Any property owner may accept the assessment of damages in his favor made by the commissioners, or acquiesce in their failure to assess damages in his favor, and shall be construed to have done so unless he gives to said commissioners, within thirty days after the assessment is filed, notice in writing that he demands assessment of his damages by jury. In such event the commissioners shall institute in the proper court in the proper county an action to condemn the lands that must be taken or damaged in making such improvements, which action shall be in accordance with the proceeding for the condemnation of property for public use provided in the chapter on eminent domain. Where condemnation proceedings are had as herein provided and an appeal is taken to the circuit court, the drainage commissioners may pay the amount awarded by the jury into the hands of the clerk of the circuit court, who shall hold the same to abide the decision of said appeal, and the drainage commissioners may proceed with the work of constructing the drain as laid out by them.