Immediately after the passage of this act, the Governor shall appoint, by and with the advice and consent of two-thirds of the Senate, the members of council who shall hold office until the first Monday of January, Anno Domini one thousand nine hundred and twelve. At the general municipal election to be held in the present year in each city of the second class now existing, and at the first municipal election occurring at least sixty days after any other city shall have entered said class, there shall be elected the full number of councilmen to which the city shall be entitled, to serve from the first Monday of January following. Said councilmen shall meet and organize on said date; and, immediately thereafter, divide themselves by lot into two classes, the odd numbers to serve for two years, and the even numbers for four years, thereafter. At each general election thereafter there shall be elected at large the number of councilmen required to fill the places of those whose terms are about to expire, to serve for four years, and also to fill any vacancies, caused by death, resignation, or removal, occurring more than sixty days before such election, to serve for the balance of the term of the member who has died, resigned, or removed.