The "Heraldic Eagle" reverse was first used in 1798. An authentic 1797 DB dollar should have the "Small Eagle" reverse.
Sorry this isn't a American silver eagle. This is a Morgan silver dollar. The mintmark is located above the DO in DOLLAR on the back of the coin.
The first silver eagle was made in 1986 not 1879. It's called a MORGAN dollar after the designer George T. Morgan and assuming it's circulated and has no mintmarks, retail value is $17.00-$26.00 the date is very common.
An 1879 "Silver Dollar" is a Morgan dollar.
1879 would make it a Morgan dollar, which has an eagle on the reverse.
It's a Trade Dollar not a Morgan dollar. If you look at the back of the coin, the phrase "Trade Dollar" is under the eagle. As to value, take it to a coin dealer for an assessment it may not be genuine. The entire series is known to have had copy's and fakes made.
No collection value but is has a scrap silver value of about 10 bucks.
Peace dollars were made from 1921 to 1935. An 1879 silver dollar is called a Morgan dollar after its designer George T. Morgan. There's more information at the Related Question
1879 would make it a "Morgan" dollar.
The value for an 1879P morgan silver dollar, uncirculated, is about $45 (Red Book) price. If you have any Morgan's that have mintmark, CC, Carson City, the value goes up.