Cattle, sheep, and other four-footed animals have four quarters, each containing part of a body and a fore-leg or a hind-leg. The Joyce glossaries do not cover “fifth quarter” as an established expression. But Joyce knew something of the vocabulary of butchers, as he refers to the “fifth quarter” as “all that raw stuff, hide, hair, horns”.
The “fifth quarter” was important. Although some people regarded it as the refuse of the slaughterhouse floor, butchers were more knowing, and the “fifth quarter” (or in Roman abattoirs the quinto quarto) was said to be the “butcher’s profit”.
We find the expression used in English from at least 1794, in Arthur Young’s Annals of Agriculture vol. 22, p. 54:1
Some value the saleable meat at 6d. per lb. allowing what is called the fifth quarter for the butcher’s profit.
It was well known in Dublin circles, appearing in the local newspapers in discussions of the cattle and dead-meat trade:
The Meat Trade of Dublin […] If a butcher therefore goes into Smithfield market at the present time he can purchase the best beef at 8d a pound, calculated upon the dead weight of the carcase; the hide, horns, feet, head, tallow, and offal of the animal are not estimated in the value; they are known to the trade as the fifth quarter; they are looked upon as the perquisite of the butcher, and the value of these was formerly held to be the measure of the butcher's profit.
Irish Times (1879) 17 June, p. 6
The butchers, on the other hand, in addition to the hide, tallow, hoofs, horns, bones, and offal, which make up what is called the fifth quarter, has almost certainly from 4d to 5½d per lb profit.
Freeman's Journal (1884) 9 October
The fifth quarter is “lost” to the Dublin trade, as Bloom laments, when beasts are sold as livestock (rather than by dead weight) for the Liverpool markets.