This is W. E. Newton's Patent No. 2650 of October 13th 1865.  
The name G. R. Wilmot is that of the person by whom the invention has been communicated to the applicant for Letters Patent. (Just what that means, I will find out later).
The information comes out of  Patents For Inventions – Abridgments of Specifications. Class 119, Small-Arms. Period A.D. 1855-1866
 
The illustration is exactly the same as your specimen.
Protecting from dust and rain.
“A muzzle-stopper consists of a hollow cylinder d of vulcanised India-rubber, which is expanded radially by compression between the plate B and head A by a screw C, a sleeve k being interposed between the screw and the rubber. The cylinder d has on its outside a layer h of vulcanised rubber covered by a layer of leather, cloth, felt, or the like.”
 
W. E. Newton produced a string of patented inventions, his “Venetian Blind”  rear sight is one I have seen on an early Whitworth..   The date November 24th, 1863 does not feature in the Abridgments.
 
30 bore as a rifle or carbine size is nothing out of the ordinary.
 
 
 
 

Happy to have found it as I am not always so lucky.  I asked my old friend George, who is retired Patent Examiner, about the Wilmot reference and he said that the systems have changed a lot since that period but he thinks it is probably the name of the agent who dealt with the Patent Office on behalf of Newton (but he cannot be sure).
 
I have a small collection of tompions  including some by Blanch incorporating an oil bottle and others which can be used as rod guides.  I will photo them some time but meanwhile here is Blanch’s advertisement as an indication.
 

 

 

This is very interesting.  As I see it, the 24 November 1863 Patent will be for the American Inventor Wilmot who had to get a UK citizen to register the patent in the UK, hence the grant of Letters Patent to Newton.  Can you confirm the earlier American Patent date for Wilmot.?
 
Going the other way, the British gunmaker Charles William Lancaster patented his Oval Bore Bolt Action Under Hammer Rifle on 28th September 1854, #2089,  with an improvement on 16th September 1857, #2400.  In the USA, one Lieut.-Colonel Durrell Greene patented this in 1857 on behalf of Lancaster, the design being exactly that of Lancaster.  BUT - to this day no-one in America believes anything other than that Greene was the inventor when he was nothing but Lancaster's representative.  The rifles were made in USA and a limited number purchased by the Federals.  I have handled a couple of them and would really like to give one a work out with the correct ammn.  This is the rifle where the bullet is pushed to the commencement of rifling by a push rod running through the bolt body.  A cartridge in reversed form like that of the P'53 is then loaded so that its bullet forms the base obturator for the next shot.  After firing, the rod pushes the bullet to the front of the chamber before the bolt is opened and a fresh reversed catridge inserted.  The problem is that before firing a number of shots, the first action is to load a loose bullet.  Another complication was the under hammer action.  I imagine troop training problems with these.  I would still like to have one though.