There are several sensory changes that occur as a result of our movements. In the case of two, it is known that a compensating process `prevents perception corresponding to the sensory input, They are the compensation for the displacement of the visual field caused by a head movement, and the compensation for the visual rotation of an object we pass during forward movement. Here we report a third case, compensation for the expansion of the retinal projection of the visual field when we move forward. In these three cases, the sensory input is covariant with the proprioception of the movement that causes it. We then ask if a compensation will develop when an artificial sensory input is made to be covariant with head movements. Two experiments are reported in which rapid adaptation was achieved in such situations.