There is and has been of ancient time a law, or rather a custom, at Halifax, that whosoever does commit any felony, and is taken with the same, or confesses the fact upon examination, if it be valued by four constables to amount to the sum of thirteen-pence-halfpenny, he is forthwith beheaded upon one of the next market days (which fall usually upon the Tuesdays, Thursdays, and Saturdays), or else upon the same day that he is so convicted, if market be then holden. The engine wherewith the execution is done is a square block of wood of the length of four feet and a half, which does ride up and down in a slot, rabbet, or regall, between two pieces of timber, that are framed and set upright, of five yards in height. In the nether end of the sliding block is an axe, keyed or fastened with an iron into the wood, which being drawn up to the top of the frame is there fastened by a wooden pin (with a notch made into the same, after the manner of a Samson’s post), unto the midst of which pin also there is a long rope fastened that cometh down among the people, so that, when the offender hath made his confession nd hath laid his neck over the nethermost block, every man there present doth either take hold of the rope (or putteth forth his arm so near to the same as he can get, in token that he is willing to see true justice executed), and, pulling out the pin in this manner, the head-block wherein the axe is fastened doth fall down with such a violence that, if the neck of the transgressor were as big as that of a bull, it should be cut in sunder at a stroke and roll from the body by a huge distance. If it be so that the offender be apprehended for an ox, oxen, sheep, kine, horse, or any such cattle, the self beast or other of the same kind shall have the end of the rope tied somewhere unto them, so that they, being driven, do draw out the pin, whereby the offender is executed. Thus much of Halifax law, which I set down only to shew the custom of that country in this behalf. -- William Harrison, A Description of Elizabethan England (1577), written for Holinshed's Chronicles
At the Halifax Gibbet website, where I found the photo, Andrew Plummage relates a macabre tale about the gibbet:
A curious note on the act of beheading is recorded by the Halifax historian Wright, in which he tells of a country woman on horseback who passed the gibbet while an execution was taking place. At her sides were large wicker baskets, and when the head of the victim was dispatched, the force of the descending axe caused it to bounce a considerable distance "into one of the hampers, or, as others say, seized her apron with its teeth, and there stuck for some time."