what was the first machine they used a carburettor on?

Carburetors were invented in the late 1800's by Hungarian dudes named Banki and Csonka. At the time, carburetors consisted of a wick-like surface that drew air across it, with the gasoline drawn into the wick. They were used on standing engines - I'm assuming they were for industrial purposes, but what industrial purposes I cannot tell you.

The first automotive carburetor was used in England - for a 5 hp auto engine by Lanchester. It was also a wick-type design.

At about the same time, Maybach and Daimler were using an atomizer carburetor for engines - this is more like the modern carb, and it was eventually used on automotive engines created by these guys, and by Karl Benz (note - Daimler-Benz.....). The wick one was first, though.