Are 済む・澄む・住む cognate?


Which of these words are cognates (share a common etymology)?

  * 住【す】む ("live") (rarely 棲む or 栖む)
  * 澄【す】む ("clear") (rarely 清む)
  * 済【す】む ("end")

According [gogen allguide](http://gogen-allguide.com/su/sumimasen.html) and
several dictionaries such as the
[大辞泉【だいじせん】](http://dictionary.goo.ne.jp/smp/leaf/jn2/120156/m0u/), `済む`
derives from `澄む`. Perhaps the English expression `I believe that the issue is
#cleared up#.` helps to illustrate this relationship.

The 広辞苑【こうじえん】 dictionary (6th ed.) speculates that `住む` derives from `巣【す】`
("nest"), and lists `巣にいる` as the first (ie oldest) meaning. It also quotes
the following phrase from the 古今和歌集【こきんわかしゅう】 providing a certain plausibility
for the suggested etymology: `花【はな】に鳴【な】く鶯【うぐひす】、水【みづ】に住【す】むかはづの声【こゑ】を聞【き】けば`.
Although, it is not quite clear to me why `住む` here would mean `巣にいる`
specifically and not `to live` in general.

This suggest that 住む is unrelated to 澄む・済む. However, I did not find any
information regarding the origin of 澄む.

Are the above mentioned sources correct? Is 澄む cognate with 住む, or are they
not related at all?




Much as described in the question comments by Yang Muye and blutorange, 1) all
of these _sumu_ verbs derive from Old Japanese in ways that make the kanji
irrelevant to a discussion of etymology, and 2) all of the modern senses of
_sumu_ arise from an underlying idea of **to settle**. Interestingly, the
English term **to settle** covers most of the same meanings as the Japanese
_sumu_ : to **live in a place** , to **become clear** (such as water), to
**finish** , to **be fully paid** (such as an account), etc.

(This same etymology was briefly mentioned [in this other
post](https://japanese.stackexchange.com/questions/17344/difference-between-
the-words-for-living-
residing-%E4%BD%8F%E3%82%80-%E6%A3%B2%E3%82%80-%E6%B3%8A%E3%81%BE%E3%82%8B-%E6%9A%AE%E3%82%89%E3%81%99#answer-17350).)




Much as described in the question comments by Yang Muye and blutorange, 1) all
of these _sumu_ verbs derive from Old Japanese in ways that make the kanji
irrelevant to a discussion of etymology, and 2) all of the modern senses of
_sumu_ arise from an underlying idea of **to settle**. Interestingly, the
English term **to settle** covers most of the same meanings as the Japanese
_sumu_ : to **live in a place** , to **become clear** (such as water), to
**finish** , to **be fully paid** (such as an account), etc.

(This same etymology was briefly mentioned [in this other
post](https://japanese.stackexchange.com/questions/17344/difference-between-
the-words-for-living-
residing-%E4%BD%8F%E3%82%80-%E6%A3%B2%E3%82%80-%E6%B3%8A%E3%81%BE%E3%82%8B-%E6%9A%AE%E3%82%89%E3%81%99#answer-17350).)

