Let me say right up front. I dont think this is your William Murphy anymore. To my knowledge (PLEASE correct me if I am wrong) your WIlliam was not a corporal, I believe, if I remember correctly he was not a corporal. Then only one who was a corporal in the family was James Westley Murphy and he entered as a corporal. Me and a few of your cousins here think it is really James Westley and the person who gave it to me was just mistaken/confused. But here is the picture.
IF it is in fact James Westley Murphy, then he is your Williams half brother.