The Only Use of

resolution
in
Dr. Jekyll and Mr. Hyde

Here Poole motioned him to stand on one side and listen; while he himself, setting down the candle and making a great and obvious call on his resolution, mounted the steps and knocked with a somewhat uncertain hand on the red baize of the cabinet door.†
p. 55.2

Definitions:

(1) (resolution as in: a New Year's resolution)
a firm decision to do something
(2) (resolution as in: a United Nations resolution)
a formal statement of decision or opinion voted on by a group

While a resolution typically expresses an opinion and has no legal force, when used in early U.S. history or in the expressions joint resolution of Congress or continuing resolution, it becomes a synonym for legislation (meaning that it carries the force of law).
(3) (resolution as in: Her resolution weakened.)
determination (firmness of purpose)
(4) (resolution as in: resolution of the dispute)
a solution or outcome
(5) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

Much less commonly, other meanings of resolution include:
- a measure of optic detail -- as in: "The photograph has excellent resolution."
- separation into different parts -- as in: "When force is applied to an inclined plane there is resolution of the force into horizontal and vertical components."
- conversion to something else -- as in: "... resolution of the chord from dissonance (an unstable sound) to consonance (a more stable sound)."
- reduction to or conversion to something else -- as in: "It permits resolution of a URL to an IP address."