答案选 D.on which to base
句意：这位教授几乎不可能找到必需的理由,以此来支持新学说.
固定短语：base sth on sth.
原句剖析：The professor could hardly find necessary grounds（ on which to base his arguments） in favour of the new theory.划线部分为定语从句,正常语序应该是which he base his arguments on介词提前可以得到on which he base his arguments ,大家都知道宾语从句中what to do=what we should do ,类比可得,此句可改成on which to base his arguments 答案：D