The owner of the land may, within said month, offer in writing to the owner of the mill or dam to accept a smaller amount than that established as said annual compensation; and if the owner of the mill or dam does not agree to pay such reduced compensation, but brings an action to obtain a diminution thereof, he shall pay the costs, unless the annual compensation is reduced by the verdict to an amount less than the offer.
Mass. Gen. Laws ch. 253, § 24