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Hiram Maxim Organization - Please visit this site
This site is intended to be a technical site, not an historical one. For a definitive discussion of Sir Hiram Maxim and the invention that made him famous, please read "The Devil's Paintbrush" by Dolf Goldsmith (released by Collector grade publications), you may find it at DS Arms or search for it on Ebay, as it is out of print. The third edition is due out "soon." I will update as soon as i receive more information.
Sir Hiram Maxim invented the first machinegun, and patented that design in 1883. Descended from that first design are a class of firearms with the ability to deal death with an efficiency never before seen. Maxim's design is infamous for being the most deadly firearm of all time, and has been credited (debatably) with changing infantry tactics more than any other firearm (the slaughter of WWI all but ended the bayonet charge).
The heart of the Maxim design is a toggle action. Below is an image showing the main internals of the Maxim. When teh trigger is pulled, the firing pin strikes the cartridge primer, ignition occurs, and the projectile is forced down the barrel. Using Newtons third law of thermodynamics (every action has an eequal and opposite reaction) the barrel, barrel extension and lock are driven rearwards.

The toggle handle cams on a bearing (not shown) forcing the handle upwards, and causing the "knee" joint to break, which in turn causes the lock to ride backwards on the barrel extension rails. This recocks the lock, and initializes the extraction of the spent cartidge and reloading of the fresh by allowing the lock extractor to drop (this action is aided by two leaf springs in the topcover).

Once in full recoil the extractor aligns the spent cartridge with the ejection port and the live round with the chamber. Upon locking, the extractor cams upwards grasping another cartridge that was moved into place by the feedblock.