Here's a write-up on these from the late Bill Goforth, who wrote "the book" on H&R Firearms:
ULTRA SPORTSMAN MODEL 777 1938 - 1939
Large frame single action top break revolver; 22 rimfire caliber (shorts, longs or long rifles); cylinder capacity 9 rounds; flat top oval shaped barrel 6 inches in length (same as used on the model 199; front sight adjustable for elevation, elevation screw on front of barrel just above muzzle, rear sight adjustable for windage; oversized one piece checkered Walnut grips (eleven different styles available); straight trigger, arched hammer spur; cylinder release is a vertical lever on the right side of barrel lug; rear of cylinder has the patented H&R safety rim; finger rest trigger guard; trigger pull factory set 2 ½ to 3 pounds; hammer mounted firing pin serial numbered in its own series U01 to at least U1000.
Markings:
Top of barrel rib: HARRINGTON & RICHARDSON ARMS CO. WORCHESTER, MASS. U.S.A. in two lines
Left side of barrel: H & R “ULTRA SPORTSMAN” No. 777
Right side of barrel 22 Long Rifle CTGE.
And this info was posted online years ago by the late by Jim Hauff:
So few of this model have been transacted over the past 5 years or so, that the valuations listed in the Blue Book are based upon a very limited set, primarily gained from less than a dozen sold on gun auction sites, several personal sales that became known to me and a few that I personally purchased or offered upon. Therefore, pricing and valuation of this model (as well as the rarer Model 196 Eureka Sportsman) are subjective and vary quite a bit from region to region and time to time. The market is limited to those who recognize the collectability of these models - others will not value them as highly and will lump them into the general valuation of the Sportsman revolvers.
Hope this info is helpful.
Old No7