quator
and the depression ofthe p oles is an inevitable conse q uence
o f the rotation
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5
%
VII
.
Inertia is the most simple and natural (sic %
law
of
)
n ature
which we can imagine L aplace M é cani que
c é leste I p 1 4
N ow wh at is this inertia of matter
romulgdif as
p
the first law of nature % A bsolute passivity p erfect ob e
dien c e total senselessness want of feeling indolence etc
”
in on e word the incarnate non possumus and all th at
in order to allow other men to act and at the same time
to submit one s self to the action of any force whatever
t o follow each impulsion
C an these q ualities really be found in matter % It is
neither to b e compressed nor to b e e xtended without
resisting but resistance is a force itself and it was not
”
without reason that th e ancients said vis inertiae
M atter h as the inclination to b e a whole its least
p arts
atoms molecules or dust it makes n o di fference
attract each other in order to aggregate themselves round
a common centre or centre of gravity ; they s quee z e they
j oin on e to another matter is therefore provided with the
attracting force it is itself a force in continual action it
cannot therefore b e inert
The activity ascribed to the parts of the earth is but
apparent and relative
each part of matter whether it b e
in the interior or on the surface of the Spheroid of the
e art h
is attracted by its centre or centre of gravity which
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70
of
course a fi x ed universe as the forces acting according
to the hypothesis can only pro ceed from fi x ed b o dies
In this manner we arrive at the idea of an absolute
immobility at th e idea of universal inertia in conse quence
of the repulsion D oes it not b ecome clear that with
much more reason we may say that the first and most
simple l aw of nature is motion %
ferent whether on e
F or the astronomy it is very indi f
does or does not imagine an inertia ; science s ees nothing
else but the movement and cannot imagine how a celes
tial body can b e susp ended motionl ess in Space T h e
fixity imagined by the theory is besides no m ore in vogu e
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V III
.
It is little more than three centuries ago that an
e x planative science began to form itself that men asked
”
“
for the w h y of phen omena The historians of astro
n omy attribute great imp ortance to this ep o ch and believe
that with it investigation the highest function of the mind
awoke from a sleep of twenty centuries But if the
mechanics of the heaven were regulated the universe would
prove to b e a great disorder a total confusion ; an nu
pardonable disobedience would manifest i t
N ow they were obliged to ask for the reasons why
the phenomena of the celestial b odies as well as the whole
heaven sho w a hostile b ehaviour and w i ll not obey the
laws imp osed up on them
V elo city once ac quired does not change the perma
nency of the distance is warranted the q uiet ever e q ual
course is s ecured the almost circles may so easily b e run
thro ugh the well trace d orbits are like rail roads the sun
do es n ot move etc etc ; n ow what may b e the reason of
th e irregularities % There must b e some deadly enemy of
established order whom one must discover as soon as
p ossible at any cost
It is N ewton who answers the w h y it is N ewto n
wh o finds the disturber who i s the sole reason of each
disorder each anomaly each disturbance and this disturber
an astrono mical Proteus
calls itself a t t r a c t l o n
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72
p oints to a force there is no doubt of that
The universal attraction presuppo ses a universal force
which as such cannot b e without activity as its action
e xtends to all celestial b odies N ow i f w e c a n k n o w
h o w a n d i n w h a t m a n n e r t h i s f o r c e i s e xe r
the irreg ularities will explain themselves N ewton
c ise d
has d e c i d e d how attraction is to behave and demean
itself and it is with him and according to him that lear
ned men have demonstrated all with the most astonishing
”
evidence
The same N ewton maintained the p osition that we
ought not to b elieve anything which is not proved But
how does on e get the pro of ; h ow does on e ac quire the
persuasion that the proof is indeed a pro of % F acts
like truth h ave no need of pro ofs for they are stronger
than these
In astronomy they make or produce the
argument and are content they are pleased with h aving
furnished it But it is hard to comprehend the phenomena
to un déstan d their meaning it is hard to recognise the
observations it is altogether imp ossible to comprehend
them as long as on e retains the fi x ed ideas about the
s olar system and the nature of forces in general but
especially those a b out attraction
The theory of attraction and the application of its
”
laws to the pro ofs of the w h y of the phenomena do
n ot satisfy reason It is on this account that m any p eople
have s ome aversion to attraction and say plainly that it
do es not exist They h ave to o repeatedly sub stitude d
other forces for it without considering that by substituti ng
on e unknown thing for another there is not made any
progress
The attraction of the earth for e x ample is observable
on its surface
by
observing
attentively
its
p
h
enome
n
a
one
;
A ttraction
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73
may b e p ersuaded tha t an attracting force e x ists rea ll y
and it is p ermissible it is even reasonable to think that
which are likewise supp ose d
th e other celestial bodies
own the same force
to b e material
But if the e xi
there
stence of an attractive force is no longer doubted
still remains unsolved th e great q uestion in what manner
Whether th i s
d o the celestial b odies act on e on another
b e answerable is another question
It is by their mutual attraction that the atoms
and form that material b ody
s trive to unite themselves
which includes their totality N ow the mass of this b ody
the
c ontains the sum of the attraction of all its atoms
c onse q uence of wh ich is that the attraction of a body is
proportional to its mass prop ortional to the accumulated
matter F rom this p osition they conclude that on e b ody
which sum
as we see
is
a cts
on another b ody
represented by the quantity of the atoms It is certainl y
intelligible that the quantity or greatness of the attraction
to o proportional
e x ists in the b o dy and in an amount
But if the molecules apply this immanent
t o its mass
force to attract each other mutually to maintain their
mutual contact they can no longer either singly or
colle ctively influence another b ody and its atoms with th e
same
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nfl
n c e s th e e arth ( acco rdi n g to t h e
u
i
u
e
)
in as man y w ays a it h a mol e cul e s ; h e i nfl
u en c es si ngl e
th e o y )
p arts of th e e arth or do es n ot b ut h e is n ot h i n d ere d by th is f o m
at trac ti n g th e c e ntre of th e pl an et acco rdi n g t o th e l aw of q u ad rate
I s it n ot a wo n derful i nven tio n th is of a va i abl e attractio n w h ic h
is at th e s ame t ime bo th s tro ng er an d w eak er % I n th e th eo y of th e
t id e s fo e xampl e att a c tio n do e s n ot ac t a ccor di n g to th e s qu a e
b ut t o th e cub e of th e dis tan c e ; th e moo n e xercis e s on th e ea th
I n th e t wo th e ori e s of p r e
a s t r o n g e r attrac tio n th an t h e sun
c e s s i o n an d n u t a t i o n th e manne r of attrac tion is s till mo re
it
T he
sun
in tr th
,
,
s
s
r
r
,
,
.
r
,
,
r
,
r
,
r
r
r
.
,
As
a distinctly observable phenomenon attraction
defines itself A ttraction appears ever in the same manner :
the final result of its infl uence is that two b odie s
approach and unite which each other The approach
and final union cannot take place without motion the
conse quence of which is that the attracting force is
at th e same time a moving force E xp erien ce has taught
that some forces as magnetism electricity light etc not
only attract but also repel ; they have been called p olar
forces and their opposite directions have b een denoted
by p ositive and negative T o rep el somethi ng is to remove
it and there appears again movement which therefore is
insep arable from attraction and repulsion The mutual
action of the forc et on each other and on matter can produc e
attraction if there did not yet e xist any it can strengthen
and weaken the e xisting attraction generate light and
warmth magnetism and electri city ; this latter is es pecially
and p owerfully th e potential cause of the p ower of th e
magnet and all bodies or substances may
with a few
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s to nis h i n g ;
c h oos es c e tai n p arts of th e su face of
th e ea th on w h ic h h e a c ts a bi t a ily in o d er t o p oduc e th e
p r e c e s s i o n ; b ut h e do e s n ot ac t at al l on th e s ame p art s in
o rd e to p oduc e th e n u t a t i o n ; acti ng an d n ot ac tin g to geth er
mi g h t b e m o e th an a
mi acl e
But h ow a e th e s e an d many si mil a i n co ngrui ti e s to b e e
c on c il e d wi th th e a ccurate d e te mi n atio n s d e mo n s tratio n s p i n cipl e s
l aws etc w h ic h th ey h ave p oduc e d wi th so muc h p ai n s % A fter
h avi n g p o ve d by th e o mnipo ten c e of an alysis t h at th e sun ac t s
on th e e a th
o tati n g sp h eroid
in suc h a man n e r as if
a
th e e nti e mass wa u n i te d in it c e n t e
th e
th at al l it p arts
t o tali ty of it m ol e cul e s of cou s e it w ate r an d atmosp h ere too
mus t b e co n sid e re d as b elo ng i n g to th e solid mass an d a e co us e
t
t
a
e
n
t
a
a
e
u
ly
lso
u
n
i
t
d
i
t
h
c
f
h
i
n
g
p
r
o
v
e
d
cl
ly
h
e
n
e
n
t
r
t
r
e
e
a
e
a
v
q
;
th e sun ac ts on th e e arth an d its m oo n as if th e s e two bodi e s w e re
u n i te d at on e c ent e e tc e tc th ey allow th e sun to ac t a bit arily
in th is o th at mann er on th e s e or th os e p arts
a
r
th ere th e
sun
r
r
r r
r
,
r
r
r
r
r
r
.
r
r
r
r
,
,
r
,
r
.
r
,
,
r
r
r
,
s
s
s
r
,
r
s
,
,
s
,
,
r ,
r
,
r
r
.
,
.
,
r
,
r
75
b e c ome magn etic al or electrical or i f they
e x ceptions
p ossessed these qualities latent attain to their mani
testation
The action of forces working upo n and in anothe r
may raise the thought that it
called correlation
is the very same natural p ower which is but represented
to us in its mo difications and that we cannot but take
these modifications for distinct separate powers independen t
of one other Which of thes e modifications is nearest to
that true p ower which effects the attraction we cannot
decide as we do not know the force N or does the word
”
attraction signify the force itself but its e xpression its
e ffect and if we may say so the result of the acting
force N ow if two b odies attract one anoth er with une
qual force the less must no doubt conce de the preference
to the greater ; that is to say if matter is falling moving
attracting etc the lesser mass must fall into the greater
one and not inversely Thu
s a little ma gnet will not
attract a greater mass of iro n b ut will itself rush towards
it ;
in this case the iron attracts the magnet But if a
little magnet is fi x e d it will be capable of attractin g a
much greater mass of iron The idea of mutual attraction
being stated as a general position the notion of a t t r a c
t i n g fo r c e s fal ls away and the magnet which attracts
the iron is attracted by it in the same manner N ow if
two b odies attract on e another e qually we can no longer
de cide which is the attracting on e an d which is the
attracted on e In conse quence of the fi x ed sun always
attracting all planets would be forced to fall up on him
which is
N ow to es cap e thi s inevitable catastrophe
rendered n ecessary by the system of C opernicus combined
with the central attraction
they must t hink of means
and they invented th e c e n t r i f u g al f o r c e A s long as
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_
_
76
the sun is fi x ed they can h ardly do oth erwise than abide
by this imagination for the celestial phenomena are in
comprehensible A S th e movement takes place in space
we have no idea of it But now it is recognised tha t the
centre is moving ; we find that the sun advances in Space
swiftly enough and as he has yet a great disk and it has
not yet been observed that he diminishes so as to b ecome
at last a fix ed Star to the earth it may b e verisimilar
th at the earth follows him or that the sun carries his
system with himself But if the centre moves there are
no closed curves no orbit and of course n o plane of orbit
remaining on the same place in s pac e the circulation e xists
i t is true but it is n ot made ro und the centre of the sun
and the radius of th e curve of revolution is no longer
th e distance of the sun
When it is said that the prop er astronomical science
i s the t h e o r y that is the do ctrine of attraction which
impresses on this s cience th e stamp of infal libility that
this do ctrine e xplai n s perfectly the mechanism ofthe heaven
after p enetrating with the help of analysis
which
demonstrates everything clearly
into the sanctuary o f
the univers e and revealing all mysteries etc on e would
supp ose that the attraction itself is known accurately
and the theory is on a firm basis It b ecomes however
simply apparent that of this immense inscrutable and
incomprehensible p ower of nature and particularly of
its being and action we do not nor can we know
anything
The soul of the laws of attraction is the law of q ua
drate
The attracting force acts inversely prop ortionally
to the quadrate of the distance T h u s N e w t o n h a s
d e ci ded
If we ask our l earned men our authorities our sages
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78
idea that the same p ower which guarantees the stability
an d h as induced th e wonderful order and h armony of the
universe destroys its own work and may th erefore cause
disorder too ; the same fancy suggests to h im that all
variations ob served in the motions and p o sitions can only
b e irregularities ine qualities and p erturbations e ffected
by attraction In conse quence of this imagination N ewton
states his laws and it may b e a matter of course that
he often got into doubts about hi s own work
The motions of the celestial bodies being regulate d
by the s ystem ensured by the laws it was n ot necessary
to apply one s self to study the movement ; if however
on e wishes to give an account of the causes of the
dis
o rders
which of cours e are not produced by the move
ment one must lo ok for them elsewhere but where to
look for them one did not know
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,
IX
.
The elements of the elliptical orbits : the half great
and the time of re voluti on depending on it ; the
a x is
eccentricity of the closed orbit ; the longitude of the
erihelion
the
longitude
f
the
ascending
knot
and
the
o
p
inclinati on of the orbit to the ecliptic don t e xist at all
in reality in the sense adopted by theory
If an astronomer of our time says : The elements of
the elliptical orbits are derived from observations of more
than 3000 years ; it is from them that the planetary tables
as well as the yearly ephemerides are calc ulated ; the results
o f the calculations
agree with the observ ations and the
p ositions of the celestial bodies ( the solar system)are
for each supposed moment nearly precisely such as pro ceed
from the tables the conse quence of which is therefore
”
the correctness of the supposed elements he may b e sure
that it will n ot occur to the thoughts of anyb ody to obj ect
to it If however this astronomer adds : It is from th e
correctness of the elements and the results of calculation
that there arises the proof that the system of C op ernicus
”
and the laws of Kepler are a fact he h as said so mething
thoroughly false and contradictory to the g e n e ra l m o v e
m e n t C op ernicus and Kepler had a fi x e d s u n but
this has since that time g o t i n t o m o t i o n
It is pretended : A stronomers don t meddle with the
”
If
abs olute movement of the celestial b odies i n space
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’
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80
they did abide consistently by this sentence what we should
read in their b o oks would b e very nearly as follo ws :
What we can and espe cially do observe are th e
p ositions and motions of the celestial b o dies ; b oth are
proj e cted on the celestial sphere on the app arent heavenly
hollow sphere in the centre of which is o ur eye ; we se e
them from the earth which moves too from our p oin t
O f observation on the surface of the earth
The move
ment of a planet p roj ects itself on th e apparen t heavenly
hollow sphere in such a manner as if it were circulating
in an ellip se the half great a xis eccentricity and in
c l in ation to
the ecl i ptic of which are such and sn c h ;
as we know the a p p a r e n t Situation of the vernal p oi n
t
and the inclination of the ecliptic to the e quator we have
the epo ch longitude and ascending knot of the planet
A s this p osition Of the movement repeats itse lf periodically
and is always the same it is evident that in order to
determine the situation of the planet with reference to
the starry heaven and the sun we can only calculate with
such elements as give th e observable p osition for a result
N ow if th e ellipses with their apperten an c es like th e
ecliptic are no reality and mere products of the imagination
this is indi fferent to th e calculation for it must brin g
forward the a p p a r e n t and does not care either for th e
reality or for the name by which one denotes the O h
served phenomena That th e orbits are close is a sup
p osition which might arise from a superficial inattentive
observation of the phenomena of movement ; that ob ser
and still are made under the
vation s have b een made
preconceived Opinion that the planets are force d to mov e
according to the system of C opernicus and the laws of
K epler is a prej udice from the in fl uence of which the
observer can hardly es cap e It is however not o nly by
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81
the solar movement that the c l o s e d o r b i t s h ave b een
abolished but it h as been proved by the observations
themselves that the orbits don t close A s to the orbit
Of the earth especially it appears clearly that the end
p oint of its curve of revolution after an accomplished
perio d does not proj ect itself on the same place Of the
celestial Sphere but on a p oint which is Situated 5 0 3
more to the east which is indicated too d i stinctly by
the yearly movement of th e sun If in Spite of all these
facts theory continues to announce ellipses and closed
orbits as an indisputable truth there is to be found in this
the proof of its labouring un der a chronical incurable
sickness
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W
believe ourselves bound to inform the readi ng
and thinking public that the astronomers and mathe
matic ian s of our time have agreed together to p ass over
with condescending silence all those endeavours of lear
ned and unlearned men which tend to demonstrate the
untenableness of the C op ern ican concepti on of the world
It is in the interest of the science that we pro test against
this pro ceeding for s cience snflers from it and is even
i nsulted S ome of the most famo us astronomers are
feeling th e impulse to comp ose p opular works to in
form the public ; it is the duty of those in the first
rank to bring clearness into th e prop osed question The
most noted in this respect of present astronomers are
N ewcomb at Washington and Weiss at Vienna the
th
of L ittrow s Wonders
editor of a new edition ( th e 7 )
”
of H eaven
e
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.
,
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’
“
.
long as th e question relating to the sun being
”
considered as at rest is n ot cleared up modern astro
theory must be looked on as a produ c t o f
n omic al
and has no greater value than the
th e i magination
AS
“
,
,
83
conception of the world of Ptol emaé us and Tycho for
x ed or immoveable thin g in the universe
there is no fi
neither a fi x ed earth nor a fix ed sun nor a fix ed
Star A ll is moving E ach celestial b ody has a triple
movement : a rotation round its axis
its own mo
tion and it must follow the chief member of its group
system
)
(
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6
*
86
10
.
b ah n e n
11
.
und K o me te n
D ie wah re Ges tal t der P l an e t e n :
F riedr ic h C a r l Gusta v S taeber
D r es d e n 1 8 6 4
'
.
S o nn e b e wegt S ich
in Be z u g auf d i e F i xs ter ne
Berli n 1 8 5 2
D ie
F ol g e rung e n
.
ne ten
un d P l a
.
.
aus
C
.
d i e s er
R
(
.
L eh r e
ohr 6a c h
)
.
.
12
.
U eb e r
tisch e Geograph ic
struirten
un d
.
E rl aute rnde Be i g ab e
.
D
er
h O h ere
Unterri c h ts ans tal ten
F
.
n e u c on
u
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P us c lz maun ,
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m
a
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o
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c
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f
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f
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g
L o gik mit de r strengb ere c h tigte n
H imme l s -M ech anik
Gru nd der induc tiven
p h il osop h i sc h en un d m ath emati s c h en
l
K
u
k
K luc z gc kg
P
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z
V e ran sc h aul ic h ungsapparaten fiir V o l kssch u l e n
S emin arob erl eh rer, Gri mma
13
fiir math ema
V eransc h aul ich ungsmittel
.
1 880
G . K R E Y S I N G , L E I P %I G
.
N ac h w e i s u n g
.
V
.