includes not only the quaternion but also the $S$-quaternion.

Since the vector terminology can describe the electromagnetic and gravitational theories, the quaternion should be able to depict these two theories also. In the paper, the quaternion space is suitable to describe the gravitational features, and the $S$-quaternion space is proper to depict the electromagnetic features. And it may be one approach to figure out some puzzles in the electromagnetic and gravitational theories described with the vector.

In recent years applying the quaternion to study the electromagnetic feature has been becoming one significant research orientation, and it continues the development trend of gradual deepening and expanding. Increasingly, the focus is being placed on the depiction discrepancy of electromagnetic features between the quaternion and vector. The related research into the discrepancy is coming out all the time.

Some scholars have been applying the quaternion analysis to study the electromagnetic and gravitational theories, trying to promote the further progress of these two field theories. V. Majernik [@majernik1] described the electromagnetic theory with the complex quaternion. W. M. Honig [@honig] and A. Singh [@singh] applied respectively the complex quaternion to deduce directly the Maxwell’s equations in the classical electromagnetic theory. S. Demir [@demir1] etc 