They will keep for months if picked and stored correctly in a cellar or basement, where it’s consistently cool and humid. Usually they were packed in clean sand or fine sawdust to keep them from drying out. If they are bruised or damaged in any way, they will get moldy and rot quickly. A barrel was commonly supposed to be enough for daily use for a large family for one winter. I could see why Everett would be upset that damaged or wormy apples were hidden in the lower layers. It means he was cheated, because the barrel will go bad. Source: 19th century housekeeping manuals by Mrs. Beeton and others.