1. The History of the “Mixed Aorist” Problem
The “mixed aorist” forms have been a subject for scholarly dispute as long as Homeric scholarship has existed. Aristarchus considered the problem of determining the correct spelling. At K 513, the scholia of Venetus A tell us that Aristarchus read ἐπεβήσετο but others ἐπεβήσατο. At Γ 262, Aristarchus preferred βήσετο, but refrained from altering the text, which had βήσατο: προκρίνει μὲν τὴν διὰ τοῦ ε γραφήν βήσετο, πλὴν οὐ μετατίθησιν, ἀλλὰ διὰ τοῦ α γράφει ὁ Ἀρίσταρχος. From these statements we see that the lectio facilior , having the appearance of an ordinary sigmatic aorist, had already become widespread in the manuscripts, but that enough philological information was still available to validate the thematic forms.
From the Roman period we have evidence of controversy over the interpretation of the forms. The generally accepted theory was that the future was transferred to the function of the present (μετάγεται εἰς ἐνεστῶτα uel sim.), and that from this present tense were formed an imperfect and an imperative (scholia on A 496, β 388, δ 1). In particular, Herodian held this view (Lentz 1.447): τὸ δὲ οἴσω, οὗ τὸ προστακτικὸν “οἶσε θέειον γρηῦ” (χ 481), “οἴσετε πῦρ” (Ω 718) καὶ δύσω, οὗ ὁ παρατατικὸς “ἐδύσετο” (β 388) καὶ βήσω κατὰ ποιητικὴν ἄδειαν μετηνέχθη ἀπὸ μέλλοντος εἰς ἐνεστῶτα. But οἴσω, of which the imperative is οἶσε θέειον γρηῦ, οἴσετε πῦρ, and δύσω, of which the imperative is ἐδύσετο, and βήσω, were transferred by poetic license from the future to the present.
In the case of ἷξον (δ 1 etc.), the Etymologicum Magnum (472, 10-25) attests a disagreement between Herodian and his father Apollonius:
‘Απολλώνιος ἀπὸ τοῦ ἵκω, τοῦ διὰ τοῦ ι γραφομένου, λέγει, ὁ δεύτερος ἀόριστος, ἷκον, καὶ τροπῇ Βοιωτικῇ τοῦ κ εἰς ξ, ἷξον. ὁ δὲ Ἡρωδιανὸς τοῦτο καὶ τὰ ὅμοια ἐκ μέλλοντος λέγει μετατεθεῖσθαι εἰς ἐνεστῶτα. ἵξω, καὶ ὁ παρατατικός, ἷξον, ἷξες, ἷξε· τὸ πληθυντικόν, ἵξοηεν, ἵξετε, ἷξον. ὅτι δὲ οὐκ ἔστι δεύτερος ἀόριστος, ἀλλὰ παρατατικός, τὰ τοιαῦτα ἐλέγχει καὶ τὰ προστακτικά. εὑρήςεις γὰρ βῆσε, καὶ ἷξε, καὶ οἶσε, ὡς τύπτε καὶ γράφε. εἰ δὲ ἧν ἀόριστος, ἧν ἂν βῆσον, καὶ ἷξον. ἔστι δὲ οἴσω μέλλων· οὗ ἄλλο κίνημα οὐχ εὔρηται πλὴν τοὺ αὐτοῦ μέλλοντος. τὸν δὲ ‘Απολλωνίου λόγον δέον εἶναι μᾶλλον ἀληθέστερον· οὐ γὰρ παράτασιν σημαίνει τὸ, “οἱ δ’ ἷξον,” ᾿αλλὰ συντέλειαν, ὅτι παραγεγόνασιν. οὐ γὰρ ταῖς φωναῖς τὰ μέρη τοῦ λόγου ἀκολουθεῖ, ᾿αλλὰ τοῖς σημαινομένοις.
Apollonius says (that ἷξον is) from ἵκω, the one written with iota (as distinct from ἥκω). The second aorist is (*)ἷκον, and by a Boeotian change of κ to ξ, ἷξον (supposedly as in εἴξασι and ἤνειξα  ). But Herodian says that this form and those like it are transferred from the future to the present: ἵξω (but the future is regularly middle, ἵξομαι) and the imperfect (*)ἷξον, ἷξες, ἷξε; the plural (*)ἵξομεν, (*)ἵξετε, ἷξον. That such forms are not second ( sic ) aorist but imperfect, the imperatives also prove: for you will find (*)βῆσε and (*)ἷξε and οἶσε, like τύπτε and γράφε; but if they were aorist, they would be βῆσον and ἷξον. But οἴσω is a future, from which no other inflexion is found than the future itself. But Apollonius’ opinion must be truer; for οἱ δ’ ἷξον does not indicate continuity but fulfillment, “they arrived.” For the parts of speech depend not on sounds but on meanings. The note concludes with a valid principle for synchronic grammatical analysis. The course of the argument, however, is obviously confused. We can hardly believe that Herodian cited βῆσον and ἷξον as hypothetical second aorist imperatives. Whether he found imperatives βῆσε and ἷξε attested anywhere we do not know. The two scholars seem to have misunderstood each other: Apollonius says ἷξον is a second aorist, and Herodian replies that it is not a first aorist (but instead comes from the future). Probably the debate has lost something in transmission. In any case, we see that the two possible derivations of the “mixed aorists” are represented already in antiquity: Apollonius makes a connection with the aorist; Herodian, with the future. These have remained the alternatives throughout the history of the question, though with certain variations. For one thing, the ancient grammarians think of the forms as second aorists where the s needs to be explained, whereas later grammarians have counted them as first aorists where the thematic vowel needs to be explained. For Greeks, the essential characteristic of the first aorist was evidently the alpha and not the sigma (consider such diverse “first aorists” as ἔθηκα and ἔμεινα).  a Moreover, the two alternatives may approach each other, depending on the relation assumed between the future indicative and the subjunctive of the sigmatic aorist. To discuss in general the nature of this relation is beyond the scope of this thesis, but certain particular cases will be treated.
From the Roman period we take up the history of the problem again in the Renaissance. Early printed editions followed uncritically whatever manuscripts came to hand. As a result, the readings with alpha were the vulgate through the eighteenth century. The first step toward an informed treatment of the subject was the publication in 1788 of an edition of the Iliad, based on the manuscript Venetus A (Marcianus 454), and including the editio princeps of the scholia of Venetus A and B, by Joh. Baptista Caspar d’Ansse de Villoison. This event made the ancient grammarians’ knowledge available. In his text, Villoison followed A, reading for example at A 496 ἀνεδύσατο, but B 35 άπεβήσετο, and θ 505 ἄξασθε, θ 545 ἄξαντο. C. G. Heyne (l802) accepted the same variation in spellings, choosing alpha or epsilon after consideration of the merits of a particular case; e.g. whether the sense required was imperfect or aorist (note on A 496), or which looked like the older form (note on B 35). At θ 505 he read ἄξασθε, but in his note he quoted the scholion on the verse and added, “debuit ergo legere ἄξασθε.” From the middle of the nineteenth century, the thematic forms were generally accepted, e.g. in the editions of I. Bekker (l843) and J. La Roche (l870). Bekker also reedited the scholia (l825).
Not only the texts but also the grammars of the nineteenth century show knowledge of the ancient grammarians, e.g. F. Thiersch (l826), C. A. Lobeck (supplements to Buttmann’s grammar, l839), H. L. Ahrens (l839). The grammarians of this period usually list the “mixed aorist” forms as irregular first aorists. An exception is R. Kühner, who mentions them under the heading of Aorist II, saying that they present a substitution of endings of the second aorist for those of the first.  The origin of the label “mixed aorist” is unclear: A. von Bamberg (1885, first edition 1874) refers to die sogenannten gemischten Aoriste;  J. van Leeuwen and M. B. Mendes da Costa speak of gemischte Aoriste (1886, from the Dutch of 1883). 
The next new development to affect discussion of the “mixed aorists” was the introduction of comparative philology, consequent upon the discovery of Sanskrit by western scholars in the late eighteenth century. Classical philologists were slow to accept the idea that evidence from another realm might be useful to them; but when they did realize the value of Indo-European studies, they tended to forget the importance of the ancient Greek grammarians. After G. Curtius (1880) and D. B. Monro (1882), who show an overlap between the study of comparative philology and the awareness of ancient testimony, Herodian and the Homeric scholia are virtually ignored. P. Wahrmann (l926) refers to “den älteren Grammatiken” meaning Kühner-Blass and Brugmann. 
The use of comparative material led scholars in more than one direction. Curtius, who is credited with introducing comparative grammar and classical philology to each other,  made an attempt to treat the “mixed aorists.” Assuming that the sigmatic aorist was a common Indo-European inheritance, and that it must have had corresponding primary forms (properly with a , but attested only with e/o as in ἀλέξομαι: ἀλέξασθαι), he interpreted λέξεο, βήσετο, δύσετο as derivatives of such sigmatic Primaria.  Curtius did not compare the Greek forms directly with Sanskrit forms. This phase appears in the works of Brugmann (l892) and (with qualifications) Wackernagel (l897): the Vedic thematic imperatives of the sigmatic aorist (nesa, parsa , rasatam ) immediately reminded these scholars of the Homeric imperatives like οἶσε and caused them to posit an Indo-European class of such imperatives. Together with the corresponding short-vowel subjunctives, these imperatives would originally have been injunctive forms. 
An alternative comparison could be made with the secondary future or conditional tense, attested in Sanskrit and Old Irish; this connection was made by V. Magnien (1912).  Of course the resemblence to the future was already evident, from an internal Greek viewpoint, to the ancient grammarians, and was again mentioned by G. Mahlow (1883).  0
Both of these comparisons between Greek and Sanskrit forms are vitiated by insufficient attention to their histories within the respective languages. If the forms are innovations in each language, they do not bear witness to an inherited Indo-European category. Therefore, the next stage in the study of the “mixed aorists” depended on a subtler philological treatment of the Homeric evidence (as also of the Vedic).  0a Already in the eighteenth century, Richard Bentley had demonstrated how the Homeric text could be made to yield linguistic-historical data when he discovered the traces of the digamma. In the first half of the twentieth century, an appreciation of the artificiality of the Homeric dialect was gradually developed; K. Meister in his Die homerische Kunstsprache (1921) showed (for instance) that artificial inflexional forms could be created within the epic language.  1 A. Debrunner (l922) applied this kind of insight to ἄξοντο (Θ 545), demonstrating that it was derived within the epic from the imperative ἄξεσθε (Θ 505)  2 Wahrmann (l926) showed how the “mixed aorists” spread in the epic language and tried to explain them all as artificial creations for metrical convenience.  3 The work of Milman Parry, who saw that the formulaic quality of the Homeric language is a characteristic of oral poetry, put the notion of “metrical convenience” in a new light. Innovations in the epic had to be seen not as arbitrary inventions but as part of a process of growth and adaptation in the formula system. Manu Leumann (l950) showed that odd words in Homer could often be explained by the derivation of one formula from an older formula misunderstood. Often the older formula was preserved alongside the derived formula, and in such cases both chronological levels could be observed in the extant Homeric text. Leumann (l953) applied Debrunner’s explanation of ἄξοντο to the other “mixed aorist” forms, deriving them (except ἷξον) from imperatives which originated as imperatival futures.  4 Trying to give a more thorough explanation than Wahrmann’s, he imposed one mold on a heterogeneous collection of material. The need for separate treatment of the various forms was recognized (after Wackernagel) by E. Schwyzer in his Griechische Grammatik (1939)  5 and by P. Chantraine in his Grammaire homerique (1948).  6 As the latter says, citing the former, “Les formes ne se trouvent pas toutes sur le même plan et ne doivent pas être envisagées en bloc.”  7
The method which will be used in this investigation depends on certain convictions about the nature of the Homeric language, derived from the work of such scholars as Milman Parry, Manu Leumann, Jerzy Kuryłowicz, Calvert Watkins, and Gregory Nagy. The epic language changed with time, as all languages do. Furthermore, the changes were not arbitrary, but followed much the same rules as do the changes in a natural language. One may refer in particular to the formulation by Kuryłowicz in his article “La nature des procès dits ‘analogiques.’”  8 In the epic, as distinct from a natural language, a special constraint was applied by the dactylic meter. Hence established formulae which fit the meter continued to be used even when the forms they contained lacked synchronic motivation. In order to say something new, a poet could create new expressions by analogy with those which already existed, using the rules of his natural language. In a few cases, like that of enallage,  8a there may have been special rules operating in the poetic but not in the natural language. Still, it must be emphasized that analogical processes did not operate arbitrarily in the epic language any more than they do in natural languages. Metri gratia is not a sufficient explanation of Homeric abnormalities. What is peculiar about the epic language is that it was no one’s native speech, but always a language to be imitated.  9 There was therefore no one who could set any definite limit to analogical development. As a result, one may find some quite remarkable innovations side by side with the most extreme archaisms. The wide chronological range represented often makes it possible to reconstruct the life history of a word and so to elucidate the analogical processes at work. In the course of this reconstruction clues can be obtained from the contexts of a word, both in Homer and in later Greek poetry, and from its metrical treatment in the hexameter. Comparative Indo-European evidence is also useful, more often to show a parallel innovation than to prove a common inheritance. In the following chapters, an effort will be made not to neglect any type of evidence which may help to solve the problems of the “mixed aorists.”