Your retracement begins at the original township
corner of Tps. 3 and 4 North, Rs. 7 and 8 west, where you have established
a true bearing by solar observations. The latitude of this cor. is
45° 34' 30" N. You traverse 4 miles westerly before you find
an original corner and determine the intermediate corners to be lost.
You now need to reestablish the corner of sections 2 and 3 only. Your
random traverse yields the following data.
Inverse from Tp. Cor. to cor. of secs. 4 and 5:

Inverse between tp. cor. and temp cor. of secs. 2 and 3:

The original survey reports the following from the tp. cor.:

The lost cor. of secs. 2 and 3 would be reestablished by single
proportionate measurement. However, if you fail to account for curvature
of the township line, how far off will your reestablished corner
be?

Using the curvature calculator you can determine how much curvature
must be factored into your final corner position. Using the single
proportion formula, determine the position of the lost corner. Do
you remember the formula?

retracement/record x record or 321.07/320.00 x 160 = 160.535

The proportionate position of the cor. of secs. 2 and 3 would be
located:

S. 88° 42’ W. 160.535 from the tp. cor.

But, you’re not finished yet. What about curvature? You need
to apply this to your single proportion answer to arrive at the
final position for the corner.