Lewes says: “The emergent is unlike its components in so far as these are incommensurable, and it cannot be reduced either to their sum or their difference” (Lewes 1875, 413)
(N.B.: consider "or their difference" - it seems half of the story is forgotten, and not reduceable to the sum has been turned into greater than the sum, which adds some factor in my view.)
Mill says: “The chemical combination of two substances produces [...] a third substance with properties different from those of either of the two substances separately, or of both of them taken together . […] There, most of the uniformities, to which the causes conformed when separate, cease altogether when they are conjoined; and we are not, at least in the present state of our knowledge, able to foresee what result will follow from any new combination, until we have tried the specific experiment.” (Mill 1843, 371, bk3, ch6, §1)
The qualifier "present state of knowledge" is important here. Today we can (better) explain why the combination of two gases forms water. This indicates that we like to take as emergent what we cannot (yet) explain.
Thus emergence is the surprising occurence of a phenomenon we cannot currently explain - but may be able to explain in the future. The modern sum is greater than its parts is obviously a qualitative interpretation: water is definitely interesting in its properties, but why should its properties be "more" than that of H and O?