According to hamilton, what are the main purposes of forming a union under the constitution?

The main purpose of forming a union under the constitution was the Common Defense of the associates including the protection of Public harmony against regional upheavals and external invasions, management of trade and commerce on the domestic and international level and the dealing of America's political and commercial intercourse with foreign countries.

The overall purpose of the Federalist Essays was to secure public assistance for the then proposed constitution and to demonstrate their service and to influence the opinion of the reader.