If the commissioners at any time either before or after the organization of the district find that other land not embraced within the boundaries of the district will be benefited by the proposed improvement or improvements already made, they shall assess the estimated benefit to such lands and shall specially report to the chancery court, or chancellor in vacation, the assessments which they have made on land beyond the boundaries of the district, as already established. It shall thereupon be the duty of the clerk of the chancery court to give notice by two (2) weekly insertions in a newspaper published in the county where such lands lie, describing the additional lands which have been assessed. The owners of real property so assessed shall be allowed not less than ten (10) days after the last required publication of such notice in which to file with the clerk of the chancery court in writing their protest against being so assessed, or included within the district. The chancery court, or chancellor in vacation, shall, within ninety (90) days, investigate the question whether the lands beyond the boundaries of the district so assessed by the commissioners will in fact be benefited by the making of the improvement, and from its finding in that regard, either the property owner or the commissioners may, within twenty (20) days, appeal to the supreme court. If the finding is in favor of the commissioners, the limits of the district shall be extended so as to embrace any lands that may be benefited by the making of the improvement.