I am still find that each time I count I get to a different number as there was variations through the time when you count.
Manson and Rostaing replaced the front wheels of the Gribeauval Garrison Carriage with the same wheel as the field and siege guns. The truck wheel was the same size for all as far as I have been able to determine. Therefore there was ony one extra wheel. The other wheel comes from the solid wheel on the meunier carriage for coast guns.
There was one wheel for each of the calibres rather than two in the previous system.
M1792 Manson Reforms
Garrison Rear Wheel truck
Field Rolling Stock
M1792 4-pdr limber
M1792 8/12-pdr limber
Caisson rear wheel
Siege / garrison guns
M1732 single draft Limber
Light / Mountain Guns [
4-pdr Swedish Guns
Moutain guns [Various]
> Surely, the wheels for the field pieces varied to take account of the physics of firing the different pieces as mounted on the (necessary) different carriage
That was the wisdom of the 16th century. It had not taken into account the work in the middle of the 18th century of Bellidor, Robins, Euler. There was no reason for having so many different wheels. By the 1780s Britiain had come to the conclusion and started to implement this. This was not complete until the 1790s with the heavy and light 5 foot wheel. The same comclusion was made by the Austians and Prussians earlier.
The size different in the wheels was in inches or upon their weight so it made little difference. Small wheels have a higher rolling resistance than smaller wheels. This was the main problem with the French Caisson.
There was no unification of the French System until the reforms by Manson shown in the Manson (1792) tables of construction. I know it does not answer the question but it is what are you counting as part and not part of the system.
I am not sure about d'Urtubie. You can always contact me offline as I do not have D'Urtunbie. I borrowed Paul Dawson's copy a couple of years ago.