direction, each by a movement of its own--are overpowered and carried along with the outer sphere, though the time of revolution, in the case of each, is more or less modified by its own inherent counter-moving force.[35] [Footnote 32: Plat. Tim. p. 31 B. [Greek: ei(=s o(/de monogenê\s ou)rano/s], &c.] [Footnote 33: Plat. Tim. p. 35 A. [Greek: Tau)to\n--to\ a)me/riston--tha/teron--to\ meristo\n--tri/ton e)x a)mphoi=n ou)si/as ei)=dos.]] [Footnote 34: Plato, Timæus, pp. 35-36. The pains which were taken by commentators in antiquity to expound and interpret this numerical scale may be seen especially illustrated in Plutarch's Treatise, De Animæ Procreatione in Timæo, pp. 1012-1030, and the Epitome which follows it. There were two fundamental [Greek: tetraktu/es] or quaternions, one on a binary, the other on a ternary scale of progression, which were arranged by Krantor (Plutarch, p. 1027 E) in the form of the letter [Greek: L], as given in Macrobius (Somn. Scip. i. 6, p. 35). The intervals between these figures, are described by Plato as filled up by intervening harmonic fractions, so as to constitute an harmonic or musical diagram or scale of four octaves and a major sixth. (Boeckh's Untersuch. p. 19.) M. Boeckh has expounded this at length in his Dissertation, Ueber die Bildung der Welt-Seele im Timäos. Other expositors after him. 1 /\ / \ 2_/_ _\_3 / \ 4 _/_ _\_9 / \ ------ ------ 8 27 ] [Footnote 35: Plato, Timæus, p. 36 C. [Greek: tê\n me\n ou)=n e)/xô phora\n e)pephê/misen ei)=nai tê=s tau)tou= phu/seôs, tê\n d' e)nto/s, tê=s tha)te/rou. tê\n me\n dê\ tau)tou= kata\ pleura\n e)pi\ dexia\ periê/gage, tê\n de\ thate/rou kata\ dia/metron e)p' a)ristera/.] For the meaning of [Greek: kata\ pleura\n] and [Greek: kata\ dia/metron], referring to the equator and the ecliptic, see the explanation and diagram in Boeckh, Untersuchungen, p. 25, also in the note of Stallbaum. The allusion in Plato to the letter [Greek: chi=] is hardly intelligible without both a commentary and a diagram.]