Law of corona and dielectric strength of air — III

Air at the surface of small wires has an apparently greater strength than air at the surface of large ones. It has been found that the breakdown gradient may be expressed
$g_v = g_0\left(1+{k \over \sqrt{r}}\right)$
This means that at breakdown the gradient is always constant and equal to g
0
, at k √r cm. from the conductor surface, independent of the size of the conductor. The explanation seems to be that energy is necessary to start rupture and that, therefore, rupture can not start at the surface, but only after the surface gradient has been increased to g
v
, in order to store the rupturing energy between the conductor surface and k √r cm. away in air, where the gradient is go. Theoretically g
0
should vary directly with the air density, or
$g_0^{\prime} = \delta g_0$
If the energy theory is true the energy storage distance should also vary with δ or energy storage distance = Φ (δ) k √r. This has been found to be the case, that is,
${\rm Energy\ storage\ distance}\ = k \sqrt{r \over \delta}$
Therefore g
v
docs not vary directly with δ but
$g_v = g_0 \delta \left(1 + {k \over \sqrt{\delta_r}}\right)$
The effect has been found to be the same whether δ is varied by change of pressure, or temperature (over range where there is still no chemical change due to temperature). According to the above theory if the wires were spaced very close together, so as to interfere with the free energy storage distance, that is, in the order of k √r cm., it would be expected that g
v
would increase in value in order to store sufficient energy to start rupture in the limited distance. It has been found that the gradient begins to increase at a spacing of 2 k √r cm. and, within the limits of the tests, g
v
values as high as 200 kv. per cm. or 500 kv. per inch have been reached. Spheres were used in these tests as it is impractical to adjust cylinders at small spacings. The electron theory may also be nicely applied to the above when the distance k √r may be thought of as the “accelerating distance.”