All 3 Uses of

principal
in
The Age of Innocence

It was what they principally sought and admired on their occasional travels abroad; considering architecture and painting as subjects for men, and chiefly for learned persons who read Ruskin.†
Chpt 5 *

principally = primarily or most importantly

The Duke of course would be their principal theme; though the appearance in Fifth Avenue of a golden-haired lady in a small canary-coloured brougham with a pair of black cobs (for which Beaufort was generally thought responsible) would also doubtless be thoroughly gone into.†
Chpt 10

principal = most important; or person that is most important

Little arduous as his professional duties were, he would have been convicted of frivolity by the whole Mingott clan if he had suggested asking for a holiday in mid-winter; and he accepted May's departure with the resignation which he perceived would have to be one of the principal constituents of married life.†
Chpt 13

Definitions:

(1) (principal)
most important; or person who is most important
The exact meaning of principal can depend upon its context. For example:
- "the principal idea" or "the principal performer" -- the most important
- "the principal of the school" -- the person in charge
- "a principal of a company" -- an owner or person with controlling authority
- "the principal in a transaction" (as contrasted to the agent) -- the person on whose behalf an agent acts
(2) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

See a comprehensive dictionary for specialized senses in finance, architecture, law, chemistry, and music.