  The paper discusses some scalar invariants in the gravitational field and
electromagnetic field by means of the characteristics of the quaternions. When
we emphasize some definitions of quaternion physical quantities, the speed of
light, mass density, energy density, power density, charge density, and spin
magnetic moment density etc. will remain the same respectively in the
gravitational and electromagnetic fields under the coordinate transformation.
The results explain why there are some relationships among different invariants
in the gravitational and electromagnetic fields.
