Here's the air as it appears in Dick's The Songs of Robert Burns, 1903.

Mick

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X:1
T:Adieu! a heart-warm, fond adieu
M:C
L:1/4
C:Robert Burns
S:Dick - The Songs Of Robert Burns, No.240
K:G
"^Lively"(B/A/)|G G D> G|E E e>
w:A_dieu! a heart-warm, fond a-dieu;
d|(B/d/)(e/d/) (B/d/)(e/d/)|B G G
w:Dear bro_thers_ of_ the_ mys-tic tye,
(B/A/)|G G D> G|E E e>
w:Ye_ fa-vour-ed en-ligh-ten'd few
d|(B/d/)(e/d/) (B/d/)(e/d/)|B G G||
w:Com-pa_nions_ of_ my_ so-cial joy!
B|(A/G/)(A/B/) G (G/E/)|(D/E/)(G/A/) B
w:Tho' I_ to_ for-eign_ lands_ must_ hie;
(A/G/)|A> B (c/B/)(c/d/)|e A A>
w:Pur_su-ing For_tune's_ slid'-d'ry ba';
B|(c/B/)(c/d/) e (d/c/)|(B/A/)(B/c/) d
w:With melt_ing_ heart and_ brim_ful_ eye,
(c/B/)|(A/B/)(d/e/) (d/B/)(A/B/)|G E E||
w:I'll_ mind_ you_ still,_ tho'_ far a-wa'.