y is encountered in
determining an equitable distribution on those parcels of land lying
partly in one zone and partly in another, but the rate may be arrived
at with reasonable accuracy by pro-rating in accordance with the exact
conditions.

In. Fig. 1, let it be assumed that the assessment area is to be two
miles wide, one mile on each side of the road and the various
ownerships to be indicated by the parcels of land numbered 1 to 8, as
shown. Each zone for the assessment of the 3-1/4 mile section is 1/4
mile wide and the rates for the several zones are 50, 25, 15 and 10
per cent respectively. Let it be assumed that the portion of the cost
of the 3-1/4 miles of road to be assessed on the area shown is
$20,000. The assessment would then be as follows:

------+-------+----------------------+------------+-------------
| | Rate x frontage on | Amount of |
Parcel| Rate | improved road = | Assessment | Assessment
| | assessment units | per unit[1]|
1 | 2 | 3 | 4 | 5
------+-------+----------------------+------------+-------------
1 | a 50 | 50 x 2640 = 132,000 | $0.016655 | $1558.46
| b 75 | 75 x 1320 = 99,000 | | 1153.90
2 | 40 | 40 x 2640 = 105,600 | | 1230.77
3 | 10 | 10 x 2640 = 26,400 | | 307.69
4 | 25 | 25 x 1320 = 33,000 | | 384.66
5 | [2]85 | 85 x 5280 = 448,800 | | 5230.88
6 | 15 | 15 x 5280 = 79,200 | | 923.08
7 | [2]65 | 65 x 7920 = 514,800 | | 6000.00
8 | 35 | 35 x 7920 = 277,200 | | 3230.77
| | ------------------- | | -----------
| | 1,716,000 | | $20000.00
------+-------+----------------------+------------+-------------

[1] The assessment per unit is obtained by dividing the total
assessment by the total of column three.

[2] On these two parcels, it is decided that more than half of
the zone rate should apply to the half of the zone toward the
improved road, but some modification of the rates adopted might be
justified.

[Illustration: Fig. 1]

The assessment of the cost of the east and west one-mile section of
road is made up in like manner, and let it be assumed that the portion
of the cost of this road that is to be assessed on th