If bonds to finance the construction or acquisition of waterworks, gas, electric, or other light works, or heating or power system, by the city are not approved under section 16-676 or sections 16-680 to 16-683, or if the city fails to obtain an adequate supply of good water, then the mayor and city council may contract with and procure individuals or corporations to construct and maintain a system of waterworks, power, heating, or lighting plant in such city for any time not exceeding twenty years from the date of the contract, with a reservation to the city of the right to purchase such waterworks, lighting, heating, or power plant at any time after the lapse of ten years from the date of the contract upon payment to such individuals or corporations of any amount to be determined from the contract, not exceeding the cost of the construction of such waterworks, power, lighting, or heating plant. In other respects such contract may be on such terms as may be agreed upon by a two-thirds vote of the city council. No such contract shall be made unless authorized by a majority vote of the legal voters of such city at a special election called for that purpose, notice of which shall be given by publication once each week for three successive weeks prior thereto in a legal newspaper in or of general circulation in such city.