A 227Kb PDF of this article as it appeared in the magazine—complete with images—is available by clicking **HERE**

Most of the programming work we’ve experienced thus far is no more than reliable math being indisputable as to its singular solution. This multiple point Resection should offer a good solution but not an exact solution in planar geometry. Statistics tells us that there’s always a better answer. I have incorporated a method that favors simplicity over the pursuit of an absolute or finite solution. The solution is derived from a series of overlapping Collin’s Point Resections and the simple linear average of the aggregate x & y values of the solutions.

The Collins Method or Bessel’s Method considers the occupied point and the two of three control points on a circumference. A fourth point is projected on the circumference from the occupied point through the third point. The relationship between all points is trigonometrically defined. For more information regarding resection methods and Collins Point refer to this link http://www.mesamike.org/geocache/GC1B0Q9/resection-methods.pdf

Program X and Program Y are quick utility programs that compose a complex number in and from rectangular coordinates (LBL X) and decompose a complex number in rectangular coordinates to polar coordinates (LBL Y).

I currently have all of the previously published routines along with Resection on my 35s. I am able to store points ranging from single digit point numbers to some where in the mid 400’s. This is the just about the limit of practical balance between program memory and data storage allocation. Please do not hesitate to send any comments, concerns, questions, or criticism to rls43185@gmail.com.

**Example Data and Running the Program**

We will reference our previous data set as follows:

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If you have carried coordinates through from the compass rule adjustment article you may find insignificant differences in solutions as noted in the May 2015 "AREA" column. The source of the error is the difference between hand entering coordinates to two decimal places versus the computed (adjusted) values that are carried out to the full 12 digit precision of the HP 35s. This is a great example toward accepting tolerance in measurement through the assessment of the source data. The amount of these differences is insignificant, however the reason they exist must be identified before considering the impact. I will be reporting will the 2 decimal coordinates listed above.

**Observation Data**

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Observation data contains a simulated natural error of -0°00’48" to the horizon. These values will be impacted by the linear averaging of the interim solutions. Your comfort level can be ascertained by comparing raw angles to post solution values. Differences may be apparent by fixing the display to a greater precision. The solutions are accumulative therefore any inclusive interim solution should vary from any given singular solution.

The solution requires the input of adjoining (co-current) angles as delineated by "A" & "B". Note that angle 1-PNT-5 is the overlapping angle. Entry should run clockwise using angle right.

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**Interim/Final Solution Notes:**

At this time the solution could be accepted and stored as point 10. A single three point solution may yield sufficient results. Observations can be added by repeating the steps through "MORE". Continue around the observation horizon clockwise until the "B-C" angle of the last observation is the same as the "A-B" angle of the first observation. In this case it’s 49°30’20" between Points 1 & 5.

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*Jason Foose is the County Surveyor of Mohave County Arizona. He originally hails from The Connecticut Western Reserve Township 3, Range XIV West of Ellicott’s Line Surveyed in 1785 but now resides in Township 21 North, Range 17 West of the Gila & Salt River Base Line and Meridian*.

A 227Kb PDF of this article as it appeared in the magazine—complete with images—is available by clicking **HERE**