In relation to some of the wagon-related issues and questions in this thread:

In wagon-terminology, the spar under the wagon is generally known as a "reach pole". On a farm wagon, for example, it would usually be straight, and fastened in the same manner, with a pin at each end (the "fifth-wheel" pin is generally called the "kingpin"). On a farm wagon, the wagon-box would be removeable, and the wheel-base could be then adjusted for other loads, as the "reach" would be long, and the tail-pin would be towards the center of the wagon body (through a plate-box on the rear "hounds"). The "reach" would have multiple rear pin-holes to make this adjustment. This was the common design that was most used on wagons in the early 19th century.

The running gear is known as "dead-axle" as it is un-sprung, as opposed to the gear on a "spring-wagon" where the axle is sprung to the body in the rear and the front axle is sprung to the "hounds" and fifth-wheel assembly. Some dead-axle designs did not have a reach pole, and would therefore have iron-bracing to replace the bracing from the wooden "hounds" in the rear-axle assembly on a reach-wagon.

Spring wagons can have small wheels up front, that can turn under the wagon-body, thus giving a large turning radius, very useful when manouvering in narrow city streets; dead-axle wagons generally have larger front wheels for increased ground clearance, and the turning radius is correspondingly less, as it is limited by the space between the higher front-wheels and the wagon-box when turning (English farm-wagons tended to have inward curved bodies to increase the turning radius).

The statement about assembling small wheel spares carried as parts is interesting; I am wondering if these wheels were intended to be shod with "hoop-tyres" or "strakes" (individual shoes, as commonly used on artillery wheels before the advent of American factory made wheels in a later era). I note that the small wheels shown had ten spokes, and thus five felloes, it was common to have an odd number of felloes for straked wheels, and an even number for hooped tyres (at least, that was the local case for farm wagons reported in "The Wheelwright's Shop" by George Sturt in 1874 when he took over his late father's shop in Farnham; their tools and wagon designs hadn't changed much in centuries at that time). I would presume, however, that the front and rear wheels referred to would both be either hooped or straked, but not mixed.

It should be noted that hooped tyres were more friendly to paved city streets, than strakes, as the latter were usually nailed on with diamond-headed hand-forged flat nails, which were fine on dirt, but harsh on paving blocks.

I have just discovered some of the other French wagons: the ambulance's (light and heavy), and the "supply" (or "baggage"). These basically used a form of dead-axle running gear, but the ambulance boxes were sprung from the wagon bed.

Hope this helps.

Regards, and thanks for posting the caisson photos and diagrams!

John