Osthoff’s Law in Latin

The sound change known as Osthoff’s Law, shortening a long vowel before a resonant-consonant cluster, was first explicitly described to have applied in the prehistory of GreekbyOsthoff (1884).Sincethen,theexistenceof asimilarsoundchangeinLatinhas been controversial in the literature, with claimed examples such as *vēntus > ventus ‘wind’. At one end, Simkin (2004) argues that Osthoff’s Law never took place in Latin; at the other, Weiss (2009) claims at least three independent rounds of Osthoff’s Law in the history of the Italic branch. I summarize the synchronic facts about pre-cluster vowel length in classical Latin using a comprehensive survey of the Latin lexicon, with a historical explanation for the vowel length in every form containing a cluster. I argue that Osthoff’s Law happened in Latin (contra Simkin), but only once (contra Weiss), around the 2nd century bce.


Introduction
In Osthoff (1881Osthoff ( , 1884, Hermann Osthoff proposed the sound change known as Osthoff's Law (abbreviated as 'OstL'): Osthoff originally proposed OstL for Greek, but the change has since been argued to have taken place in Germanic, Celtic, Balto-Slavic, and Latin. This paper is the first work dedicated specifically to the question of OstL in Latin: the evidence for it, and when in the history of Latin it was active. My goal is to do this by summarizing the synchronic facts about pre-cluster vowel length with a survey of the whole Latin lexicon, together with a historical discussion of each form and an explanation for the length of each vowel. I conclude that OstL did apply in Latin, some time in or after the 2nd century bce.
In section 1, I discuss the background to OstL elsewhere in Indo-European and in Latin. In section 2, I give all the data relevant to the question of whether or not OstL applied in Latin, consisting of etymologies that appear to have undergone OstL and those that contain surface sequences of long vowels followed by rc clusters (i.e. synchronic 'counterexamples' to OstL). I conclude the positive examples give evidence for OstL applying in Latin in much the same environments as Osthoff concluded for Greek. In section 3.1, I discuss some further exceptions, and the sound changes that need to be ordered later than OstL to explain them; in section 3.2, I give a chronology of OstL relative to other Latin sound changes. Section 4 concludes the paper.

1.1
OstL in Indo-European As Sihler (1995) comments, 'Osthoff's Law' is properly the name for the Greek sound change proposed by Osthoff (1881) in the quote above, but here I use it to refer to similar sound changes in Latin and other Indo-European branches. Osthoff's sound law started with his (1879) etymology of the dative plural ending -ois; the vowels of both Sanskrit -ais and Lithuanian -ais must reflect a pie instrumental plural ending with a long vowel *-ōis, and so Greek -ois (and not **-ōis) comes from a shortening of long vowels in some position in the word (Collinge, 1985). In Osthoff (1881), he proposed that this shortening applied to all long vowels before rc clusters, as in the Greek Zeús next to Sanskrit dyáus with the reflex of a long *ē; Simkin (2004) points out that this converges on the idea Schmidt (1877) had used to explain the short vowels in forms like éstan(t) 'they stood' < *e-stā-nt.
"Before rc clusters" is a pre-theoretic way of describing this environment, and (as a phonological rule) seems to operate without reference to syllable Indo-European Linguistics 5 (2017) 147-177 structure; it corresponds to "before coda resonants in non-final syllables and coda resonant-consonant sequences in final syllables", assuming the grammar syllabifies rc sequences with the resonant in a coda. Byrd (2015) assumes a special exemption for final syllables, citing Ringe (2008) as taking word-final resonants in ancient ie languages to be extrametrical; this would mean OstL does apply to all coda resonants. Yates (2015) gives a detailed description within Optimality Theory. There are some shortening rules before single word-final resonants, e.g. the -m#, -r# and -l# shortenings listed by Weiss (2009) for Latin, but these must be separate changes to OstL: they have their own idiosyncratic restrictions (the shortening before -l# only applies to polysyllables, for example).
As well as in Greek, OstL has been claimed to apply in Celtic (e.g. Osthoff 1881;McCone 1996), Balto-Slavic (e.g. Osthoff 1879), Germanic (e.g. Ringe 2008), and Latin (e.g. Parker 1986, Weiss 2009). As we've commented with Sanskrit -ais < *-ōis, OstL did not apply in Indo-Iranian, and it seems not to have applied in Tocharian either (Ringe 2008; see later discussion of ventus). Trivially, then, we can't treat OstL as a pie process. I'll argue later, in section 3, that the application of OstL is fed by several late sound changes acting specifically within Latin: this means the Latin version of OstL is independent of similar-looking laws in other branches, and that we can give specific detail of when in the history of Latin OstL took place.
The existence of OstL at all in Latin isn't universally accepted: Simkin (2004: 49) comments in passing that "the whole case for OstL in Latin" is "not indisputable". At the other end of the scale, Weiss (2009) argues for three separate rounds of OstL in Latin, based on the etymologies he takes to involve OstL combined with the relative chronology of Latin sound changes argued for by Parker (1986); I'll discuss Weiss' case in section 3. I take the general position that, by Ockham's razor, we should prefer a single round of OstL to three separate rounds; when possible, we should prefer analyses that don't involve proposing new sound changes. My conclusion in this case will be that this more parsimonious analysis is in fact possible, and so we can conclude that OstL applied once in the history of Latin, at some point in the 2nd century bce or later.

Data
In this section, I give all the evidence I've been able to find that bears on the existence, and dating, of OstL. These etymologies come in two categories: examples where OstL applies, and apparent counterexamples that make OstL historically 'opaque' in a counterfeeding sense. The data themselves come from Lewis and Short's (1879) dictionary, online via the Perseus Digital Library; and from the Thesaurus Linguae Latinae (tll), online via de Gruyter. Vowel length isn't often marked in written classical Latin, and potential OstL environments scan heavy in verse, whether or not the vowel is long, due to the coda resonant. Much of our evidence depends on the reliability of transcriptions using either a double vowel ⟨vv⟩ or an apex ⟨V́⟩ (or, in the case of i, the 'i longa' ⟨I⟩). As discussed by Flobert (1990), in the imperial period, the apex and i longa came to be adopted for spelling features other than vowel length: the apex for heavy or accented syllables and for word boundaries, and the i longa for /i/ in initial position. The fact that not all long vowels are marked as long, and that not all apparent length marking reflects long vowels, means that we can't be fully confident about the synchronic length of a vowel. The evidence for OstL, of course, depends on how accurate our guesses about length are; unless otherwise stated, vowel lengths are taken from tll. I'll also use later sound changes, in particular Romance reflexes, as evidence for length. In the development of the vowel system into Vulgar Latin (Alkire and Rosen 2010), the language loses vowel length, but indirectly distinguishes original long vowels from short vowels by vowel quality: -long ī, ū stay as i, u; -short ĭ, ŭ merge with long ē, ō as high-mid e, o; -short ĕ, ŏ become low-mid ɛ, ɔ; -short and long ă and ā merge as a.
In particular, we can distinguish short high and mid vowels from their long counterparts by the height of the Romance reflex.

2.1
Potential sources of long vowels To treat an etymology as an example of OstL, we need evidence that the form contained a long vowel at some earlier stage; so one issue to be dealt with before discussing particular etymologies is the question of where a long vowel before a consonant cluster could in general come from. As we'll see, there are a range of possible sources. An inherited long vowel could be an original lengthened-grade (as in *ōrbis). In new inflectional or derivational forms, OstL contexts appear productively when a stem-final long vowel is followed by an affix beginning with a cluster, creating a sequence *V:-RC (as in *amā-nt next to amā-re); or when a stem ending in a long vowel and a final resonant is followed by a consonant-initial affix, giving us *V:R-C (as in *līn-teum next to līnum). Within a form, the context for OstL could be produced from original *V:RVC by syncope (as in *sēnciput < *sēmi-kaput), or by monophthongization from *V1V2rc (as in *ūncia < *oin-kia). These examples will be covered in more detail in section 2.2. But a problematic category of etymologies consists of those where the (potential) long vowel comes from a laryngeal, in a context like *eHRC or *R̥ HRC.1 In other environments, we'd expect an inherited sequence *eH or *R̥ H to give a long vowel *V: (depending on the laryngeal) and *Rā respectively (Weiss 2009: 97, 100). Naïvely, we might expect *V:RC and *RāRC in earlier Latin. The problem is that according to the standard picture of pie syllabification (Schindler 1977), these forms should syllabify as *eHR̥ C and *R̥ HR̥ C in the parent language. When the intervocalic laryngeal deletes without lengthening, given that only coda laryngeals cause compensatory lengthening, we should ask what we'd expect to happen to the new sequences *eR̥ C and *R̥ R̥ C.
We can consider what the learner perceives at the time that laryngeals were deleted. In the case of an adult sequence [eHR̥ C], the new generation of learners lacking laryngeals is faced with what they perceive as a phonetic sequence [eR̥ C]-the question is how a learner analyses this [eR̥ C], which presumably is impossible according to the phonotactics of early Latin. One possibility is that the learner interprets the sequence as /eRC/, so the end result is a sound change *eHRC > eRC with no intermediate *ē stage; if this is true, etymologies that show short vowels from original *eHRC aren't examples of OstL. This is the development described by Ringe (2008: 77) for ventus, ultimately following Kuryłowicz (1935). Alternatively, the learner might preserve the weight and phonetic duration of [eR̥ C], and interpret it as /ēRC/; if this is true, *eHRC gives *ēRC as we'd naïvely expect, and so these etymologies do involve OstL. I don't know of any way to distinguish between these options.2 From *R̥ HRC, our task is easier. The vocalism in Latin planta < *plh₂-nt-shows that *l ̥h₂ must have given its usual long-vowel reflex as lā; otherwise, a short syllabic *l ̥ would give **ol, and a short syllabic *n̥ would give **en. Suppose that *R̥ H becomes *Rā via an intermediate stage of a long syllabic resonant *R̥ : (Sihler 1995: 101); planta is evidence that *R̥ R̥ C is somehow analysed as *R̥ :RC. The fact that learners seem here to be preserving the duration or weight of the syllable as a whole, rather than the length of the vowel, should count at least as weak evidence for the same treatment of *eR̥ C; so tentatively, I will treat these as examples of OstL. This won't affect the conclusion of the paper or the relative chronology I give in section 3.

2.2
Examples of OstL with etymologies Here, I list candidate examples of OstL, together with discussion of possible alternative (non-OstL) explanations for the relevant data when appropriate. I start with examples from inflectional paradigms, where the phonological environment for OstL appears consistently in particular morphological categories, and then move on to examples from the etymologies of individual words.

2.2.1
Examples from morphology The clearest examples from inflectional morphology are in the verbal system, and they mostly come from instances where an affix beginning with a cluster rc is added to a stem ending with a long vowel. Some of these are from the theme vowels defining the stem of each conjugation (Morwood 1999): the first conjugation ā (amāre) and the second conjugation ē (docēre). (The fourth conjugation theme vowel ī, as in audīre, is never immediately followed by a cluster.) We also have the long theme vowels of the present subjunctive-ē for the first conjugation and ā for the second, third, and fourth conjugationsthe long ā of the imperfect subjunctive in -bā-, and the long ī of the perfect subjunctive in -erī-(from the pie optative; Weiss 2009: 420).
Aside from these three environments in which the theme vowel is shortened, one other context of inflectional morphology is claimed to undergo OstL: the dative plural in -īs, supposedly from *-ōis, in both the first and second declensions (Sihler 1995: 263;Weiss 2009: 207, 236). For the o-stems, Sanskrit and Avestan instrumental plurals in -āis and -āiš respectively attest *-ōis with a long vowel (Simkin 2004: 35); and the fact that Greek has a dative plural -ois < *-ōis was Osthoff's original motivation for proposing OstL in Greek. But in both Old Latin and Oscan (Sihler 1995: 263), we see inscriptions with dative plurals in -ois, which in Latin regularly became -īs; for the change *oi > ī in final syllables, cf. the nominative plural *-oi > -ī. If this Italic *-ois is from *-ōis, we have an instance of OstL parallel to the one in Greek. Although it's possible that ⟨ois⟩ is spelling -ōis in Latin, it seems unlikely that there was a direct sound change *ōi > ī; the dative singular -ō has to come from *-ōi (cf. the Greek dative singular in -ōi), as still survives in the Duenos inscription (Weiss 2009: 222). The Oscan spelling ⟨ois⟩ has to reflect *-ois, given that *ō > u is spelt ⟨u⟩.4 The traditional explanation for this difference between the reflexes of *-ōi and *-ōis is that the latter was shortened by OstL.
Indo-European Linguistics 5 (2017) 147-177 -pinguis 'fat, greasy' < *pīnguis < *piH-n-. Sanskrit pivan-'fat' (adj.) < *piH-wen-and Lithuanian píenas attest a laryngeal in the root *piH- (de Vaan 2008: 466), so the vowel looks to have been shortened by OstL. The origin of the -n-or the -gui-elements aren't clear, but Walde and Hoffmann (1930) suggest analogy with unattested *finguis < *bʰn̥ gʰ-u-i-(which ought to mean 'thick'); the case for OstL in this word would be weakened if this analogy is right, but there's no other evidence for that suggestion. -Herculēs < Greek Hērakles. This word shows an irregular syncope of a, which perhaps feeds OstL in shortening the vowel, but we would regularly expect **Hēreclēs (Weiss 2009: 3). Given Etruscan Hercle (Rix 2004), the actual Latin word is probably a borrowing, in which case the short vowel could equally be an Etruscan development rather than a Latin one. -surculus 'twig' . This has a short vowel, and is a diminutive from surus 'post' , which has a vowel of unclear length (de Vaan 2008: 602). As de Vaan comments, if this is connected to sūra 'calf of the leg' , then there should be a long vowel in sūrus, and so surculus would involve OstL-but this etymology is only speculation. -perna 'thigh, upper leg' < *pērsna- (Meiser 1998: 75). This must be connected to Sanskrit parṣṇi-and Gothic fairzna (acc.sg.), both 'heel' (de Vaan 2008: 461); the loss of s in *-RsN-is probably regular, as in *alsnos > alnus 'alder' (Weiss 2009: 179 Sen's (2012) archaic parsing syncope. Although this word is traditionally given (e.g. by Weiss) with a long vowel as prīnceps, Sihler (1995: 78) points out that Roman grammarians give the vowel as short, and that archaic Italian has a form prence explicitly reflecting a short vowel. To account for the spelling ⟨príncipi⟩ in Latin using the apex in cil 13.1644, I follow Allen's (1965: 73) suggestion that this letter before a velar nasal is meant to reflect quality, not length (see section 2.2.1). The usual Romance form with a vowel i, as in prince, is a learned borrowing directly from Latin that takes on the original vowel quality.

'Counterexamples' to OstL, and etymologies
In this section, I list some apparent 'counterexamples' to OstL: if a classical Latin word contains a long vowel followed by a resonant-consonant cluster, it looks superficially as if OstL hasn't applied. The explanation in all these cases is either that the word was only formed after OstL applied, or that the word is old but its long vowel was only formed after OstL applied. Two broad classes of exceptions relating to later vowel lengthening rules will be dealt with in section 3.
I'm only considering words that are judged to be native Latin vocabulary. There are examples of loans containing long vowels before rc-e.g. hīrmos 'first troparion of a canon' < Greek heirmós, or place names like Crēmna-but in the absence of knowledge about when these were borrowed, I take it these aren't probative.

2.3.1
Synchronic long vowels before OstL clusters vīndēmia 'grape harvest' < vīnum 'wine' + demō 'take away' (Meiser 1998: 76 case, we can't describe it as a later univerbation. As I'll argue in section 3, the weakening of a to e in medial syllables preceded OstL, and this weakening explains the third-conjugation theme vowel of vēndere given original dare. This means the collocation of vēnum dare as a single word has to precede a-weakening-so it also preceded OstL, which means OstL should have applied to this form to give *vĕndere. But from the same root, we have a family of words like vēnum 'sale' , vēneō 'be sold' , and vēnālis 'for sale' , all of which weren't compounded with dare and so didn't undergo OstL. I take it that the vowel in vēndere is just analogy with all the other forms of this family. -fūrtum 'theft' , fūrtim 'secretly' (i.e. 'like a thief'), and other members of this derivational family. The agent noun fūr < *bʰōr (cf. Greek phṓr) has an inherited long vowel, and this vowel spread analogically into the rest of the family. -ūndecim < *oino-dekem (Meiser 1998: 172). The evidence about the length of this vowel is inconsistent: on the one hand, grammarians explicitly give the vowel as being long (Sihler 1995: 78), and some Romance reflexes like Italian undici reflect a long vowel. But most Romance languages show a short vowel o < *ŭ: French onze, Spanish once, Portuguese onze. Given *oi regularly produces Latin ū, the only explanation for the short vowel is OstL; we can sensibly explain the long vowel as an analogy with ūnus 'one' , which OstL doesn't touch. -nūndinae 'market day' < *noweno-dinai. This literally means 'on the ninth day' (Meiser 1998: 172, de Vaan 2008, where *e syncopates giving *ou > ū, and then the syncope of *o leaves this long vowel in an OstL environment. The vowel here is marked as long (Allen 1965: 75), so these instances of syncope must be later than OstL. This means that, contra Sen (2012), this syncope isn't an example of the archaic alignment syncope that feeds OstL. -nōngentī 'nine hundred' < *novem-centī. This ō is from contracted *-owe- (Meiser 1998: 174, de Vaan 2008). -nūntius 'messenger' < *nowentius. Weiss (2009: 268) treats this as from *new-'shout' , cf. Sanskrit návate, where the outcome of syncope must have been *-owe-> *-ou-> *-ū- (Parker 1986: 160), cf. the doublet providentia and prūdentia. This problematic syncope is apparently not one of the regular syncopes identified in Sen (2012), as an anonymous reviewer points out, but it counterfeeds OstL. Parker follows Sommer and Pfister (1977: 102) in giving French annoncer 'announce' < *annuntiāre as evidence that there was a late round of OstL shortening the vowel of nūnt-; but there are easier interpretations than a new sound change.  (2008: 289) gives the traditional etymology as a derivative *ho-jōr-ino-from *joHr-'year' , but points out that we'd expect a long vowel **horīnus, rather than the apparent actual development *hōrĭnus > hōrnus. In both accounts, the environment rn comes from a syncope of short i that it's possible to assume is later than OstL. -dēnde 'then' . tll gives this as a variant of deinde. This monophthongization must be later than the usual *ei > *ẹ > ī (Weiss 2009: 101), given deinde is the usual form in the classical language. -prōrsus 'forwards' < *pro-worsos (Meiser 1998: 87 (Allen 1965: 24). In principle, this new rc cluster fits the conditioning environment for OstL, but there are some inherited long vowels that stay long in this environment in Latin: rēgnum 'kingdom' < *rēg-nom (cf. rēx), sēgnis 'slow' < *sēg-nis (cf. Greek heka 'slowly'), and abiēgnus 'made of fir' from abiēs 'silver fir' . We also have stāgnum 'pool'; although there are no cognates with long vowels directly, de Vaan (2008: 585) takes this to be a full grade of *steh₂g-cognate with zero-grades in Old Breton staer < *stagrā and Greek stagṓn 'drop' . Eichner (1992: 66) gives the vowel in sēgnis as short, as evidence for shortening by OstL, but Allen (1965: 72) gives inscriptional evidence for both sēgnis and rēgnum. As I'll argue in section 3, the fact that sēgnis doesn't raise to **signis is also evidence that the vowel was long, because (pace Eichner) OstL happens earlier than the raising of ĕ > ĭ before nc clusters; this raising otherwise happens before gn, as in dignus 'fitting' < *dek-nos or lignum 'firewood' < *leg-nom.
One possibility is that there was a lengthening before gn, and indeed there are some inscriptional cases of inherited short vowels before gn being spelt as long (Sommer and Pfister 1977: 121;Meiser 1998: 79): we have spellings ⟨seignvm⟩ (cil 1².42) and ⟨sIgnvm⟩ (cil 6.10234) with the i longa ⟨I⟩ for signum, ⟨dIgnI⟩ (cil 10.5676) for digne, ⟨Ignis⟩ (cil 11.826) for ignis, and ⟨privIgno⟩ (cil 6.3451) for prīvignō. But Diomedes describes dignitās as an anapaest,8 meaning the first vowel was short. The Romance evidence also implies short vowels for words of this form: from signum, Italian has segno, and French has a doublet seing (with an inherited short ĭ) and signe (a cultismo with ĭ borrowed as Proto-Romance i); and from dignus, Italian has degno. Allen (1965: 73) suggests the i longa is being used here to spell a short vowel with the quality of a long /i:/, assuming short i became allophonically tenser before sayeed Indo-European Linguistics 5 (2017) 147-177 [ŋ] without actually lengthening. The spelling ⟨ei⟩ is also sensibly treated as a spelling of a tense vowel distinct from /i:/; cf. the high vowel inscriptionally spelt ⟨ei⟩ from the original *ei that eventually raises to merge with ī (Weiss 2009: 101). If neither ⟨I⟩ nor ⟨ei⟩ reliably spells length, then these aren't clear examples of long vowels, as is backed up by the Romance reflexes with short vowels. If there was no lengthening before gn, then the long vowels of rēgnum and sēgnis can't be the result of a post-OstL lengthening-so OstL didn't apply before gn. I take it that gn was still pronounced [gn] at the point OstL applied, and the change to [ŋn] happened later.

Other rules affecting vowel length
In the previous section, I gave the etymologies of Latin words involving OstL, and the etymologies of some synchronic 'counterexamples' . In this section, I discuss two broad classes of more exceptions to OstL in particular phonological environments, and the sound changes (ordered later than OstL) that create them.

3.1.1
Lengthening before r In this category, I list instances of long vowels in the environment _rC not explained by any sound changes covered so far. we can also compare ōrnō 'furnish' < *ōrd-nō, as a long vowel from the same source (Meiser 1998: 122 *dʰer-. De Vaan (2008: 223) suggests Proto-Italic *fermo < *dʰer-mo-'holding' , with the raising to i being part of a (supposed) general raising after a labial (Watkins 1973). We have use of i longa in cil 4.175, but the Romance evidence (French ferme, Italian fermo) points to a short vowel in fĭrmus (Ernout andMeillet 1959: 422, Allen 1965: 74;Meiser 1998: 79). -vīrtūs 'manly qualities' . The vowel is marked with i longa in cil 6.449. This abstract noun is from vir 'man' < *wiH-rō-, where the short vowel is due to Dybo's law (de Vaan 2008: 681). We also have i longa used for vīrgō in cil 6.2150, which Ledo-Lemos (2002) etymologizes as a derivative of vir. -lārgus 'large' . We see use of the apex in cil 6.32521. De Vaan (2008: 327) explains the length of the vowel as a secondary lengthening, rather than following the Walde and Hoffmann (1930) etymology as ultimately from a stem *laj-es-'fat' as in lāridum 'bacon' . -ārma 'arms' . Grammarians describe the long-vowel form ārma as a 'barbarism' (Allen 1965: 73), which tells us that both ārma and arma must have existed (the former being stigmatized). Allen also points out that the weakening in inermis 'unarmed' means that the vowel must have been short at some point, given that only short vowels undergo weakening. De Vaan (2008: 54) treats the word as from *h₂er-'join' , so a short vowel is etymologically expected. -ārca 'chest' . The vowel is marked with the apex in one inscription from Lyon (Boissieu 1846), but as Allen (1965: 73) points out, the fact we have weakening in compounds (exerceō, coerceō, etc.) of the corresponding verb arceō means the vowel must have once been short. -hōrtus 'garden' . We have use of the apex in cil 6.9493, but no obvious etymological reason for a long vowel (de Vaan 2008: 290).
In sum, the evidence seems to suggest that some words underwent a lengthening before rC sequences. Obviously, this means that some of the examples of later formations in section 2.2 above-quārtus, hōrnus, etc.-could in fact have been shortened by OstL and then lengthened again by this pre-rC lengthening, which would undermine the explanations in that section. I haven't been able to find an interpretation of the etymologies under which this lengthening was completely regular in any environment, with plenty of short vowels in _rC position still surviving in Latin as well as near-minimal pairs like fōrma 'form' but fŏrmus 'warm' , so I take it this rule only applied sporadically. 3.1.2 Lengthening before nct clusters 3.1.2.1 nct and nx In this category, we have more surface exceptions to OstL not explained by any of the above rules; these are instances of long vowels before nct, nx, or mpt clusters. The solution is a lengthening before nct and nx (Weiss 2009: 130), but a morphological explanation for the examples with mpt. In most of these cases, the vowel length is disputed by different sources, which suggests this lengthening was sporadic or dialectal.
Most of the examples with nct and nx are from paradigms, either in past participles or perfects: cingere, cīnxī, cīnctus. Meiser (1986) and De Angelis (2016)  In one form, we have a verbal noun with no form in the corresponding paradigm to compare it to: pānctiō 'fastening' next to pangō; the verb has pepigī, pāctus for the perfect and past participle respectively, so there's no trace of the nasal other than in the present stem forms. The long vowel in pāctus < *ph₂ǵto-s (de Vaan 2008: 443) is expected from Lachmann's Law after devoicing of an original voiced stop, and not necessarily from an original nasal.
In the one word quīnque 'five' and its derivatives, we see a long ī: quīnque 'five' , quīndecim 'fifteen' , quīnquāgintā 'fifty' , quīntus 'fifth' < *kʷénkʷe < *pénkʷe. Traditionally (e.g. de Vaan 2008: 509, Sihler 1995 it's assumed that the length started in the ordinal quīntus < *quīnctus < *kʷenkʷ-tos, and then was analogically introduced into all the other forms. This makes it part of the set of words with nct originally, with loss of *k in between a resonant and a stop (Weiss 2009: 180).
And finally, one adjective is reliably marked with length before nct (e.g. in cil 9.60): cūnctus 'all' . One Roman folk etymology (Maltby 1991) was that this is a contraction of coniūnctus 'joined together' from iungō, which would mean the length comes from the length of iūnctus; de Vaan (2008: 154) cites the traditional scholarly etymology as from *kon-kitos, the past participle of conciēre 'called together' .
For all of these forms, the Romance reflexes have inconsistent vowel length. As Allen (1965: 67) and Sommer and Pfister (1977: 121)  iŭnctus, and tĭnctus; Weiss (2009: 130) also points out the discrepancy between Italian giunto, implying a long vowel, and French joint, impying a short one. Allen assumes analogy with the presents pŭngō, iŭngō, and tĭngō; Parker (1986: 160) assumes a sporadic late round of OstL in Romance. The latter is possibleif 'long-vowel' forms like Italian giunto are actually learned borrowings from 'short-vowel' forms like iŭnctus, the data are all consistent with a shortening in early Romance. Given lengthening was sporadic before nct and nx, it could alternatively be that these just carry on the unlengthened variants.
From these examples, it's sensible to conclude there was a lengthening before nct and nx. Given *quīnctus > quīntus and the Greek loan sphinktḗr > spinter 'bangle' , Weiss (2009: 180) analyses the regular outcome of the sequence *nkt as deletion of the k. This would follow a general *RCt > Rt rule, as in *forktis > fortis 'strong' , as well as being backed up by spellings ⟨defuntus⟩ for defūnctus and ⟨santus⟩ for sānctus (Sihler 1995: 221), and late-attested hypercorrections ⟨Crysanctus⟩ and ⟨Sanctipe⟩ for Greek chrúsanthos and xanthíppē respectively (De Angelis 2016). Weiss takes it that all instances of nct and nx in past participles are newly created, with a new devoiced c by analogy with the g in the present tense. One problem is that cūnctus and cūnctor don't have any obvious models for analogy: Sihler assumes that the *nkt > nt change doesn't apply before back vowels, while Leumann (1977) and de Vaan (2008) analyse these nct clusters as having been created later by alignment syncope, as in the two etymologies above.
If it's true that *nkt > nt is counterfed by alignment syncope in forms that then undergo lengthening, as in cūnctus and cūnctor, then this can't just be analysed as compensatory lengthening after the loss of the stop. It's standardly assumed (Allen 1965: 66, Parker 1986: 113, Meiser 2003) that these nct and nx lengthenings are just a special case of the sound change lengthening vowels before nf and ns, or n + fricative clusters. In Oscan and Umbrian (Parker 1986: 113), there's a regular spirantization k > χ before t and s, followed by loss of nasals before fricatives with compensatory lengthening of the preceding vowels. This means there are Sabellic parallels to the Latin nct and nx lengthening cases: Latin sānctum next to Oscan saahtum, and Latin cīnctum next to Umbrian šihitum10 Meiser (1986: 55). The assumption is that Latin also had k > χ in these environments, followed by the normal lengthening before n + fricative clusters.
This isn't convincing: for one thing, the Latin lengthening has to be a separate development from the Sabellic lengthening in saahtum and šihitum. Although Meiser (1986: 55) argues the latter lengthening has to be ordered earlier than Indo-European Linguistics 5 (2017) 147-177 Proto-Sabellic, such that we see Umbrian i and not e as would be expected by the 'ursabellische Vokalverschiebung' , Weiss (2009: 130, 177) points out that the Latin lengthening must have happened within Latin: lengthening before n + fricative clusters is fed by a-weakening, a change specific to Latin, in *an-anslō > *an-en-slō > anēlō 'pant' . If lengthening were in Proto-Italic, these clusters would also be affected by OstL, and this rule is meant to explain the exceptions to OstL by being ordered after it. Clackson (2015) points out that South Picene has unspirantized forms of k in deiktam 'shown' (< *deiḱ-) and molk [t]ah 'many' (< *molkt-, cf. Latin multus), meaning the spirantization in Oscan and Umbrian is also a later development than Proto-Italic.
The rule would have to have a different conditioning environment in the two branches, in any case. The Sabellic spirantization rule also seems to apply to *pt as well as kt-cf. Umbrian screhto 'written' , with no change in Latin scriptus (Clackson 2015). A second reason is that the change kt, ks > χt, χs is unconditioned in Sabellic, while in Latin it would have to be limited specifically to the environment n_t. Parker (1985: 111) prefers this to a general Latin kt, ks > χt, χs, which would then require a 'Rückverwandlung' where all instances of χt, χs later revert to kt, ks after the lengthening. Even in the restricted form of the rule, we'd need a later reversal of unattested χ to k.
A final argument against analysing nct and nx lengthening as n + fricative lengthening is that the two have different mechanisms. Allen (1965) gives inscriptional evidence that n was actually deleted before fricatives, as in ⟨cosul⟩ (cil 1².8) for cōnsul, ⟨cesor⟩ (cil 1².8) for cēnsor, ⟨meses⟩ (cil 9.714) for mēnses, ⟨cofeci⟩ (cil 1.560) for cōnfecī, meaning we can analyse the lengthening of the vowel as compensatory lengthening. The n was then restored analogically, except when there was no base for analogy, cf. Spanish mesa, French moise from mēsa < mēnsa 'table ' .11 In nct, it's the stop that deletes, so quīntus rather than **quīctus; all the cases I've found of long vowels before ct come from Lachmann's Law, rather than from any process of nasal deletion. This isn't strong enough evidence for a general mpt lengthening; these long vowels are all from coalescence of a suffix vowel with the e of the root, or (in the case of other more transparent compounds from emō) analogies with ēmptus itself. Given the long vowel in the perfect ēmī, as expected from a lengthened grade, the vowel in ēmptus is probably analogy. The main reason that it's difficult to rule out a regular lengthening before mpt is that we should predict *mpt > *mt > nt by the general cluster simplification rules given above, so there are no native mpt sequences. In the verbs above, I take it mpt is by analogy with the m of the present and perfect paradigms; the other two instances I've been able to find are cŏmptō 'reckon' < computō (cf. French compter) by a late syncope and cămpter 'angle' < Greek kamptḗr. In the absence of any better evidence for a regular lengthening, the morphological explanation for the emō forms is preferable.

3.2
Relative chronology of OstL In this section, I discuss the chronology of OstL relative to other Latin sound changes. First, I list sound changes that need to i) precede and ii) follow OstL, based on the etymologies in section 2. Next, I discuss the case for an early OstL shortening before glides, and judge that none of the arguments in favour are conclusive. Finally, I respond to some potential objections and problematic etymologies.
Leaving aside the shortening of long vowels before glides, which I discuss in section 3.2.2, the evidence for OstL in early Italic isn't very strong. Parker (1986: 149) comments in passing that the short í in the nominative singular of Oscan n-stems like statíf < *stat-īns (Buck 1904: 130) is down to an instance of OstL in Sabellic, but this wouldn't be a convincing case that there was another OstL in any ancestor (as opposed to cousin) of Latin. As an alternative, statíf could from *stat-ēns with no OstL. There's even some evidence that length before nt was maintained from Proto-Italic at least into early Sabellic, as in the Oscan third person plural stahínt, which has to reflect *sta-ēnt.12 Without evidence Indo-European Linguistics 5 (2017) 147-177 for a round of OstL specifically shared between Sabellic and Latin, I conclude there was no early round of OstL.

3.2.1
The chronology From the etymologies in section 2, we can read off which sound changes preceded OstL and which followed it. I've summarized these in the lists below.
Rules that take place before OstL: In terms of absolute dates, the key constraint is that OstL needs to follow *oi > ū. The absolute chronology in Weiss (2009: 192) dates *oi > ū as happening in the early 2nd century bce. Although I haven't found any examples of the parallel change *ei > ī feeding OstL, we have early records of a spelling ⟨e⟩ probably reflecting some intermediate ẹ (Allen 1965: 53); if the two monophthongizations can be thought of as part of the same change, it was already underway in the 3rd century. I place OstL in the 2nd century or later, after monophthongizaion was complete.

3.2.2
OstL before glides In Weiss' (2009: 104, 125) discussion of OstL, he proposes that the sound change applies at three separate points in the history of Latin. His first round, Round a, applies early on-before monophthongization and a-weakening-and part of the evidence for this is in the few examples of OstL before glides. In other words, these are cases where long diphthongs *V:j, *V:w shorten to Vj, Vw, the Greek equivalents of which were Osthoff's (1879) original reason for proposing OstL. I've been able to find four arguments in the literature for a specifically 'Osthoff' shortening of long diphthongs.
The first is from the merger of reflexes of *ēi and *ei as ī in medial position, as in dīxī 'I said' < *dēixī with a lengthened grade, cf. Old Avestan dāiš (Weiss 2009: 104). I agree with Simkin's (2004: 185) comment that this is only probative if we have a good case that unshortened *ēi would have changed into something other than *ī; the fact that *ēi > ī in itself doesn't imply that it went through a stage of *ei.
The second argument is from the dative plurals in -īs (Sihler 1995: 263, Weiss 2009; see section 2.1.1). The argument is that the second declension -īs reflects *-ois < *-ōis, where the normal reflex of *ōi would be ō, as seen in the dative singular -ō < *-ōi; and that the first declension -īs reflects *-ais < *-āis. Sihler (1995: 253) suggests that the first of these dative plurals is actually from the locative *-oisu, as in Sanskrit -eṣu, which has a short vowel; the Latin ending would then reflect an apocope *-oisu > *-ois > -īs, with no OstL. Michael Weiss (p.c.) has suggested that *-oisu would regularly give **-ēse, given that final short *-u is preserved as -e (Weiss 2015). This may be true, but as James Clackson (p.c.) points out, the Greek variant -oisi is plausibly relevant; if early Latin shared the same irregular development to *-oisi, then the loss of final -i would be expected, as happens in the present tense verbal endings -s, -t, -nt < *-si, -ti, -nti. As described in section 1, when we have alternative etymologies, Ockham's razor would have us choose the one that doesn't involve proposing a new sound change; and so we should prefer the *-oisu etymology to *-ōis.
Indo-European Linguistics 5 (2017) 147-177 In the case of the first declension -īs, Weiss' (2009: 236) proposed origin of *-āis is by analogy with a masculine *-ōis. If Italic speakers innovated *-ais straight away by analogy with *-ois < *-oisi < *-oisu (as is more plausible under my account than a form *-āis), there was no OstL involved; and even if we take the variant form -ās as evidence for *-āis, a shortened form *-ais by analogy with *-ois would be a sensible analogy anyway, so again there need not have been any round of OstL involved.13 For a third argument, Parker (1986: 181ff.) points out an unexplained difference between the vowels of nōn and nūllus. He takes it that these come from *ne oinom and *ne oinelos respectively, where the vowels are in some way the outcome of a contraction *eoi. Comparing the dative singular *-e-oi > *-ōi > *-ō, we might expect that *ne oinom > *neoin > *nōin > *nōn is the right development, which raises the question of why we don't have **nōllus. Parker rejects an account based on some ad hoc raising of oi > ō in an unstressed syllable, which would be consistent with the data (and the rest of the evidence from Latin) but not independently confirmed by any other facts. The explanation from Juret (1938: 64) is that nūllus underwent OstL: *ne oinelos > *neoillos > *nōillos > *noillus > nūllus, with the ū coming regularly from monophthongization of oi. But as Parker points out, there's no explanation given as to why *nōillos should be an OstL environment if *nōin isn't. I propose nūllus is more sensibly treated as analogy with ūllus < *oinelos, with no long *ōi, meaning this isn't an Osthoff form.
A fourth argument is pointed out by Sommer and Pfister (1977: 124). Next to gaudeō 'rejoice' , we have a past participle gāvisus with a long ā; de Vaan (2008: 255) compares Greek gēthéō 'rejoice' < *geh₂-dʰ-with a different root extension, as evidence the vowel should be etymologically long in Latin. Sommer and Pfister's explanation is that the original present *gāvideō < *geh₂-wid-irregularly syncopated to *gāudeō, where *āu > au by OstL. It's possible that a sound change creating a new phoneme āu would have been automatically analysed as au without involving OstL, given we have no evidence that Latin allows long diphthongs, and a change to a single word wouldn't be powerful enough to alter the phonology of the language. Even if it is an example of OstL, this OstL is late-fed by syncope within Latin-and so not evidence for an early round of OstL shortening long diphthongs. 13 An anonymous reviewer argues that speakers could have analogized an ending *-āis based on other forms of the a-stem paradigm with a long vowel in the suffix, like the locative plural *-āsu. This is possible, but even then wouldn't be evidence that the shortening to *-ais is sound change rather than analogy. sayeed Indo-European Linguistics 5 (2017) 147-177 3.2.3 Weiss' chronology In Weiss' (2009: 125) short discussion of OstL, he argues that OstL happened not once, but three times independently in the history of Latin. Round a, which he argues takes place in parentēs 'parents' and calendae 'calends' , feeds the weakening of *a to e in medial unstressed syllables. Round b is fed by both archaic parsing syncope and alignment syncope, and feeds raising of *e, o to i, u before the velar nasal as in nuncupāre and sinciput (see above). Round c applies late, after monophthongization, as in undecim. My proposal that there was a single OstL will have to explain these apparent ordering facts. Given the sound changes he cites, there's actually nothing distinguishing Round a from Round b: there's no argument that the sporadic instances of syncope feeding Round b have to be later than weakening. Round c really is separate, though, importantly because it's fed by monophthongization.
The crucial fact from absolute chronology distinguishing Round c from Rounds a and b is that weakening precedes monophthongization: while weakening was prehistoric, *oi > ū only took place at the start of the 2nd century bce (Weiss 2009: 192). If the other monophthongization from *ei > ī was part of the same sound change as *oi > ū, then we have internal evidence for this relative chronology as well: weakening *a > e feeds *ei > ī, as in *ok-kaidō > *occeidō > occīdō 'kill' (cf. caedō 'cut' for the base form). Based on examples like iuncus, uncia, and undecim above, I've argued that monophthongization feeds OstLand Weiss' case for distinguishing Round a from later rounds is that there are examples of OstL feeding weakening.
Because only short ă undergoes weakening to e, if any instances of *āRC undergo OstL to *ăRC and then weaken to *eRC, we'd have a case of a preweakening OstL (cf. talentum 'talent' < Greek tálanton for weakening in this environment (Sihler 1995: 61)). And because monophthongization follows weakening and some OstL follows monophthongization, we'd need multiple rounds, as Weiss proposes. To argue against OstL preceding weakening, it'd suffice to give an example of a long vowel *ā shortened by OstL but not later affected by weakening.
The theme vowels from section 2.1.1 show exactly this development, where OstL counterfeeds weakening, rather than weakening feeding OstL. Next to amāre, we have the 3pl. amant, not *amānt > *amant > **ament; the gen.sg. participle amantis, not **amentis; and the gerundive amandus, not **amendus. Weiss' response to this (2009: 126) is that the vowel quality was restored analogically to amant after OstL; the ē:e correspondence in docēre:docent caused by OstL isn't obscured by weakening rules, so in principle could be the basis for a four-part analogy ē:e :: ā:X. Sihler (1995: 78) is skeptical, pointing out that the only other vowel in the paradigm of amāre after OstL-then-weakening would sayeed Indo-European Linguistics 5 (2017) 147-177 syllable underwent weakening as expected, having not been produced by OstL. By the alacer rule (Weiss 2009: 118), this syllable is blocked from weakening to e by undergoing harmony with the first syllable, giving forms like *calatiō and *calator; I take it these were then remodelled with the first conjugation theme vowel and become calātiō and calātor. Weiss' two problematic etymologies, then, needn't be convincing.
One case not mentioned by Weiss as an argument for a round of OstL preceding weakening is vēndō 'sell' . As commented earlier, this superficially gives us a chronology problem: vēndere < vēnum + dāre shows weakening of the theme vowel a to e, but if weakening precedes OstL, any forms created early enough to undergo weakening should also undergo OstL. As above, we can quite reasonably invoke analogy with the rest of the derivational family: vēnum 'sale' , vēneō 'be sold' , and vēnālis 'for sale' , all of which are outside the environment for OstL and so keep their long vowels.
In short, then, I think the evidence for a round of OstL before a-weakening isn't conclusive-meaning the parsimonious solution, by Ockham's razor, is that there was only a single round of OstL.

Conclusion
I've discussed the evidence for Osthoff's Law-the shortening of long vowels before sequences of a resonant followed by a consonant, originally proposed for Greek-in the history of Latin. I've surveyed every word in the recorded Latin lexicon that contains the environment for OstL, and discussed the evidence for the etymology of each word that has been (or could be) claimed to involve OstL shortening. For each of the synchronic 'counterexamples' , I've given an explanation in terms of later sound changes, especially the sporadic lengthenings before rC and nct/nx. In terms of the chronology of OstL, I've shown that (contra Weiss' 2009 account), there was only one application of OstL in the history of Latin; and that it happened some time in or after the 2nd century bce, following the monophthongization *oi > ū.