That when two or more counties unite and form a county engineer district and jointly employ a county engineer, in compliance with this act, the salary and expense of such engineer and his assistants shall be paid by the counties in the district and the amount each of such counties shall pay shall be agreed, in writing, by the boards of county commissioners of the several counties in the district. In agreeing as to the pro rata share to be paid by each county, the several boards of county commissioners shall consider the engineering services probably required by each of such counties and such consideration shall include the following factors with respect to each of such counties: (a) area, (b) mileage of county roads, (c) number of watercourses, (d) population, (e) assessed tangible taxable valuation, and (f) the total amount of funds being spent for county roads and bridges.