The HP 35s Calculator—A Field Surveyor’s Companion: Part 7—Adjustment

A 276Kb PDF of this article as it appeared in the magazine—complete with images—is available by clicking HERE

The current price range of the HP35s is $50-$60 in the United States. In 1972 a new HP35 cost $395. Adjusting $395 to 42 years of inflation equates to about $2,200 according to internet fodder. Going backwards, $60 in 2014 bucks equates to about $10.75 in 1972. It’s no big secret that electronics are really cheap now-a-days and who really cares? Well, I do! I’m teaching you how to wring every single dime out of a $60 dollar black box that is really worth $2,200. Our next few programs require your elbow grease to squeeze the lemonade out of the old black box.

This Month’s Program

Why do we even bother to adjust our surveys if our modern measuring capabilities are ridiculously precise to begin with? Least squares network adjustment will resolve the most probable statistical value of measurements and positions. That type of adjustment truly improves consistency of expectations when comparing positional values. Positive applications include baseline networks and level networks. Contrary to our judicial function as boundary retracement surveyors, the objective of control work is resolving the most absolute positional value for a particular station. For example as in the NGS case the station mark itself is subordinate to the values assigned, adjusted, published, updated, and republished as the geodesy is refined. I really don’t think that Michael Dennis and Dave Minkel sneak out at night with a hammer and bang every mark on the continent over a smidge. Of course not, they simply report the updated adjustment values which lend the appearance of a "floating" mark to us dirt surveyors. I can assure you that NGS marks are very static and don’t "move"! However, when introducing NGS control into a network, the expectation is to adjust the physical measurement between control points to the known adjusted control values. That is somewhat contrary to our expectations as boundary retracement surveyors. We most often and comfortably report varying measurements between legal corners and place our emphasis on the evidentiary value of a position as controlling rather than the mathematically derived coordinate. {If you feel any challenge to my last statement please unsubscribe from The American Surveyor. You are not practicing Land Surveying. You are engaging in some sub professional measurement exercise and you are a FRAUD!!!}.

Our predecessors did not necessarily seek to resolve the most probable statistical value of a position but rather aimed to accurately identify the location of legal evidence. Their purpose for adjusting measurements was to promote consistency for retracement rather than a truly "most probable value". They measured linearly and thus they adjusted measurements linearly. According to "Surveying" by Davis, Foote, and Rayner circa 1928, "Many surveyors, however, rely upon their own judgment, in large measure disregarding any established rule, and arbitrarily distribute the error in accordance with their estimation of the difficulties met in the field. Manifestly, if certain courses are over rough ground, the error of chaining these courses would be expected to be relatively large, and the correction to the observed distance should be correspondingly great; also when sights are steep and visibility is poor, larger angular errors would be expected than where conditions of observing are more nearly ideal, and hence in balancing the survey it is fair to assume that the larger changes in direction should be in the courses where conditions surrounding the observations were relatively unfavorable." It should be apparent that the quest for the absolute mechanical position of a point is of little relevance in retracement work. However, employing the compass rule adjustment simply provides a consistent method to distribute error through your measurements.

Compass Rule can logically be applied to aid in recovery of evidence when a consistent difference is noted between plat reports and observed measures. Where original subdivision lines were physically run the difference between the physical end points and the platted positions could be prorated through the line points. The thought being that accumulated field error was accepted on the ground but not accounted for on the plat. This computation may lead the retracement surveyor closer to the original evidence of the work as laid out on the ground. Frederick W. Boreman P.S. 6855 (Ohio) used to say "Jase, they’re like clams. When one coughs, it gives them all away." (see Figure 1)

The benefits of least squares adjustments are negligible if not perhaps misleading (too good for the intended purpose) when applied to modern retracement survey work. The compass rule method is well suited to retracement efforts because of its simplicity and repeatability. It is quite a simple premise: any error is proportionally distributed to every measurement in a lineal set according to each measure’s magnitude. Traversing is linear and stations are generally physically dependent upon only the adjoining stations. When measurements are made with consistency they are considered equal in weight so there’s little if no need to apply any sort of arbitrary or statistical weighting.

Please do not hesitate to send any comments, concerns, questions, or criticism to

The Program
Program B: Compass Rule Traverse Adjustment

This program is very dependent on the order and format of the traverse entry. The objective is to get the foresight point number to match the input leg number. The reasoning is that the program operates on a loop counter and requires sequential addressing with the order of the legs as entered. Traverse legs will be overwritten by the values of the computed coordinates as they are addressed to the same register. This may take some rearranging on your part or a change in field numbering discipline. Remember to enter azimuths/ angles in decimal degrees. Final report of angles and azimuths is in DMS format.

Example Data and Running The Program
Create a traverse sketch and use field notes to construct a data table like the examples below. Raw coordinate values are listed to demonstrate differences but are not apparent while running the routine. Raw coordinates are computed by simply assuming the backsight azimuth of N35E between points 4 and 5 and simply running around the polygon. The program uses the statistical accumulator and registers. Access  registers through keystrokes  BRS  – for the "SUMS" menu.

Continued Online…
Due to the length of this month’s program listing, please refer to the online PDF at

Did You Know?
Do you actually know the name of the division symbol? You know, the minus sign wedged between a colon? Well apparently Bill Gates forgot to put it in my Microsoft Office Suite so I set sail in that ocean of knowledge we call the internet. I found that the division symbol is named "obelus" and is available in MS Windows through keystrokes Alt+0247 on the keypad ÷ there, see I just did it! I’ll do it again ÷ this is fun ÷ oh, BTW, sorry Bill I stand corrected!

Polecat of the Month
Mark E. Hummel, hailing from a certain un-named city holding six Superbowl titles and the rings to prove it, pointed out that Line I021 of the January 2015 Inverse Routine should include the keystroke .EQN.. Mark Hummel’s great catch is second only to Franco Harris’ Immaculate Reception in Iron City lore. Thanks Mark for pointing it out!

Jason Foose is the County Surveyor of Mohave County Arizona. He has been licensed for  441,504,000 seconds…no wait, 441,504,001 seconds…no wait, 441,504,002 seconds…

A 276Kb PDF of this article as it appeared in the magazine—complete with images—is available by clicking HERE