Special Taxes.
—Special taxes are those levied upon property for a particular improvement that is demanded by public interest. They are not uniform but must be levied in proportion to the benefits accruing to the property from the improvement. This class of taxes is very popular for financing the building of roads and the paving of streets as well as other public construction. The area adjacent to the road or pavement for a certain specified distance back, or possibly, halfway to the next thoroughfare, is assessed for the improvement and in road work is technically known as “fronting property.” Each piece of fronting property is required to pay toward the whole cost of improvement an amount proportional to the benefits derived from the improvement.
These benefits evidently decrease as the distance from the improvement increases. They may not always vary in the same ratio, but appraisers will usually follow some definite rule and deviate from it only in extreme cases and as local conditions demand. That they should not decrease directly as the distance but in some geometrical ratio, most engineers agree. Law courts have frequently upheld assessments made upon some such basis.
For the purpose of initiating an improvement by petition it is customary to adopt a fixed scale for the measure of the benefits, based upon distance, that will probably be derived from the improvement. Some legislative bodies have enacted definite rules for evaluating “influence” in petitioning. Generally the rule is based upon some mathematical variation. For example that the assessed value or influence of property of uniform width extending back from the roadway shall vary as the square root of the maximum distance back. In the [figure] on page 313, a lot of one-unit area fronting the street is given a value of 31.62. This is from the mathematical formula
y2 = 1000x
where y represents the assessed value or influence in petitioning, and x, the distance back, considering the value of y = 100 for x = 10.
To draw the curve mark off on a straight line ten equal distances; at the mid-point of these distances or units erect perpendiculars. From the formula calculate values for y as shown in the [table]; lay these off on the verticals and plot the curve through their extremities. To clarify this some, suppose that upon the center of the first space, there being one unit area or lot here, there is stacked up the value of the assessed benefits 32 (31.62) silver dollars. On the next space, since there are two lots extending back from the street, the stack would contain 45 (44.72) silver dollars—continue this for each space and for the number of lots extending back. A curved line passing through the tops of the stacks representing the assessed values will be the influence curve plotted.
| 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.