All 4 Uses of

principle
in
Washington Square, by Henry James

Mrs. Penniman even took for granted at times that other people had as much imagination as herself; so that when, half an hour later, her brother came in, she addressed him quite on this principle.†
Chpt 6

principle = basic rule or belief

There passed through Morris Townsend's mind a rapid wonder as to what he might, even under a remote contingency, be indebted to from the action of this principle in Dr. Sloper's breast, and the inquiry exhausted itself in his sense of the ludicrous.†
Chpt 16

Yes, but you see that on that principle Catherine has duties to him as well.†
Chpt 16

Definitions:

(1) (principle)
a basic rule or belief
The exact meaning of principle can depend upon its context. For example:
- "our guiding principles" -- basic moral beliefs that guide decisions and behavior
- "electromagnetic principles" -- rules describing how the world works
- "She lacks principles." -- lacks moral guidelines
- "We agree in principle." -- about important basic beliefs
(2) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

See a comprehensive dictionary for more specialized senses including one in chemistry.