I came along eventually Baz (and with my "technical" hat on too!)
For simplicity (and for those who wish to read no further!) -
Gauge '3' is built to a gauge of 2.5" (63.5mm) and this (for standard gauge railways) gives a scale of 1:22.6.
The history is a little more convoluted however. Gauge ‘3’ (or N° 3, as 2½" gauge was originally known) was one of five standard model gauges recommended by a subcommittee of the Society of Model Engineers on February 1st, 1899, making this gauge now more than a century old. At the time, 2½” gauge allowed the construction of fairly successful and reasonably to-scale live-steam locomotives - although the scale used back then was generally 1/2" (e.g. 1/24th). This changed between the 1st & 2nd World Wars to the more accurate scale of 17/32nds (13.5mm) to the foot. It should therefore be noted that G3 is firmly based on an Imperial gauge (e.g in inches) - as were the other four standard gauges.
Much confusion exists in this area because in the early days of "toy" trains, most toy train products were imported from the "Continent" - as Europe was then called in this country!
In 1891 at the Leipzig Toy Fair, Marklin introduced three new train ‘sets’ which were remarkable then, because for the first time a manufacturer had introduced the concept of a ‘Railway’ by matching train to track and accessories. Prior to this, manufacturers had simply sold an engine and maybe some carriages or wagons to accompany it – most had no track to run on and the concept of “gauge” was unknown. Here for the first time was a company marketing toy train sets and in three different sizes. Marklin called them Gauge I (48mm), Gauge II (54mm) and Gauge III (75mm). It should be noted that these measurements were made from the centre of each rail (and not the inside rail edges).
Other Continental manufacturers quickly followed with their own ranges.
Schonner adopted Gauges I, II and III but also added a 67mm gauge, which it called Gauge IIA.
Bing (Marklins greatest rival) followed with the same gauges used by Schonner but designated 75mm track as Gauge IV and 67mm track as Gauge III. Carette had two track gauge sizes it designated as Gauge I (48mm) and Gauge III (initially at 65mm, later at 67mm). So although the toy industry was moving towards standardising their actual track gauges, there was less agreement on what to call these gauges.
In summary, Bing and Carette both had 67mm track (as measured between rail centres) they called Gauge III, as did Schonner – although they called it Gauge IIA. Both Marklin and Schonner had 75mm track they called Gauge III but which Bing called Gauge IV. It is perhaps unsurprising that this caused much confusion in Britain at the time, compounded by the use of ‘centre of rail’ track measurements.
However, Gauge '3' as we know it today, goes back to the Society of MEs sub-committee of 1899 and is based on a track gauge of 2.5" and therefore scales at 1:22.6 exactly.
Regards,
IanT