The Carcel lamp was patented in Paris by the watchmaker Guillaume Carcel on October 24, 1800. Two different models are on display at the Musée des Arts et Métiers in Paris
The Carcel lamp is a mechanical lamp that puts a definitive end to the problem of the bad capillarity of vegetable and animal oils. The clockwork movement (in the foot) controls a pump located in the oil tank to raise the oil directly to the nozzle.
The first generation of lamps (1800-1810) had to be lifted to wind the movement for the underside of the lamp (Mulum model). The second generation of lamps (from 1810), was to be lifted up to the side (pair on display at the Grand Curtius). Other Parisian inventors, including Gagneau, would later modify the pump(s).
The Carcel lamp, and Carcel type, will always be a "Rolls Royce" for big budget. From 1837, a simpler and less expensive mechanical lamp will be manufactured in Paris then elsewhere: the lamp with moderator (spring and leather piston).
These lamps have nothing to do with the oil lamps (mineral oil) that will be manufactured in the second half of the 19th century.
Head of the “Musée du Luminaire” (Museum of Lighting)
More information about the Mulum (Musée du Luminaire), here: https://lesmuseesdeliege.be/mulum/