Statistical or numerical information I think.
This part of the excerpt seems to be correct as it reveals that the diet alone is responsible for his ninth birthday: "It had plenty of room to expand, thanks to the spare diet of the establishment; and perhaps to this circumstance may be attributed his having any ninth birth-day at all."
Answer:
The underlined phrase is Adjectival
Explination:
It describes the bond they had/it describes the bond.
It’s kinda like figurative language but it’s not literal. The term “Summer spoke to me” most likely meant, reaching but not in a literal way.