Upon the day specified in the notice required by the preceding section for the meeting, the board of directors, which is hereby constituted a board of equalization for that purpose, shall meet and continue in session from day to day as long as may be necessary, not to exceed ten days, exclusive of Sundays, to hear and determine such objections to the said assessment roll as may come before them; and the board may decide the same. The secretary of the board shall be present during its session, and note all changes made at said hearing, and on or before the fifteenth day of January thereafter shall have the assessment roll completed as finally equalized by the board.