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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 . ' “ ; ‘ ’ » - , ’ . ' , , , . , , ” , , . , ’ - - . , . , , , . . , , , . , . , , , , . , , . , , , 15 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 , , . , , , , . , , . , ~ , , , . . , , , . , . , , . , . . , . 16 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 , . , W , , , . , , , , , , , , . , , , , , . . , , . , , , , , . , , . , , ‘ 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 . , - , , , . . , , , , , ’ . , fi . , . , . , ‘ , , . , , , 2 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 , , , , , , , . 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 . , . . , , . , , , , . , , , , , . , l9 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 , , , , , , . , , , . . , . , , , , , . , , . , , , , , , , , - . . 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 lf , , , , . , , . , , , , , , , . , , , , . , 22 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 , , , . , , , , , , , , . , . , , , , . . , , , , . . , , , 23 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 . / , . . , , , , . . , , . , , , , , , . , , , , , . , , , ' , w , , , , . , , , , , , , 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 , , , , . , , , . , , . , , . , , . , ’ . , . , . , , , . , , ’ . , 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 . ' , , , , , . - , . , , . , , , , , , , , , . , , , , , , , , , , , , . , 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 , , , . , , , , , , , , . , , , , , , , ‘ . , , , , , . , , , , , , , , , . 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 , , , . , . . , , , , , , , , , . . , , . 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 , , . , , , , , , , . , , . , , , , , , , , , . , , . , , , , , , , , , , . , , 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 ” , , , , , . . , , , , , , , , , , , , , , , - , , . , , , . , , . , , , , , , . . 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 , , , . , , , , “ . 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 , . . , , , , . , , . - - . . - , , ’ . , , , , , , , , . 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 s , , . , , , , , . . , , “ , , , , ’ ’ . . . , , , , , ’ . , . . , , , . , , . 3 , 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 , , , , . . , , , , , . “ “ . . , , , - , , , , , . ' , , , , “ . , “ . , . , . , , . “ , , “ , , , . . , 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 , , , , , , , . . . , ‘ “ , , , , , . , , , , . 3 * 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 , , “ , , , , , , - , , 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 , , , , . , , , . , , , , . , , . , , ' . , , , , , , , . , ’ . 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 , ' , , ’ . , , , , , , , , , , . , , , , , . , , . . . , , , , , . , , , 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 , , , , . , , , , . , . . , , , . , , . , , , , . , , , , , , , . 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 , , . , , . 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 , , . , , , . , , , , , , . , , , . 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 , , i , . , , . “ , , . , , , , . , , , . ‘ . . . , , , , . , . , , , 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 , , , , , , , . , , , , . , , , , , , . , , , , , , , , , , . , . , . , , , 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 . , , . , , . , . , , 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 , , , , , , . , , . , - , , . , , , , . , , , , , , 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 , . , , , , - , , , , . , , r , , , , - , , . , , , , . , , , , , , . , , , , 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 , , , , . , . , . , , , , , , , , , , . , , , . , , 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 , , . - , , . , , , , , , , , , , , , , , , , , , , . . 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 , , , . ” ” 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 , , , ’ , . 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 , , , . , , . , . , . , , , ’ , , , , . , , , , “ , , ’ , . , , , , , . 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 , , , , , . . , , , , , . “ 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 , , , , , , , . , , , ’ , , 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 . , , , , . , , , . , , , , , , . , , , . IV . 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 , , . , , , ’ . , , . , , , , , , , , , , , . . , , , , , , 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 , , , , , . , , , . , , . , , . . , , , , , , , . . , , . , . , 60 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 , , . . . . , - , . , , - , . , . , , . , , , , , , , , . . 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 , , . , . ’ , , ’ , . , . , . . , , , , . . 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 , . . , , . , , , , . , . , . . , , . , . , , , , . , , , 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 ( ) , . , . , , , . . ' , ‘ , , , , , , . , , . , , . , , , , , . , , , . , , , , . 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 , . , , , , , , . , , , . . , , , , . , , , , , , . 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 , , , , % , . ' , , . , , ’ “ , , . , , . , . , , , , . , , , , , , , “ . , , 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 , - . , , ’ , , . , , . , , , , . 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 , , . . . , ' , , , . , , , “ , , ’ , . , , , “ . , , , , , , , , . , , , , 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 , . , . , , , , , , . . 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 , , . , , . , , . , . , , , - , - - , , - . . , . , , , , . 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 . , , , , , , . . , , , , “ . , . , , , , . , . . , , , , , . “ . , , . , , , . , , 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 , , , , . , , . , . , , . , , , . , , . , , , . , , , , 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 . , . , , . , . , , , , . , , . , , , , , 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 ‘ , , , . , , , , . , , . , “ , , , . , , , , . , , , . , , . , . , , , . , , , , . . , , , . _ _ 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 , , . , . , , , , , , , , . , , , . , , , , , . , , , . , , , , . . , . , , , 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 , , , , , . , , . , , ’ , , , , , , , . , 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 , , ’ , . “ , , , “ . , , , . , . “ ’ . 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 , , “ , , , , , , , , . , , , , . , , , , . , , , , , . , , , , . , , 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 , , ’ . , , “ , , , . , , , , , . 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 , . , , . . , ’ “ . 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 ) ( ‘ , , , . , . , , . 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 . A P us c lz maun , ' . . i r m a e o n z l c h f u f a e R 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 . 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 .