In years of looking for a Savage made Brayton tubeless scope I ended up finding a lot of information on similar setups and even found a couple examples, newest acquirement is a circa 1910 Alex Martin Galilean sight. Galilean seems to be the term used in England to describe what in the Sates would just be called a 'tubeless scope'. The Martin sight has a magnification of about 2X and is used like a peep sight with the black dot in the center of the front lens used for aiming, in contrast the Brayton used standard type rifle sights and the lenses could be folded down if magnification was not needed.

Here is the sight set temporarily mounted on a rifle, the rear eyepiece contains a small lens and is made more for a receiver type sight because the edge contacts the sight before the threads bottom out, also, because the sight line is much higher (about 1.2" above bore center), this sight barely has enough elevation adjustment so you can just see through it (and it's not sighted in, so it may have to go higher).

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This sight is unmarked other than a number, but other sights that are almost identical are marked 'Alex Martin', the patent is in the name of John Elsden Martin -
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There were several makers of similar sights from this time period and during WWI several, including the Alex Martin, were issued for use on Lee-Enfield rifles for sniping - some of the others were Lattey, Neil and Gibbs. One article I found stated that British War office records showed there were 9000 Lattey, 4,250 Neill, 775 Martin and 100 Gibbs sights issued to frontline regiments. All were about 2X and of course none of these sights worked well in the rain.

Here is the patent for the Martin front sight for use on the Enfield, you can see it is a much more robust design -
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The Martin and Neil used a dot on the front lens for aiming, the Gibbs had a pointer & cross line on the front lens and the Lattey used the existing rifle sights and worked much like a Savage/Brayton with the rear lens forward on the barrel sight. There is a Enfield with a Lattey sight set pictured at the bottom of the page in this link - rifleman.org.uk/Enfield

Some of the other British manufactured sights and variations are pictured in the two links -
www.milsurps.com/35259
www.milsurps.com/24821

This type sight was improved on and was still being marketed by Parker-Hale at least into the1930's - and it was it was marketed as fitting on Savage & Steven's rifles -
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Gene