Hello Pentire,
His Master's Certificate was #38,207. It was issued at Liverpool on 5 August 1851.
You can see his entry in The National Archives file BT 124 free online at the CLIP (Crew List Indexing Project) website here:
http://www.crewlist.org.uk/masters/masters.php?mode=IMAGE&row=WILLIAM;DAY;1812;APPLEDORE;DEVON;MASTER;38207;;LIVERPOOL;5;8;1851;BT124_1b;2;102;8;1;321;1851%20-%201860;35000%20-%2038999;207Unfortunately, you will not be able to make any sense out of the three columns of coded notations beside his name. Those represent his voyages as a master for 1852, 1853 and 1854. None of us can interpret them without having access to the Customs House Registers for those particular ports for those particular years.
However, it is safe to assume that in 1853, his vessel was registered in one of the largest ports because it appears to be Vessel #7176 in that year's "Annual List of Shipping Registered to the Port of x" as the voyage begun in 1853 carried over into early 1854 when he died. Upon the vessel's return to her home port, she would have been added to the 1854 "Annual List" but under a different number.
However, you may be able to fill in gaps in his past work history. Ancestry has the "UK Masters and Mates" database. His certificate should be there. Once you find it, use both the backwards and forwards scrolling arrows to search for other pages in his file. Oftentimes there is the "Record of Service" which he would have had to submit detailing the vessels he had previously served on, his dates aboard same and his ranks aboard same.
Both Ancestry and FindMyPast have some other merchant navy records. There may well be other hits for him, including the one that gives a physical description - height, hair colour, eye colour, details of scars and tattoos.
Not having any subs myself, I can't look for you.
Cheers,
Westoe
EDIT: After posting this I tried the link but the image doesn't load. Try this one instead and fill in the blanks for William Day born 1812.
http://www.crewlist.org.uk/masters/masters.php