One thing I always recommend, if you have found a copper that looks in bad shape, but you can see some details, TAKE A PIC of it BEFORE any type of cleaning is attempted. A good habit to get into is the "Before" and "After" photos.
A lot of times the details you see are just the now corroded metal/hardened dirt, which is going to wash away with almost any type of cleaning, it sort of like just an impression of what used to be solid metal and no longer is, cleaning off dirt, never really "ruins" the coin the coin was already destroyed by corrosion. Also, never rub much on the iffy coppers if you want to save what corroded details are left, it takes experience to know when to do what with a coin or a button.
With that said, I do not think it is a Farthing, cannot tell exactly how much smaller than your CT copper to the right, but it could a a small, light weight KGIII copper of some type, usually size in diameter and weight in grains or grams helps in determining some intelleigent guesses on unknown coppers....
Don