1816, 2nd edition, vol.1, footnote on p.67:
classis Insecta 
1. ordo Coleoptera
consisting of Beetles
2. ordo Strepsiptera 
consisting of genera Xenos and
Stylops
3. ordo Dermaptera
consisting of the Earwigs
4 ordo Orthoptera
consisting of Cockroaches, Locusts, Grasshoppers,
Crockets, Spectres, Mantes, &c.
5. ordo Hemiptera
consisting of Bugs, Cicadae, Water-scorpions,
Water-boatman, Plant-lice, Cochineal insects, &c.
6. ordo Trichoptera
consisting of flies, produced by the various species of
Case-wormes, Phryganea L.
7. ordo Lepidoptera
consisting of Buterflies, Hawkmoths, and Moths.
8. ordo Neuroptera
consisting of Dragon-flies, Ant-flies, Ephemerae, &c.
9. ordo Hymenoptera
consisting of Bees, Wasps, and other insects armed with a
string or ovipositor, and its valves.
10. ordo Diptera
consisting of Flies, Gnats, and other two-winged insects.
11. ordo Aphaniptera 
consisting of the Flea genus.
12. ordo Aptera
consisting of Mites, Lice, &c.
1826, 2nd edition, vol.4:
classis Insecta
1. ordo Coleoptera
= Eleuterata (:368)
2. ordo Strepsiptera
= Rhipiptera (:369)
3. ordo Dermaptera
(:370)
4 ordo Orthoptera
(incl. Dictyoptera Leach )
(:371)
5. ordo Neuroptera
(:371)
6. ordo Hymenoptera
(:373)
7. ordo Hemiptera
= Ryngota F. (:376)
8. ordo Trichoptera
(:378)
9. ordo Lepidoptera
= Glossata F.
(:380)
10. ordo Diptera
= Antliata F. (:381)
11. ordo Aphaniptera
From
αφανης, inconspicuous; so named because something like elytra
appeaer (:382)
12. ordo Aptera
(:383)
subordo Hexapods
Thysanura Latr. =
Anoplura Leach
subordo Octopods
1. Aranidea McL. 
= Aranea L. = Araneidae Latr.
2. Scorpionidea McL.
= Scorpio L.
3. Galeodea 
Galeodes=Silpuga
4. Phrynidea
subordo
Polypods
= classis Myriapoda Leach