Andrew Eastbourne has kindly translated for us all the section on December from John the Lydian, De Mensibus, book 4. The hand-written copy which alone preserves this work is, unfortunately, badly damaged in this section, leading to various restorations and gaps.
153. December was so named as being itself the tenth [month] from March.
154. …with harmony having been divided……everything and it is guarded……<the> experience of <Phaeth>on and  the actions of the <wat>er <at the time of Deucali>on <h>int at <a certain image> of th<e passions that> have <become apparent in t>he universe. <But the Phoeni>cians have<a> somewhat different opinion about Cronus, by w<ay o>f homonymy, <or in accordance with> a certain a<llegor>y, as <one can determi>ne <from th>e second [book] of Phoenician [History] of Herennius Philo. And the history tea<ch>es that he also reigned o<ver> Libya <and> Sicily <and the western re>gions, <as> I related <earl>ier, and that he founded a city, as Charax says—t<he one then ca>lled Cronia, but now Hierapolis, as Isigonus <On the Pal>ic Gods and Polemo and Aeschylus in his Aetna ha<ve taught, or as> Euhemerus’ <whol>e history, adorn<ed> with details, [says], setting o<ut cleverly> his spec<ulations> about the so-called gods……hides <away>…<of al>l sor<ts>…divine; <so that also> P…… says <f>in<ely in h>is [work] On Dionysus that the <just among ki>ng<s and pri>ests were honored by <the> gods thems<elves> with equal honors and titles and thus <were called gods> in a <myth>ical manner, while the history <has b>een transmitted <in a> fic<tionalized form>.
But there are some who  say that Cron<us—or, b>y a ch<ange of letter, Ch>ronus ["time"]—was the child of Uranus ["sky / heavens"]; for indeed, time derives from the <movem>ent of the heavens. And in his temple, as Phyl<archus says in the> 17th [book] and Menander in <the> 1st [book], no woman or <dog o>r fl<y> would enter.
Such thin<gs, th>en, have <been said> by “those outside”;
And Cronus <indeed>, being fourth, <both> receives the scepter of his father <by force> and hands it on to his <child> under <comp>ulsion, according to the outward appea<rance> of the myth. And the myth-writers  appear to have taken the cause of <this sor>t of verbal elaboration from the particular character<istics of the g>od. For he is the leader of the Titan<ic> or<der>, on account of his separative [faculty] and <the> highest of intel<lectual> [entities], among which difference shone forth—and for this reason <they say that he> both receive<s> and gives kingship, as <the power> that struggles in a warlike and <forcible> manner <to add> the second things to the fir<st>. For the ge<nus> of difference is truly ill-dispo<sed and> anti-social, <as> Plato says. Hence indeed <the son is said> to separate <himself> from the father, and <the s>on [is said] to seize his <rule in turn>,  <for>cing <the> harmony <toward> both on account of the particular Titan<ic> nature.
Such things he too wrote in his <ex>planation of the sacred m<yths>.
At the new moon  of the month, they would refr<ain from [eating] cab>bage and would <pr>ay to Poseidon and Aphrodite and Amphitrite, <and> f<urthermore the> powers [would pray] to Cronus on behalf of <the> coming winter—<and> lik<ewise> also to Tyche [i.e., Fortune] the Overseer, to Sophrosyne ["moderation / self-control"], and to Eros, whom the myth-writers consider to be the child of Z<ephyrus the gi>ant, as Eurytus the Laced<aemonian l>yric poet says. He begins thus: “Eros, of delightful appearance.” And Plato in the Symposium says that at the birth of Aphrodite, Penia ["poverty"] came up and plotted in secret against Porus ["resources"], who was drunk on nectar, and in this manner Eros was conceived. O<n this basis> the great Moses speaks allegorically about the generation of mankind.
On this day, Varro says that the Hyades set and [it is] w<inte>r from this point on.
155. On the next day, Eudoxus predicts the rising of Sagittarius, and the winter / storm.
And they would also celebrate the festival called Agonalia  in honor of Helios Daphnêphoros and Genarchês, just as at Athens the rites at the Daphnephoria [were celebrated]. On this [day] also the festival <they> called <“Septi>mundius” was celebrated—that is, the circuit around  the ci<ty, since> the walls of Rome were spread <over seven h>ills. <And> the name<s> of the<se> are: <Pa>latium, Esquilium, Tarpeium, Aventinum, Tibu<rtium, Pra>en<es>tium, Viminalium. But <among> the ancients, [they were named] differently, as follows: Aven<t>inus, Caelius, <Esq>uilius, Capitolinus, Velinensius, Qui<rina>lius, Pala<tinus>.
156. On the third day before the Nones of Decem<ber> is a <day> without work, on which Euc<te>mon s<ays> the Dog [i.e., Canis Major] rises and <the wint>er be<gi>ns.
And a chariot-race was held, at which abom<inable [?]>…
157. The dipundii, meaning “new soldiers,” whom the Italians also call tirones from the fact that they serve because of their need for sustenance.  And they called them dipundii from their having been recently summoned to military service; for [it is] not [the case]…and they called them <dipun>dii from the fact that they endured military service, and were content with [wages of] just two coins—for the Romans customarily called two obols a dipundius.
158. The Romans customarily divided their citizenry into three [groups] and distinguished those who were suitable for arms, those [who were suitable] for farming, and those [who were suitable] for hunting; and the season of winter brings an end to these [pursuits]. For in it, neither do they arm themselves, nor do they practice farming, because of the season’s cold and the shortness of the days—and hence in the old days they named it bruma, meaning “short day.” And Brumalia means “winter festivals”;  so at that time, until the Waxing of the Light, ceasing from work, the Romans would greet each other with words of good omen at night, saying in their ancestral tongue, “Vives annos“—that is, “Live for years.” And the farming people would slaughter pigs for the worship of Cronus and Demeter—and hence even now the “Pig-Slaughter” is observed in December. And the vine-dressers would sacrifice goats in honor of Dionysus—for the goat is an enemy of the vine; and they would skin them, fill the skin-bags with air and jump on them. And the civic officials would also [offer as] the firstfruits of the collected harvest wine and olive oil, grain and honey and as many [products] of trees as endure and are preserved—they would make loaves without water and they would bring [all] these things to the priests of the [Great] Mother. And this sort of custom is still observed even now; and in November and December, until the “Waxing of the Light,” they bring [these] things to the priests. For the [custom] of greeting [people] by name at the Brumalia is rather recent; and, the truth [is], they call them “Cronian festivals”—and because of this the Church turns away from them. And they take place at night, because Cronus is in darkness, having been sent to Tartarus by Zeus—and they mysteriously signify the grain, from its being sown in the ground and thereafter not being seen. And this is quite true, as has been said: The attention to [these] things goes on at night, such that finally, in truth, the Brumalia are festivals of the subterranean daemones.
159. The natural [philosophers] say that at one time, before the “setting in order,” this universe was formless  matter—and hence the philosophers call matter Hades and Tartarus—in that it is disturbed [tarattomenên] and unstable by nature on account of its formlessness. And [they say] it is timeless, but not without a beginning, and nonetheless [it is] originated and caused; from eternity waiting for the empowerment of <the> Father himself, having received by his will an existence that is wholly timeless. Hence, the Chaldaean names matter “Father-originated” in the Oracles; and it is worth hearing how Iamblichus speaks [of it] in the first [book] of his Chaldaica:
On the one hand, matter is eternal, because it subsists along with the absolute first causes from eternity, and it has its existence among them and with them. On the other hand, it never stands on its own, because it has been set firmly among the common [things] in accordance with the same-named and unitary power. And it is not incomplete and limitless, but rather shares in a certain perfection, since nothing proceeds from the paternal triad incomplete, and it is led forward of itself into [its] perfection and limit. So then, when the basic elements had been brought forth in this way after it [i.e., matter in general], but nevertheless were in a state of confusion, the Demiurge, taking up all that was then without order, not at rest, but moving unharmoniously, brought it into order, according to the Timaeus. But when the elements were separated—the fire shining above on account of its natural lightness, the water falling to the depths because of its natural heaviness—then the myth-makers put Cronus in Tartarus, as [if to say that] when the fire went up the water  lurked in the hiding-places of the earth. And yet they say that he is the father of Zeus, because of his watery nature, which is known to tradition as the eldest of all the elements, according to the poet, who says: “Ocean, the origin of the gods, and mother Tethys.” And they named the water “Tethys” similarly, from the fact that it naturally lies bounded by the dry earth on the one hand, and by the thick air on the other.
And thus the natural [philosophers spoke] about Cronus.
But we nevertheless find that he is also described in books as the child of Uranus, as being the rain-storm that is born from the air; hence, he is called hyetos ["rain"], as though [to say] hyios ["son"], or because after the heavens, there is the cold zone, and then the warm [zone]. And concerning the imprisonment of Cronus in Tartarus, Ammonius says that Cronus is the mind, or rather the soul—for [these are] not the same thing—while Zeus is generation / birth; and that before generation / birth, the soul has been confined in the body, and thus also the body is named demas, as the equivalent of desmos ["bond / imprisonment"]. And the “cutting off” [of Uranus' genitals] is the last [step (?)], and is generative and productive of everything; such is the nature of the genitals. Cronus, the father of the Cronian nature, cast these down so that the heavens’ power of eternity would subsist also in the sea, that is, in the sublunar world (which indeed has been likened to the unstable and much-twisting [nature] of the sea), “where [there are] murder and ill-will and the other kinds of death.”
Such things the Greeks [say].
160. Dionysus is the spirit [pneuma], that is, the warmth, that arose from the fire, and hence he was called Fire-born and Thigh-bred and Male-female by the Greeks, since  they were unaware of the philosophical treatment regarding him and of what he actually was. For [as "Fire-born"] he is the warm spirit that from every sowing of every living, spiritual creature is inserted at the same time for the production of the life and growth of all things that are in the world. And he was called “Thigh-bred” because in the membranes and the genital parts and the veins that are in the thighs, this sort of material has been given a home in every living creature—and from this everything has taken solid form. And he was termed “Male-female” because of the fact that male-and-female sowings result in two, the male and the female natures, and it is not possible for one thing to be engendered from another, if [the two] do not come together. And the things fashioned by this [pneuma / Dionysus] will produce the living creatures. They have surmised that he is dissolved and is regenerated, because also the things engendered by him are likewise incessantly consumed and again brought to life.
161. The circle is the most perfect of shapes. Hence, the Egyptians, when they depict the world, inscribe a round, air-like and fiery circle, and a serpent with a hawk’s form stretched out in the middle of it as the connective Agathos Daimon. And the whole shape is like our T [theta].
162. The number eight is feminine and unbounded and imperfect. Hence it is also called alitomênos ["missing-the-month"] by Nicomachus. For the eight-month period is manifestly not in proportional relationship with any of the harmonics; hence, the eight-month-old [fetuses] are not brought to perfection. For, being between the perfection-bringing numbers [i.e., 7 and 9], it is itself found to be imperfect. For since it partakes in every material power, it has been allotted the powers concerned with matter.
 The damaged opening of this section must have introduced an association between December and Cronus and the symbolic significance of Cronus; the “homonymy” mentioned early on in the surviving portion would seem to have been that between Gk. kronos (the god’s name) and chronos (“time”).
 Gk. pathos, sometimes to be translated “passion” (as later in this sentence).
 Cf. De Mensibus 4.71: “And Crates says that Cronus reigned over Sicily and Italy and most of Libya, harshly…”
 Gk. theôria.
 Hase suggested “Plutarch” as a supplement here; Wuensch guesses “Polycharmus,” and cites FGH 4:480.
 In Christian authors, this expression is frequently used to refer to pagans; here, however, it seems to refer to run-of-the mill historians, as opposed to esoteric philosophers like Proclus, who is quoted next.
 Gk. hieros logos.
 For this quotation, which is not verbally identical to any extant passage of Proclus, cf. Proclus, Comm. in Platonis Timaeum 3.169; Comm. in Platonis Timaeum 3.188; and especially Comm in Platonis Cratylum 149. Wuensch cites Theologia Platonica p. 258C.
 Gk. mythikoi.
 Alternatively, “<to urge on> the second things against the fir<st>.”
 Plato, Laws 3 [701c].
 Further “separating” his kingdom from that of his father: In Platonis Timaeum 2.225.
 I.e., the first day of the month (from the terminology strictly proper to a lunar calendar).
 “Powers” (dynameis) could be a reference to military “forces.”
 Gk. agalmoeidês, which could also mean “of glorious appearance” or “statue-like”; Wolff emended to aglaomeidês, “brightly smiling.”
 Symposium 203b.
 Cf. Warde Fowler, Roman Festivals, p. 280-82. This word or related words are associated with various days in the calendar, including Dec. 11 (in conjunction with Septimontia).
 That is, “the Sun Laurel-Bearer and Ancestor.” This may be a reference to Sol Indigetes; but Wissowa, Religion und Kultus, p. 372, does not try to identify the old Roman god involved here. Cf. also Diodorus Siculus, 37.11, for an oath of allegiance at the time of the Social War, sworn by “Helius Genarchês.”
 A Daphnephoria is attested in Boeotia (Proclus [probably different from the Neoplatonist philosopher quoted by John Lydus earlier] in Photius, Bibliotheca 239 [p. 321b Bekker]), but the epithet Daphnêphoros for Apollo is found more widely.
 The remains of a word here could point to an original meaning “deprecatory (prayers / rites).”
 The explanation perhaps depends on a connection with the Greek verb teirô, “to distress or weaken”; or the Latin tero, “to wear down / away.”
 Cf. OLD s.v. dupondius, meaning “two asses (small copper coins).” The transference of the term to new military recruits does not appear to be attested in Latin.
 Gk. Βρουμάλια δὲ οἱονεὶ χειμεριναὶ ἑορταί; alternatively, “…[function] as winter festivals,” but οἱονεί introduces the significance of a term just before, with bruma.
 Gk. τὰ Αὐξιφωτία, presumably referring to 25 Dec., as (e.g.) in the “Calendar of Antiochus” the date is marked: ἡλίου γενέθλιον· αὔξει φῶς. For the phrase, cf. also Cosmas of Jerusalem, Comm. in S. Greg. Naz. carm. [PG 38:464].
 Lit., “you will live for years.”
 I.e., Saturn and Ops, who were considered husband and wife, and whose festivals were associated at this time of year; some further considered them the equivalents of Heaven and Earth (Macrobius, Sat. 1.10).
 Cf. askoliasmos / Askolia, the name for such an “event” at the Rural Dionysia.
 I.e., the Magna Mater (Cybele) (?).
 Gk. τὸ…ἀληθέστερον; lit., “the truer [thing]” / “the quite true [thing].”
 I.e., Saturnian festivals (Saturnalia).
 Gk. ἀποτρέπεται; alternatively, “turning [people] away from them.”
 Gk. αἰνίττονται.
 Gk. aneideos.
 Gk. (H)aidês, which was often interpreted as being derived from a negative prefix (a-/an-) plus the root id- meaning “to see,” like the word aneideos.
 Gk. genêtos.
 Gk. aitiatos.
 I.e., his commentary on the Chaldaean Oracles.
 Gk. stoicheia.
 Cf. Plato, Tim. 30a.
 Hom., Il. 14.201.
 Empedocles, fr. 221.
 The epithets in Greek are Pyritokos, Mêtrotraphês, and Arsenothêlys.
 Cf. Herennius Philo, fr. 9 [= Eusebius, Praeparatio Evangelica 1.10.51].
 The image relates to a foetus which has not yet reached full gestation.
 Cf. Ps.-Nicomachus, Theologumena Arithmeticae p. 55 Ast = Ps.-Iamblichus, Theologumena Arithmeticae, p. 74 De Falco.
 Cf. Ps.-Nicom., Theol. Arithm., pp. 42, 58 = Ps.-Iambl., Theol. Arithm., p. 55, 78 De Falco.