  The paper aims to apply the algebra of octonions to explore the contributions
of external derivative of electric moments and so forth on the induced electric
currents, revealing a few major influencing factors relevant to the direct and
inverse piezoelectric effects. J. C. Maxwell was the first to adopt the algebra
of quaternions to describe the physical quantities of electromagnetic fields.
The contemporary scholars utilize the quaternions and octonions to research the
physical properties of electromagnetic and gravitational fields. The
application of octonions is able to study the physical quantities of
electromagnetic and gravitational fields, including the octonion field
strength, field source, linear moment, angular moment, torque and force. When
the octonion force is equal to zero, it is capable of achieving eight
independent equations, including the force equilibrium equation, fluid
continuity equation, current continuity equation, and second-precession
equilibrium equation and others. One of inferences derived from the
second-precession equilibrium equation is that the electric current and
derivative of electric moments are able to excite each other. The external
derivative of electric moments can induce the electric currents. Meanwhile the
external electric currents are capable of inducing the derivative of electric
moments. The research states that this inference can be considered as the
underlying mechanism for the direct and inverse piezoelectric effects. Further
the second-precession equilibrium equation is able to predict several new
influencing factors of direct and inverse piezoelectric effects.
