Someone wondered what he was holding in it. It's a camera lens, the sort that goes on the type of big brass and mahogany plate camera that he used. He is apparently polishing it with a cloth. The photo was taken by the celebrated Rejlander, whom Carroll consulted when building his own photographic studio.
LEWIS CARROLL IN HIS OWN ACCOUNT: THE COMPLETE BANK ACCOUNT OF THE REV. C.L. DODGSON [ Edited with Notes and an Introduction by Jenny Woolf ] Paperback – 2005