The Baculus Cantoralis, to give it one of its many names, is a large staff held by a Choirmaster or Cantor which originates in Benedictine Monasteries of the 10th and 11th centuries. It is sometimes called a Baculus Choralis or a Baculus Praecentoris. At Solesmes, where it is still in use, it is referred to as Le Bâton de Chantre. When I was there recently I saw it being used at Vespers on Trinity Sunday. It can be seen beside the Cantors just to the right of the Eagle, resting on a stand:
At the top of the Baculus is a small ivory carving of St Peter, the patron of Solesmes Abbey, imparting a blessing and holding the Basilica of St Peter in Rome:
Its use is purely ceremonial nowadays, although in medieval times it was reportedly used as a 'corrective' instrument when dealing with inaccurate singers. (I wonder where I might acquire one...) The photograph below shows Dom Umberto Bertini of Farnborough holding a Baculus. The photograph was taken before Solemn Vespers at Clairvaux before the First World War.
I came across an article from 1940 about Dom Uberto Bertini in the Catholic Herald's online archive. Do go and read it if you have a moment: he was an extraordinary man. My thanks to the Monks of Farnborough for providing the photograph.