This is the formula for length contraction. As there existed a proper time for time dilation, there exists a proper length for length contraction, which in this case is "". The proper length of an object is the length of the object in the frame in which the object is at rest. Also, this contraction only affects the dimensions of the object which are parallel to the relative velocity between the object and observer. Thus, lengths perpendicular to the direction of motion are unaffected by length contraction.