Both Uses of

resolute

in

Moby Dick

However, Starbuck, who had the ordering of affairs, hung on to it to the last; hung on to it so resolutely, indeed, that when at length the ship would have been capsized, if still persisting in locking arms with the body; then, when the command was given to break clear from it, such was the immovable strain upon the timber-heads to which the fluke-chains and cables were fastened, that it was impossible to cast them off.†
Chpt 79-81 *

resolutely = with firm purpose or belief

So with poor Queequeg, who, as harpooneer, must not only face all the rage of the living whale, but—as we have elsewhere seen—mount his dead back in a rolling sea; and finally descend into the gloom of the hold, and bitterly sweating all day in that subterraneous confinement, resolutely manhandle the clumsiest casks and see to their stowage.†
Chpt 109-111

Definition:

firm in purpose or belief