The school ink bottles

An original account written in a nineteenth-century voice; a period simulation, not an archival document.

Every Monday I filled the school’s ink bottles before the children arrived. I used to pour each to the brim, believing that a full bottle was the most useful. The master showed me the black stains left beneath their desks. A bottle with no space above the ink spilled when a child pushed in a pen, and a tightly stoppered one overflowed when the stopper was forced down. Thereafter I left a small empty space at the top; the ink lasted no less well, and the desks suffered less.

Explain two actions that caused the overfilled ink bottles to spill.