[The Bird Fancyer's Delight, or Choice Observations And Directions Concerning the Teaching of all sorts of Singing Birds after the Flagelet and Flute [recorder] when rightly made as to Size and tone, with Lessons properly Compos'd within the Compass and faculty of each Bird, viz. for the Canary-Bird, Linnet, Bull-Finch, Wood-Lark, Black-Bird, Throustill [thrush], Nightingale and Starling. The whole fairly Engraven and Carefully Corrected]
[’Tis still in memory, the old manner of Playing on the Flute, which was by the way of Dots, a memorial of which remains in the Gamut for that Instrument to this time, but it being so impracticable and never to be attain’d to at sight, that the use of the Instrument was almost lost, till introduced by Gamut rules, which has not only brought it much in vogue, but the Performers on it are as ready at sight as on any other Instrument, ’tis not doubted but the like Improvement will be made on the Flaggelet by this Method, which Instrument is not only delightful, but also profitable, particularly to Bird Fanciers, it having been often known that Birds after being taught by the Flagellet has been sold for great value, all Lessons or Airs that are made for the Flute may now be play’d on the Flagellet, which must of Consequence be very grateful to all Lovers of the Instrument, the improvement of which is owning to the Ingenious Mr. Hill, who has made several Incomparable Peices [sic] for the Flagellet, and is an excellent performer on it, and to encourage the Lovers of it, he is willing to instruct in this new Method, any that is desirous to learn.]
Here is a link John Walsh's 1715 book that offer's the ingenious Mr. Hill's method.
It actually turns out that if you follow the pun (which I always do), and consider that the word "flageolette" (or "little flag" for the diamond shape that replaces the note-head in fingered harmonics), these little tunes make great fingered harmonic exercises for violinists and violists.