Discuss the evidence that the farmers of the constitution meant for popular rule to be only one element of the new government in which ways did the new government limit the power of majorities?

The checks and balances that the Framers built into the Constitution extended not only to balancing the three branches of government but also in balancing the influence of larger and small states, balancing the more volatile House and the more deliberative Senate, and balancing the rights of minorities in the face of majorities. The Framers specifically wanted to prevent any "tyranny of the majority"--the phrase was coined by Alexis de Tocqueville, but it is a concept from the Federalist Papers (the concept is often there called "the violence the majority faction") and previous in debates about parliamentary power in Britain.

The Framers meant that, just because a majority of the people think a certain thing should be so does not mean that the basic rights of the people not in the majority can be infringed upon. A modern example might be one that involves free speech: just because a majority of Americans believe that Nazi Propaganda is evil and offensive does not mean that the small minority of people who choose to exercise their right to free speech to express Nazi ideas can be silenced by the majority. Another example might be, just because the majority of Americans at one time thought that black children should be educated in separate schools just for blacks, did not make it right to apply segregation to the schools. This is partly why the Supreme Court eventually ruled against this kind of segregation, and today we see that blacks--although a minority--are entitled to exactly the same access to schools and education as anyone else (although this is implemented imperfectly still). You might also imagine futuristic/nihilistic scenariOS (sometimes explored in fiction, e.g. "24" on TV) where the majority of Americans might believe that all Muslims should be locked into camps, although this is repugnant to American ideals of liberty. All of these examples are examples of how a democratic majority can sometimes be just as oppressive and repugnant to liberty as a dictator might be.

Aware of this, the Framers built certain checks into the American political system to help prevent such instances of the tyranny of the majority. The main way this is implemented is in the Bill of Rights, a set of principles that are essentially unchangeable by a simple democratic majority; they can be altered only through a difficult amendment process requiring widespread consensus and long debate. The amendment process to the Constitution can be regarded as another check against any tyranny of the majority.

The Electoral College can be viewed as another example of this: the Electoral College system requires a candidate not merely to win a popular vote but actually to have widespread geographic support--the Electoral College forces presidential candidates to be mindful of more diverse interests than a simple popular vote would and to pay attention more often to smaller states and more than one region, or more than just city dwellers.