He goes far enough into open ocean that they will be dragged out to sea. There the depths drop to almost bottomless. Then the fish eat the body parts by working their way into rips or small holes.
I wonder how people from the 1940's would feel about our casual discussion of body parts and how to dump them properly.
They get found at one point thats why instead he starts putting them in a stream so they wash away making it harder to find.