Can anyone advise how to scan this line from a fragment of Euripides’ Erechteus (sorry haven’t figured out how to add breathings and accents!)?
ως θεων βωμου πατριδα τε ρυωμεθα
I can only see you must lengthen either the epsilon of theon or the iota of patrida?
I can’t make it scan, but it looks like a iambic trimeter to me except for the beginning. Where did you find this? Are you sure it is supposed to scan as it is? If we scanned θεων as a single long syllable and added a short syllable x between θεων and βωμου, like this? 
ως θεων x βωμου | πατριδα τε ρυωμεθα
“|” stands for caesura. With “-δα τε” two shorts replaces a long, it’s called resolution.
It’s from here: http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.01.0151:speech=1:section=100#note-link9
And Paul’s guess appears correct, though I don’t know if it’s from the editor or the manuscript:
ὡς θεῶν τε βωμοὺς πατρίδα τε ῥυώμεθα.
ὡς θεῶν-- L L
τε Βω-- S L
μοὺς πατρ-- L | L
ίδα τε-- S S S
ῥυώ-- S L
μεθα-- S L
ὡς θεῶν τε βωμοὺς πατρίδα τε ῥυώμεθα.
After the caesura there’s a resolved longum: πατρί- scans uu. τε is long: ῥ- regularly acts as a double consonant. (And the υ of ῥύομαι is always long, so the 5th foot is spondaic.)
The world goes on. For now.
Thank you. I had looked up “ῥυόμαι” in the LSJ (online), but couldn’t find the length. With mwh’s corrections:
ὡς θεῶν-- L L spondee (allowed 1st, 3rd, 5th feet)
τε Βω-- S L iambus
μοὺς πατρί-- L | S S dactyl (allowed 1st, 3rd)
δα τε_-- S L iambus
ῥῡώ-- L L spondee
μεθα-- S L iambus
That said, I can’t see how to tell whether the first syllable in πατρίδα should be long or short. τρ can allow either, and 3:dactyl 4:iambus or 3:spondee 4:tribrach would both be allowable, as far as I know.
It’s better to think in terms of resolutions (uu substituting for a long) than of dactyls and tribachs and suchlike. And once you get the idea of the iambic trimeter as a trimeter (x—u— being a metron) and as bipartite (breaking into two unequal parts, before a longum) you can better grasp the line as a whole, without needing to segment it into six feet of variously admissible forms.
Here if you read πατρ- as long you immediately find the rest of the line won’t scan. Encountering πατριδα following caesura you should assume resolution unless contraindicated.
There must be something that I don’t understand. The rest of the line does scan, because ίδα τε would be a tribrach, right?
I would have thought it worked the same as this: ἀλλ’ οἱ μὲν ἐκβαλόντες ἀνοσίως ἐμε
No, τε is long, on account of ῥ- following. Even if it weren’t, -δα τε would make an ugly resolution. In ἀλλ’ οἱ μὲν ἐκβαλόντες ἀνοσίως ἐμέ, as in the Erectheus line, you have a resolution directly following the caesura (here 4th-ft not 3rd-). ἀνοσίως is a word which fits into iambics only if there is resolution, and ἀνο- (uu = —) is in the same word, like πατρι- here. Lexical articulation comes into play. There’s more than individual syllables and individual feet involved. I think you are going about this the wrong way.
I see what you’re saying now. I had assumed that the enclitic made it the same word, and that was enough.
ἐθρέψαθ’ Ἑλλάδι με φάος. (dimeter)
ὀψέ γε φρονεῖς εὖ, τότε λιποῦσ’ αἰσχρῶς δόμους.
But apparently this is rare, making your explanation much more likely. See the footnote here for more examples from Euripides (this is also where I got these two examples from): https://books.google.com/books?id=GOURAAAAYAAJ&pg=PA461
You need to learn to distinguish normal from abnormal. Don’t bother about the abnormal until and unless you encounter it. But if it’s split resolutions in tragic iambics you’re interested in, West’s Greek Metre pp.86f. is what you should be consulting, or whatever he says in his abridgment, Intro to GM. (Eur.Bac.807 κοινῇ τάδ’, ἵνα is an even more notable instance than those he mentions.) But in our Erectheus line there’s no question of a split resolution. There’s only one possible way to read the line. Once you develop a feel for the iambic trimeter you’ll find that all trimeters effectively scan themselves.
In ὀψέ γε φρονεῖς εὖ, τότε λιποῦσ’ αἰσχρῶς δόμους (again late Euripides) the most important thing to register is the resolution following the caesura, just as in the Erectheus verse and in the other one you adduced.