Sure it would reduce accuracy. The inner cylinder is approximately a 10:1 ratio. One inch of rain fills 10 inches of cylinder. The outer cylinder is approximately 1:1 ratio, so one inch of rain (over the first one inch) fills the outer cylinder one inch. So the accuracy of the overflow would be 1/10 the accuracy of the inner cylinder.

Why are you proposing to treat the two designs differently? You can still decant the overflow into the inner cylinder to get 1/100ths of an inch. The only change is that you would be able to read rainfall over 1 inch to the nearest 1/10th without disassembling the gauge, which is an

*improvement* over the current design.

With an inner diameter of 4 inches, every inch of rainfall will fill a 1.155-inch ID tube with 12 inches of water. This is approximately the current design, and it works well enough. However, the entire outer cylinder is the same diameter as the funnel. Since the inner cylinder displaces some water, the depth of the water in the overflow doesn't relate in a meaningful way to the actual rainfall. If the inner diameter of the outer cylinder was changed to 4.239 inches, and the funnel kept at 4 inches, the water level in the overflow would rise one inch for every inch of rain that fell into the funnel (assuming the inner tube's walls are 1/8-inch thick).Everything would still work the same. The first inch would be readable in 1/100ths and the overflow would fill the outer cylinder. You would still decant the overflow into the inner cylinder to get 1/100ths of an inch. The only change is that while the gauge is still assembled you can glance at it and see that 2.4 inches of rain has fallen (for example). With the current design you cannot tell how much rain is in the overflow by glancing at the gauge, so I would say the accuracy has been improved in that respect without disturbing the ability to decant the overflow for higher accuracy.

EDIT: When you try to do math without double-checking your work first, you get mistakes. I corrected the calculations of diameters.