Let me make one thing clear. This is all based on the geometrical fact that spheres are proportional to the cube of their diameters. Obviously, when the British made their proof charts giving the diameters of the various gauges they used this formula. The 1 gauge diameter was rounded off to three places, so listed as 1.699" on the charts. If one simply uses 1.669" as the base it will result in some very slight errors while going through the entire chart. The only part I played in this was to just set down & calculate the exact number was needed for the 1 gauge to make all gauges fit the existing chart. As I said you Must go with 1.66928x, & I now do not recall exactly how much that X can vary, but 5 works out & is convenient to remember. When working with either a calculator or a Keypad on a computer after putting in the 1.669 & moving to the center 285 is bottom, top &, middle numbers.
