One major variety of the 1878 Morgan Silver Dollar features 8 Tail Feathers on the eagle at the reverse of the coin. Other later versions were changed to 7 tail feathers.
One major variety of the 1878 Morgan Silver Dollar features 7 Over 8 (7/8) Doubled Tail Feathers. The initial die originally had 8 feathers but was later changed to 7. This resulted in what looked like 7 feathers struck on top of 8 feathers - and gave it a doubled feather look.
One major variety of the 1878 Morgan Silver Dollar features 7 Tail Feathers and also features the reverse design of 1878. The reverse of 1878 is actually the earlier design which can be identified by noticing how the eagle had an unnaturally flat or concave breast. The easiest way to identify this variety is to look at the arrow feathers on the arrows that the eagle is holding in it's claw. The top feather is straight and parallel along with the rest of the arrows.
The later reverse of 1879 variety was changed to give the eagle a rounder and more convex breast appearance that looked more natural. Again the easiest way to identify the reverse of 1879 is to also look at the arrow feathers. Unlike the reverse of 1878 - the reverse of 1879 features a prominently slanted top feather on the arrow.