In each of the two years succeeding the triennial assessment, except in counties of the first class, and except as in counties of the second and third classes otherwise provided, the commissioners, or board for the assessment and revision of taxes, as the case may be, of the respective county shall send a transcript of such triennial assessment to the elected or appointed assessors of every ward, borough, town, township and district therein, together with their precepts, requiring them to take an account of all personal property taxable by law, together with a just valuation of same, and all persons, and also a valuation of all offices and posts of profit, professions, trades and occupations taxable by law, enjoining such assessors to make a just return to them and to note in such return such alterations in his ward, borough, town, township or district, as may have been occasioned by the transfer or division of real estate, or by the destruction of buildings, or by the mining out of coal, ore, or other minerals assessed under the triennial assessment, and also noting all persons who have arrived at the age of eighteen years since the last triennial assessment, and all others who have since that time come to inhabit in such ward, borough, town, township or district, together with the taxable property such persons may possess, and the valuation thereof, agreeably to the provisions of this act; and to reassess all real estate which may have been improved by the erection of buildings or other improvements subsequent to the last preceding triennial assessments, subject to appeals as now provided by law.