Any taxpayer who, on the effective date of this act, is making payments on delinquent taxes under the provisions of the act of July twenty-second, one thousand nine hundred and thirty-six (Pamphlet Laws, sixty-seven),¹ or the act of May twenty-sixth, one thousand nine hundred and thirty-seven (Pamphlet Laws, eight hundred ninety-three),² may secure the benefits of this act by making payments on the balance due on such delinquent taxes at the times and in the fractional parts prescribed herein.