Noggin
Modern equivalent
¼ imperial pint = 142 millilitres
A quarter of an imperial pint, the spirit measure of the public house.
A noggin is a quarter-pint, and so is a gill, and for most purposes the two words name the same quantity. The noggin was the one you heard in a public house, particularly in Ireland, where spirits were sold by it; the gill was the one in the statute.
Where it becomes interesting is that the gill did not mean a quarter-pint everywhere. Across much of Lancashire and Yorkshire a gill meant half a pint, and a quarter-pint was a noggin and nothing else, so the two words were not interchangeable at all but necessary to tell apart. A southerner ordering a gill in a northern pub got twice what he expected.
The word also means a small wooden cup, which is almost certainly where the measure came from, and it survives in the sense of a head — as in to be knocked on the noggin — by a route nobody has satisfactorily explained.