| x | y2 | y |
|---|---|---|
| 1 | 1,000 | 31.62 |
| 2 | 2,000 | 44.72 |
| 3 | 3,000 | 54.77 |
| 4 | 4,000 | 63.25 |
| 5 | 5,000 | 70.71 |
| 6 | 6,000 | 77.46 |
| 7 | 7,000 | 83.67 |
| 8 | 8,000 | 89.44 |
| 9 | 9,000 | 94.87 |
| 10 | 10,000 | 100.00 |
Assessment curve.
For the purpose of initiating an improvement the unit in which the prospective benefits are to be measured is usually adopted by the governing or assessing authorities. Dollars will not do because the cost will not be known until after the improvement has been finished. In the case of roads and streets the unit quite generally used is the “front-foot.” The number of front-feet in any paving district will be the same as the number of abutting feet along the street to be improved. A different definition for “front-foot” is given on [page 318]. The petitioning power or influence of the several properties constituting the whole frontage is proportional to the number of front-feet assigned to each property, and these are assigned according to the adopted rule which is supposed more or less closely to measure the benefits to be derived from the improvement.
When it comes to paying for the improvement the total cost up to the time of payment, including all charges against the district of whatsoever character, is divided by the number of front-feet giving the cost per front-foot, from which may readily be determined the cost to be assessed to each property according to the number of front-feet assigned to it.
To illustrate this more concretely, consider a road one mile long. Its abutting length is 2 miles, one on each side, or 10,560 feet. The total number of units of influence in the whole assessed area, and the number of units of assessed benefits, is 10,560 front-feet. The number of these units assigned or assessed to a particular plot of land is technically called its “frontage.” Since all land for a specified distance from the roadway must share in the benefits and in the cost, therefore, a piece of property may have frontage even though it does not touch the street or roadway to be improved.
In order to facilitate computation, more or less arbitrary variations are made from the theoretical curve of assessment thought to be ideal. Each infinitesimal portion of land bears a different assessment value according to its position in relation to the improvement. It would be impracticable to divide the land into an infinite number of strips of infinitesimal width and calculate the assessment for each. This could be done by mathematical analysis if all the boundary lines were straight lines and mathematical curves, but the work would be even then too laborious to pay. It is customary to divide the assessed territory along each side of the roadway into zones with edges parallel to the road, and to each zone is given a weight or proportional part of all the assessed value. The weights are obtained from the mathematical curve and are given values corresponding approximately with theoretical calculations.
Zone Weights.
—To determine the proper zone weights the influence curve is plotted as in [figure] on page 319. The base line, AB, is divided into as many parts as it is desired to have zones; from the mid-point of each part a perpendicular to the base line is erected to meet the curve, shown in the table, as mid-ordinates. These are each multiplied by 100 and divided by the longest, in the case of five zones, 94.85, to get them into percentages of the whole. These are now adjusted to near numbers for easy multiplication. For example, to multiply by 331⁄3 add two ciphers and divide by 3; to multiply by 25 add two ciphers and divide by 4; and so on.
Five-zone Table