How to pronounce "Ephemerides"?
I've always pronounced "Ephemerides" (plural of Ephemeris) using four syllables, the fourth being "Ides" as in the "Ides of March".
But in this talk at a few seconds after 10:10, it is pronounced with five syllables, the last two sounding like "Pleiades."
Are both acceptable, are there rules or guidelines for choosing a preferred pronunciation between the two?
All sources I've found say ephemerides is pronounced /ɛfɪˈmɛrɪdiːz/ ("effih-MERRih-deez", which for some speakers is the same as "effuh-MERRuh-deez").
Nobody uses the /aɪdz/ ("ide's") pronunciation, as far as I know. It would be justified if the singular were ephemeride ending in /aɪd/ ("ide"). However, "ephemeride" doesn't seem to exist as a singular noun.
The singular is instead ephemeris, from Ancient Greek ἐφημερῐ́ς (ephēmeris).
According to Wiktionary, the plural of ἐφημερῐ́ς was ἐφημερῐ́δες (ephēmerides). Basically, it's just become conventional to pronounce the letters "es" as /iːz/ ("eez") at the end of plural words of this type (ones that follow the Greek or Latin form rather than being formed with normal English pluralization rules).
"Ides" is a different type of loanword. It's not just a transliteration of a Greek form. The Latin word was īdūs, a plural of the fourth declension. This developed to French and English ides where the e just represents a schwa or the length of the preceding vowel, and the "s" is the usual plural suffix.
As a supplement to @herisson's excellent answer, the following three online dictionaries provide an audio link for the pronunciation of the plural noun. The audio is embedded in each web page so I can't insert the audio links here, but I've included a link to the page and an edited excerpt of the dictionary entry in each case:
Merriam-Webster
ephem·er·is | \ i-ˈfe-mə-rəs \
plural ephemerides \ ˌe-fə-ˈmer-ə-ˌdēz \
Collins
ephemeris (ɪˈfɛmərɪs)
plural ephemerides (ˌɛfɪˈmɛrɪˌdiːz)
Dictionary.com
ephemeris [ ih-fem-er-is ] [IPA: / ɪˈfɛm ər ɪs /]
plural e·phe·mer·i·des /ˌɛf əˈmɛr ɪˌdiz/.