Final answer:
Historical evidence from different societies suggests that military rank could affect family structures and the number of children. For instance, Roman fathers with more children were granted certain privileges, while other societies prescribed children inheriting the lower rank in rank-discrepant marriages. Thus, while direct correlation varies, status, including military, could influence family size and privileges.
Step-by-step explanation
When examining historical societies and their military and societal structures, it becomes apparent that there were indeed correlations between terminal military rank and various socio-economic outcomes, including the number of children. In some cases, military rank could affect the legal and social status of an individual's offspring, such as in societies where children inherited the lower rank of a parent if a marriage occurred across social or rank boundaries. However, in ancient Rome, a policy was employed to encourage population growth among the upper-class citizens, in which fathers with three children who survived to adulthood received extra privileges, including exemptions from mandatory public service.
These historical anecdotes reveal that while there may not be a straightforward, uniform correlation between terminal military rank and the number of children across all societies and time periods, military rank and legal status did influence family structure and the privileges bestowed upon individuals and their families. Considering this, military rank had indirect effects on family size through incentives or penalties which correlated with rank.
Moreover, societal prestige and military rank could be directly linked, as officials could earn not just office rank but personal rank as well. The perception of being composed of finer qi (vital energy) was prevalent among the gentry class, indicating that social status, including military rank, had far-reaching implications on family and societal structures.