Col. Thorton was one of the most famous air gun shooters in history. His book, "A Sporting Journey Through France" has always been a tough book to get ahold of. I picked up a set of this big 2 volume book years ago on Ebay. Nice copies can go for thousands. Now it's available to all.
Written about his journey through France in 1802, it's a fascinating look into France just after the French Revolution.
One small bit of this book seems to have escaped any attention can be found on page 37.
The "re-loaded instantaneously" is what caught my attention. It would seem that Col. Thorton might have been shooting a Girandoni-style air gun or perhaps one of the other Staudenmayer's repeater air gun designs. That Col Thorton would have been aware of Staudenmayer is pretty sure, since Thorton was a customer of the London Gunmaker Joseph Manton where Staudenmayer apprenticed prior to opening his own shop in 1799.
There's a couple more air gun mentions, see page 71, and also some air gun diagrams on a plate between pages 70-71. The plate does not show a repeater air gun. Instead, the air guns shown are an old butt pump with barrel surround tank, another older ball tank design, and an old air cane design. These same diagrams can be found in other scientific books of the time showing the basic concepts of the air gun, so, they are almost certainly not the air guns carried by Thorton.
There is also a discussion by some French officers about how they saw another officer apparently shot by an air gun and how they would hang any soldier found with an air gun.
Pretty neat 1802 stuff.