keithhagan
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The chambers on a X frame are on about a .560 radius
That means a 1.12 dia circle with circumference of 3.517
divided by 5 it is .703 and by 7 it is .502
A 500 has an outside wall thickness of .100. If the 350 uses the same radius it would have about .236 outside wall and at least .11 space between the chambers. Actually a bit more as the closest spot between the chamber is outside the radius of chamber centers.
Your idea of using a 30-30 case and a 40 cal bullet is interesting as there would be no shoulder.
The place where the space between chambers is narrowest lies on the straight line between two adjacent chambers. Since the centers of the charge holes lie on the circle with radius 0.560, these lines form the heptagon inscribed within this circle (in general, for a cylinder with n charge holes, this point will lie on the n-gon so inscribed).
This means that the distance between the centers of the charge holes will be a little less than 0.502 (for large numbers of charge holes this difference tends toward zero).
I get a distance for the center of adjacent charge holes in the 350 of
Code:
y = 2 * R * cos(450/7) ≈ 0.560*0.86776747823 ≈ 0.48594978781
This leaves about 0.063" between chambers at their narrowest at the mouth assuming a 30-30 cartridge sized chamber (.423" at the mouth). This is more thickness than an N frame in 45 Colt, but a bit less than the thickness in an N frame 44 magnum (~0.075").