The first way leaps from scattered particulars straight to the most general axioms, then works back down to derive intermediate truths from them — the method of the schools, fast, satisfying, and, in Bacon's diagnosis, almost guaranteed to entrench error, because the leap to generality happens before the evidence can discipline it.
The second way climbs gradually — particulars to lesser axioms, lesser axioms to broader ones, broader ones only eventually to the most general — never outrunning what the evidence at each stage can support. Bacon calls it 'the true but unattempted way,' a phrase that doubles as his book's whole thesis: the right method has simply never been tried at scale.
Drawn from Book I, Aphorism XIX of Novum Organum.