The design discussion separates the main battery's capital-ship role from the secondary battery's defensive work. Four-inch guns are weak in a ship-to-ship duel with large opponents, but useful against destroyers, smaller craft, and aircraft. Those targets call for weapons smaller than the 18-inch main guns. The distinction explains the defensive role of a battleship's secondary battery.
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What four-inch secondary guns are for
Four-inch secondaries may be weak against major warships, but they remain valuable for engaging destroyers, smaller craft, and aircraft.