This is where life gets complicated.
The arms as I have them, full heraldic description somewhere in my files. appear to have been granted to a de Mansfeld family in Yorkshire back in the 1500s but we have no evidence to suggest that the Mansfields are descended from them. Nor indeed is there any evidence that the family used their arms. A new Spring Hill College was built between 1854 and 1856, after their deaths and it may simply be that the architect went searching for a device associated with the name Mansfield with which to adorn his building.
This became tricky in 1955, when Mansfield College applied for full membership of Oxford University and the College of Heralds queried their right to the arms, lifted from Spring Hill. It was at this point that they engaged a professional genealogist, who seems to have made a complete dog's breakfast of his research (I have his notes), with the result that the college was obliged to commission a new coat of arms.
My interest stems from the fact that I attended Moseley Grammar School, then housed in the old SHC building, between 1956 and 1962, at which time the entire history of the building had been lost. A few years ago the then Deputy Head of the successor school, of which I was then a governor and which was still housed in the same building, and I determined to investigate and we are now almost ready to publish our findings.
Needless to say, Mansfield College also have a keen interest in resolving this particular puzzle.
Keith