Question

how might a second born son hope to achieve success under the system of primogeniture

Answer 1

Primogeniture is the right, by law or custom, of the firstborn son to inherit the entire estate, to the exclusion of younger siblings (compare to ultimogeniture). Historically, the term implied male primogeniture, to the exclusion of females. In the absence of children, inheritance passed to collateral relatives, in order of seniority of their lines of descent. The eligible descendants of deceased elder siblings take precedence over living younger siblings, such that inheritance is settled in the manner of a depth-first search.
The principle has applied in history to inheritance of real property (land) and inherited titles and offices, most notably monarchies, continuing until modified or abolished .
Variations on primogeniture modify the right of the first-born son to the entirety of a family's inheritance (see appanage) or, in the West since World War II with the wider promotion of feminism, eliminate the preference for male over female siblings. Six monarchies in Europe have eliminated male preference: Sweden, Norway, Netherlands, Belgium, Denmark and Luxembourg. The type of marriage prevalent in each culture plays a crucial role in the adoption of differing primogenitures.

Answer 2

I hope I helped =)