Plato's Doctrine respecting the rotation of the Earth and Aristotle's Comment upon that Doctrine Part 1

Plato's Doctrine respecting the rotation of the Earth and Aristotle's Comment upon that Doctrine.

by George Grote.

PREFACE.

The following paper was originally intended as an explanatory note on the Platonic Timaeus, in the work which I am now preparing on Plato and Aristotle. Interpreting, differently from others, the much debated pa.s.sage in which Plato describes the cosmical function of the Earth, I found it indispensable to give my reasons for this new view. But I soon discovered that those reasons could not be comprised within the limits of a note. Accordingly I here publish them in a separate Dissertation. The manner in which the Earth's rotation was conceived, ill.u.s.trates the scientific character of the Platonic and Aristotelian age, as contrasted with the subsequent development and improvement of astronomy.

PLATO--ON THE EARTH'S ROTATION.

In Plato, Timaeus, p. 40 B, we read the following words--[Greek: Ge=n de trophon men e(mete/ran, ei(llome/nen de peri ton dia pantos po/lon tetame/non phu/laka kai demiourgon nukto/s te kai e(me/ras e)mechane/sato, pro/ten kai presbuta/ten theo=n, o(/soi e)ntos ou)ra/nou gego/nasi.] I give the text as it stands in Stallbaum's edition.

The obscurity of this pa.s.sage is amply attested by the numerous differences of opinion to which it has given rise, both in ancient and in modern times. Various contemporaries of Plato ([Greek: e)/nioi]--Aristot. De Coelo, II. 13, p. 293 b. 30) understood it as a.s.serting or implying the rotatory movement of the earth in the centre of the Kosmos, and adhered to this doctrine as their own.

Aristotle himself alludes to these contemporaries without naming them, and adopts their interpretation of the pa.s.sage; but dissents from the doctrine, and proceeds to impugn it by arguments. Cicero mentions (Academic II. 39) that there were persons who believed Plato to have indicated the same doctrine obscurely, in his Timaeus: this pa.s.sage must undoubtedly be meant. Plutarch devotes a critical chapter to the enquiry, what was Plato's real doctrine as to the cosmical function of the earth--its movement or rest (Quaestion. Platonic. VII. 3, p. 1006.)

There exists a treatise, in Doric dialect, ent.i.tled [Greek: Ti/maio** to= Lo/kro Peri Psucha=s Ko/smo kai Phu/sios], which is usually published along with the works of Plato.

This treatise was supposed in ancient times to be a genuine production of the Lokrian Timaeus, whom Plato introduces as his spokesman in the dialogue so called. As such, it was considered to be of much authority in settling questions of interpretation as to the Platonic Timaeus. But modern critics hold, I believe unanimously, that it is the work of some later Pythagorean or Platonist, excerpted or copied from the Platonic Timaeus. This treatise represents the earth as being in the centre and at rest. But its language, besides being dark and metaphorical, departs widely from the phraseology of the Platonic Timaeus: especially in this--that it makes no mention of the cosmical axis, nor of the word [Greek: i)llome/nen] or [Greek: ei(loume/nen].

Alexander of Aphrodisias (as we learn from Simplikius ad Aristot.

De Coelo, fol. 126) followed the construction of Plato given by Aristotle. "It was improbable (he said) that Aristotle could be ignorant either what the word signified, or what was Plato's purpose" ([Greek: a)lla to=| A)ristote/lei, phesin, ou(/to le/gonti _i)/llesthai_, ou)k eu)/logon a)ntile/gein; o(s a)letho=s gar ou)/te te=s le/xeos to semaino/menon ei)kos e)=n a)gnoei=n au)ton, ou)/te ton Pla/tonos skopo/n.] This pa.s.sage is not given in the Scholia of Brandis). Alexander therefore construed [Greek: i)llome/nen] as meaning or implying rotatory movement, though in so doing he perverted (so Simplikius says) the true meaning to make it consonant with his own suppositions.

Proklus maintains that Aristotle has interpreted the pa.s.sage erroneously,--that [Greek: i)llome/nen] is equivalent to [Greek: sphiggome/nen] or [Greek: xunechome/nen]--and that Plato intends by it to affirm the earth as at rest in the centre of the Kosmos (ad Timaeum, Book iv., p. 681 ed. Schneider). Simplikius himself is greatly perplexed, and scarcely ventures to give a positive opinion of his own. On the whole, he inclines to believe that [Greek: i)llome/nen] might possibly be understood, by superficial readers, so as to signify rotation, though such is not its proper and natural sense: that some Platonists did so misunderstand it: and that Aristotle accepted their sense for the sake of the argument, without intending himself to countenance it (ad Aristot.

De Coelo, p. 126).

Both Proklus and Simplikius, we must recollect, believed in the genuineness of the Doric treatise ascribed to Timaeus Locrus.

Reasoning upon this basis, they of course saw, that if Aristotle had correctly interpreted Plato, Plato himself must have interpreted _incorrectly_ the doctrine of Timaeus. They had to ascribe wrong construction either to Plato or to Aristotle: and they could not bear to ascribe it to Plato.

Alkinous, in his Eisagoge (c. 15) gives the same interpretation as Proklus. But it is remarkable that in his paraphrase of the Platonic words, he calls the earth [Greek: e(me/ras phu/lax kai nukto/s]: omitting the significant epithet [Greek: demiourgo/s].

In regard to modern comments upon the same disputed point, I need only mention (besides those of M. Cousin, in the notes upon his translation of the 'Timaeus', and of Martin in his 'etudes sur le Timee') the elaborate discussion which it has received in the two recent Dissertations 'Ueber die kosmischen Systeme der Griechen,'

by Gruppe and Boeckh. Gruppe has endeavoured, upon the evidence of this pa.s.sage, supported by other collateral proofs, to show that Plato, towards the close of his life, arrived at a belief, first, in the rotation of the earth round its own axis, next, at the double movement of the earth, both rotation and translation, round the sun as a centre (that is, the heliocentric or Copernican system): that Plato was the first to make this discovery, but that he was compelled to announce it in terms intentionally equivocal and obscure, for fear of offending the religious sentiments of his contemporaries ('Die kosmischen Systeme der Griechen, von O. F.

Gruppe,' Berlin, 1851). To this dissertation M. Boeckh--the oldest as well as the ablest of all living philologists--has composed an elaborate reply, with his usual fulness of ill.u.s.trative matter and sobriety of inference. Opinions previously delivered by him (in his early treatises on the Platonic and Pythagoreian philosophy) had been called in question by Gruppe: he has now re-a.s.serted them and defended them at length, maintaining that Plato always held the earth to be stationary and the sidereal sphere rotatory--and answering or extenuating the arguments which point to an opposite conclusion ('Untersuchungen uber das kosmische System des Platon, von August Boeckh,' Berlin, 1852).

Gruppe has failed in his purpose of proving that Plato adopted either of the two above-mentioned doctrines--either the rotation of the earth round its own axis, or the translation of the earth round the sun as a centre. On both these points I concur with Boeckh in the negative view. But though I go along with his reply as to its negative results, I cannot think it satisfactory in its positive aspect as an exposition of the doctrine proclaimed in the Platonic Timaeus: nor can I admit that the main argument of M.

Boeckh's treatise is sufficient to support the inference which he rests upon it. Moreover, he appears to me to set aside or explain away too lightly the authority of Aristotle. I agree with Alexander of Aphrodisias and with Gruppe who follows him, in p.r.o.nouncing Aristotle to be a good witness, when he declares what were the doctrines proclaimed in the Platonic Timaeus; though I think that Gruppe has not accurately interpreted either Timaeus or Aristotle.

The capital argument of Boeckh is as follows: "The Platonic Timaeus affirms, in express and unequivocal terms, the rotation of the outer celestial sphere (the sidereal sphere or Aplanes) in twenty-four hours, as bringing about and determining the succession of day and night. Whoever believes this cannot at the same time believe that the earth revolves round its own axis in twenty-four hours, and that the succession of day and night is determined thereby. The one of these two affirmations excludes the other; and, as the first of the two is proclaimed, beyond all possibility of doubt, in the Platonic Timaeus, so we may be sure that the second of the two cannot be proclaimed in that same discourse. If any pa.s.sage therein seems to countenance it, we must look for some other mode of interpreting the pa.s.sage."

This is the main argument of M. Boeckh, and also of Messrs. Cousin and Martin. The latter protests against the idea of imputing to Plato "un melange monstrueux de deux systemes incompatibles"

(etudes sur le Timee, vol. ii. p. 86-88).

As applied to any person educated in the modern astronomy, the argument is irresistible. But is it equally irresistible when applied to Plato and to Plato's time? I think not. The incompatibility which appears so glaring at present, did not suggest itself to him or to his contemporaries. To prove this we have only to look at the reasoning of Aristotle, who (in the treatise De Coelo, ii. 13-14, p. 293. b. 30, 296. a. 25) notices and controverts the doctrine of the rotation of the earth, with express reference to the followers of the Platonic Timaeus--and who (if we follow the view of Martin) imputes this doctrine with wilful falsehood to Plato, for the purpose of contemptuously refuting it "pour se donner le plaisir de la refuter avec dedain."

Granting the view of M. Boeckh (still more that of Martin) to be correct, we should find Aristotle arguing thus:--"Plato affirms the diurnal rotation of the earth round the centre of the cosmical axis. This is both incredible, and incompatible with his own distinct affirmation that the sidereal sphere revolves in twenty-four hours. It is a glaring inconsistency that the same author should affirm both the one and the other." Such would have been Aristotle's reasoning, on the hypothesis which I am considering; but when we turn to his treatise we find that he does not employ this argument at all. He contests the alleged rotation of the earth upon totally different arguments--chiefly on the ground that rotatory motion is not natural to the earth, that the kind of motion natural to the earth is rectilineal, towards the centre; and he adds various corollaries flowing from this doctrine which I shall not now consider. At the close of his refutation, he states in general terms that the celestial appearances, as observed by scientific men, coincided with his doctrine.

Hence we may plainly see that Aristotle probably did not see the incompatibility, supposed to be so glaring, upon which M.

Boeckh's argument is founded. To say the least, even if he saw it, he did not consider it as glaring and decisive. He would have put it in the foreground of his refutation, if he had detected the gross contradiction upon which M. Boeckh insists. But Aristotle does not stand alone in this dulness of vision. Among the various commentators, ancient and modern, who follow him, discussing the question now before us, not one takes notice of M. Boeckh's argument. He himself certifies to us this fact, claiming the argument as his own, and expressing his astonishment that all the previous critics had pa.s.sed it over, though employing other reasons much weaker to prove the same point. We read in M.

Boeckh's second 'Commentatio de Platonico Systemate Coelestium Globorum et de Vera Indole Astronomiae Philolaicae,' Heidelberg, 1810, p. 9, the following words:--

"Non moveri tellurem, Proclus et Simplicius ostendunt ex Phaedone.

Parum firmum tamen argumentum est ex Phaedone ductum ad interpretandum Timaei loc.u.m: nec melius alterum, quod Locrus Timaeus, quem Plato sequi putabatur, terram stare affirmat: quia, ut nuper explicuimus, non Plato ex Locro, sed personatus Locrus ex Platone, sua compilavit. At omnium firmissionum et certissimum argumentum ex ipso nostro dialogo sumptum, _adhuc, quod jure mirere, nemo reperit_. Etenim, quum, paulo supra, orbem stellarum fixarum, quem Graeci [Greek: a)plane=] appellant, dextrorsum ferri quotidiano motu Plato statuebat, non poterat ullum terrae motum admittere; quia, _qui hunc admitt.i.t, illum non tollere non potest_." (This pa.s.sage appears again cited by M.

Boeckh himself in his more recent dissertation 'Untersuchungen uber das kosmische System des Platon,' p. 11). The writers named (p. 7) as having discussed the question, omitting or disregarding this most cogent argument, are names extending from Aristotle down to Ruhnken and Ideler.

It is honourable to the penetration of M. Boeckh that he should have pointed out, what so many previous critics had overlooked, that these two opinions are scientifically incompatible. He wonders, and there may be good ground for wondering, how it happened that none of these previous writers were aware of the incompatibility. But the fact that it did not occur to them, is not the less certain, and is of the greatest moment in reference to the question now under debate; for we are not now inquiring what is or is not scientifically true or consistent, but what were the opinions of Plato. M. Boeckh has called our attention to the fact, that these two opinions are incompatible; but can we safely a.s.sume that Plato must have perceived such incompatibility between them? Surely not. The Pythagoreans of his day did not perceive it; their cosmical system included both the revolution of the earth and the revolution of the sidereal sphere round the central fire, ten revolving bodies in all (Aristotel. Metaphysic.

i. 35, p. 96 a. 10. De Coelo, ii. 13, p. 293 b. 21). They were not aware that the revolutions of the one annulled those of the other as to effect, and that their system thus involved the two contradictory articles, or "melange monstrueux," of which Martin speaks so disdainfully. Nay, more, their opponent, Aristotle, while producing other arguments against them, never points out the contradiction. Since it did not occur to them, we can have no greater difficulty in believing that neither did it occur to Plato. Indeed, the wonder would rather be if Plato _had_ seen an astronomical incompatibility which escaped the notice both of Aristotle and of many subsequent writers who wrote at a time when astronomical theories had been developed and compared with greater fulness. Even Ideler, a good astronomer as well as a good scholar, though he must surely have known that Plato a.s.serted the rotation of the sidereal sphere (for no man can read the 'Timaeus' without knowing it), ascribed to him also the other doctrine inconsistent with it, not noticing such inconsistency until M. Boeckh pointed it out.

It appears to me, therefore, that M. Boeckh has not satisfactorily made good his point--"Plato cannot have believed in the diurnal rotation of the earth, because he unquestionably believed in the rotation of the sidereal sphere as causing the succession of night and day." For, though the two doctrines really are incompatible, yet the critics antecedent to M. Boeckh took no notice of such incompatibility. We cannot presume that Plato saw what Aristotle and other authors, even many writing under a more highly developed astronomy, did not see. We ought rather, I think, to presume the contrary, unless Plato's words distinctly attest that he did see farther than his successors.

Now let us examine what Plato's words do attest:--[Greek: ge=n de trophon men e(mete/ran, ei(llome/nen] (al. [Greek: ei(lome/nen, i)llome/nen]) [Greek: de peri ton dia pantos po/lon tetame/non phu/laka kai demiourgon nukto/s te kai e(me/ras e)mechane/sato, pro/ten kai presbuta/ten theo=n, o(/soi e)ntos ou)ra/nou gego/nasi.]

I explain these words as follows:--

In the pa.s.sage immediately preceding, Plato had described the uniform and unchanging rotation of the outer sidereal sphere, or Circle of The Same, and the erratic movements of the sun, moon, and planets, in the interior Circles of the Diverse. He now explains the situation and functions of the earth. Being the first and most venerable of the intra-kosmic deities, the earth has the most important place in the interior of the kosmos--the centre. It is packed, fastened, or rolled, close round the axis which traverses the entire kosmos; and its function is to watch over and bring about the succession of night and day. _Plato conceives the kosmic axis itself as a solid cylinder revolving or turning round, and causing thereby the revolution of the circ.u.mference or the sidereal sphere._ The outer circ.u.mference of the kosmos not only revolves round its axis, but obeys a rotatory impulse emanating from its axis, like the spinning of a teetotum or the turning of a spindle. Plato in the Republic ill.u.s.trates the cosmical axis by comparison with a spindle turned by Necessity, and describes it as causing by its own rotation the rotation of all the heavenly bodies (Republ. x. p. 616, c. 617 A). [Greek: e)k de to=n a)/kron tetame/non A)na/gkes a)/trakton, di' ou(= pa/sas e)pistre/phesthai tas peri/phoras ... , kuklei=sthai de de strepho/menon ton a)/trakton o(/lon men ten au)ten phoran . .

. . stre/phesthai de au)ton e)n toi=s A)na/gkes go/nasin.][1]

[Footnote 1: Proklus in his Commentary on the Platonic Timaeus (p.

682, Schn.) notes this pa.s.sage of the Republic as the proper comparison from which to interpret how Plato conceived the cosmical axis. In many points he explains this correctly; but he omits to remark that the axis is expressly described as revolving, and as causing the revolution of the peripheral substance:--

----[Greek: ton de a)/xona mi/an theo/teta sunagogon men to=n ke/ntron tou= pantos sunektiken de tou= o(/lou ko/smou, _kinetiken de to=n thei/on periphoro=n_, peri e(n e( ch.o.r.ei/a** to=n o(/lon, peri e(n ai( a)nakukle/seis, a)ne/chousan ton o(/lon ou)ranon,**

e(n kai A)/tlanta dia tou=to proseire/kasin, o(s a)/trepton kai a)/truton e)ne/rgeian e)/chousan. kai me/ntoi kai to tetame/non** e)ndei/knutai** t.i.te/nion ei)=nai ten mi/an _tau/ten du/namin, ten phrouretiken te=s a)nakukle/seos to=n o(/lon_.]

Here Proklus recognises the efficacy of the axis in producing and maintaining the revolution of the Kosmos, but he does not remark that it initiates this movement by revolving itself. The [Greek: Theotes], which Proklus ascribes to the axis, is invested in the earth packed round it, by the Platonic Timaeus.]

Now the function which Plato ascribes to the earth in the pa.s.sage of the Timaeus before us is very a.n.a.logous to that which in the Republic he ascribes to Necessity--the active guardians.h.i.+p of the axis of the kosmos and the maintenance of its regular rotation.

With a view to the exercise of this function, the earth is planted in the centre of the axis, the very root of the kosmic soul (Plato, Timaeus, p. 34 B). It is even "packed close round the axis," in order to make sure that the axis shall not be displaced from its proper situation and direction. The earth is thus not merely active and influential, but is really the chief regulator of the march of the kosmos, being the immediate neighbour and auxiliary of the kosmic soul. Such a function is worthy of "the first and eldest of intra-kosmic deities," as Plato calls the earth. With perfect propriety he may say that the earth, in the exercise of such a function, "is guardian and artificer of day and night." This is noway inconsistent with that which he says in another pa.s.sage, that the revolutions of the outer sidereal sphere determine day and night. For these revolutions of the outer sidereal sphere depend upon the revolutions of the axis, which latter is kept in uniform position and movement by the earth grasping it round its centre and revolving with it. The earth does not determine days and nights by means of its own rotations, but by its continued influence upon the rotations of the kosmic axis, and (through this latter) upon those of the outer sidereal sphere.

It is important to attend to the circ.u.mstance last mentioned, and to understand in what sense Plato admitted a rotatory movement of the earth. In my judgment, the conception respecting the earth and its functions, as developed in the Platonic Timaeus, has not been considered with all its points taken together. One point among several, and that too the least important point, has been discussed as if it were the whole, because it falls in with the discussions of subsequent astronomy. Thus Plato admits the rotation of the earth, but he does not admit it as producing any effects, or as the primary function of the earth: it is only an indirect consequence of the position which the earth occupies in the discharge of its primary function--of keeping the cosmical axis steady, and maintaining the uniformity of its rotations. If the cosmical axis is to revolve, the earth, being closely packed and fastened round it, must revolve along with it. If the earth stood still, and resisted all rotation of its own, it would at the same time arrest the rotations of the cosmical axis, and of course those of the entire kosmos besides.

The above is the interpretation which I propose of the pa.s.sage in the Platonic Timaeus, and which I shall show to coincide with Aristotle's comment upon it. Messrs. Boeckh and Martin interpret differently. They do not advert to the sense in which Plato conceives the axis of the kosmos--not as an imaginary line, but as a solid revolving cylinder; and moreover they understand the function a.s.signed by the Platonic Timaeus to the earth in a way which I cannot admit. They suppose that the function a.s.signed to the earth is not to keep up and regularize, but to withstand and countervail, the rotation of the kosmos. M. Boeckh comments upon Gruppe, who had said (after Ideler) that when the earth is called [Greek: phu/laka _kai demiourgon_ nuktos kai e(me/ras], Plato must have meant to designate some active function ascribed to it, and not any function merely pa.s.sive or negative. I agree with Gruppe in this remark, and I have endeavoured to point out what this active function of the earth is, in the Platonic theory. But M. Boeckh (Untersuchungen, &c., p. 69-70) controverts Gruppe's remark, observing, first, that it is enough if the earth is in any way necessary to the production of the given effect; secondly, that if active force be required, the earth (in the Platonic theory) does exercise such, by its purely pa.s.sive resistance, which is in itself an energetic putting forth of power.

M. Boeckh's words are:--"Es kommt nur darauf an, da.s.s er ein Werk, eine Wirkung, hervorbringt oder zu einer Wirkung beitragt, die ohne ihn nicht ware: dann ist er durch seine Wirksamkeit ein Werkmeister der Sache, sey es auch ohne active Thatigkeit, durch bloss pa.s.siven Widerstand, der auch eine machtige Kraft-ausserung ist. Die Erde ist Werkmeisterin der Nacht und des Tages, wie Martin (b. ii. p. 88) sehr treffend sagt 'par son energique existence, c'est a dire, par son immobilite meme:' denn sie setzt der taglichen Bewegung des Himmels bestandig eine gleiche Kraft in entgegengesetzter Richtung entgegen. So _muss_ nach dem Zusammenhange ausgelegt werden: so meint es Platon klar und ohne Verhullungen: denn wenige Zeilen vorher hat er gesagt, Nacht und Tag, das heisst ein Sterntag oder Zeittag, sei ein Umlauf des Kreises des Selbigen--_das ist, eine tagliche Umkreisung des Himmels von Osten nach Westen, wodurch also die Erde in Stillstand versetzt ist:_ und diese tagliche Bewegung des Himmels hat er im vorhergehenden immer und immer gelehrt." ... . "Indem Platon die Erde nennt [Greek: ei(lome/nen], nicht [Greek: peri ton e(aute=s po/lon], sondern [Greek: peri ton dia pantos po/lon tetame/non], setzt er also die tagliche Bewegung des Himmels voraus" (p. 70-71).[2]

[Footnote 2: "We are only required to show, that the Earth produces a work or an effect,--or contributes to an effect which would not exist without such help: the Earth is then, through such operation, an _Artificer_ of what is produced, even without any positive activity, by its simply pa.s.sive resistance, which indeed is in itself a powerful exercise of force.**

The Earth is Artificer of night and day, according to the striking expression of Martin, 'par son energique existence, c'est-a-dire, par son immobilite meme:' for the Earth opposes, to the diurnal movement of the Heavens, a constant and equal force in the opposite direction. This explanation _must_ be the true one required by the context: this is Plato's meaning, plainly and without disguise: for he has said, a few lines before, that Night and Day (that is, a sidereal day, or day of time) is a diurnal revolution of the Heaven from East to West, whereby accordingly the Earth is a.s.sumed as at rest: And this diurnal movement of the Heaven he has taught over and over again in the preceding part of his discourse."--"Since therefore Plato calls the Earth [Greek: ei(lome/nen], not [Greek: peri ton e(aute=s po/lon], but [Greek: peri ton dia pantos po/lon tetame/non], he implies thereby the diurnal movement of the Heaven."]

I not only admit but put it in the front of my own case, that Plato in the Timaeus a.s.sumes the diurnal movement of the celestial sphere; but I contend that he also a.s.sumes the diurnal rotation of the earth. M. Boeckh founds his contrary interpretation upon the unquestionable truth that these two a.s.sumptions are inconsistent; and upon the inference that because the two cannot stand together in fact, therefore they cannot have stood together in the mind of Plato. In that inference I have already stated that I cannot acquiesce.

But while M. Boeckh takes so much pains to vindicate Plato from one contradiction, he unconsciously involves Plato in another contradiction, for which, in my judgment, there is no foundation whatever. M. Boeckh affirms that the function of the earth (in the Platonic Timaeus) is to put forth a great force of pa.s.sive resistance--"to oppose constantly, against the diurnal movement of the heavens, an equal force in an opposite direction." Is it not plain, upon this supposition, that the kosmos would come to a standstill, and that its rotation would cease altogether? As the earth is packed close or fastened round the cosmical axis, so, if the axis endeavours to revolve with a given force, and the earth resists with equal force, the effect will be that the two forces will destroy one another, and that neither the earth nor the axis will move at all. There would be the same nullifying antagonism as if,--reverting to the a.n.a.logous case of the spindle and the verticilli (already alluded to) in the tenth book of the Republic,--as if, while Ananke turned the spindle with a given force in one direction, Klotho (instead of lending a.s.sistance) were to apply her hand to the outermost verticillus with equal force of resistance in the opposite direction (see Reipubl. x. p.

617 D). It is plain that the spindle would never turn at all.

Here, then, is a grave contradiction attaching to the view of Boeckh and Martin as to the function of the earth. They have not, in my judgment, sufficiently investigated the manner in which Plato represents to himself the cosmical axis: nor have they fully appreciated what is affirmed or implied in the debated word [Greek: ei(lo/menon--ei(lou/menon--i)llo/menon]. That word has been explained partly by Ruhnken in his notes on Timaei Lexicon, but still more by b.u.t.tmann in his Lexilogus, so accurately and copiously as to leave nothing further wanting. I accept fully the explanation given by b.u.t.tmann, and have followed it throughout this article. After going over many other examples, b.u.t.tmann comes to consider this pa.s.sage of the Platonic Timaeus; and he explains the word [Greek: ei(lome/nen] or [Greek: i)llo/menen] as meaning--"_sich drangen oder gedrangt werden_ um die Axe: d. h.

von allen Seiten her an die Axe. Auch la.s.se man sich das Praesens nicht irren: die Krafte, welche den Weltbau machen und zusammen halten, sind als fortdauernd thatig gedacht. Die Erde drangt sich (ununterbrochen) an den Pol, _macht, bildet eine Kugel um ihn_. Welcher Gebrauch vollig entspricht dem wonach da.s.selbe Verb.u.m ein _einwickeln_, _einhullen_, bedeutet. Auch hier mengt sich in der Vorstellung einiges hinzu, was auf ein _biegen_ _winden_, und mitunter auf ein _drehen_ fuhrt: was aber _uberall nur ein durch die Sache selbst hinzutretender Begriff ist_," p. 151. And again, p. 154, he gives the result--that the word has only "die Bedeutung _drangen_, _befestigen_, nebst den davon ausgehenden--die von _drehen_, _winden_, aber ihm _ganzlich fremd_ sind, _und nur aus der Natur der Gegenstande in einigen Fallen als Nebengedanken hinzutreten_."[3]

[Footnote 3: "To _pack itself_, or to _be packed_, round the axis: that is, upon the axis from all sides. We must not be misled by the present tense: for the forces, which compose and hold together the structure of the universe, are conceived as continuously in active operation. The Earth _packs itself_, or _is packed_, on to the axis--_makes or forms a ball round the axis:_ which corresponds fully to that other usage of the word, in the sense of _wrapping up_ or _swathing round_. Here too there is a superadded something blended with the idea, which conducts us to _turning_, _winding_, and thus to _revolving_: but this is every where nothing more than an accessory notion, suggested by the circ.u.mstances of the case. The word has only the meaning, to _pack_, to _fasten_--the senses, to _wind_, to _revolve_, are altogether foreign to it, and can only be superadded as accessory ideas, in certain particular instances, by the special nature of the case."]