Both Uses of

consequence

in

A Modest Proposal

They cannot get work, and consequently pine away from want of nourishment, to a degree, that if at any time they are accidentally hired to common labour, they have not strength to perform it, and thus the country and themselves are happily delivered from the evils to come.
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consequently = resultantly (as a result)

Fifthly, This food would likewise bring great custom to taverns, where the vintners will certainly be so prudent as to procure the best receipts for dressing it to perfection; and consequently have their houses frequented by all the fine gentlemen, who justly value themselves upon their knowledge in good eating; and a skilful cook, who understands how to oblige his guests, will contrive to make it as expensive as they please.

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)
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."