Paschen's law

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Original poster: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br> 

Hi:

Some update about the final form of the translation of Paschen's
article? And about the pictures? (usually in the last pages of
the Annalen).

I am thinking about how to apply the law to determine the breakdown
voltage of gaps that would break down at low voltages, or because
the distance is small, or because the radius of curvature of the
surfaces is small, always at normal pressure.

For example, assuming a maximum electric field of 30 kV for each
cm of radius for a ball, a 0.2 mm ball would have breakout at 300 V,
and a 2 um ball at just 3 V. In this case there is no distance to
consider, so how to apply the law?

For a gap between two flat plates, the law says that the breakdown
voltage is a function of the product of pressure and distance, with
a minimum of about 340 V for p*d=0.2 cm.mmHg. With 760 mmHg, the
minimum corresponds to d=0.00026 cm, or 2.6 um. Below this distance
the law says that the breakdown voltage increases. Very strange.

And about gaps between points with small radius of curvature and
small distances? The strange effects appear to occur at um distances,
what is not so small.

I think that there is something missing in this law. Specially a
reason for it being as stated.

Antonio Carlos M. de Queiroz