Coleman lantern is a generic trademark, also called genericized trademark or proprietary eponym, where the brand name became the synonym for the product itself. Some examples are escalators (a brand name by Otis) or aspirin (a brand name by Bayer). It is the name of a kerosene lamp, where the fuel is pressurized by a manual pump and has a carburetor, which allows a brighter and steadier flame. Unfortunately it is as fragile as any other kerosene lamp, especially the glas and mantle, and thus not really suitable for caving, at least for the sportive kind. But it was popular during the 19th and early 20th century due to the lack of alternatives and because people generally tended to explore only the "easy" parts of cave. As far as we know it was never used for mining.
The lanterns were originally created and produced by Irby & Gilliland in Memphis, Tennessee. The official name was The Efficient' Pendant Arc lamp No. 6. William Coffin Coleman was selling the gasoline fueled lamps with his company Hydro-Carbon Light Company, incorporated 1900. However, despite the obvious advantages, sales were poor. Since the lamps could not be cleaned, they became clogged with soot, which caused the light to go out after some time. He acquired the patent for the lamp and redesigned it, and in 1903 he started production. In 1914, he introduced the Coleman Lantern, a design incorporating various improvements, such as a bug-screen and a flat base. Since that time more than 50 million of the lanterns have been sold throughout the world.
The German version Petromax was developed in 1910 by the Berlin commercial councillor Max Graetz at his company Ehrich & Graetz. Max Graetz was called Petroleum-Maxe by his friends, and this nickname was shortened to Petromax. The lamp was very popular for decades, as it provided light and even warmth, it was used by farmers, flea market owners, and by the German army. During the 1930s the Graetz AG dominated the world market for such petroleum lanterns with a market share of 80 %. After World War II most lamps were sold abroad, in countries where electricity was not available nationwide. In the late 1970s the sales collapsed, and despite the popularity among campers, it was not produced in Germany anymore. For some time it was produced in high quality in Portugal, but after two decades in which the patent was sold numerous times it is not produced anymore. Still there is a company of the same name which sells camping gear and even lamps of the same name, which seem to be Chinese copies.
The third main lamp of this type is the British Tilley Lamp. It is named after John Tilley, who invented the hydro-pneumatic blowpipe in 1813. William Henry Tilley was manufacturing gas lamps in Stoke Newington since 1818. The Tilley company moved to Brent Street in Hendon in 1915 during World War I, and began developing a kerosene pressure lamp. The lamps were sold from 1919 by the Tilley High-Pressure Gas Company, and sold them widely to railway companies and the Armed Forces. Many sailors, soldiers and airmen used a Tilley Lamp during World War II. And again the name Tilley lamp became the eponym for high pressure lamps in Britain.
This type of lamp is called pressure lamp, which is basic idea of the lamp. But actually there are three components which make this kind of lamp possible, the pressure, the carburettor, and the mantle instead of a wick. It burns multiple liquid fuels such as petrol, paraffin, diesel, kerosene, petroleum, gas or spirit. The lamps are usually portable, consist of a pressure tank with an integrated hand pump, and a glass cylinder with the mantle. You fill the fuel up to a mark, then the air in the container is compressed to 2 atmospheres with the pump, for both of which measuring instruments are attached. Now you can open the nozzle and light the mantle. A turning wheel is used to adjust the flow rate and thus the brightness.