Final answer:
The query deals with historical ship designs for transporting slaves, highlighting the cramped and inhumane conditions wherein individuals had only 2 feet 7 inches of height between the beams on the lower deck.
Step-by-step explanation:
The question refers to historical blueprints of a ship used for the transportation of slaves, specifically detailing the construction and dimensions of platforms or shelves. The passage provided describes a plan for increasing the capacity for additional slaves around the wings or sides of the lower deck, employing platforms or shelves in the manner of church galleries. Notably, it highlights the inhumane conditions, with a height of only 2 feet 7 inches between the beams, which is an inadequate space for humans, further emphasizing the brutal and squalid conditions enslaved people were subjected to during the transatlantic slave trade.
The exact measurement required for the platform extension over the centerline of its support is not provided in the historical context. Usually, such specifics would be dictated by historical building practices or safety standards of the time, which are not given in the provided references. Contemporary building standards for platform extensions may differ greatly from those of historical periods.