All 3 Uses of

consequence
in
The Importance of Being Earnest

That was in consequence of a misunderstanding between myself and a young person.
Act 1 *

consequence = result

You see, it is simply a very young girl's record of her own thoughts and impressions, and consequently meant for publication.
Act 2

consequently = resultantly (as a result)

You are the son of my poor sister, Mrs. Moncrieff, and consequently Algernon's elder brother.
Act 3

Definitions:

(1) (consequence as in: a direct consequence of)
a result of something (often an undesired side effect)
(2) (consequence as in: of little consequence)
importance or relevance
(3) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

In classic literature, consequential may refer to someone with too much feeling of self-importance as when Dickens wrote "Because he's a proud, haughty, consequential, turned-up-nosed peacock."

Self-consequence was used in a similar manner, but is more easily understood by modern readers since important is one of the modern senses of consequence.

Another classic sense of consequent that is similar to importance or significance refers to "material wealth or prominence" as when Jane Austen wrote: "They had each had money, but their marriages had made a material difference in their degree of consequence."