TRIMMING THE WICK

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In his translation of a book by the Banu Musa brothers, Donald Hill possibly modifies an illustration of an oil lamp (which actually showed a knob and a rack and pinion gear) to add a float pulling a chain to pull out more wick as the flame burns. Donald Hill’s fictitious chain pulls in the wrong direction. In another book, Donald Hill replaces the fictitious float with a fictitious vacuum device.
An illustration of another lamp shows what might or might not be a wind barrier.
Donald Hill claimed this as the Muslim invention of the hurricane lamp, but modern hurricane lamps do not look like this.
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banu_musa_mechanical

TRIMMING THE WICK

The flaming wick is located at the upper far left of the diagram. The function of the circular object at the top right corner of the diagram is unclear, but Donald Hill guesses it is a tank of oil. Donald Hill takes a guess in one book that a partial vacuum (created when oil flows out of the oil tank) pushes up the wick. This explanation does not make much sense, because a vacuum at the right side of the lamp would suck the wick in, not push more wick out.
In another book, Donald Hill either copied a different drawing of the lamp from a different book by the Banu Musa brotbers, or else Donald Hill altered the illustration to add a float inside the tank of oil. He claims that the float was attached to a chain that pulled the wick. Not only is Donald Hill possibly adding something that is not in the original illustration, but a float that falls as fuel is consumed would pull on the wick from below, shortening the wick when the wick needs to be lengthened.
In my interpretation of the diagram, the circle at the top right corner of the diagram is not a tank of oil. I see a rack and pinion gear that converts rotary motion into linear motion. The wick of the lamp is operated by someone turning a knob. I am guessing that circular objects inside the lamp form a counterweight pushing on the rack to counter the weight of the rack, thus preventing the rack from sliding back down into the lamp.
An animation of a rack and pinion gear can be found at https://en.m.wikipedia.org/wiki/Rack_and_pinion
The Romans knew about rack and pinion gears, having used them in devices to lift water.
It is likely that this device in the diagram was copied from a Byzantine book, rather than being actually invented by the astronomer Banu Musa brothers. The brothers worked in the same building in Damascus that contained a huge library of Byzantine books written in Greek.

HURRICANE LAMP?
Another illustration shows what might or might not be a wind barrier (consisting of a semicircular vertical wall that may be surrounding the flame on 2 sides.
Donald Hill described this as the Muslim invention of the hurricane lamp, but modern hurricane lamps have a full 360 degree cylindrical shield, the shield is transparent instead of non-transparent, and instead of air blowing from the side, use a convection current from below to supply the air.

Image made by one of the Banu Musa brothers, via Wikimedia Commons.
image credit
https://commons.wikimedia.org/wiki/File:Banu_musa_mechanical.jpg#mw-jump-to-license

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