The Real Constitution: Article I, Section III (Structure of the Senate)

The Senate of the United States shall be composed of two Senators from each State, chosen by the Legislature thereof for six Years; and each Senator shall have one Vote.


Immediately after they shall be assembled in Consequence of the first Election, they shall be divided as equally as may be into three Classes. The Seats of the Senators of the first Class shall be vacated at the Expiration of the second Year, of the second Class at the Expiration of the fourth Year, and of the third Class at the Expiration of the sixth Year, so that one third may be chosen every second Year; and if Vacancies happen by Resignation, or otherwise, during the Recess of the Legislature of any State, the Executive thereof may make temporary Appointments until the next Meeting of the Legislature, which shall then fill such Vacancies.


No Person shall be a Senator who shall not have attained to the Age of thirty Years, and been nine Years a Citizen of the United States, and who shall not, when elected, be an Inhabitant of that State for which he shall be chosen.


The Vice President of the United States shall be President of the Senate, but shall have no Vote, unless they be equally divided.


The Senate shall chuse their other Officers, and also a President pro tempore, in the Absence of the Vice President, or when he shall exercise the Office of President of the United States.


The Senate shall have the sole Power to try all Impeachments. When sitting for that Purpose, they shall be on Oath or Affirmation. When the President of the United States is tried, the Chief Justice shall preside: And no Person shall be convicted without the Concurrence of two thirds of the Members present.


Judgment in Cases of Impeachment shall not extend further than to removal from Office, and disqualification to hold and enjoy any Office of honor, Trust or Profit under the United States: but the Party convicted shall nevertheless be liable and subject to Indictment, Trial, Judgment and Punishment, according to Law.

Recall that even those members of the Convention that supported direct election of Representatives (as opposed to election by state legislatures) were comfortable with the idea of "successive filtration" for the Senate and Executive. Under Edmund Randolph's original Virginia Plan, Senators would be elected by the House of Representatives from nomination by state legislatures. Richard Spaight of North Carolina, concerned about the withdrawal of power from the states, was the first to propose that the state legislatures elect Senators directly; but since the convention was at the time thought to be likely to pass a system of assigning representatives according to state populations, and Randolph believed that the Senate should be "so small as to be exempt from the passionate proceedings to which numberous assemblies are liable", and Rufus King pointed out that under proportional representation "there must be 80 or 100 members to entitle Delaware to the choice of one of them", the motion was laid aside for the time being.

James Wilson, who had defended direct election of Representatives, believed the Senate should be independent of both the House and the state legislators and called for direct election of Senators, perhaps by uniting several different districts, which Madison opposed on the grounds that if a large and small state voted as a group, all its senators would be chosen from the large state even if someone from the small state was more qualified. Even at this early point, Roger Sherman proposed electing one member from each state legislature. Ultimately Randolph's scheme was effectively rejected, with only Massachusetts, Virginia, and South Carolina being happy with it.