Page:A Dynamical Theory of the Electromagnetic Field.pdf/35

where $\alpha ,\beta ,\gamma$ are the components of magnetic intensity. If R be the resultant gravitating force, and R' the resultant magnetic force at a corresponding part of the field,

$R=-R'\ \mathrm {and} \ \alpha ^{2}+\beta ^{2}+\gamma ^{2}=R^{2}=R'^{2}$

Hence

$E=C-\sum {\frac {1}{8\pi }}R^{2}dV$

(47)

The intrinsic energy of the field of gravitation must therefore be less wherever there is a resultant gravitating force.

As energy is essentially positive, it is impossible for any part of space to have negative intrinsic energy. Hence those parts of space in which there is no resultant force, such as the points of equilibrium in the space between the different bodies of a system, and within the substance of each body, must have an intrinsic energy per unit of volume greater than

${\frac {1}{8\pi }}R^{2}$

where R is the greatest possible value of the intensity of gravitating force in any part of the universe.

The assumption, therefore, that gravitation arises from the action of the surrounding medium in the way pointed out, leads to the conclusion that every part of this medium possesses, when undisturbed, an enormous intrinsic energy, and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction.

As I am unable to understand in what way a medium can possess such properties, I cannot go any further in this direction in searching for the cause of gravitation.

PART V. — THEORY OF CONDENSERS.

Capacity of a Condenser.

(83) The simplest form of condenser consists of a uniform layer of insulating matter bounded by two conducting surfaces, and its capacity is measured by the quantity of electricity on either surface when the difference of potentials is unity.

Let S be the area of either surface, a the thickness of the dielectric, and $k$ its coefficient of electric elasticity; then on one side of the condenser the potential is $\Psi _{1}$ and on the other side $\Psi _{1}+1$, and within its substance

${\frac {d\Psi }{dx}}={\frac {1}{a}}=kf$

(48)

Since ${\tfrac {d\Psi }{dx}}$ and therefore $f$ is zero outside the condenser, the quantity of electricity on its first surface $=-Sf$, and on the second $+Sf$. The capacity of the condenser is therefore $Sf={\tfrac {S}{ak}}$ in electromagnetic measure.