This piece is somewhat of an anomaly.  It is on a separate piece of paper, albeit found roughly folded in the Song Time book.  Like the other pieces, it is written on a four-line stave, with no key signature, and the minims are written with stems on the opposite side to other notes (as also found in the William Dixon manuscript↗̱). However, the manuscript is much larger, with the stave drawn clumsily by hand rather than being carefully ruled.  There is also no time signature, and only two bar lines, each towards the beginning of the systems.  

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It can't be ruled out that this is just a sketch rather than a complete piece, but when played it is reminiscent of the Border ballad Chevy Chase (Roud No. 223; Child No. 162).  Assuming the two barlines present indicate anacruses, the melody has a distinct 3/4 feel.  The lack of further barlines suggests the piece should be played freely, befitting an air.