And here is the tune that Anderson intended for Jenny's Complaint, taken in this case from Johnson's Scots Musical Museum (vol.I, 1787, no.50, p.50):

X:1
T:Nancy's to the Green-wood Gane
B:Scots Musical Museum, I 50.
N:Tune prescribed by Robert Anderson for "Jenny's Complaint".
L:1/8
Q:1/4=100
M:4/4
K:Bb
F2|F3 G F2 (ED)|(EDC) B, G3 B|F3 G (F3/2G/F) D|
F4 B3 F|(G2 G/A/B) F2 (ED)|(ED)(C B,) G3 B|F3 G (F3/2G/B) D|F4 B2 F2|
B2 d2 d2 (cd)|(edc) B G2 (F3/2G/)|B2 d2 (ed) (cB)|(d3 e) f2 z g|
f2 d2 {e}d2 (cd)|(edc) B G2 e2|(d3/2e/) f2 (F3/2G/F) D|F4 B2|]