77. For the purpose of obtaining a partial remission or refund of tax, the owner of a building composed of separate tenements may request the Board, at the time of the assessment of the building, to enter in the assessment list, in addition to the annual value of the whole building, a note recording in detail the annual value of each separate tenement. When any tenement, the annual value of which has been thus separately recorded, has remained vacant and unproductive of rent for sixty or more consecutive days, such portion of any tax assessed on the annual value of the whole building shall be remitted or refunded as would have been remitted or refunded if the tenement had been separately assessed.