The details were obtained from Harrison himself, who was present.

He had made use of two balances situated in the same plane, but vibrating in contrary directions, so that the one of these being either way assisted by the tossing of the ship, the other might constantly be just so much impeded by it at the same time.

As the equality of the times of the vibrations of the balance of a pocket-watch is in a great measure owing to the spiral spring that lies under it, so the same was here performed by the like elasticity of four cylindrical springs or worms, applied near the upper and lower extremities of the two balances above described.
Then came in the question of compensation.

Harrison's experience with the compensation pendulum of his clock now proved of service to him.
He had proceeded to introduce a similar expedient in his proposed chronometer.

As is well known to those who are acquainted with the nature of springs moved by balances, the stronger those springs are, the quicker the vibrations of the balances are performed, and vice versa; hence it follows that those springs, when braced by cold, or when relaxed by heat, must of necessity cause the timekeeper to go either faster or slower, unless some method could be found to remedy the inconvenience.
The method adopted by Harrison was his compensation balance, doubtless the backbone of his invention.