Coin collector, coin shop, ebay, flea market.
You are describing the "mercury dime". The portrait is actually Miss Liberty, but the liberty cap she's wearing makes her look like the god Mercury, hence the coin's nickname. They aren't rare at all, in circulated condition. It's probably only worth about a dollar. If it's uncirculated still no more than $10 or so. All dimes before 1965 are worth about a dollar right now for the silver content.
Other than size, appearance, and monetary value... not much. If both were minted pre 1965, then they are both 90% silver. Both underwent a few different styles. For the silver dollar, there were Liberty, Morgan, and Peace designs. Dimes were Liberty, Barber, Mercury and Roosevelt.
Dime Sumka died on October 20, 1999, in Skoplje, Macedonia.
All "Mercury" dimes (aka Winged Liberty Head Dimes) struck at the branch mints of Denver (D) and San Francisco (S) have their mint marks near the bottom of the reverse, just to the right of the word "ONE".
The cast of Design on a Dime - 2011 includes: Casey Noble as Herself - Host
A 1857 nickel is also called: a Seated Liberty half dime. Its value in good condition (G-4) is: $20; if the mint state is MS-60, the value increases to: $250.
It's a Roosevelt dime not a liberty dime and all are considered common, value is about $2.00
The Winged Liberty, or Mercury Dime. Most people call it the Mercury Dime, but its real name is the Winged Liberty dime.
It isn't a liberty dime, it is a Roosevelt dime, it isn't silver and only worth 10 cents.
The Liberty dime minted in 1943 was 90% silver. The current rate for a circulated 1943 Liberty Dime is the current value of the silver of the coin, presently $5.50
1857 is not a rare date for Seated Liberty Dimes. In circulated condition, as long as it has complete rims on both sides, will be worth $10 to $15
You can find a picture of a 1936 liberty dime at the related link below.
A US dime dated 1867 is a Seated Liberty dime. To see one, in your search box type in Seated Liberty dime and click on images.
That's off by about 65 years. Mercury dimes were minted from 1916 to 1945. A dime from 1853 would be called a Liberty dime or Liberty Seated dime.
The Liberty Seated Dime (1837-1891)
The value of a 1842 seated liberty dime is about $20 in G-4(good) condition.
Miss Liberty is on the 1904 Barber dime, the first dime to have the portrait of a real person is the 1946 Roosevelt dime.