On the 1881 Census William's occupation is "Foreman of Examiners Rl(?) Arsenal".
Had you seen the 1861 Census? (reference RG09 408 119 10)
William Dawson, Br. in Law, age 43, occpn. Shell examiner, born Woolwich.
Was "your" William the William Dawson, Royal Sappers and Miners, discharged Adelaide, 6 May 1856?