Portsmouth Garrsion Hospital Records

[Steve Bridges]

Hi-
I have just learned that my g-g-grandfather William Bridges died at what is called the Station Hospital in Portsmouth, in March 1876 (source: British Newspaper Archive). I am assuming this is what was called the Garrison Hospital?
He was in a the army (sources Marriage Cert., 1871 Census), but a lowly rank as far as I can tell (no regimental records survive of his service). The death notice in the paper calls him a 'smith', however. Unfortunately, he does not appear in the BDM Index.
Does anyone have suggestions as to whether there are surviving records from the hospital that might help me discover how he died?
Steve Bridges
Sydney, Australia.