----+------------+----------+------+---------------+------- Zone|Mid-ordinate|Percentage|Weight|Adjusted Weight| Sum ----+------------+----------+------+---------------+------- 1 | 31.62 | 33.3 | 33.3 | 33¹⁄₃ | 33¹⁄₃ 2 | 54.77 | 57.7 | 24.4 | 25 | 58¹⁄₃ 3 | 70.71 | 74.6 | 18.9 | 16²⁄₃ | 75 4 | 83.67 | 88.5 | 13.9 | 15 | 90 5 | 94.87 | 100.0 | 11.5 | 10 | 100 ----+------------+----------+------+---------------+------- To get weights for six zones take the mid-ordinates at 8¹⁄₃, 25, 41²⁄₃, 58¹⁄₃, 75, and 91²⁄₃, as follows: ----+------------+----------+------+--------+-------+--------+------- | | | | | |Another | | | | |Adjusted| |Adjusted| Zone|Mid-ordinate|Percentage|Weight| Weight | Sum | Weight | Sum ----+------------+----------+------+--------+-------+--------+------- 1 | 28.86 | 31 | 31 | 30 | 30 | 33¹⁄₃ | 33¹⁄₂ 2 | 50.00 | 52 | 21 | 20 | 50 | 20 | 53¹⁄₃ 3 | 64.45 | 67 | 15 | 15 | 65 | 16²⁄₃ | 70 4 | 76.70 | 80 | 13 | 12¹⁄₂ | 77¹⁄₂ | 10 | 80 5 | 87.02 | 91 | 11 | 12¹⁄₂ | 90 | 10 | 90 6 | 95.73 | 100 | 9 | 10 |100 | 10 |100 ----+------------+----------+------+--------+-------+--------+------- =To Calculate the Frontage.=--As has already been stated, in some states in order to initiate a road improvement to be paid for by special assessment a petition for the same signed by the owners of a majority of the frontage is necessary. To determine the frontage for this petition general rules are laid down by proper authority or laws enacted, stating the necessary procedure and the weights allowed for calculating frontage based upon distance from the roadway to be improved. In one state the land up to a distance of 2 miles back on each side of the roadway may be formed into an improvement district which constitutes the fronting territory or frontage. The frontage on each side of the roadway is divided into four zones equal in width. The first zone, the one nearest the road, has a weight of 50, or it may be said to contain 50 per cent. of the total frontage; the second zone has a weight of 25, or contains 25 per cent. of the frontage; the third, 15 per cent.; and the fourth, 10 per cent. Along a mile of the road there are, of course, two miles or 10,560 front-feet frontage. This 10,560 front-feet is not considered to be uniformly distributed over the entire 4 square miles (assuming the district 2 miles each side the road) of assessed territory abutting the mile of roadway. Nor to be decreased according to the mathematical laws stated above. But the distribution is by arbitrary rule laid down by legislative authority.