Abstract: It has been considered that the image compensation displacement caused by swinging of compensator is equal to the sum of the object swing and image swing around the centre of the pendulum.Based upon this new concept,a mathematical model for the self-levelling compensation function has been presented.As a consequence,the consistency in principle between the"turning" and"parallel displacement" modes,which are admittedly deemed to be traditional in the theory of automatic level,has been obtained.The model has also made it possible to provide a simple and general method for the calculation of compensation function for various types of compensators.