What this coin looks like (obverse, reverse, mint mark location, special features, etc.): There were multiple varieties of the 1878 Morgan Silver Dollar - 7 Tail Feather Type. These varieties deal only with the coins that had only 7 tail feathers on the eagle depicted on the reverse of the coin. The earlier version originally had 8 feathers before the number was reduced. One major variety is actually 7 feathers struck over 8 feathers (7/8 doubled tail feathers) - which resulted when the engraver was updating the die to strike 7 feathers over the original 8. The difference between the 7 vs 7/8 vs 8 tail feathers 1878 Morgan dollar is depicted above in the example comparison image.
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. The difference between the Reverse of 1878 vs Reverse of 1879 Morgan Silver Dollar is depicted below in the example comparison image with the features depicted by the arrows: