The book History of Modern U.S. Military Small Arms Ammunition, Vol. 1 (Revised) by Hackley, Woodin & Scranton describes the experimental Cal. .22 1895 Experimental Cartridge in some detail.  Gene Scranton provided one of his excellent pen and ink drawings of a loaded cartridge.

Springfield Armory made at least one .22 caliber barrel and perhaps one in .20 caliber.  Frankford Arsenal made 250 unprimed cases, 250 118 grain bullets, 25 112 grain bullets and 25 250 grain bullets.  The cases were tinned brass, Case length was 2.745".  Head diameter was 0.430" and rim diameter was 0.512".  Bullet diameters were .225".  Overall length of a loaded round was 3.471".

The case looked like a stretched-out Krag, but was smaller in diameter and longer.  With only 250 cases and 300 bullets made, there were probably only one or two test rifles made.  The cartridges were probably too long to function through the Krag magazine, but they could have been loaded singly, all that would be necessary for an experimental cartridge.  Muzzle velocity with the 120 grain bullet was about 2,600 fps.  Since there is no further record of the cartridge, it was apparently not a great success.

Note that the bullet diameters are greater than the diameter reported with the earlier Army document.  The same is true for the diameters of the .30 and .45 bullets.  These guys used bore diameters, not groove diameters.

My adventures with an early Gallery Practice Rifle, with a groove diameter of .226" make me think that the internal barrel dimensions may have doomed the experiment from the start.  Deep grooves in excess of bullet diameter are not conducive to good accuracy.