  The paper aims to apply the complex-octonions to explore the variable
gravitational mass and energy gradient of several particles in the external
ultra-strong magnetic fields. J. C. Maxwell was the first to introduce the
algebra of quaternions to study the physical properties of electromagnetic
fields. Some scholars follow up this method in the field theories. Nowadays,
they employ the complex-octonions to analyze simultaneously the physical
quantities of electromagnetic and gravitational fields, including the field
potential, field strength, field source, linear momentum, angular momentum,
torque, and force. When the octonion force is equal to zero, it is able to
deduce eight independent equilibrium equations, especially the force
equilibrium equation, precession equilibrium equation, mass continuity
equation, and current continuity equation. In the force equilibrium equation,
the gravitational mass is variable. The gravitational mass is the sum of the
inertial mass and a few tiny terms. These tiny terms will be varied with not
only the fluctuation of field strength and of potential energy, but also the
spatial dimension of velocity. The study reveals that it is comparatively
untoward to attempt to measure directly the variation of these tiny terms of
gravitational mass in the ultra-strong magnetic field. However it is not such
difficult to measure the energy gradient relevant to the variation of these
tiny terms of gravitational mass. In the complex-octonion space, the
gravitational mass is a sort of variable physical quantity, rather than an
intrinsic property of any physical object. And this inference is accordant with
the academic thought of `the mass is not an intrinsic property any more' in the
unified electro-weak theory.
