Breakdown Voltage Gradient and Paschen's Law - Doesn't make sense ?

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Original poster: "Mccauley, Daniel H by way of Terry Fritz <teslalist-at-qwest-dot-net>" <daniel.h.mccauley-at-lmco-dot-com>



Something isn't making sense to me.

I'm looking at some derivations of Paschen's Law in Lucas' High Voltage
Engineering Book which states the following:

**********************
Under constant atmospheric conditions, it is found that the breakdown
voltage of a uniform field gap may be expressed
in the form:

V = A*d + B*SQRT(d)       where d is the gap spacing

For air under normal conditions:
A = 24.4kV/cm
B = 6.29kV/cm^1/2

It then states that the breakdown voltage gradient is about 30kV/cm in
gaps on the order of 1cm
and about 6kV/cm for large gaps on the order of several meters

**********************

Using the above equation for say 1cm, I do indeed get approx. V =
30kV/cm

However, if I use d = 300cm (3 meters), i get about 24kV/cm, which is
way off from 6kV/cm.

Is there an error in the above equation, or am I missing something???

Any help appreciated.

Thanks

The Captain