The county commissioners, or the board for the assessment and revision of taxes, as the case may be, may, in their discretion, issue their precepts to the elected or appointed assessors of the respective wards, districts, boroughs, towns and townships, on or before the first day in March of each year, for the assessment of such persons as may remove into the respective township, ward, borough, town or district since the last assessment, and for the reassessment of such property as may have been transferred since the last assessment, and for the assessment of those who may have been omitted from the last assessment. And it shall be the duty of such assessors to make such assessment, and return the same before the twenty-fifth of May. For such service the said assessor shall receive, out of the county funds, such compensation as may be fixed by the county commissioners, not, however, exceeding the per diem compensation fixed by this act.