J. C. Maxwell applied simultaneously the vector terminology and the quaternion analysis to study the electromagnetic features. Nowadays the spaces of electromagnetic and gravitational fields can be chosen as the quaternion spaces, and the coordinates of quaternion spaces are able to be the complex numbers. The quaternion space of the electromagnetic field is independent to that of the gravitational field. These two quaternion spaces can combine together to become one octonion space. Contrarily the octonion space can be separated into two subspaces, the quaternion space and the S-quaternion space. In the quaternion space, it is able to deduce the field strength, field source, angular momentum, torque, force, and mass continuity equation etc. in the gravitational field. In the S-quaternion space, it is able to infer the field strength, field source, and current continuity equation etc. in the electromagnetic field. The results reveal that the quaternion space is suitable to depict the gravitational features, including the gravity and the mass continuity equation etc.. Meanwhile the S-quaternion space, it is suitable to describe the electromagnetic features, including the electromagnetic force and the current continuity equation etc..