the classical field theory. Therefore it is able to be said that the component selection are the essential ingredients for the field theory too.

In the quaternion space, it is able to deduce the gravitational field equations as well as the gauge condition of gravitational potential etc. The Newton’s law of universal gravitation in the classical gravitational theory can be derived from the gravitational field equations described with the quaternion. Two components of the gravitational strength are the counterpart of the linear acceleration and of the precession angular velocity. In general, the component of the gravitational strength, which is corresponding to the precession angular velocity of the gyroscopic torque dealt with the angular momentum, is comparatively tiny.

In the $S$-quaternion space, it is able to reason out directly the electromagnetic field equations as well as the gauge condition of electromagnetic potential etc. The electromagnetic field equations described with the $S$-quaternion can be equivalently translated into the Maxwell’s equations of the classical electromagnetic theory in the three-dimensional vector space. Moreover the definition of electromagnetic strength and the gauge condition of electromagnetic potential both can be equivalently translated respectively into that in the classical electromagnetic theory.

It should be noted that the 