Identity:
Miss Crosby had, according to Whistler, a brother who was a soldier. This may have been Herbert Ball Crosby (ca 1872-1936) who graduated from the US Military Academy at West Point in the class of '93, on 12 June 1893.
Life:
The only record of Whistler's contact with Miss Crosby is a draft of a letter that may never have been sent (#00763). In it he changed his form of address from 'lady' to 'young lady', and it is unlikely that he had actually met her.