If ten per cent of the landowners owning lands adjoining or adjacent to any existing district operating under the provisions of this chapter shall petition the chancery court to extend the boundaries of any such existing district, describing generally the region which it is intended shall be embraced within the boundaries of such drainage district as extended, it shall be the duty of the chancery court, or chancellor in vacation, to enter an order directing the commissioners of such drainage district to forthwith proceed to cause a survey to be made, and to ascertain the limits of the region which will be benefited by the proposed system of improvements, giving a general idea of its character and the cost of drainage and other improvements necessary and making such suggestions as to the size of the drainage ditches and their location and of levees, dams, and pumping stations, if any of such be necessary, to properly drain and protect said territory, or if the commissioners may deem such levees, dams, pumping stations, or any or either of them advisable, and to file their reports with the clerk of the chancery court. All expenses of making such survey, preparing the plans and estimates of the costs of the improvements, costs of publication, attorneys’ fees, and other necessary expenses shall be paid as the work progresses by the existing drainage district to which the land and territory is proposed to be added, or by the board of supervisors as the court or chancellor may order. All such expenses shall be repaid out of the first money received from taxes upon the additional lands embraced in such drainage district, or from the sale of bonds from the district as extended, if that be done; but if that be not done, then the board of supervisors shall levy an ad valorem tax upon the land which it was proposed to add to such existing drainage district to repay the costs advanced by such existing drainage district or the board of supervisors, as the case may be.