Page:An Enquiry Concerning the Principles of Natural Knowledge.djvu/44

 stands for what is called the vector product of the two vectors, namely the vector

It is evident that $${curl_\alpha}(X_\alpha, Y_\alpha, Z_\alpha)$$ can be expressed in the symbolic form

The vector equation

is an abbreviation of the three equations

Let $$(F_\alpha, G_\alpha, H_\alpha)$$ be the electric force at $$(x_\alpha, y_\alpha, z_\alpha, t_\alpha)$$, and let $$(L_\alpha, M_\alpha, N_\alpha)$$ be the magnetic force at the same point and time. Also let $$\rho_\alpha$$ a be the volume density of the electric charge and $$(u_\alpha, v_\alpha, w_\alpha)$$ its velocity; and let $$(P_\alpha, Q_\alpha, R_\alpha)$$ be the ponderomotive force: all equally at $$(x_\alpha, y_\alpha, z_\alpha, t_\alpha)$$. Finally let $$c$$ be the velocity of light in vacuo.

Then Lorentz’s form of Maxwell’s equations is

It will be noted that each of the vector equations (3), (4), (5) stands for three ordinary equations, so that there are eleven equations in the five formulae.