All 3 Uses of

on the other hand

in

Moby Dick

By the above definition of what a whale is, I do by no means exclude from the leviathanic brotherhood any sea creature hitherto identified with the whale by the best informed Nantucketers; nor, on the other hand, link with it any fish hitherto authoritatively regarded as alien.†
Chpt 31-33 *

When I stand among these mighty Leviathan skeletons, skulls, tusks, jaws, ribs, and vertebrae, all characterized by partial resemblances to the existing breeds of sea-monsters; but at the same time bearing on the other hand similar affinities to the annihilated antichronical Leviathans, their incalculable seniors; I am, by a flood, borne back to that wondrous period, ere time itself can be said to have begun; for time began with man.†
Chpt 103-105

…what made this incident of the Rachel's the more melancholy, was the circumstance, that not only was one of the Captain's sons among the number of the missing boat's crew; but among the number of the other boat's crews, at the same time, but on the other hand, separated from the ship during the dark vicissitudes of the chase, there had been still another son; as that for a time, the wretched father was plunged to the bottom of the cruellest perplexity; which was only solved for him by…†
Chpt 127-129

Definition:

(on the other hand)
from another point of view; or in a way that is different (a phrase used to introduce a different perspective or idea)