Brass tokens with the inscription "In memory of the good old days" were issued between 1787 and 1799. They typically have a bust of George III (British monarch from 1760 - 1820) on the obverse surrounded by the inscription "Georgius III dei gratia" and a Coat of Arms surrounded by the inscription "In memory of the good old days" on the reverse. Smaller pieces roughly the size of the half guinea are also common.
There is some evidence that these tokens were restruck in the 1860's. They are quite common with a value of a few dollars at most, and it is possible to put together a quite attractive collection of spade guineas for a modest cost. Their exact function is not known, but it is quite possible that they functioned as gambling tokens in a manner similar to today's Poker chips.
The end of the Campaign of Italy of 1796-1797 and the signature of The Peace of Campoformio on Oct. 17, 1797.
George I died during 1797 and was succeeded by George II. So, both George I and George II reigned during 1797.
John Adams was the Vice President from 1789 to 1797.
1797
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If the inscription in total reads GEORGIVS II REX on the obverse, with BRITANNIA on the reverse, your description lines up with a copper coin, but there were no copper coins minted in 1757 and all Pennies prior to 1797 were a small silver coin. You may have a privately minted coin or a medallion.
A real 1796 or 1797 Draped Bust dollar has values from $1,300.00 to about $100,000.00 dependong on type and grade.
In circulated condition it has no extra value. It's brass, not silver, and was minted in 2007 as part of the Presidential Dollar series. 1789-1797 are the years Washington served as president.
It's not made of gold and it's worth one dollar. 1789-1797 were Washington's years as President.
Its value would depend upon which coin it was and its condition.
Please look at the coin again. No US quarters were struck in 1797 and the Washington series started in 1932. Post new question.
Please look at the coin again. No US quarters were struck in 1797 and the Washington series started in 1932. Post new question.
Draped Bust Small Eagle, 1797 & 1798 are worth thousands in good condition. In uncirculated condition they are worth many thousands of dollars.
Please post a new, separate question with the coin's denomination.
There were no British Halfcrown coins minted from 1752 to 1815 inclusive.
One dollar.
Your coin is either a British 1797 "Cartwheel" Twopence 41mm in diameter, or a British 1797 "Cartwheel" Penny 36mm in diameter. If somebody has drilled a hole in it, it might be worth a few Pence. Modified coins have no collector value.