  We use superconducting rings with asymmetric link-up of current leads for
experimental investigation of winding number change at magnetic field
corresponding to the half of the flux quantum inside the ring. According to the
conventional theory, the critical current of such rings should change by jump
due to this change. Experimental data obtained at measurements of aluminum
rings agree with theoretical prediction in magnetic flux region close to
integer numbers of the flux quantum and disagree in the region close to the
half of the one, where a smooth change is observed instead of the jump. First
measurements of tantalum ring give a hope for the jump. Investigation of this
problem may have both fundamental and practical importance.
