What is Madison discussing in the first half of this essay?

James Madison begins his Federalist Paper 51 by explaining that the purpose of this essay is to help the readers understand how the structure of the proposed government makes liberty possible. Each branch should be, in Madison's opinion, mostly independent. To assure such independence, no one branch should have too much power in selecting members of the other two branches. If this principle were strictly followed, it would mean that the citizens should select the president, the legislators, and the judges. But the framers recognized certain practical difficulties in making every office elective. In particular, the judicial branch would suffer because the average person is not aware of the qualifications judges should possess. Judges should have great ability, but also be free of political pressures. Since federal judges are appointed for life, their thinking will not be influenced by the president who appoints them, nor the senators whose consent the president will seek.