All the corporate powers of every such corporation shall be vested in and be exercised by a board of directors, who shall be stockholders of the corporation, and shall be elected at the annual meetings of stockholders at the public office of such corporation within this state. The number of such directors, the manner of their election, and the mode of filling vacancies, shall be specified in the by-laws, and shall not be changed except at the annual meetings of the stockholders. The first board of directors shall classify themselves by lot in such manner that there shall be, as nearly as practicable, three directors in each class. Those belonging to the first class shall go out of office at the end of one year, those of the second class at the end of two years, and in like manner those of each class shall go out of office at the expiration of a number of years corresponding to the number of his class; and all vacancies occurring by reason of expiration of term shall be filled by election for a term of years equal to the number of classes.