[bjornsing]

Wow! :) A quick read seems to indicate that the case where the "metal plate with holes in it" approaches a wire mesh (holes are large compared to spacing) is treated in "Reflectors for a Microwave Fabry-Perot Interferometer" published by W. Culshaw in 1959 [1].

It's still locked up behind a paywall though, some 57 years later! :( Anybody have access (or can afford the $13 / $33 to buy it)? I checked if I could access it through DeepDyve but, no.

(Perhaps this is the answer to Q1, that it really hasn't "remained unanalyzed for 180 years", but that our broken way of archiving scientific knowledge has hid the analysis?)

1. http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=112468...

[duaneb]

Here it is: http://sci-hub.cc/10.1109/tmtt.1959.1124685#

[bjornsing]

Thanks! :)

To me it seems not entirely implausible that both the OPs main conclusions can be derived from Culshaw's 1959 paper:

1. "First of all, the radius of the wires matters. As r→0, the shielding goes away. This, we now realize, must be why your microwave oven door has so much metal in it, and is not just a sheet of glass with a thin wire grid."

This conclusion could possibly be derivable from Eq 26 in Culshaw's paper. There's a clear dependence on r there. It's not completely obvious (to me) though, as it seems Culshaw is studying a more general case with a 3D structure of rods/wires.

2. "Secondly, the shielding is linear in the gap size, not exponential."

This conclusion too could possibly be derivable from Eq 26; there's a linear dependence on a there. But for the same reasons as above it's not entirely obvious (to me).

Seems to me that Trefethen should at the very least read Culshaw's paper though, if he hasn't already. :P

Can anyone with some electrical field theory knowledge/experience make a better comparison? :)

[Iv]

> but that our broken way of archiving scientific knowledge has hid the analysis?

A thousand times this.

What we need is a wikipedia of academic science where edits are peer-reviewed.