|Funk & Wagnalls New Practical Standard Dictionary. Britannica World Language Edition. 1946, 1957.|
The word was coined in 1834 by the English physicist Sir Charles Wheatstone (1802-1875) from Greek rheos "a flowing, stream" + -stat "regulating device." I'm assuming that the name also inspired the Canadian indie rock band, the Rheostatics.
Wheatstone also happened to invent the telegraph, coin the word "microphone," invent the stereoscope, come up with the Playfair cipher encryption and, perhaps most importantly, make improvements to the accordion, renaming it the "concertina."
Below, a simple sliding rheostat in my possession: