Hello jedburgh
If you have a look at findmypast.co.uk there seems to be a little bit of info on Private McCormick - not a full service record (though a more diligent search may find one, I only looked quickly) but follow
this link.
That includes the info that he attested in Dec 1866 and was discharged Feb 1885.
Apart from that I think you'd have to check the census returns - 1841 (?), 51, 61, 91, 01 and 1911 and then see if you can dig out any birth, marriage or death records. You can either use the Scottish transcriptions on findmypast.co.uk (they don't yet include 1911) or view the original census documents at scotlandspeople.co.uk - this is presuming he resided in Scotland (is McCormick an Irish name?).
If you're related you probably have more info with which to find the right William McCormick!
With best wishes - Garen