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# AZ: Cardinal Equivalents for Single and Double Proportion

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(@gromatici)
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What is the practice in Arizona for single proportion and DP: 1.  straight inverse and then proportion or 2. reduce to cardinal equivalents and then proportion as the Manual stipulates?  Some states accept either one since both been in practice.

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There are  no cardinal equivalents in single proportion.

If you dont use cardinal equivalents for double proportion it's not a double proportion.

As usual the correct method depends on the specific situation. The primary methods in the manual assume the township was subdivided by the standard method given in the manual. For example, double proportion makes no sense if the township was subdivided by GPS survey.

If the township was subdivided by the "standard" method, and the corner is truly lost (no evidence at all) you would have a hard time justifying not using the manual methods in any state.

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Jerry Wahl has a paper on it with an illustrated example.

or

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(@gromatici)
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So in CA, the practice was for surveyors to simply inverse their measured data, and not reduce to CE.  It seems like the other states I've gotten licensed in, never developed that bad habit!  So in CA, there was two ways to do it, one by inversing and comparing it to the record, and one by reducing it to CE and then comparing it to the record.  It's been many years since I've studied for that exam, so I don't know what the standard is now.  Glad that I don't have to deal with it!

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@gromatici

How does the CA alternative method work? What do you do after you inverse and compare?

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@aliquot

I don't know about what Gromatici is saying but...

Curt Brown's method was single proportion the north-south line and the east-west line which establishes two points (or temporary stakes as he puts it)  then run an astronomical north or south line out of the east-west point and a east or west line out of the north-south point, the intersection of the two cardinal lines is the restored corner position. He cites "Restoration of Lost Corners" for this method.

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@dave-karoly

That would work until the upper tier of sections, there is often a bearing kink along the north-south lines for the last mile, sometimes fairly strong.

I've even seen coordinates prorated in for a double proration using SPC bearings, needless to say that doesn't work at all.

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@aliquot

It's been about 15 years, but here is how i remember it:  So in CA, the actual old exams from the 1980's and 1990s that were released to the public had DP questions on them.  The answer involved simply inversing the measured coordinates (not subtracting northing from northing to get C.E.) to get a measured length that WAS NOT reduced to Cardinal Equivalents.  You compared that to the record (which also was NOT reduced to cardinal equivalents).  Then, you did your proportion, and then the "moves" from the temporary stakes for the DP corners.  In other words, the correct answer was not the method in the Manual, but a hybridized version of it where you simply inversed between found corners, and did not reduce either the measured or record data to C.E.  OF course this WAS NOT the correct method, but was commonly in practice in CA.  Interestingly a candidate used the proper method while taking the exam (20 years ago or so), and was graded wrong.  She sued, and won in court, or won in front of the board (can't remember that detail). So when I took the exam, they told me I could do it either way.  Sounds confusing doesn't it????  I've always wondered if other states had the same issue to deal with.

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@gromatici

That sounds like a person who is making up the test, had his way of doing it and it became the SOP when giving the test. I can't imagine California coded that into their statutes, or regulations.

When in doubt do it correctly, it's clear why Cardinal Equivalents are used, but often they only make a very minor difference.

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@gromatici

That is the method given in the BCLP books. Brown cites "Restoration of Lost Corners."

A classmate in about 2001 said he failed because he did the Brown method.

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@dave-karoly

OH!  So maybe that is the nexus on why they used that in California........................  I wonder if CA still accepts that an an answer, now that the test is multiple choice.  The fifth edition doesn't seem to discuss it on page 267.........the only statement that I found intriguing was:  "On occasions, the instructions for double proportionate measures have been misinterpreted".  It's more in the context of angles vs. distances and isn't real clear what they are talking about.  Then they go on to illustrate a DP by use of a diagram, but the figure shown is all in cardinal directions (both for the record and measured data), and it would have been better for the reader had they broke down an example were the data needed changed to CE.  In fact there aren't the words "cardinal equivalents" in Browns book, for either edition i have.

They do state in Brown's 5th ed.:  "Primary weight is given to distance, not to angle or bearing".  I guess that's their way of saying "reduce distances to Cardinal Equivalents"?  I like how the 3rd edition stated it, although still lacking the phrase "Cardinal Equivalents":  "It is to be noted that original reported bearings play no part in the restoration of a corner by double proportionate measurements; distance is a subdivision is superior to angle.".  They don't explicitly state the same for MEASURED data!

I guess that's proof that in CA, they were doing DP's this way and that's why that had that policy.  Seems like a good subject for an article.  My experience with other states, is that there is only ONE way to do this........less confusing!

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California does not have a code adopting the methods of the manual for subdividing sections. That's why you have to split a section by area if it says "one-half" or the "east half".  Like I mentioned before, you can obtain all the old copies of the exams and the "correct" answer was doing it incorrectly until someone called them on it.  Anyways, this is ancient history and I wanted to make sure no other state was doing the same thing.

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@gromatici

Wood v. Mandrilla, 167 Cal. 607 (1914) has been cited for the proposition that half in California means one-half by area. The case is pretty much a derelict on the waters of the law having only been cited a couple of times in California in cases not involving boundaries, in other words, our courts have ignored it. The two properties involved appear to be currently split by Plat measure, not half by area. The case was cited in a Kansas probate case, the Kansas Court saying the better rule is descriptions in the PLSS should be read in context of the system.

In the case Mandrilla received the Deed to the east half of the southwest quarter (180 acres approximate) of Section 30 from Wood. Mandrilla proceeded to occupy one-half by area then Wood sued to recover 10 acres saying that the east half only contained 80 acres per the Plat (an old Plat which did not show lots, only two unequal halves). I think the fact that Mandrilla took possession of 90 acres motivated the court to apply the rule "Words used in a conveyance are to be given their ordinary and popular meaning, unless used in a technical sense, or having a special meaning, or the context shows that they are used in a different sense. The word “half” has a plain, common, and natural meaning, and when used in describing lands is to be understood literally."

My opinion is that if the Plat shows lots then the technical meaning exception would override the plain meaning rule. The California Courts, however, are always on the lookout for evidence of practical construction of the meaning of words by the parties.

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