Why the 10-inch naval gun fell between useful calibres

Why was there no enduring 10-inch naval gun between common cruiser and battleship calibres?

It did not offer enough extra penetration over eight inches or enough advantage over twelve inches to offset its rate-of-fire and weight penalties.

Penetration, rate of fire, and mounting weight explain the missing 10-inch step. Once eight- and twelve-inch guns were available, the intermediate calibre did not add enough performance to justify its compromises. Its rate of fire was broadly comparable with a 12-inch gun and roughly half that of an 8-inch weapon. A later exchange also notes the heavy mounting penalty relative to an 8-inch gun. Ten inches made more sense in earlier periods when it approached the largest practical calibre, but later cruiser and battleship choices left it stranded between better-supported alternatives.