Thank you for the quote that came from the American Edition of 1804 which was a pirated copy of the 1802 2nd edition. This was written in 1799 and was printed by T Egerton in 1801. The manuscript was submitted in late 1799.
The Royal Artillery in the 1790s were going through a transition and Adye was referring to the AWI equipment that plagued the RA at the time. The only unifed system was that used by the RHA. Introduction of the Butler Carriage with its iron axle, double draft and the abandoming of battalion guns came in c1800. Adye was writing before this.
By the Peninsular War, there was a rational system. The old pattern equipment had been retired or fallen to bits. The Brigade artillery did not receive block trails until c1813. It should be noted that the RHA always had block trail howitzers of the Desaguliers design apart from a short period when they received Heavy 5.5in howitzers from the Brigade (Foot) Artillery.