In this paper, J. Jacobi’s Theorems [9] have been considered for the spherical curves drawn on the unit dual sphere during the closed space motions. The integral invariants of the ruled surfaee corresponding, in the line space, to the spherical curve dtawn by a fixed point on the moving unit dual sphere during the one-parameter closed motion were calculated with a different approach from the area vector used by H. R. Müller [11], In addition, the ruled surfaces corresponding to the curves drawn by the unit tangent vector, principal normal vector or a unit vector on the osculating plane of the mentioned curve, were seen to be cones with this approach.