This is a great piece of history a set of 17 glass hydrostatic balls, originally there would have been 19 balls, this is a big set of glass balls,  rarely do you find this number still remaining.
Each glass ball is numbered and would have been placed in alcohol to measure the specific gravity of a given liquid.If the ball floated, it would be cross-referenced against the number on the list on the inside of the lid.  These were used in the 18th and early 19th before modern hydrometers were available.
This circular rosewood  box with glass balls is by Baldy Bombaly, Whitehaven.
The box measures 8.5cm in diameter.
There is a set of these hydrostatic balls by Baldy Bombaly in the Science Museum.