(1):

(n.) The quality or state of being hard, literally or figuratively.

(2):

(n.) The peculiar quality exhibited by water which has mineral salts dissolved in it. Such water forms an insoluble compound with soap, and is hence unfit for washing purposes.

(3):

(n.) The cohesion of the particles on the surface of a body, determined by its capacity to scratch another, or be itself scratched;-measured among minerals on a scale of which diamond and talc form the extremes.