Why treaties settled on six- and eight-inch cruiser guns

Why did the naval treaties choose six- and eight-inch cruiser-gun limits rather than other sizes?

Six inches marked the practical lower end for a cruiser, while British Hawkins-class interests and negotiation produced the eight-inch upper category; larger 9.2-inch proposals raised fears about powerful Italian Mediterranean cruisers.

Six-inch guns combined cruiser-level striking power with a useful rate of fire, while the British did not want their 7.5-inch Hawkins class excluded. Negotiators eventually settled on eight inches, after British consideration of 9.2-inch guns on 12,000-ton ships. French 155 mm weapons also help explain the familiar 6.1-inch treaty wording.