6. If there be no choice of a senator or senators at the annual election, the governor shall issue his warrant to the town and ward clerks of the several towns and cities in the senatorial district or districts that may have failed to elect, requiring them to open town or ward meetings for another election, on a day not more than fifteen days beyond the time of counting the votes for senators. If, on the second trial there shall be no choice of a senator or senators the governor shall certify the result to the speaker of the house of representatives; and the house of representatives, and as many senators as shall have been chosen, shall forthwith elect, in joint committee, a senator or senators from the two candidates who may receive the highest number of votes in each district. 7. If there be no choice of governor at the annual election, the speaker of the house of representatives shall issue his warrant to the clerks of the several towns and cities requiring them to notify town and ward meetings for another election, on a day to be named by him, not more than thirty nor less than twenty days beyond the time of receiving the report of the committee of the house of representatives, who shall count the votes for governor. If, on this second trial there shall be no choice of a governor, the two houses of the General Assembly, shall, at their next session, in joint committee elect a governor from the two candidates having the highest number of votes, to hold his office for the remainder of the political year, and until his successor be duly qualified. 8. If there be no choice of governor and lieutenant-governor at the annual election, the same proceedings for the choice of a lieutenant-governor shall be had as are directed in the preceding section; provided that the second trial for the election of governor and lieutenant-governor shall be on the same day; and also provided, that if the governor shall be chosen at the annual election and the lieutenant-governor shall not be chosen, then the last named officer shall be elected in joint committee of the two houses from the two candidates having the highest number of votes, without a further appeal to the electors. The lieutenant-governor, elected as is provided in this section, shall hold his office as is provided in the preceding section respecting the governor. 9. All town, city and ward meetings for the choice of representatives, justices of the peace, sheriffs, senators, state officers, representatives to Congress and electors of president and vice-president, shall be notified by the town, city and ward clerks at least seven days before the same are held. 10. In all elections held by the people under this constitution, a majority of all the electors voting shall be necessary to the choice of the person or persons voted for.