The Federalist Papers were published under the author Publius, but individual authorship has been determined for the discrete papers. Federalist No. 10, which was written by James Madison, continues the theme of Federalist No. 9, written by Alexander Hamilton.
The Federalists were in favor of a strong union, or republic. They saw this as a way to protect the young nation and to ensure more equal participation of all areas. The strength of the union would offset what they saw as the likely danger from diverse factions that could prevent further development or, at worst, tear the country apart.
Madison used the concept of "republic" in reference to organized units of governance of various scales, especially states and countries. He worried that an individual state might gain too much power. Jefferson, in contrast, saw a powerful, controlling federal government as a greater danger. He was in the anti-federalist camp.