...all of these concepts of usefulness are rather limited, and we only mean by them, that each science should have applications outside its own area, and that there is some general direction in this sequence of applications towards practical ones...

This phrasing suggests an "(in)exact sequence" of sciences, in which the image of a foundational science for a discipline (ex: Physics for Chemistry) is in the kernel of applications to an overlying science (ex: Chemistry to Biology).