Riviere La Tranche is now known as the Thames River. The Hesse District became the Western District (in 1792) before it became the counties of Essex and Kent (as well as the London district).
The Ontario GenWeb described Hesse as follows:
"Established 24 July 1788 as one of four districts within Upper Canada. Consisted of the area that is now the current counties of Brant, Bruce, Dufferin Elgin, Essex, Grey, Huron, Kent, Lambton, Middlesex, Norfolk, Oxford, Perth, Waterloo, and Wellington."