Perigosto stick

A perigosto stick looked like a thin, silver probe with a tiny sphere on top. (NA: Love and War) Students at the Time Lord Academy used them to play games of four-dimensional juggling. (EDA: Seeing I) However, on one occasion, the Third Doctor claimed that it was a musical instrument. (PDA: Deadly Reunion)

The First Doctor and his friend Ruath once electrified Cardinal Borusa's perigosto stick. (MA: Goth Opera)

The Doctor was in his early nineties before he could bring himself to admit that he still liked to play with his perigosto stick. The other students teased him mercilessly about that for about fifty years. (EDA: Beltempest)

On an occasion when the Master believed he had killed the Third Doctor, he ruefully thought back to a youthful prank when the Doctor and he had put glue on the Lord President's perigosto stick. (DWN: Doctor Who and the Dæmons)

The Third Doctor once told a humorous story in which the punchline was "never trust a Venusian shanghorn with your perigosto stick." (DW: The Green Death)

Behind the scenes
The perigosto stick was the basis of a minor running joke by Doctor Who novelists. Building upon the minor mentions in The Green Death and Doctor Who and the Dæmons, novelists would make elaborate mention of perigosto sticks without explaining all that much about what they actually were or might have been used for.