Final answer:
The authors feared the United States might form alliances with former enemies of Britain, potentially threatening British interests. They hoped shared cultural and institutional bonds would encourage a stronger relationship between Britain and the U.S. instead.
Step-by-step explanation:
The authors expressed a fear of the United States forming alliances with former enemies, which in the context likely refers to Britain's concern over the possibility of the U.S. aligning with France or other European powers against British interests. This concern arises from the historical tensions and the Revolutionary War where the U.S. fought for independence from British rule. The authors hope that the shared cultural and institutional bonds between Britain and America will prevent such an outcome and favor a rekindling of a closer relationship, avoiding further division and hostility. This sentiment echoes the broader themes of unity and the preservation of British influence, concerns that were particularly relevant in the aftermath of the American Revolution and during subsequent discussions about British foreign policy.