The particular type of sludge being discussed here (because there are several different types) is the stuff found in the bottom of fermentation vessels:
When settling-vessels are used, a similar sludge settles out at the bottom of these vessels, and the same care should he taken to retain it in these vessels as is so necessary in the case of fermenting-vessels. The beer associated with the sludge, whether in the fermenting- or settling-vessel, need not be wasted. It should be taken to the presses, and the clear beer mixed off in small proportions with that particular beer for which there is the most assured quick consumption, preferably black beer. If there be any difficulty about effecting a separation in the presses, that difficulty will generally be removed by adding finings to the sludge and beer about twelve hours before pressing. If there are no presses, bags answer equally well.
A case which came before me a few years ago bears very closely upon what I have been saying, although applying rather to the sludge which forms in beer storing vessels than to that in fermenting or settling plant, but the principle is the same.
A brewer was in the habit of bottling a light pale ale himself, and the contents of each storing-vessel were, when bottled, stacked and kept separate. In all cases the beer contained in the bottles on the top layers of the stacks showed floating particles (apparently of finings), while the rest was perfectly free from any such defect. It seemed inconceivable that the mere fact of certain bottles lying above the rest should produce a precipitation exclusive to those top-most layers ; but whatever was tried the result was the same.. The beers were then brought to me, and I found that the floating particle in the top layer beer were not finings at all, but agglomerations of wild yeast, and this led me to suppose (as indeed was the case) that these top layer beers representing the bottom strata of beer in the storing vessels had got practically the whole of the wild yeast sediment which had collected in the storage vessels, whilst the lower layers of bottles which were taken from the upper strata of beer in bulk got practically none of it."
"Journal of the Federated Institutes of Brewing, Volume 1, 1895", pages 493-494.
A cautionary tale. Watch out for sludge, brewers. You never know what might be in it.