the moment of conscious perception, object and organ are qualified alike), combined with the statement ý ỏσμì кaπvúdns Tís ¿otiv ȧvalvμíaois. In ch. v. (443a, 21, seqq.) this statement is sharply criticised, if not, as Baeumker thinks, altogether rejected. Neuhaeuser, however, disagrees with him. Of the statement in question the latter says:'Indessen wird sich zeigen, dass sie mit einer gewissen Modification auch von der eigenen Meinung des Aristoteles. nicht gar zu weit absteht' (Aristoteles' Lehre, &c., p. 22). I cannot now reproduce Neuhaeuser's reasons for this assertion, and, as I think it needless to add to them, I must be content to refer my reader to his pages. It is to be observed that in ch. v. we find Aristotle implicitly repeating the assertion here made of the association between ὄσφρησις and πῦρ. For in 444, 24 we read:—ἡ γὰρ τῆς ὀσμῆς δύναμις θερμὴ τὴν φύσιν ἐστί.

On the whole, as Alexander evidently read si before dɛī, this is probably correct, but we must not, with Baeumker and Neuhaeuser treat this particle as indicating that Aristotle argues, from premisses not his own, for a conclusion with which he does not agree. There should then be a comma, instead of a full stop, after σroxεiwv. 438b, 23:

ὥσθ ̓ ὑπάρχειν ἀνάγκη αὐτὴν τὴν αἴσθησιν] δυνάμει πρότερον.

It appears that the 8 of two MSS., before duváμɛ, must be accepted. The required sense is not that 'alo@nois must exist potentially before it exists actually' (though this is true), but that it must, from the first, possess the quality which exists potentially prior to the moment of perception.' For as the actualized alo@nois possesses the actual quality of its αἰσθητόν, so the potential αἴσθησις (τὸ ὀσφραντικόν) possesses the potential quality of the aio@nróv, which is prior to the actual. Hence, δυνάμει θερμὸν τὸ ὀσφραντικόν.

439, 25, seqq. :

Ἔστι μὲν οὖν οὕτως ὑπολαβεῖν πλείους εἶναι χρόας παρὰ τὸ λευκὸν καὶ τὸ μέλαν, πολλὰς δὲ τῷ λόγῳ· τρία γὰρ πρὸς δύο, καὶ τρία πρὸς τέτταρα, καὶ κατ ̓ ἄλλους ἀριθμοὺς ἔστι παρ ̓ ἄλληλα κεῖσθαι, τὰ δὲ ὅλως κατὰ μὲν λογὸν μηδένα, καθ ̓ ὑπεροχὴν δέ τινα καὶ ἔλλειψιν ἀσύμμετρον, καὶ τὸν αὐτὸν δὴ τρόπον ἔχειν ταῦτα ταῖς συμφωνίαις. τὰ μὲν γὰρ

ἐν ἀριθμοῖς εὐλογίστοις χρώματα, καθάπερ ἐκεῖ τὰς συμφωνίας, τὰ · ἥδιστα τῶν χρωμάτων εἶναι δοκοῦντα, οἷον τὸ ἁλουργὸν καὶ φοινικούν καὶ ὀλίγ ̓ ἅττα τοιαῦτα, δι' ἥνπερ αἰτίαν καὶ αἱ συμφωνίαι ὀλίγαι, τὰ δὲ μὴ ἐν ἀριθμοῖς τἆλλα χρώματα, ἢ καὶ πάσας τὰς χρόας ἐν ἀριθμοῖς εἶναι, τὰς μὲν τεταγμένας, τὰς δὲ ἀτάκτους καὶ αὐτὰς ταύτας, ὁτὰν μὴ καθαραὶ ὦσι, δια τὸ μὴ ἐν ἀριθμοῖς εἶναι τοιαύτας γίνεσθαι.

Here Aristotle states what he considers a possible theory of the origin of different colours from the primary black and white, by the juxtaposition in varying proportions of invisibly small blacks and whites; and he illustrates this by the theory of the combination of sounds; conjecturing, further, that the production of pleasing colours may be analogous to that of pleasing chords, as based upon, or involving, numerically definite ratios between the components in both cases. 'Or (he concludes) we may conceive all the various colours as involving numerical ratios between their component blacks and whites, some, however, determinate in ratio and some indeterminate, and suppose that colours, when they are not καθαραί, derive this quality (τοιαύτας γίνεσθαι) from their not involving numerical ratios.' Here there is a contradiction: for the hypothesis is that all colours really involve such ratios, only that while some are τεταγμέναι, others are ἄτακτοι. We must read τοιούτοις before τοιαύτας. The χρόαι are not καθαραί, when the ἀριθμοί which they involve are not καθαροί, i.e. not definitely calculable. Aristotle's meaning may be stated at length as follows:It occurs to him that all combinations whatever of blacks

and whites must involve in each case a certain number of whites and a certain number of blacks. But, as he goes on to say, if the colours resulting from the combinations are to be pleasing, the numbers they involve must be calculable, or capable of being numerically defined. In Acoustics every combination of sounds involves the composition of certain vibration frequencies: of this there can be no doubt but only in comparatively few cases are the proportions between the combined elements calculable, and only in these cases is the result pleasing. Thus, in the octave the ovμpwvía is the product of a pwvý involving vibration-frequencies of n per second combined with another pwvý involving those of 2n per second. Now when the numbers which form the terms of a λóyos or proportion can be thus definitely stated, they are said to be Kalapoί to be cleared up. When a bank account is balanced, i.e. when the arithmetical relation between the credit and the debit sides has been determined, this account is said to be exactly calculable or calculated— the proper expression being καθαραὶ αἱ ψήφοι (cf. Dem. 303). Similarly here when the ratio of the blacks and whites (which, doubtless, has always at its basis certain numerical totals) is such as can be determinately formulated (as in musical chords), the numbers involved are кalapoí (or clear), and their representative colour also is кaðapóv

1 In this passage Dr. Blass (whom I mention with all the honour due to such a scholar) readsἂν καθαιρῶσιν αἱ ψῆφοι κἂν μηδὲν περιῇ. But the sense, at least, of the formerly accepted by καθαραὶ ὦσιν αἱ ψῆφοι is beyond question, viz., 'Just as... whenever you proceed to a λoyouós, if the account has been balanced, and nothing found to his credit, &c.' The KalaρEιÓTηs consists not in the fact of the opposite amounts cancelling (àvraveλeîv)

one another, which they may or may not do, but in the fact that the state of the figures on both sides is arithmetically clear, this 'clearness' being the condicio sine qua non of the λογισμός. The tense of kalaιρŵσ is against it: we want an aorist, as in the corresponding phrase of Aeschines, émeidàv ὁ λογισμὸς συγκεφαλαιωθῇ; and ὦσιν in the old reading is virtually an aorist. So too is repin, its co-ordinate.

(or pure). It is not necessary to ask whether Aristotle had actually calculated the components of any colours. He had not: but he had a strong faith in the analogy (in whatever terms expressed) between the spectrum and the scale. On this faith in the possibility of a calculation not yet made, his present hypothesis is based. He therefore speaks of certain colour-ratios as calculable in contradistinction to others which are not so, neglecting or forgetting that no ratios in the composition of colours-whether agreeable or not—had as yet been definitely made out: that no one had done for the spectrum what Pythagoras did for the scale. The propriety of reading τοιούτοις, to go with ἀριθμοῖς, is manifest from the above considerations, while the need of emendation is equally manifest from the fact that the received text makes the sentence self-contradictory. How easily TOLOÚTOs may have been lost before Tolaúraç is obvious. Alexander's text contains no positive evidence that he read τοιούτοις. His interpretation of μὴ καθαραί seems incorrect. He explains thus:— By μὴ καθαραί Aristotle must mean juxtapositions of dissimilars (un ὁμοίων). For the resultants would be kalapá if, for example, in the whole mixture-process, side by side with every two parts (of e.g. black) one part (of white) were placed; but not кaðapá if, in the course of one and the same mixture-process, we had one part of one opposite sometimes juxtaposed with two parts of the other, sometimes with three parts of the other, and sometimes with one.' Thus, he thinks, the impure colour would result from the combination, or juxtaposition, in the same colour of dissimilar, but still definite, ratios. If this were so, no doubt the difficulty of calculating the general ratio between the separately invisible blacks and whites would be increased: but its calculableness would appear to be established. Aristotle's point, however, is that the numbers which underlie the colours called impure-the

numbers of the particles of black and white, respectively, which enter into each such colour, and therefore the ratio of these numbers to one another, cannot ever be definitely made out. Similarly one might say a noise is an 'impure' sound, as being (unlike a ovμpwvía) representative of no calculable ratio. There is doubtless, or would be from the Creator's point of view, some numerical ratio to express the relation between the diáμerpoç and the Tλεupά of a square, but this ratio is for human reason incapable of determinate arithmetical expression: it is an ἄλογος λόγος. Now if φύσις had mixed blacks and whites in a ratio equal to that between the diagonal and the side of a square, the resulting colour would be in this sense v ἀριθμοῖς, but the ἀριθμοί would not be καθαροί, and the colour would not belong to the class called καθαραί χρόαι. The qualitative impurity of the colour-another form of expression for its andía-would be the sensible correlative of its numerical

impurity'-of the fact that it baffles men's powers of arithmetical analysis.

ồn

443, 26 seqq. Aristotle has distinguished two on of odours. The first sidoç depends for its agreeable or disagreeable qualities on its association with the taste of food: when we are hungry we find the smell of food agreeable: when we have satisfied our hunger the same smell is not agreeable, or is positively disagreeable. The second sidos consists of odours agreeable or disagreeable per se. He goes on:

Αἱ δὲ καθ ̓ αὑτὰς ἡδεῖαι τῶν ὀσμῶν εἰσίν, οἷον αἱ τῶν ἀνθῶν· οὐδὲν γὰρ μᾶλλον οὐδ ̓ ἧττον πρὸς τὴν τροφὴν παρακαλοῦσιν, οὐδὲ συμβάλλεται (leg. συμβάλλονται) πρὸς ἐπιθυμίαν οὐδέν, ἀλλὰ τοὐναντίον μᾶλλον· ἀληθὲς γὰρ ὅπερ Εὐριπίδην σκώπτων εἶπε Στράττις [Phoen. 1.]

ὁτὰν φακὴν ἕψητε μὴ ἐπιχεῖν μύρον.

He condemns a practice which had come into vogue of seasoning meats with odours of the latter class: Biálovrai