Yes, that is odd about the bluing loss on the cylinder; not normal for sure, but as long as it functions/fits OK, you could use Brownell's Oxpho-Blue to add back some deep/rich color (as it's the best cold blue formula I've ever used; but it may take several applications).
Is there a partial (3 digits) of the serial number on the cylinder or extractor star? If so, that will confirm it is the original factory cylinder for that frame.
Enjoy shooting it; I have one too, but I'd suggest you only use standard velocity 22's in it.
Also, to "keep it tight" for the frame-to-barrel lockup, it is always a great idea on older H&R top breaks to open the top-break latch when opening -- and when closing it too. Sure, it's neat to snap it open, quickly eject all the empties, load it up, and snap it back closed -- but that will accelerate slight loosening of the lockup over time. You can tell on the older guns where that was done a lot...
Below, I've posted some information about this model, as compiled by either the late Bill Goforth or Jim Hauff.
Tight groups.
Old No7
H&R "22 SPECIAL"
The H&R "22 SPECIAL" model was first catalogued circa 1926. The 1st Variation (1926-28) was chambered for 7 shot .22 rimfire (long rifle, long and short) and had the same frame and upper works as the H&R "AUTO EJECTING" model from that era and was equipped with two piece walnut grip panels with a hump at the top ("saw handle").
In late 1928 - 29, the chambering was changed to 9 x .22lr and also 7 x .22 Winchester Rim Fire. This is the 2nd Variation. NOTE: the .22 WRF chambering is extremely scarce - some experts have estimated that only around 200 pieces were made with this chambering.
In 1930, the grip panels were changed to rounded top/no hump checkered walnut and this is considered the 3rd Variation (1931- 32).
In 1933, the grip frame was changed to the "RICE" type, with a bird's head shaped grip frame and one piece monogrip - attached to the frame by one bolt through the rear of the grip screwing into the now covered back strap. The cylinder now came equipped with a raised rim around the back face - the "H&R SAFETY RIM. This is considered the 4th Variation (1933 - 1938).
The 5th Variation (1939 - 1940?) There is the possibility of a 6th Variation with some other changes internally. Markings on the barrel were pretty much consistent, except when the .22 WRF chambering was introduced - the right side was stamped either: ".22 LONG RIFLE CTG" or ".22 W.R.F. CTG". The rear cylinder face for the 7 shot .22 WRF will be marked with a W.R.F. stamp, along with the last three digits of the s/n.
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