13. As soon as may be after the Senate first meets, and after each first meeting of the Senate following a dissolution thereof, the Senate shall divide the senators chosen for each State into two classes, as nearly equal in number as practicable; and the places of the senators of the first class shall become vacant at the expiration of three years, and the places of those of the second class at the expiration of six years, from the beginning of their term of service' and afterwards the places of senators shall be vacant at the expiration of six years from the beginning of their term of service.

The election to fill vacant places shall be made within one year before the places are to become vacant.

For the purpose of this section the term of service of a senator shall be taken to begin on the first day of July following the day of his election, except in the cases of the first election and of the election next after any dissolution of the Senate, when it shall be taken to begin on the first day of July preceding the day of his election.