Actually I've always understood Ought gauge (not scale) to have been chosen at 1.25" (1-1/4") just as a nominal measurement by toy train makers back in the dark ages and the size (scale) of the models to run on that track in a likewise manner. "OO" or as Hornby called it "Dublo" was just 5/8", or half of "O" and the "scale" of the trains, just as abitrary. Being that 3'6" gauge works out at as the perfect size for 1/64 scale for OO/HO track in the imperial foot and inches measuring criteria, suited me fine in NZ, although I never did get past doing anything more than draw drawings of loco plans in that scale from photos and known overall lengths and heights. I was very surprised many years later to come across printed drawings in a hobby shop, that showed that my drawings were pretty accurate generally. I was helped by my mother, who went with me to the railyards in town, where we wandered around the locos near the train shed, while I took photos with her old Box Brownie camera and took measurements of bits and pieces, sometimes on engines that were standing, hissing steam. Not another soul to be seen, never got "shooed" away. Was that what's referred to as "The good old days"?It doesn't work out, it just happened sort of backwards. Take a 7mm track gauge for "Ought" scale, take 1/2 of that for Half Ought or 3.5mm. So make that equal to standard gauge of 4' 8.5" and what work out what scale ratio that ends up being?