(a)

(1) In the event that the board shall have voted to accept any offer of gift, shall have voted to purchase any improvement, or shall have voted to construct any improvement, it shall thereupon appoint an assessor to assess the benefits which will accrue to the real property within the district from the acceptance of the gift of improvement, the purchase of the improvement, or the construction of the improvement.

(2) The assessor shall take an oath that he will well and truly assess all benefits that will accrue to the landowners of the district by reason of the acceptance, purchase, or construction of the proposed improvement. He shall thereupon proceed to assess the lands within the district.

(b)

(1) The assessor shall inscribe in a book each tract of land and shall place in one column his valuation of each tract or parcel of land prior to the improvement, which may be marked "Assessed Value of Lands Prior to Improvements," and in another column he shall place what he thinks will be the value of each tract or parcel of land after the improvement, which may be marked "Assessed Value of Lands After Improvement."

(2) (A) (i) If the assessed value of land after improvements is greater than the assessed value of land before improvements, as assessed by the assessor for the district, then the difference between the two shall be the assessed benefits that will accrue to each tract by reason of the improvement.

(ii) If the assessed value of land, as assessed by the assessor of the district, after the improvement is acquired or made is less than the assessed value of land before improvements are acquired or made, as assessed by the assessor for the district, then the difference between the two shall be the assessed damages that will accrue to the particular parcel or tract of land by reason of the improvement.

(B) The assessor shall enter the assessment of benefits or damages opposite the description of each piece of property in appropriate columns, one of which may be marked "Assessed Benefits" and the other may be marked "Assessed Damages," and in another column the assessor shall show the estimate of the probable cost to the landowner, which may be marked "Estimated Cost."

(c)

(1) The assessment shall embrace not merely the lands, but all railroads, tramroads, telegraph lines, telephone lines, pipelines, and other improvements on real estate that will be benefited by the acquiring or making of the improvement.

(2) No assessment shall apply against any pipelines or other improvements which are extensions of or connected to the pipeline distribution system or other improvements within any city adjacent to the district.

(d)

(1) The assessor shall place opposite each tract the name of the supposed owner as indicated by the deed records, but a mistake in name shall not vitiate the assessment.

(2)

(A) The assessor shall also assess all damages that will accrue to any landowner by reason of the proposed improvement, including all injury to lands taken or damaged.

(B) Where the assessor returns no such damages to any tract of land, it shall be deemed a finding by him that no damages will be sustained.

(e) The assessor shall hold his office at the pleasure of the board, which can fill any vacancy in the position of assessor.