Sergeant Early’s jig

From O’Neill’s Dance Music of Ireland

is as played by Adele Farrell. This setting is pretty close to O’Neill’s as posted by treecipitation, but it has that c natural in bar 2 which is quite essential to the tune IMO. I think bar 1 of the B part is also played with a c natural sometimes (or even the whole tune in Dmix?). Anyway, here’s Adele:
http://comhaltas.ie/music/detail/comhaltaslive_319_4_adele_farrell_and_holly_geraghty/lang/en/

is from Harry Bradley’s piping… for a few c naturals more.
http://errantelbows.podbean.com/e/sergt-earlys-jig/

is another rather mixolydi-ish version from the playing of Jimmy Noonan:
https://www.youtube.com/watch?v=tBCRIERl3t4

play video

is from O’Neill’s 1001 (Chicago 1907, p. 21)… for the sake of completeness.

Paul McGrattan at 10:32 in the video of “Scoil Samhraidh Willie Clancy online highlights from the Irish Traditional Music Archive”, flute and whistle (the tune, first in Paul’s set of three jigs, was introduced as “no name for”, as noted by ITMA).
https://www.youtube.com/?gl=GB