The lines of force of a magnetic field extending through an infinitely conducting fluid between footpoints on the planesz=0 andz=Lcan be wrapped and interwoven by bounded continuous motions of the footpoints into a random sequence of arbitrary topological patterns along the field. The sign of the topological helicity of the winding pattern of the field vanes at random along the field. On the other hand, in force-free equilibrium the relative helicity (α=B. ▿B/B2) is rigorously constant along each line of force. Indeed in the limit of an endless random sequence of independent winding patterns along the field, the helicity falls asymptotically to zero and the field becomes curl free. A field with constant helicity along each line of force is obliged to create internal tangential discontinuities (in which the sign of the curl and the helicity is arbitrary) if it is to follow the varying topological helicity imposed by the twists and turns of the succession of independent winding patterns.