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San Juan and Ponce: Newsletter Challenge (10/09/07)

Posted October 07, 2007 5:01 PM
Pathfinder Tags: challenge questions

The question as it appears in the 10/09 edition of Specs & Techs from GlobalSpec:

When the government of the United States assumed authority of Puerto Rico, the U.S. Coast and Geodetic Survey was called upon to complete a survey of the island. The astronomical latitudes of San Juan and Ponce were calculated with results indicating a north-south distance between the two cities of 30 miles. However, by triangulation the surveyed distance differed by nearly a mile. How could this be? And where have other, similar discrepancies occurred?

(Update: Oct 16, 8:33 AM EST) And the Answer is...

San Juan is north of the mountains near the Atlantic Ocean while Ponce is south of the mountains near the Caribbean. The gravitational influence of the mountains, the lesser density of sea water compared to island rock, and the higher density of underwater rocks versus island rocks shift plumb bobs off the vertical line allowing for incorrect transit measurements. Similar discrepancies have been noted in India and other mountainous regions

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#1

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/08/2007 4:14 AM

Curvature of the Earth vs line of sight? Something to do with latitude, so anywhere else on on that latitutde?

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#2
In reply to #1

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/08/2007 8:07 AM

It is interesting to consider curvature but the curvature is not that pronounced as you might think. Now my numbers my not be entirely accurate (any mariner's out there are welcome to correct me), but it is said if you are 70 feet above the ocean, you can see for 7 miles to the horizon.

Now since Porto Rico is not that large, I find it hard to believe that curvature plays a factor in this measurement. Another thought, though is if the satellite image is taken with a scanning type camera, it could be time delay. Think about it, at the earth's equator, the surface of the plant is traveling at approximately 1000 miles per hour. Factor in if the satellite is going a different direction and you have got a lot of relative speed. So could it be that the discrepancy is caused by the time delay in the satellite camera? It is hard to believe that NASA would make that kind of mistake, but worst has happened.

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#37
In reply to #2

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 9:30 PM

Close. The distance to the horizon formula is 1.17 times the square root of the height of eye. So at 70 feet, the horizon would be 9.79 nautical miles away, or around 11 1/4 statute miles.

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#42
In reply to #1

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 11:29 PM

Astronomical calculations are obtained with a sextant. Astronomical items at 45 degrees above the horizon are chosen for accuracy. From the one city, items to the North would be chosen, from the other, items to the South. While erroneous astronomical data tables could have played a factor I doubt it. Rather I would think that refraction is the key. To the South is very Moist, to the North is quite dry.

I'm not smart enough to do the math.

tom

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#49
In reply to #42

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 4:54 AM

I half suggested this, but it wasn't really a serious possibility. But the index of refraction of air is only 1.0003. So, at 45-degrees, a compete absence of air would result in a change of angle of 1 minute of arc; that would correspond to an error of one mile. But even considering extreme pressure, temperature* and humidity variations the maximum angle variation we might see is in the order of five percent of that - which might correspond to about 100-yards.

Fyz

*N.B. I believe that temperature is capable of giving the largest contribution. The 5% corresponds to 30-degreesC +/-5, +/- 0.5% atmospheric pressure variation, and humidity from 0 to 100%. [Reference: NIST calculator for air refractive index]

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#3

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/08/2007 8:09 AM

That sounds far too much for truly local variations in the curvature of the Earth, and the general oblateness has been understood for some time. The following is just a first guess:

Presumably these measurements would have been made quite early last century. So the latitude would have been determined using a sextant? In that case, I could think of two possible causes - variation in the direction of the gravitational vertical due to the mass of the island and hills between, and differences in atmospheric distortions over the sea and over the land?

There would be little that surveyors of the time could do to counter the variation in measurement of the vertical, but first thoughts are that 1-mile does sound rather a lot for this; the second could be reduced by making measurements both by day and by night, with reference to stars with known separations so all the measurements could be made over the sea.

Fyz

*1-mile only corresponds to an error of about 1-minute.

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#5
In reply to #3

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/08/2007 10:14 AM

I assumed that new measurements were taken rather than relying on old ones. That was my inference from the way the question was worded - although it did seem strange that they would "survey" by two methods at the same time, unless two different agencies were involved...

Ah - just reread the question: and I'm missing a bit of background info: Just when did the US assume authority over said island?

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#7
In reply to #5

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/08/2007 11:20 AM

In practical terms, at the invasion. Formalised in the relevant* 'Treaty of Paris'. Both 1898, I think.

Although I'm no expert, I imagine that duplicate measurements would have been commonplace. Triangulation measurements were (presumably) optimum for landlubbers, but latitude and longitude might be more relevant in a boat (should that be ship?).

Fyz

*Just to add to any confusion, there have been several treaties of that name.

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#18
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Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 6:56 AM

Thanks Fyz.

boat (should that be ship?

Depends on the size and whether, in normal operation, it is capable of submerging.

Small surface vessels = boats
Large surface vessels = ship
Submersible = boat (irrespective of size)

Of course, they're all female

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#21
In reply to #7

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 7:59 AM

1898, I surely mis-read this question. Satellites are likely not a factor, but if they are using naval instruments of the period, there is a lot of places error can creep in.

Firstly altitude, naval readings assume you are or very near sea level not on a hill.

After one takes readings one needs to look up in tables the positional information for accuracy. To do this you need very accurate time and time pieces of the day were notoriously inaccurate. They could have done a lot better with a Quartz Timex, even though Quartz watches are not considered precision time pieces even today.

The tabulations for determining positioning for naval purposes where not themselves accurate, as they were meant to afix ones rough position in an ocean of hundreds of miles. Plus or minus 1 mile error would be quite acceptable in that regard. In general most ships of the day relied on readings to maintain a reasonably constant latidute while the ship sailed across the ocean. The latitudinal changes where made typically close to land, so they did not typically worry too much about the longitudinal position while in open ocean.

Using the triangulation on land would most likely be the most accurate method as it is most like the surveying methods of today.

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#23
In reply to #21

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 8:27 AM

Although it's not relevant for latitude, Harrison chronometers and their successors did a pretty good job in absolute terms, plus it would only be a matter of a couple of days to sail all the way around the island to take "ABA" readings. However, if you were considering East-West variation it would be worth remembering that 1 second (time) corresponds to 15 seconds of arc, or 1/4 of a mile. Oh, and longitude is pretty critical when in straits (Dire or otherwise)

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#80
In reply to #3

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 6:44 PM

Just North of San Juan is a very deep trench in the ocean. That would mean the absence of a lot of mass just north of the Island, so I think that nailed it with the gravitational vertical observation.

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#4

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/08/2007 9:50 AM

I thing that it may be due to gravitational variation using satellite readings. a satellite does not have a perfect orbit, but is influenced by the GEOID. The geoid is a map of the varying gravitational areas of the earths surface, the height of a satellite in orbit varies according to the geoid. The geoid has recently been remapped with the event of the GRACE programme. ( Gravity Recovery and Climate Experiment ). I think this error and others where found after corrections in the geoid?

Regards JD.

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#6

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/08/2007 10:29 AM

The difference between common latitude and geocentric (which I believe adjusts for the curvature of the earth) can be as far off as twelve or thirteen minutes from equator to poles.

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#8
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Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/08/2007 11:26 AM

Such an error, even if left uncorrected (which no seaman or surveyor worthy of his salt would do) would represent a peak slope error of about one part in 270 - or 1/9 of a mile.

Fyz

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#9

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/08/2007 1:08 PM

Kudos to ER for thinking about the historical aspect of this question. I haven't checked the timeline yet, but I'm sure the survey began in late 1898 or 1899, so we can rule out satellites.

The difference could be due to two different methods being used, ocean navigation and land surveying. I'm not for sure about this yet.

Both cities are ports, and before the Spanish American War, I'm sure ships from the US Navy used both for supplies. The Navy must have had the lat-lon of both ports recorded and this information supplied to their ships in the area.

However, before the war, the US did not have access to the interior of the island. Once land surveyors took their measurements, they discovered the dsicrepancy. According to Wikipedia, surveying starts with a benchmark, a position of known location and elevation. Oceans and seas do not have fixed benchmarks.

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#11
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Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/08/2007 2:45 PM

I'll be interested in what you can find.

Late 1898/1899 would certainly be pretty quick for the survey on land, particularly as there seems to be no reason why US would have been set up to administer distant conquered territories before that date (and the treaty was only signed in December). Apart from that, I seem to recollect that a specific project to survey the US island territories by triangulation was started in 1900, this specific project continuing until about 1940 (the duration having lodged in my memory for no particular reason). But this is only from general reading, and it may be false memory in any case.

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#55
In reply to #9

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 9:14 AM

Could it have to do with the tide? GM

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#10

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/08/2007 2:35 PM

That does not seem too bad. According to Wikipedia, "the best possible accuracy of celestial navigation is about 0.1 nautical miles (200 m). At sea, results within several nautical miles, well within visual range, are acceptable. A highly skilled and experienced navigator can determine position to an accuracy of about 0.25 nautical mile (460 m)."

Statistically, it is possible that you could be .25 miles off in each site and if they are of in opposite direction, you have .5 mile between the two. Given that is a highly skilled operator, a less skilled operator will haver a harder time to approach those numbers.

The error in distance between the two cities was cited in the challenge as nearly 1 mile.

Krakatoa went ballistic in 1883, which was too early, but perhaps a subsequent eruption of another volcano could have distorted the atmosphere and cause distortion in the apparent position of the stars at lower elevations and impacted the survey.

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#12

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/08/2007 3:16 PM

Finally, a site with numerical information on gravitational anomalies. Puerto Rico is rather exceptional, and the N/S component of the vertical deflection in that area covers a range exceeding 112-seconds of arc. According to the map, as best as I can judge*, the difference between the two locations corresponds to about half of this, or just under 1-minute of arc. At ~4000 mile earth-radius, that would indeed be about a mile.

Fyz

*Unfortunately, I couldn't find a complete colour key

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#19
In reply to #12

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 7:25 AM

If this is the correct reason (sounds plausible to me, but what do it know?), than Fyz's link also answers the "Where else?" part of the question.

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#22
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Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 8:07 AM

The method used was astromonical, which means they did rely on gravity to make the instruments work. This is certainly another place for error to enter the equation.

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#25
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Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 8:42 AM

Nice work!

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Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 10:20 AM

Thanks. Another for my miniscule collection.

Fyz

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#52
In reply to #12

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 5:18 AM

Astronomical surveys were done with high precision theodolites which oriente in the vertical component using spirit level bubbles the same as a spirit level or builders level. The difference in vertical deflection would affect the observed vertical angles to the stars (sun included) which are used to calculate latitude. Longtitude is related to time, latitude to vertical angle from the horizon. In earlier times this error would not have been know and so could not have been corrected for.

Triangulation again uses precision theodolites and solves the missing distance knowing observed angles and at least one known distance. This distance was usually a precisely measured shorter distance. This is essentially a horizontal triangle and would not have been affected greatly by the vertical deflection.

From Sir Veyor.

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#63
In reply to #52

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 9:46 AM

OK, so are you saying that the triangulation method is essentially more accurate and correct, and unaffected by local variations in gravity?

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#64
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Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 9:56 AM

I think that the triangulation method could have some similar proportional errors due to gravitational anomalies. But the proportionality is against the relevant distances. For the astronomically-based data the relevant distance is to the centre of the Earth. For the triangulation method it would be the distances over which the triangulation is made** - in this case the difference in errors would be a factor of about 100.

**without doing the full geometry, I would expect that north-south error would primarily be determined by the west-east spacing and vice versa.

Fyz

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#13

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/08/2007 11:31 PM

Ok, this is a old question, been told several ways, but I feel this is similar to the many others.

Drive 30 miles South,

then 30 miles East,

then 30 miles North,

then 30 miles West.

You will not finish where you started, its nothing to do with gravity, its all to do with the curvature of the earth.

also, if your using astronomical measurements, Gravity has no bearing, could be the inaccurate time keeping of the era.

When was Long-Lat defined to be non-square, and shipboard time keeping devices invented?

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#15
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Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 5:36 AM

The Harrison chronometer was adopted in the 18th century (more than 100 years earlier).

Navigators have been making curvature corrections since before Galileo (Vatican or not).

You would need to be within 900 miles of the North pole* for the latitude issue to cause an error as large as a mile, and in any case this error would be solely East-West.
*Puerto Rico is, of course, in the tropics.

Regarding "gravity has no bearing": what is your reference for the angle the stars subtend? Ideally, it would be the line to the centre of the Earth. But the only reference you have for that is Gravity.

Time on the other hand is irrelevant to this question, as it only affects East-West measurements.

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#14

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 12:06 AM

Yes I agree that the earth surface is not perfectly spherical. But to just clarify a few points, I think we are talking about the distance as the crow flies, as they say, not land miles, up hill and down dale? The geoid is the true shape of the earths surface, and this is due to gravity, the distribution of mass. This agrees with what you are saying I think. I therefore speculated that when early surveyors done there calculations this effect was not taken into account, it will need someone better at maths than I am to follow up on that as a possibility.

Regards JD.

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#16
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Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 5:46 AM

Over this 30-mile range, geoid effects would be related solely to variation in the diameter of the Earth. The total geoid variation (polar versus equatorial radius) is just 0.3%, or 1/10th of a mile. And they should by then have been using appropriate radii for their calculations in any event.

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#17
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Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 6:41 AM

Yes the dia of the earth is 7899.8 miles between the poles and 7926.28 miles at the equator not a great deal of difference as you say. And as you say one would think of them as being competent, in doing there calculations. So if an error has been found in there calculations, then one is drawn to the possibility of it being related to modern technology, satellites? So looking a bit closer at the geoid, and trying to make some sense of it, have come up with the following possibility. The geoid is referred to as the spirit levels reference of flatness, if that the correct term? the spirit level aligns itself to the geoid. so if the distance was surveyed in the past where a spirit level is used in the instrumentation, then just maybe an error crept in. I know its a long shot, but maybe someone can enlighten me on the method they used, or would of used?

Regards JD.

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#20
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Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 7:56 AM

I think you should assume competence - and no errors in the calculations. The different surveys are for different applications. Latitude-longitude is for seafarers to get to the ports and avoid hazzards, triangulation for general land use. Seafarers are dependent on the 'flat' surface of the sea as a reference for looking at the stars - and 'flat' is relative to the local gravitational direction, rather than to the geode. The only data on local gravitational anomalies at that time would have been the results of such surveys - and it would make no sense to "correct" either set of data, as this would only cause problems for the users. BTW, seafarers often used "dead reckoning" (e.g. dropping stuff overboard) as a supplement for local navigation, so their charts could get quite complex. I imagine that was one of the reasons that a full commercial master's certificate would have been so challenging.

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#27
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Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 9:07 AM

The following taken from the internet support your remarks regarding the sea level as a reference, I think you have put it together nicely. The geoid and flatness at sea are much the same thing but on land its the centre of gravitational attraction that effects the outcome?

Dr. Byron Tapley, Grace principal investigator at UT's Center for Space Research, called the new model a feast for oceanographers. "This initial model represents a major advancement in our knowledge of Earth's gravity field. "Pre- Grace models contained such large errors many important features were obscured. Grace brings the true state of the oceans into much sharper focus, so we can better see ocean phenomena that have a strong impact on atmospheric weather patterns, fisheries and global climate change".

Grace is accomplishing that goal by providing a more precise definition of Earth's geoid, an imaginary surface defined only by Earth's gravity field, upon which Earth's ocean surfaces would lie if not disturbed by other forces such as ocean currents, winds and tides. The geoid height varies around the world by up to 200 meters (650 feet).

"I like to think of the geoid as science's equivalent of a carpenter's level, it tells us where horizontal is," Tapley said. "Grace will tell us the geoid with centimeter-level precision."

Regards JD.

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#30
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Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 10:19 AM

"The geoid and flatness at sea are much the same thing" Er... no - water can only respond to physical effects - in this case a combination of gravity and centripetal acceleration. So the horizontal sea surface is perpendicular to the combination of the geode and any gravitational anomalies. The anomalies are created by a comination of the local thickess/density of the earth's crust and thetopography. This applies just as much under the sea as on land - as you will see from the maps if you follow my previous link.

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#38
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Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 9:37 PM

Yes I agree with your interpretation, Centripetal acceleration; in oceanography I believe is referred too as the Coriolis deflection. It seem my terminology is not the best. And your ability to bring that bit extra helps.

Regards JD.

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#29
In reply to #20

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 9:39 AM

Prior to 1990 shipboard navigators used several different methods to fix a ships position.

Loran

Omega

SATNAV

Radar

Celetial

Visual

Before 1990 they were just establishing GPS, there were only a few satilites available so fixing a position wasn't very accurate. By 1990 there were several more satilites established and positioning a ships position became as accurate as to within a few yards.

Before GPS navigators thought themselves pretty good if they could estimate the ships position to within a few thousand yards of the ships actual position on the open ocean.

Before then visial fixes would be considered the most accurate method.

Since 1898, nautical charts have been updated and corrected several times. This would also included the fixed reference points used for taking a visual fix.

Curvature of the Earth would play a big part in the accuracy of a satilite positioning.

IF you were to take a section of land from a round object like a globe and lay it flat it would take on a different shape. It doen't have to be a big section either.

30 miles would create a difference in distance.

In the waters off San Diego a nautical mile is around 2000 yards. In the waters outside the Puget Sound a nautical mile is about 1820 yards.

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#24

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 8:34 AM

Latitudes are calculated a mean sea level, or an of elevation zero. The survey probably was not corrected for elevation difference.

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#34
In reply to #24

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 3:56 PM

Wrong. Triangulation is a 3-D system and does correct for elevation differences. Fyz is probably right though that anomolies in local gravity could create errors in determining angles off of horizontal, since horizontal is determined by the local gravity!

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#51
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Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 5:17 AM

Maybe the tide influenced the measurement of the latitude???

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#26

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 9:03 AM

Rounding errors.

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#28

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 9:28 AM

All of the answers so far consider both cities to be a point source. Both cities are fairly large, and the Lat/Long of the center of the city could be quite different for each survey. I have several GPS units and one of them uses City Hall to calculate distance to a particular city, while my Garmin units seem to use the geographical center of the city. Also, if the method used was the geographical center, then that would change over time. If the surveys were taken several years apart, then it is probable that the center of the city would have moved.

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#35
In reply to #28

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 4:13 PM

I was thinking the same thing, where are the reference points? I would hope that the two measurements would be considering the same references points!!

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#41
In reply to #28

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 11:03 PM

I believe that you are correct as the surveys were done by the "U.S. Coast and Geodetic Survey".

U.S. Coast might take distant from the sea ports & Geodetic Survey might take distance from cities centers.

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#47
In reply to #41

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 4:25 AM

Why do you people insist on assuming incompetence when there are more interesting (and potentially correct) reasons. Is it something to do with your life experiences?

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#53
In reply to #47

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 7:25 AM

Dear Guest #47,

Guest #41 did not assume incompetence, but rather that two organisations might use different datums (data?). No value judgements were given in his post, unlike in yours. Have your life experiences given you to assume that everyone's else's remarks are derogatory? And why the anonymity?

Blessings

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#60
In reply to #53

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 9:35 AM

Dear ER

My understanding is that this was a single organisation. But even if it was split into two groups, this would at best be a trivial basis for a "challenge". Plus, I'd certainly call it incompetence if survey results were issued with apparently identical datums** that were in fact different.

I have to admit that I find the consistent attempts by many to assign what appear to me to be obvious, trivial, and uninteresting answers to every challenge to be a waste of mouse-clicks. Sorry if you consider this is an inappropriate value judgement - and also that my irritation is showing.

And... I have yet to observe universal competence, let alone attain it. And no, I still don't always log on.

Blessings reciprocated

Fyz

**My understanding is that when datum is used to represent a basis for measurement it generally takes "datums" as the plural.

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#87
In reply to #60

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/11/2007 4:12 AM

LOL - now I understand Kris's comment!

'Twasn't me who suggested there were two organisations, and I didn't believe #41 was right on that score, I just didn't choose to express my opinion on that point (mea culpa).

I agree with you that some of the responses are trivial; I tend to ignore those. I responded to your post #47 as it seemed to be a personal attack rather than a factual/theoretical disagreement and we've seen enough of those in CR4 lately.

I'm sorry you're feeling irritated - would you like an Indian head massage to relax you?

And... I have yet to observe universal competence, let alone attain it.
True for me too, in spades.

I knew you'd respond to the datums/data issue...I was thinking of you as I typed it

Peace is restored?

PS I wasn't Guest #41

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#90
In reply to #87

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/11/2007 5:41 AM

LOL - now I understand Kris's comment!

Pretty good going since I've only been reading so far ! Oh the mysteries of CR4. I was watching to see a custard-pie fight develop. You must have read my mind.

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#92
In reply to #90

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/11/2007 7:22 AM

I think that was the one about helping me (in a different thread)

Fyz

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#93
In reply to #87

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/11/2007 7:28 AM

"knew you'd respond to the datums/data issue...I was thinking of you as I typed it"
I 'guest' as much

"Peace is restored?"
Other than what appeared analogous to "paternal instincts", I didn't have an issue with you (though there may have been issues the other way around)

PS I wasn't Guest #41
I never thought for one moment that you were (see above).

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#95
In reply to #93

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/11/2007 7:48 AM

No issues here either, other than trying to convey non-verbal info in typeface! And finding that some of my attempts at jokes are not understood

Without being sycophantic, I enjoy your posts and learn a lot from them. These replies have simply been an attempt (clumsy?) to make sure none arose. Now we've got that sorted, I'll shut up!

Well, about this subject anyway (before Kris starts...)

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#99
In reply to #95

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/11/2007 9:03 AM

Clumsiness competition? I win every time. Whoups, buttervingers.

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#107
In reply to #95

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/12/2007 3:39 AM

Hello Kris!

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#108
In reply to #107

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/12/2007 3:42 AM

LOL. I'm just so obvious aren't I - you were quicker off the mark than I expected.

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#109
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Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/12/2007 6:53 AM
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#57
In reply to #41

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 9:25 AM

Uh, #41? I believe that the "US Coast and Geodetic Survey" (formed in 1878) was one single organization at the time of the original Puerto Rico survey (around 1900) and as such had one standard benchmark (pardon the pun) for city location points. Why did you try to split it into two organizations? That is like saying NASA is two organizations, National Aeronautics and the Space Administration! Granted that there may have been sub-divisions within the organization, but when it comes to cartography, one standard would prevail.

Since 1970 the US C&GS has been two separate organizations under the National Ocean Service (NOS) of the National Oceanic and Atmospheric Administration as the National Geodetic Survey (NGS) and the Office of Coast Survey (OCS), so I can understand your confusion. It is likely though they still use the same standards, just each has a somewhat different mission.

I am wondering how this fits in with the mission of the US Geological Survey (USGS), which is also responsible for mapping, but primarily in the interior. So where does the interior stop and the coast begin?

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#32

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 10:46 AM

Is the north-south alignement perfect? If not, it will account for the discrepancy.

Guillermo, gvanrees@fibertel.com.ar

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#33
In reply to #32

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 12:07 PM

The North-South alignment is a very long way out, as you will see if you look at a map. This would result in a discrepancy of several miles if the surveors were incompetent; if they were competent, a different cause would be needed for any discrepancy

Fyz

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#36

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 9:21 PM

I'm not clear on the time line here. Was the triangulation done prior to the US taking over? There is some indication the magnetic declination was not well charted prior to this and that could well account for the discrepancy. Of course, any Bermuda Triangle nut (Oops, I mean buff) will tell you this is a part of the world where true N and magnetic N are very close and that weakens compasses which are then attracted to magnetic storms which burst forth from the earth.

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#39
In reply to #36

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 9:42 PM

And, in fact, that would have been about the time the declination switched from E to W. mmm?

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#54
In reply to #39

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 8:50 AM

And, in fact, that would have been about the time the declination switched from E to W. mmm?

Mmm, indeed. Magnetic declination (angular difference between True North and Magnetic North for any particular location on the Earth) does not just flip suddenly "from E to W". It is a gradual change that happens as the solid crust of the Earth floats over its molten core (which is magnetized). Declination must approach zero and pass through zero before it can increase in magnitude in the other direction. Any good cartographer or surveyor (or even a Boy Scout!) will easily keep up with the changes and make the appropriate adjustment so, guess again!

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#56
In reply to #54

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 9:21 AM

That might apply to your "Good Surveyor, Boy Scout and Cartographer" but what about your run of the mill?

Who take short cuts, cut corners, think they can skip steps because they've been doing it for 20 years and no ones questioned them so far.

You know, the bulk of the work force that really do need supervision, even though they think they don't.

You bring up a good point but you don't have to be arrogant about it.

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#61
In reply to #56

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 9:38 AM

#56, I was not being arrogant, just incredulous. Magnetic declination is so basic to mapping (although possibly obsoleted with GPS now) that it hardly seems possible that anyone would possibly ignore it, no matter how many short cuts, cut corners, or skipped steps they may have taken. It is like saying the infant's parent or nurse forgot or decided not to put the nipple on the baby bottle and shoved it into the baby's mouth anyway!

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#101
In reply to #61

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/11/2007 9:41 AM

agreement from cr3. Actually I am miffed that I missed it! It is very elementary.

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#62
In reply to #56

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 9:44 AM

I've just been ticked off for making a "value judgement" regarding another's comment. So here I am being hypocritical and commenting on yours.

How is it that the Japanese can allow their workers to take full responsibility for what they do when Western companies can't? Note that this even applies to several Japanese companies in their operations outside Japan.

How is it that most of these "run-of-the-mill" seem to manage to get from A to B, feed themselves, and undertake quite complex tasks in their private lives without the assistance of their employer supervisors?

Personally, I've observed more unacceptable short-cuts being initiated by 'managers' (many of whom, like myself, carry the label "engineer") than by the "run of the mill" workforce

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#88
In reply to #62

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/11/2007 4:14 AM

On this we are most definitely in agreement, Fyz.

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#94
In reply to #62

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/11/2007 7:43 AM

I agree, the managers are more than likely the initiaters of really big problems. Not that they are incompetent, but instead because they are not in close touch with the real work. It is those managers who refuse to listen to their workers and respond to the problems that have the biggest problems. For those managers that listen to their workers closely, those managers will be the most successful.

As the old axiom tells, the workers can cause a company to loose some profit, but it is the management that will utterly destroy it. Look at Westinghouse and now Mattel. It was not the workers that cut those corners to buy cheap paint for those toys, it was management.

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#98
In reply to #94

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/11/2007 9:01 AM

"Not that they are incompetent"
What does than mean? Surely managerial competence includes the ability to stay sufficiently in touch with the requirements to make appropriate decisions.

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#118
In reply to #62

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/12/2007 3:37 PM

I'm sorry I didn't notice this comment sooner or I would have responded earlier.

The Japanese adopted a management plan presented to them around 1948 by a man named Deming. He is a forefather to "Total Quality Management."

He first proposed this to United States companies but was rejected because CEO's didn't think anyone could tell them how to run their company.

The products produced in Japan was considered 2nd rate and they were desperate to break from that mold and adopted Deming's plan, even the Japanese business men that were skeptical about it. Within 5 years Japanese product quality surpassed expectations.

The United States still didn't adopt the quality mentality until about 1980. By then everyone was wanting to buy Japanese because everything made in the US was junk especially in the automotive industry.

It wasn't until some journalist came across Deming and wondered what happened to this guy that Deming was found and interviewed.

Deming made the statement "IF the Japanese can do it, why can't we?"

The CEO's of Ford and GM both saw this interview and started towards establishing a Quality Program in their companies, which saved them from bancruptcy back then.

We still have a lot of companies that are slow in adopting the importance of QualityManagement Principles. Especially in the small companies.

One of the principles is empowering the employees with being part of the decision making process. Something many American Supervisors Won't allow.

Toyota gets 3 million suggestions in the company suggestion boxes every year. 85% of them are implemented. Not because they are all good ideas, but to demonstrate that their ideas are valued.

That is why Toyota is one of the leading automobiles in the world today.

Just so you know. I'm the guy that someone later asked me to register. I'm the one with the navigational experience. I'm the one that made the Smart comment about the stars not being aligned. I am also 45 years old.

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#119
In reply to #118

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/12/2007 4:28 PM

Just so you know. I'm the guy that someone later asked me to register. I'm the one with the navigational experience. I'm the one that made the Smart comment about the stars not being aligned. I am also 45 years old.

Will the mystery Guest please enter and sign in!

Thanks for playing "What's my Gripe"!

ROFL

Regulars on CR4 are well aware of W. Edwards Deming and his contributions to the worldwide Quality Improvement movement. I think that Fyz's question was more of a rhetorical one. The problem in the US, and possibly other western countries, is that many of those in management pay lip service to Quality Improvement, but then don't follow through with what it takes to do the job right.

This is especially true in smaller companies, especially those owned and managed by a single individual or a family.

Hey, when you register be sure to pick a nice screen name that fits your personality, background, interests, or whatever. Avatars are fun, too. Some even post actual photos of themselves as their avatar, like mine! <grin>

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#120
In reply to #119

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/12/2007 6:51 PM

Ok, here I am.

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#124
In reply to #120

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/13/2007 11:57 AM

Dude - you are now soooooo screwed! Just joking. (not really)

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#121
In reply to #119

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/13/2007 11:03 AM

Me too!

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#123
In reply to #118

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/13/2007 11:55 AM

Hi Janissaries

Thanks for filling out the detail. Good to see you joined as well.
Off-topic can be good too...
May the paws be with you.

Fyz

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#45
In reply to #36

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 4:18 AM

All utterly irrelevant to latitude measurements, as south is measured against the passage of the sun. But the question specifically states that the surveys were requested when the US took over; surely that would mean that they would not start until after that.

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#40

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/09/2007 10:15 PM

"And where have other, similar discrepancies occurred."

If one has a good hypothesis, then there is the onus of proof by predicting an outcome, any thoughts on that?

Regards JD.

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#46
In reply to #40

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 4:23 AM

Plenty of candidates shown in my link. It would also happen in the European Alps (or indeed near any significant topographical feature) if anyone were equipped to use celestial navigation in those regions (given the lack of well-defined horizontal references...)

Fyz

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#48
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Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 4:41 AM

Yes I also thought maybe the celestial use of the North Star who's position moves a few deg over time relative to the earth axis, but I think they corrected that by the end of the 1600 century? Drake is recorded as have made such latitude errors.

Yes Ive looked at a few possibilities and there a few as you say.

Regards JD.

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#50
In reply to #48

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 5:03 AM

True, the drift of the Earth's axis could result in a shift of the basic references. But in any case the astronomical (coastal) measurements would have been made over a period of a few days and using repeat measurements (ABA) to minimise discrepancies due to elapsed time, (such as orbital and tidal variations). This is to give the best practicable datum for local navigators.

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#59
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Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 9:32 AM

Yes I think the error would cancel out, if there was one? as it would be common to both. But there is one other thing in regard to the earths axis, Angular momentum, this is a slight wobble in the earths axis, just a fraction of a deg, that occurs a few times a month, I don't know the actual frequency, but if they did not take the readings at the same time, then there is a possibility of an error. Not sure of my facts, as to whether they could correct for this? I think the North Star position was corrected against other star positions. But I still think your properly correct regarding gravity.

Regards JD.

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#86
In reply to #59

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/11/2007 3:29 AM

The drift in the earth axis is referred to as the Chandler wobble, and appears to cycle over longer intervals than I stated above. regards JD.

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#43

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 12:46 AM

There was old San Juan and New San Juan. The old was the original city at the entrance of the port, a fortress area. The new was just inland and abutted to it. Many old towns were built around the fort at the entrance to the harbor only to be moved inland. This is just a guess.

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#44

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 2:30 AM

Gravitational disturbance. (as mentioned above). Caused by the mass of a mountain or more dense formations under the ground.

A plumb line would hang skew due to the horizontal gravitational vector caused by the mass of the mountain.

If the distance around the mountain must be measured there will be a discrepancy because the 2 base lines would not be parallel (as expected by the surveyor).

Something similar happened in Cape Town (South Africa).

When the area was surveyed in the late 1600 or early 1700's. The surveyor intend to set out a baseline and started the survey started next to Table Mountain.

Because of the gravitational disturbance the base line was at an angle.

The original conclusion was that the curvature in the southern hemisphere were different from that in the north.

The error were corrected but even then there were a discrepancy of some 15m overlap between the Cape and Port Elizabeth datums. The result was what we called "red line borders" on farm diagrams and compilation sheets.

The Cape datum has only recently been replaced with WGS84.

I am not sure wither America might have had the same problem. I had a look at some

property compilations in America (NY - but not sure it was in 198x). The map had to be corrected by the (original) cut and paste method.

Another similar case was noticed on areal photography take next too a mountain range. The navigational system of the plane and the leveling device of the camera were not consistent, resulting in distorted photos.

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#58
In reply to #44

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 9:30 AM

Best explantion I have heard so far (improving on earlier gravitational explanations), and the only one to seriously answer the second part of the challenge.

Kudos to you!

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#65

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 10:39 AM

This is interesting. On the one hand we have Hendrik (in #44) and others saying that triangulation method may be off because of a local gravitational anomaly causing an error in the original baseline angle (from vertical), that may be different from the vertical that determines the astronomical calculation of latitude.

Then we have Sir Veyor (in #52) saying, I think, that triangulation must be essentially correct, since it never varies in angle from its baseline, once established, while astronomical surveys depend on two different measurements, each with a separately established vertical, to determine latitude difference, and therefore creating an error in the North/South distance.

Is this a case of "six of one, or half dozen of another" or put another way "same difference"? Or even, "Don't raise the bridge, lower the water!", or the classic "Cup half full or half empty?"

I think they are both correct in that, as Hendrik says, the baseline may be off as compared to the initial astronomical observation, but, as I think Sir Veyor is saying, this does not really matter, as what we are seeking is not the latitude, but the difference in North/South distance between the two points, and unless you re-set the baseline somewhere in the process (by reference to the theodolite at a different location), the North/South component of distance should be very accurate.

On the other hand, and I am not a surveyor so I do not know this answer, is triangulation with a single baseline measurement always used? Apparently not, as Hendrik gives the examples of the overlapping measurements between the two cities in South Africa. So, IF the triangulations was started at one point, say San Juan, and never had a second baseline measurement (like say, at Ponce, or another city which included Ponce in its triangulation). I am GUESSING that with an area the size of Puerto Rico, only one baseline was used, and so the error is likely to be in the astronomical observations of latitude, not in the triangulation method.

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#66

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 12:00 PM

My guess is that the largest error was in the astronomical measurement. The error found was 1 mile, and this is the equivalent of 0.0144 degrees, or just slightly over 1 minute of arc. While this may seem like a small angle, I believe that the folks making the measurement had equipment capable of making measurements of sufficient accuracy that this was not the problem.

I don't know much about Puerto Rico, but I would bet that like most semi-tropical islands it has a wet side and a dry side. Since San Juan is on the north side and Ponce is on the south, I'll assume that San Juan is on the dry side and Ponce is on the wet. Standing on the coast in Ponce, the astronomer would be looking up through two layers of air, with different temperatures and humidities, and therefore slightly different indices of refraction. In effect, the astronomers were looking up through a very weak prism, with a south facing wedge of warm dry air at the surface and a north facing wedge of cool wet air above. Therefore the line of sight to a reference star would be bent very slighty toward the south. In the north at San Juan the situation would either be reversed, or perhaps the dry and wet layers would be parallel. Therefore this prism would either be reversed or absent.

A second source for this error could be the method used to establish true vertical and horizontal references. I don't think that the astronomers would use the horizon as a reference since they would be on land somewhat above sea level. More likely they would have used a very accurate spirit level. Between Ponce and San Juan lies the Cordillera Central, a significant mountain range. The mass of these mountains would cause a level in Ponce to point slightly downward toward the south, while in San Juan it would dip slightly to the north. These errors in the reference plane would compound the error due to the atmospheric effects.

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#67
In reply to #66

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 12:39 PM

Sextants aren't that accurate of an instrument. At least not the ones used on Navy ships. Back then nothing was digital. Everything was computed using long equations and pre-determined charts.

Ship navigators consider themselves lucky to be within a few thousand of the ships actual position in accuracy on the open ocean. I know I used to navigate naval ships. I used to navigate minesweepers in actual minefields in the Arabian Gulf, where our accuracy had to be within a few yards using gps and visual fixes.

I've observed modern day surveyors determine pre-existing property lines being 4 feet off from previous surveys.

Navigators receive chart corrections from DMA all the time. These corrections involve water depths, navigational aids, revised coastlines and elevations. They give pictures in Notice to Mariners to cut out and tape over areas that have changed or incorrect to begin with. I can garrantee you the discrepency between Ponce and San Juan was published in a Notice to Mariners.

Back then the discrepency could have been attributed to which way the instrument users head was tilted when taking his reading.

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#68
In reply to #67

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 1:11 PM

It's true that the navigator's sextant is not a very accurate instrument, particularly when it is hand held on board a ship, even in the relatively calm waters of a tropical harbor. But my guess is that they would have had and used more accurate equipment, and set it up on land to have the most stable working platform available. They almost certainly had some pre-existing maps of Puerto Rico, and knew the island was relatively small, and that a small sextant error from the deck of a rolling ship would have put Ponce north of San Juan.

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#69
In reply to #68

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 2:58 PM

Wikipedia indicates that the U.S. Coast and Geodetic Survey was first established by President Thomas Jefferson in 1807 as the Survey of the Coast. Progress moved ahead slowly and haltingly during the first 25 years. Not until August 29, 1811 did Mr. F. R. Hassler sail for Europe to obtain the proper instruments.

Until that time you are possibly correct, that they would have been limited to ships' sextants. But surveyors' instruments (under suitable conditions) were capable of remarkable accuracy even them (though skilled operation was required)

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#70

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 3:03 PM

I wonder if the altitude of the 2 cities was taken into account. San Juan is about 2 meters above sea level, while ponce is around 50.

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#73
In reply to #70

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 4:03 PM

Do you really think that 48 meters difference in height could account for a mile difference in horizontal distance?

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#71

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 3:05 PM

The survey route would be up one side of the mountain range and down the other, and the gravitational effect of the mountain would distort the readings of vertical and horizontal, so that "vertically down" was actually angled toward the mountain. In addition, there is an interior volcanic plug with higher density than the coastal limestone, and there is also a trench five miles deep off the coast. These would have resulted in further errors. The surveyor's spirit level saw the mountainside as closer to horizontal than it actually was, and overestimated the horizontal distance.

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#72
In reply to #71

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 4:01 PM

This may be true in ordinary land surveying where only short distances are covered and so the local horizontal is established w.r.t. gravity using a spirit level. But topographic surveying by triangulation requires a more precise methodology. But then, if you were correct, that gravity would introduce error every time a reading was taken (Sir Veyor says not, see #52, as the baseline angle is set with a spirit level one time only to establish "horizontal" in the triangulation method and carried forward by using a theodolite), as one went up and then down the mountain, wouldn't the errors be averaged out since they would be in one direction going up and the other direction coming back down (assuming you were proceeding in a relatively straightline path over the surface and finished at relatively the same altitude, namely sea level)?

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#77
In reply to #71

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 4:48 PM

Actually this is in principle a contributor, for precisely the same reason as the astronomically determined distance is so far in error. However, the astronomically determined distance represents the angular separation (in radians) time the radius of the earth, so any angular error there is multiplied by the Earth's radius. For going over mountains, the equivalent distance over which the angular error can accumulate is only the height of the mountain; as the highest mountain on Puerto Rica is less than a mile, you'd need an discrepancy of something like 50-degrees between the measured verticals to account for this. Of course, the same sort of principle also applies to the effect of the combination of East-West angular error to the North-South measurement, but again this distance is only about 40-miles, so this would need an error in the N-S orientation of 1.5-degrees.

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#74

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 4:13 PM

Okay, I admit that I have not read every reply, but I did see some discussion re curvature. The curvature is .66 v feet/ arc mile.

If the survey was done by overhead photo then not curvature but elevation would most likely be the culprit. Photo pairs (orthopairs) are not true to size as a result of the 3rd dimension Z.

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#75

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 4:21 PM

Since point to point distance calculated from latitudes is dependant on the distance from the center of the earth (altitude) is it possible that the two points have significant differences in altitude causing this error?

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#76
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Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 4:32 PM

I am not sure tht I agree with your terminology.

Typically we have above and below sea level which is ELEVATION. And we have Distance above earth which is ALTITUDE.

This is not a hard and fast rule but, one that is common in the present context.

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#78
In reply to #76

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 4:57 PM

Hey Rummy,

Not to be nitpicky, and the guest was definitely wrong in calling altitude the distance from the center of the earth, but aren't elevation and altitude really the same thing, i.e. distance above mean sea level? Elevation is usally applied to land measurements and altitude to heights one might ascend in, say, a balloon, rocket, or airplane, but you also often hear altitude used in the context of mountain climbing. Of course altitude when flying can be measured as being relative to the surface below, but usually the reference is based on mean sea level, so it amounts to the same thing as elevation.

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#82
In reply to #78

Re: San Juan and Ponce: Newsletter Challenge (10/09/07)

10/10/2007 8:13 PM

When dealing with matters of geological features, altitude is generally in reference to a distance from which a measurement was taken above earth and elevation the height of a point on the earth.

Yes altitude is used in regards to mountains and such as it sort of co-mingles due to the extreme elevation.

Look at a map and see if Taum Sauk Mountain is shown at an elevation of 1,772 feet above sea level or an altitude.

It's just one of those things where people say, "oh, so this is not an area you are familiar with".

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