Drew, Burrard in volume 3 of," The modern Shotgun- The gun and cartridge," reviews improved cylinder and its relation to choke.In 1887 when the British rules of Proof changed, eliminating the "Not for Ball" mark,replacing same with the word, "Choke", the rule of proof was, "any barrel with a restriction at the muzzle must be impressed with the word choke".
Burrard defines improved cylinder as, "Any barrel with a muzzle diameter [choke] normally reduced by .003-.005" that results in a pattern density of 50% approx; using #5or6 shot [British] at 40 yards . This represents a 10% approx; improvement over a gun bored true cylinder.Expanding on this issues, Burrard states that some makers infact increase the degree of choke on improved cylinder barrels to .008 max; in order to achieve the desired pattern density.
In my opinion the term Improved cylinder was adopted by the british trade in 1887 so as to differentiate between the more common and better understood definitions of choke namely 1/4 ,1/2, 3/4, and full choke.
