The Constitution – Article I, section 3, clauses 1-2

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.”

Altered to election by the people of each State by the Seventeenth Amendment, ratified April 8, 1913.

Classes and Vacancies Clause

“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.]”

Altered to state executive-issued writs of election until popular election can fill the vacancy according the Seventeenth Amendment, April 8, 1913.