When any extension of or addition to any existing system of improvement shall be thus constructed, the cost thereof shall be assessed to all the property, counties, cities and towns in the enlarged district benefited thereby in proportion to the benefits received therefrom. Any new lands thus brought into the district shall be assessed in addition a proper and equitable share of the then value of the original system of improvement in proportion to the benefits which such new lands derive therefrom. In determining the value to be so assessed the board of appraisers shall take into consideration the amount, if any, which the property to be assessed has already paid toward the construction of the original system and all other matters that may be pertinent. If at any time it shall appear to the board of supervisors of any drainage or diking improvement district that any lands without the boundaries of such district are being benefited by the improvements of the district and are not being assessed for the benefits received, they shall file a petition with the board of county commissioners praying the benefits received by such lands be determined and an assessment made upon such lands for the benefits so received. Thereupon, the board of county commissioners shall appoint a board of appraisers as provided in RCW 85.08.360 for the apportionment of the cost of construction of the original system of improvement, and an apportionment of the then value of the improvements of the district shall be made to such lands in proportion to the benefits received therefrom as nearly as may be in the manner provided for the apportionment of the cost of the original system of improvement. In determining what share of the value of the improvements of the district shall be apportioned to such lands the board of appraisers shall take into consideration the benefits already received by such lands and all other matters that may be pertinent. The amount of the value of the original system assessed upon any new property brought within the district shall be rebated pro rata upon the assessments, if any, outstanding against the lands of the district on account of the construction of such original system. If the assessment against any land has been paid in full, or if the assessment remaining outstanding against such land is less than the rebate apportioned to such land, the amount so rebated or excess of rebate over assessment shall be paid into the maintenance fund of the district and a proper credit on any existing or future assessment for maintenance shall be entered in favor of the land entitled thereto. The lands in the original district shall remain bound for the whole of the original unpaid assessment thereon for the payment of any outstanding unpaid warrants or bonds secured to be paid by such assessments.