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Papa-Bear-NYC

Adjustment of locations (tri-stations) over the years

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I have noticed something recently which is a little disconcerting and if someone from the NGS or other knowledgeable person can explain the "adjustment" process, it would help me to understand what's happening.

 

Here's an example: One of the primary stations of the early Borden Survey (1830-38) in Massachusetts was "Watatick" which Borden set on top of the mountain of that name (Worcester County) in 1833. In 1895, the CGS set another mark "Watatick 2" very close to Borden's station. A good source which I look at for early Massachusetts stations is the CGS Special Publication No. 76 "Triangulation in Massachusetts" (1922). Unfortunately there was no description of the Borden station but there was for "Watatick 2".

 

81c0253e-f99d-49b6-a9e1-3dd02447166c.jpg

 

This station was reset in 1937, and the current data sheet has none of the early information in it. The datasheet for the Borden station "Watatick" was non-published since there was no description at all. So the only reference to the location of the Borden station was from the old CGS Special Publication.

 

But although the CGS S.P.. had no description, it did have a valid latitude and longiutude (to 3 decimals in the seconds, equivalent to about 1 inch) for the Borden station and the angles to surrounding stations. Furthermore the publication stated that marks with locations specified to 3 places such as these, were fully adjusted.

 

Here are the locations and azimuths to other stations:

 

fb71dd0e-f15e-49e6-9ef8-66b05dc940d9.jpg

 

Just for fun, I ran the INVERSE on the early locations for the stations.

 

Here's what I got:

  First  Station : Watatick 2					
  ---------------- 
LAT =  42 41 48.48400 North 
LON =  71 53 34.84000 West  

 Second Station : Watatick					  
  ---------------- 
LAT =  42 41 48.55300 North 
LON =  71 53 34.87000 West  

 Forward azimuth		FAZ = 342 13  6.7945 From North
 Back azimuth		   BAZ = 162 13  6.7742 From North
 Ellipsoidal distance	 S =		 2.2360 m

 

2.236m is equal to 7.3 feet. Excellent! So the old estimate of 7 feet was correct and 162 degrees is very close to SE as the early documentation specified (Note - 162 is the back azimuth since that's the way I specified the stations).

 

SO I went searching for the stations, found WATATICK 2 RESET but found that the old station was under a huge cairn, which I had not the time or energy to dismantle. Hopefully I may go back and try to find it.

 

I logged the RESET station on GC and NGS, put a note in my GC log about the old station being under the cairn, and logged the Borden station with NGS as a NOT FOUND, with a complete description. This was to get it published. And about a month later there it was. (see MY3831).

 

So what's the problem with adjustment I mentioned at the beginning of this post? This: once the datasheet was published for WATATICK, I now had two much more accurate positions and presumably the adjustment was a better fit to the shape of the earth, etc. So I ran another INVERSE and got this result:

 

  First  Station : Watatick 2					
  ---------------- 
LAT =  42 41 48.29635 North 
LON =  71 53 33.12769 West  

 Second Station : Watatick					  
  ---------------- 
LAT =  42 41 48.31904 North 
LON =  71 53 33.10116 West  

 Forward azimuth		FAZ =  40 46 35.5841 From North
 Back azimuth		   BAZ = 220 46 35.6021 From North
 Ellipsoidal distance	 S =		 0.9246 m

 

Oops! The distance is suddenly .9246m (= 3.03 feet) and the azimuth is completely wrong! Wha Happened?

 

The modern adjustment is much worse than the original (in a relative sense, not in an absolute sense). With this data (absent the early reference of 7 feet southeast) one would NEVER find this station.

 

I've checked and rechecked those numbers - but please check them again for me if you will.

 

BTW: it makes no difference which spheroid you use with INVERSE. At such short distances, one wouldn't think it would. And in case you might say the INVERSE would not be expected to work at such short distances, I would just say I use it all the time (along with FORWARD) and generally have good results. Early surveyors apparently used it all the time. This from the same special publication gives exactly this method:

 

94e48fa5-ce48-4b59-b3ab-50a037602744.jpg

 

This really is bothersome and makes me question if I can continue to use INVERSE between a found station and a missing station to find it.

 

Please take the time to read this through and see if I did something wrong or if there's another explanation.

Edited by Papa-Bear-NYC

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Looks like an interesting problem. I have seen something like it before near here. Perhaps Dave Doyle can look up that actual observations that were used in the more recent adjustment. I would tend to believe most the old data. It is very unlikely that the 7 foot difference was observed or used in the adjustment, so each station might be subject to errors coming in from long lines out into the network.

 

One interesting thing shows up on the old control listed for 2 reset:

MY6361

NAD 83(1996)- 42 41 48.29596(N) 071 53 33.12705(W) AD( ) 2

NAD 83(1992)- 42 41 48.29509(N) 071 53 33.12681(W) AD( ) 2

NAD 83(1992)- 42 41 48.29487(N) 071 53 33.12684(W) AD( ) 2

NAD 83(1986)- 42 41 48.29001(N) 071 53 33.09528(W) AD( ) 2

 

Note about a 3 foot shift from the first NAD83 value to the second.

 

- jerry

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Papa Bear--

 

Your first run of INVERSE was on two contemporaneous--and old--sets of coordinates. The second uses as the first station the new coordinates for WATATICK, which use the NAD 83 (1996) datum. You can't successfully run INVERSE on two sets of coordinates from very different datums. We had an example recently in Washington, a little east of Bellingham, where on the same disk NGS had coordinates in NAD 83 (1996), and WSDOT had them in NAD 83 (2007). Running INVERSE put the station eighteen inches from itself.

 

This of course raises the question: what is the exact datum of the current version of INVERSE? We don't know.

 

We hope we're on the right track here, and have been helpful. We very much enjoy your reports.

 

Cheers,

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Well, we seem to have stopped thinking just before we raised "another question." Sorry.

 

Of course INVERSE requires no tweaking for datum adjustments; it just requires consistent input.

 

Cheers,

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Maybe I am misreading the information, but it looks to me like both data sheets give coordinates described as being in "NAD 83(1996)" datum and match the ones inversed in the second example.

 

WATATICK 2 RESET is given as a second order station.

 

Also it was recovered in 1983 and so it is possible that it has updated GPS coordinates on it that may have been used in later adjustments.

 

WATATICK is given as a third order station.

 

To make it a little more clear what I was trying to say before. Adjusted coordinates for these stations would be a result of a least squares adjustment of a number of angles from a variety of other stations in the network. Some of those observations were made a long time ago and they were of varying accuracies and often quit distant. Since it was often the case that only angles were used there can be some error in the adjusted coordinate. Also these stations may even be connected to different stations of varying accuracy.

 

I would trust the old data sheet as to how far away the station was over a computation made from many miles away which could result in a few feet of error in one or the other station coordinates. When you try to match them up with another station that close, the errors show up. If the stations had been tied together by a distance or direction observation in the recent adjustment then the relationship would have been maintained.

 

Least squares gives the most probably answer or solution given a specific set of observations, but not an absolute true value. The adjustment probably spit out error ellipses which are not published, but which may be several feet for a 3rd order station determined from stations from 23 - 83 km distant.

 

I don't know if that puts any perspective on it or not. The locations of the two stations are only partially interdependent and were derived from different data of differing quality.

 

- jlw

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Papa Bear--

 

Your first run of INVERSE was on two contemporaneous--and old--sets of coordinates. The second uses as the first station the new coordinates for WATATICK, which use the NAD 83 (1996) datum. You can't successfully run INVERSE on two sets of coordinates from very different datums.

 

Cheers,

The first INVERSE used the two sets of locations from the 1922 publication (the ones which I illustrated in my post just above the INVERSE output). This was on the North American Datum (predecessor to NAD27) which was adopted in 1901.

 

The second used the two sets of locations from the 2 data sheets (not illustrated but you can see them here: MY3631 and MY6361), both having the latest "NAD 83(1996)" adjusted locations.

 

Both should be self consistent. I would never try to mix a station's location from the old publication with a data sheets "NAD83(1996)" location.

 

As for the Order of the stations, yes there would be different levels of errors. But the 1922 publication had the same input (namely the triangles measured in 1833 and 1896) as the later adjustment. No GPS observations were used in the 1996 adjustment (I think that first came in 2005 or 2006). In other words no new data accumulated on any of the stations involved after 1896. The only difference (as far as I understand) was the spheroid shape and newer stations outside these triangles whicch may have shifted the triangles around a slight amount.

 

Another way to state my problem is "why should a datum change" (if that's all that happened) affect the relative distance of 2 stations 7 feet apart".

Edited by Papa-Bear-NYC

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PS to my last post. The early instructions you quote on using nearby stations to find an obscured on is still valid. But you must keep in mind that those stations all have error in them.

 

So the one station would have gotten you within about a meter in a search for the other, good enough to probably recover the other station.

 

That was of course written before the day of hand held GPS that can get you nearly that accuracy in the first place. The nearest data point is always the most likely to get you into the right area, but it is not perfect in the same way your GPS handheld is not perfect.

 

- jlw

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To answer your last question, the NAD83 adjustment was not just a change in the ellipsoid. But was based on a slightly different subset of observations. Some observations were undoubtedly dropped out, considerably more data was added and the adjustment was constrained to more certain control. One would hope that the new adjustment would give better results or closer to the truth, but this doesn't always happen given a large sparse network, sometimes the errors get shoved around in funny ways or revealed.

 

Do we have NAD27 coordinates to compare? I only see them on one of the stations. It would be interesting to see how they related compared to the 1986 and then the most recent adjustments. I suspect the 1986 values look more like the NAD27 differences.

 

I would have to review history to see how the pre NAD27 North American Datum was actually computed. I would doubt that it was a large scale rigourous least squares. I seem to recall reading that NAD27 didn't even adjust many stations and they were just translated in from the North American Datum. But I do not recall what methods were used for it.

 

As for the Order of the stations, yes there would be different levels of errors. But the 1922 publication had the same input (namely the triangles measured in 1833 and 1896) as the later adjustment. No GPS observations were used in the 1996 adjustment (I think that first came in 2005 or 2006). In other words no new data accumulated on any of the stations involved after 1896. The only difference (as far as I understand) was the spheroid shape and newer stations outside these triangles whicch may have shifted the triangles around a slight amount.

 

Another way to state my problem is "why should a datum change" (if that's all that happened) affect the relative distance of 2 stations 7 feet apart".

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Oops. Sorry. Did indeed misread the INVERSE clips. Beg pardon.

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Do we have NAD27 coordinates to compare? I only see them on one of the stations. It would be interesting to see how they related compared to the 1986 and then the most recent adjustments. I suspect the 1986 values look more like the NAD27 differences.

Only MY3831 WATATICK lists NAD27 coordinates.

Here are the NAD 83(1986) locations:

 

WATATICK 2 RESET - NAD 83(1986)-  42 41 48.29001(N)	071 53 33.09528(W) AD(	   ) 2
WATATICK -		 NAD 83(1986)-  42 41 48.32015(N)	071 53 33.09954(W) AD(	   ) 3

And here is the INVERSE result

 Ellipsoid : GRS80 / WGS84  (NAD83)		
 Equatorial axis,	a   =	6378137.0000
 Polar axis,		 b   =	6356752.3141
 Inverse flattening, 1/f =  298.25722210088

 First  Station : Watatick 2					
  ---------------- 
LAT =  42 41 48.29001 North 
LON =  71 53 33.09528 West  

 Second Station : Watatick					  
  ---------------- 
LAT =  42 41 48.32015 North 
LON =  71 53 33.09954 West  

 Forward azimuth		FAZ = 354  2 52.9182 From North
 Back azimuth		   BAZ = 174  2 52.9153 From North
 Ellipsoidal distance	 S =		 0.9351 m

Interestingly, the distance .9351 m is close to the 1996 result (0.9246 m) but the azimuth is much closer to the old NAD (1901) result.

 

Looks pretty hit and miss to me. :unsure:

Edited by Papa-Bear-NYC

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I would have to review history to see how the pre NAD27 North American Datum was actually computed. I would doubt that it was a large scale rigorous least squares. I seem to recall reading that NAD27 didn't even adjust many stations and they were just translated in from the North American Datum. But I do not recall what methods were used for it.

There is a short description in the 1922 publication pages 1-5. Basically they say that the "Precise Triangulation points" (those from the Eastern Oblique Arc - Special Pub. No. 7) were held fixed and the other triangles, both from Borden and the more recent, were fitted to them.

 

There is a similar set of statements from Appendix 10 of the Report for 1894 which I have also looked over. The Borden point (WATATICK) has identical values in that publication. WATATICK 2 of course did not yet exist in 1894.

 

It should also be noted that the two stations had 2 stations in common for their triangles (Holt and Prospect Waltham). These two as well as Wachusett (which was in the EOA) are first order stations and were surveyed by both Borden in the 1830s and C&GS in the 1840s-90s. So both of the Watatick stations were strongly controlled by some of the same stations.

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Question related to this:

When an old station like WATATICK is caused to be published (like Papa-Bear did), are all the years of adjustments done? Have all those years of adjustments been done "behind the scenes" and we just never "saw" them? In other words, are the now-published NAD (XXXX) coorinates for WATATICK "correct"? If it wasn't published, was it still used in the least squares adjustment?

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Question related to this:

When an old station like WATATICK is caused to be published (like Papa-Bear did), are all the years of adjustments done? Have all those years of adjustments been done "behind the scenes" and we just never "saw" them? In other words, are the now-published NAD (XXXX) coorinates for WATATICK "correct"? If it wasn't published, was it still used in the least squares adjustment?

I believe it is. But furthermore, I believe the "datasheet" doesn't exist until we ask for it. You always see a statement at the top

"DATABASE = ,PROGRAM = datasheet, VERSION = 7.61

1 National Geodetic Survey, Retrieval Date = AUGUST 30, 2008".

 

My take on that is that the items making up the datasheet are cells in a large database and the output we see is simply generated by some SQL program which grabs the various pieces of information, formats it in a standard way, and spits it out.

 

An adjustment can take place without regard to publishable or non-publishable. An adjustment program simply needs to cycle through the database making several passes until it gets all the input locations, crunches them, and then sticks back a new adjusted value and moves the previous one down to the list of past adjusted values. Of course this may take weeks (it used to take years) for system wide adjustments. Certainly a flag like "No geodetic control at this mark" would cause the adjustment program to skip the point, but "No Descriptive Text available" is hardly such a reason assuming all the data points are present and valid.

 

At least that's the way I imagine it works. We'll have to wait till Dave D or NGS Surveyor talk to the notorious "Data base guy" to find out the real story. :unsure:

Edited by Papa-Bear-NYC

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I'll add a few more thoughts and then shut up.

 

First the number of digits that coordinates are reported to does not reflect the accuracy of the position. It didn't in 1916, and it doesn't today. That is just the way they have always done things. We do know that they truncated scaled coordinates though as opposed to adjusted coordinates. But do not believe that because the data sheets report the position to .00001 seconds that the position is actually to a millimeter.

 

The station WATATICK was reported as third order, and even though it may have been observed from first order stations, the reason it is classified as third order is that for those triangles the observations were only done to third order standards and only third order results can be expected.

 

There are statements in the preliminary pages to the publication which indicate that the distances given in the table with the positions (which are of course derived from the solutions of the triangles) are reported to 2 more decimals than might be justified by the solution. For WATATICK all the distances are reported to the decimeter, so I think it is safe to say they did not expect the sides to have been solved to better than 1 or 2 meters.

 

Third order is often specified as 1:5000 or 1:10000 depending on the class. Work of that kind can often exceed those minimums, but it would not be unreasonable on that specification to expect a meter or two of error.

 

A lot of this is discussed in various forms in the Massachusetts triangulation publication itself.

 

There could, of course, be blunders in the data capture that show up in the NAD83 adjustment, or some other reason that can only be evaluated if you know specifically what observations were adjusted and the errors found in the network leading to the position.

 

- jlw

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...

The station WATATICK was reported as third order, and even though it may have been observed from first order stations, the reason it is classified as third order is that for those triangles the observations were only done to third order standards and only third order results can be expected.

...

- jlw

I think you may have hit on something.

 

In the 1922 publication No. 76, Watatick is listed as a "Principal" station. It was part of triangles with 6 stations - Holt, Prospect Waltham, Blue Hill (Borden), Wachusett, Grace and Packard - all of which are also principal stations except Wachusett, which was a "Precise" station (part of the Eastern Oblique Arc). Thus the adjustment used for Watatick in the 1880s and 1890s was probably fairly rigorous. See also Maps 29 & 21 of that publication. So the good results vs. the "facts on the ground", namely the observation from the 1897 party that the new station was "about 7 feet southeast of Watatick" was reflected in the coordinates and produced the good INVERSE.

 

Now, the station is "downgraded" so-to-speak, due to perhaps the paucity of original observation records, etc., and the modern adjustment produces poor results relative to the newer station.

 

This is not exactly what I would call progress, would you?

Edited by Papa-Bear-NYC

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I believe that when the NGS did a readjustment, they were not simply applying a conversion from one datum to another, but rather were recomputing the positions of all the stations according to the original angles measured between the stations, holding certain positions and distances to known values.

 

If you look at the Watick 1833 listing in the special pub 76, it was part of a triangulation network that included Holt, Prospect Waltham, Blue Hill(Borden), and Wachusett. Those were the stations that formed the vertices of the figures that included Watatick 1833.

 

Holt				MY2568  NAD83(1996) 42 38 27.80076(N)   071 06 23.07706(W) 
						SP 76	   42 38 28.026  (N)   071 06 24.872  (W)

Prospect Waltham	MY3638  NAD83(1996) 42 23 18.62697(N)   071 15 13.57089(W) First Order
						SP 76	   42 23 18.831  (N)   071 15 15.333  (W) 

Blue Hill (Borden)  MY3471  NAD83(1996) 42 12 43.46794(N)   071 06 50.94772(W) Third Order
						SP 76	   42 12 43.676  (N)   071 06 52.709  (W) 

Wachusett		   MY3791  NAD83(1996) 42 29 20.58516(N)   071 53 12.26232(W) Third Order
						SP 76	   42 29 20.784  (N)   071 53 13.984  (W)

Watatick 1833	   MY3831  NAD83(1996) 42 41 48.31904(N)   071 53 33.10116(W)
						SP 76	   42 41 48.553  (N)   071 53 34.870   (W)

 

Within that portion of the network, the NAD83 adjustment changed the positions of the triangulation vertices by

Holt				41.4782 m, direction  99 38 45.8580 from north
Prospect Waltham	40.7944 m, direction  98 52 39.4558 from north
Blue Hill (Borden)  40.9063 m, direction  99 01 44.1062 from north
Wachusett		   39.7939 m, direction  98 52 08.9536 from north
Watatick 1833	   40.9033 m, direction 100 09 56.7478 from north

There was a more or less consistent local shift of about 41 meters, in the direction roughly 100 degrees from north.

 

Looking at Watatick 2, its adjustment figures included two stations shared with the Watatick 1833 network, but also 4 stations that were not part of the 1833 network:

Holt				MY2568  NAD83(1996) 42 38 27.80076(N)   071 06 23.07706(W) 
						SP 76	   42 38 28.026  (N)   071 06 24.872  (W)

Prospect Waltham	MY3638  NAD83(1996) 42 23 18.62697(N)   071 15 13.57089(W) First Order
						SP 76	   42 23 18.831  (N)   071 15 15.333  (W) 

Fay Mountain 2	  MY3700  NAD83(1996) 42 14 23.61982(N)   071 37 40.84817(W) Second Order
						SP 76	   42 14 23.796  (N)   071 37 42.562

Wachusett 2		 MY3792  NAD83(1996) 42 29 20.59612(N)   071 53 12.26962(W) First Order
						SP 76	   42 29 20.776  (N)   071 53 13.979  (W)

Mount Grace 2	   not available

Monadnock		   MZ1473  NAD83(1996) 42 51 40.96587(N)   072 06 29.05525(W) GPS
						SP 76	   42 51 41.174  (N)   072 06 30.776  (W)

Watatick 2 Reset	MY6361  NAD83(1996) 42 41 48.29635(N)   071 53 33.12769(W)
						SP 76	   42 41 48.484  (N)   071 53 34.840  (W)

Within that portion of the network, the NAD 83 adjustment changed the positions of the triangulation vertices by

Holt				41.4782 m, direction  99 38 45.8580 from north
Prospect Waltham	40.7944 m, direction  98 52 39.4558 from north
Fay Mountain 2	  39.6680 m, direction  97 52 34.8169 from north
Wachusett 2		 39.4298 m, direction  98 05 31.5874 from north
Watatick 2 Reset	39.4022 m, direction  98 27 01.4747 from north

There was a more or less consistent local shift of about 40 meters, in the direction roughly 99 degrees from north.

 

Unfortunately, Watatick 1833 and Watatick 2 Reset were in two different networks, each of which was adjusted slightly differently, so that the resulting change between them occurred:

Watatick 2 Reset -> Watatick 1833   SP 76	   az=342 13 04.3641  dist=2.2360 m
								NAD83(1996) az= 40 46 35.5841  dist=0.9246 m

The combined effect of the two networks' adjustments were to change the published positions of Watatick 1833 and Watatick 2 Reset by about 1.3 meters and to switch their relative east-west positions.

 

If the NAD83 adjustment had included an extra measurement or constraint that Watatick and Watatick 2 Reset were to remain about 7 feet apart at some known azimuth, then all the other stations would have been slightly adjusted and the relationship between the two would have remained roughly the same. Unfortunately, that 7 foot measurement was only an informal note, and so the adjustment ignored it and rearranged their positions to fit other constraints that were more consistent with the original triangulation measurements.

 

The moral is to be careful about using FORWARD or INVERSE to locate stations that are in different networks, based on historical information that has undergone subsequent adjustment.

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...

Within that portion of the network, the NAD83 adjustment changed the positions of the triangulation vertices by

Holt				41.4782 m, direction  99 38 45.8580 from north
Prospect Waltham	40.7944 m, direction  98 52 39.4558 from north
Blue Hill (Borden)  40.9063 m, direction  99 01 44.1062 from north
Wachusett		   39.7939 m, direction  98 52 08.9536 from north
Watatick 1833	   40.9033 m, direction 100 09 56.7478 from north

There was a more or less consistent local shift of about 41 meters, in the direction roughly 100 degrees from north.

...

Within that portion of the network, the NAD 83 adjustment changed the positions of the triangulation vertices by

Holt				41.4782 m, direction  99 38 45.8580 from north
Prospect Waltham	40.7944 m, direction  98 52 39.4558 from north
Fay Mountain 2	  39.6680 m, direction  97 52 34.8169 from north
Wachusett 2		 39.4298 m, direction  98 05 31.5874 from north
Watatick 2 Reset	39.4022 m, direction  98 27 01.4747 from north

There was a more or less consistent local shift of about 40 meters, in the direction roughly 99 degrees from north.

 

Unfortunately, Watatick 1833 and Watatick 2 Reset were in two different networks, each of which was adjusted slightly differently, so that the resulting change between them occurred:

Watatick 2 Reset -> Watatick 1833   SP 76	   az=342 13 04.3641  dist=2.2360 m
								NAD83(1996) az= 40 46 35.5841  dist=0.9246 m

The combined effect of the two networks' adjustments were to change the published positions of Watatick 1833 and Watatick 2 Reset by about 1.3 meters and to switch their relative east-west positions.

...

I see what you have done.

 

One surprising thing is that Wachusett (MY3791) is Third order, since it was part of the Eastern Oblique Arc and stations in that net were considered the highest order and were kept stationary while other stations were fitted to them. (i.e. it was higher than first order.) It was destroyed around 1895 and replaced by Wachusett 2, but I don't know why that would downgrade it's order.

 

I guess a global question would be why is there a change in the horizontal order of some of these stations between S.P. 76, and the current data sheets.

 

And the other question is if they had treated all the stations as one gigantic network (in fact that's what I thought they did) in the adjustment, how are weights assigned.

 

In the "good old days", when such calculations were not possible, they would fit stations in a hierarchy: in this case first the "precise" stations (the EOA stations), then the "primary stations" (I think all of these were "primary") holding the precise stations fixed and then on down to secondary and tertiary, holding the stations above them fixed.

 

I find it hard to intuitively see if network 1 moved about 41 m at 100 degrees, and network 2 moved about 40 m at 99 degrees, how the relative position moved so much. Basically they all moved more-or-less the same amount (within about half a meter) in the same direction (within about 1 degree). But you will say, sorry, it just falls out of the math. So it would be nice to know if there is anything more going on here, such as different weighting in the least squares calculation depending on order, etc.

 

As far as you final warning

The moral is to be careful about using FORWARD or INVERSE to locate stations that are in different networks, based on historical information that has undergone subsequent adjustment.

It would be next to impossible to check this in most cases, and (again) in most cases I'm interested in - that is finding an old station by measuring from a new station - they'll never be in the same network since all the old station's partners are also long gone. You're almost saying, "You just cant get there from here". The situation seems to nullify the method described in that nice blurb in S.P. 76 about how an engineer can find a missing station.

 

DaveD sent me a note saying he would look at this when he gets back to the office.

 

Edit: I just did a quick check: Wachusett is the only station in the Eastern Oblique Arc in NH, MA or CT that is not a first order station. That sounds wrong.

Edited by Papa-Bear-NYC

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I find it hard to intuitively see if network 1 moved about 41 m at 100 degrees, and network 2 moved about 40 m at 99 degrees, how the relative position moved so much. Basically they all moved more-or-less the same amount (within about half a meter) in the same direction (within about 1 degree). But you will say, sorry, it just falls out of the math. So it would be nice to know if there is anything more going on here, such as different weighting in the least squares calculation depending on order, etc.

 

Without plotting, it would be hard to see and I haven't plotted it. But basically, Watatick 1833 was moved about 1.5 meters further than Watatick 2 Reset, even if they both moved in approximately the same direction (a little south of east). That was enough to place Watatick 1833 (according to the final NAD83 published coordinates) about 3 feet northeast of Watatick 2 Reset instead of the 7 feet northwest according to the SP 76 coordinates and the note.

 

What I found confusing in SP 76 was the statement on page 12: "It should be noted that the positions contained in these tables are based upon the original adjustment of the primary triangulation made in 1866 and not upon that adjustment contained in Special Publication No. 7".

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What I found confusing in SP 76 was the statement on page 12: "It should be noted that the positions contained in these tables are based upon the original adjustment of the primary triangulation made in 1866 and not upon that adjustment contained in Special Publication No. 7".

That is one thing I do understand.

 

The adjustment done in S.P. 7 was specifically for the Eastern Oblique Arc insofar as it related to the calculations of for the figure of earth (or whatever it was called). It was basically based on a different spheroid, and it was not used before or after in any other adjustment.

 

The "primary triangulation" referred to is that of the EOA stations, but without regard to the special purpose involved. In other words it was a "regular" adjustment based on the datum built on the Clarke Spheroid of 1866, upon which the NAD of 1901 was also based.

 

There is a statement to this affect in SP 7 but I can't find it right now.

Edited by Papa-Bear-NYC

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There is a statement to this affect in SP 7 but I can't find it right now.

Here is the statement, it's actually in S.P. 76, explaining this

 

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See also S.P. 76, pp 6 & 7 for a discussion of the differing needs for a consistent datum as regards geographic positions, map making and figure-of-earth calculations. It's a bit too long to quote here.

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