Why did Henry Cavendish conclude that excess electric fluid lies on the outer surface of an electrified sphere?

Henry Cavendish concluded that excess electric fluid resides on the outer surface of an electrified sphere based on his mathematical theory of electricity, which he published in 1771.1

His reasoning was rooted in the relationship between electric force and distance: he demonstrated that if the intensity of electric force is inversely proportional to the square of the distance between charges, then any excess electrical fluid must necessarily distribute itself on the exterior of a closed conducting sphere. Cavendish confirmed this theoretical conclusion through precise quantitative experiments. This work served as an early, though unpublished, determination of the inverse square law, which was later famously established by Charles-Augustin de Coulomb.12