Section 26. In the order for the construction of a new sidewalk or the reconstruction of a sidewalk with material of more permanent character than that with which it was originally constructed, the board making the order may provide for the assessment of a reasonable amount, not exceeding one half the cost, upon the abutting estates. If an ordinance or by-law so provides, the total assessed upon any individual estate shall not exceed one per cent of the value thereof as fixed by the last preceding annual assessment for taxes.