Green’s Dictionary of Slang

a pipe; thus cock one’s organ v., to smoke a pipe.

1785, 1788, 1796		Grose Classical Dict. of the Vulgar Tongue n.p.: Organ. A pipe. Will you cock your organ? will you smoke your pipe?
1798		‘St Giles’s Greek’ in Sporting Mag. Dec. XIII 164/1: The cull [...] remained at the bowsing ken, cocking his organ.
1811		Lex. Balatronicum [as cit. 1785].
1823		Egan Grose’s Classical Dict. of the Vulgar Tongue [as cit. 1785].
1862		E. de la Bédollière Londres et les Anglais 316/2: organ, pipe. Will you cock your organ? Voulez-vous fumer votre pipe?