Good morning Jason.
They used exceptionally detailed " Lithographs " for their advertisements, you can almost make out the horizontal flyball governor.
Judging from the size of the flyballs I'd suggest that it's at least a 1 1/2 HP engine. There aren't many Barkers left in preservation and I, personally haven't seen anything bigger than the 1 HP. What is worthy of note is that they seemed to use different flywheel spoke patterns for the sizes. The 1/2-3/4 have 5 curved spokes. The one horse have 5 straight spoke and your picture shows 6 straight spokes. Obviously, different diameters and weight too.
The engines are of a very simple but effective design, the air and gaseous fuel are drawn through an atmospherically operated, horizontally orientated inlet valve. The exhaust is mechanically operated by an
" L " shaped lever driven via a roller/cam arrangement from the sideshaft. The governor, hit and miss style acts upon the exhaust lever roller and " props " it open on overspeeding.
The ignition is of the " Hot tube " variety which was a very cheap option at that time when compared to the very expensive and new fangled " Electric " systems.
Water cooling is, quite simply effected by the use of a cavity around the cylinder and thermosyphon to a large capacity water tank. As with most of the smaller engines of the day, the cylinder head is cooled by conduction into the cylinder jacket.
Well, that concludes the introduction, I just need that sleeve for my Clarkson " Autolock " chuck and we can begin....
Cheers Graham.