Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/289

of volume, and $v$ and $w$ are the components of electric currents referred to unit of area perpendicular to $y$ and $z$ respectively. Hence,

Similarly

$X=\alpha m+v\gamma -w\beta$ $Y=\beta m+w\alpha -u\gamma$, $Z=\gamma m+u\beta +v\alpha$.

(Equations of Electromagnetic Force.)

(20)

644.] If we adopt the theories of Ampère and Weber as to the nature of magnetic and diamagnetic bodies, and assume that magnetic and diamagnetic polarity are due to molecular electric currents, we get rid of imaginary magnetic matter, and find that everywhere $m=0$,and

so that the equations of electromagnetic force become,

$X=v\gamma -w\beta$, $Y=w\alpha -u\gamma$, $Z=u\beta -v\alpha$.

(22)

These are the components of the mechanical force referred to unit of volume of the substance. The components of the magnetic force are $\alpha$, $\beta$, $\gamma$, and those of the electric current are $u$, $v$, $w$. These equations are identical with those already established. (Equations (C), Art, 603.)

645.] In explaining the electromagnetic force by means of a state of stress in a medium, we are only following out the conception of Faraday^[1], that the lines of magnetic force tend to shorten themselves, and that they repel each other when placed side by side. All that we have done is to express the value of the tension along the lines, and the pressure at right angles to them, in mathematical language, and to prove that the state of stress thus assumed to exist in the medium will actually produce the observed forces on the conductors which carry electric currents.

We have asserted nothing as yet with respect to the mode in which this state of stress is originated and maintained in the medium. We have merely shewn that it is possible to conceive the mutual action of electric currents to depend on a particular kind of stress in the surrounding medium, instead of being a direct and immediate action at a distance.

Any further explanation of the state of stress, by means of the motion of the medium or otherwise, must be regarded as a separate and independent part of the theory, which may stand or fall without affecting our present position. See Art. 832.

1. Exp. Res., 3286, 3267, 3268.