Section 18B. The state treasurer, without further appropriation and upon certification of the commissioner, shall annually distribute to the several cities and towns in accordance with the provisions of section thirty-one of chapter eighty-one that portion of the Highway Fund allocated therefor. Said amount shall be distributed in four equal payments. Said payments shall be made annually, in each fiscal year, on or before September thirtieth, December thirty-first, March thirty-first and June thirtieth.

The commissioner of highways shall notify the commissioner of revenue of the estimated amounts required to be distributed under this section. The commissioner of revenue shall include said amounts in his notification to the assessors of each city and town under section twenty-five A and said amounts shall be included by the assessors in estimated receipts in determining the rate of taxation to be levied upon taxable property in each city and town.

If upon any date of distribution the amount available for distribution under this section is insufficient to make the full distributions required by said section thirty-one of said chapter eighty-one, the distributions thereunder shall be the amount otherwise due each city or town under said section multiplied by a fraction, the numerator of which shall be the amount available for distribution under this section and the denominator shall be the total amount otherwise due for the several cities and towns under the provisions of said section thirty-one of said chapter eighty-one. If upon any date of distribution the amount available for distribution under this section exceeds the amount necessary to make the full distributions required by said section thirty-one of chapter eighty-one, the distributions thereunder shall be the amount otherwise due each city or town under said section thirty-one of chapter eighty-one increased by an amount which shall be the total amount available for distribution less the total amount required for distribution multiplied by a fraction, the numerator of which shall be the amount otherwise due each city or town under said section thirty-one of chapter eighty-one and the denominator of which shall be the amount otherwise due the several cities and towns under said section.