Section 41. The expenses incurred under sections thirty-five to forty, inclusive, shall be paid primarily by the commonwealth; and the state treasurer shall issue his warrant requiring the assessors of the cities and towns concerned and of the towns in which such district is located to assess a tax to the amount of said expense, and such amounts shall be collected and paid to the state treasurer as provided by section twenty of chapter fifty-nine. Any balance due shall be assessed, collected and paid in the succeeding years in like manner.