Upon receiving such petition and any annexed exhibits the commission shall appoint and contract with two competent surveyors, who shall not be residents of any county to be cut by the lines of the proposed new county, and these two surveyors shall name and call in a third similarly qualified to settle any points of difference between them. These surveyors shall ascertain and settle all necessary questions as to area, both of the proposed new county and of the old counties after being diminished by the new, and as to the distances of the lines of the proposed new county from any existing courthouse. They shall also make a survey of the proposed new lines and plainly mark the same, so as to clearly define the population and wealth taken and left and so as to provide a guide as to who can vote by reason of residence, if the election be finally ordered. They shall make full return and report of their finding, with plats of their work, to the commission, who shall annex the same to the petition. The surveyors shall be paid by warrant of the commission on the treasurer of each old county involved for the prorata cost of the survey made within the territory of each and to this end the surveyors shall render an itemized bill of their work for each county to be cut by the new lines.