Re-crunch Summer1875 Celestial Navigation Numbers

[kayakbird]

I spent most of yesterday hiking in the vicinity of Carroll (Aban'd), Fergus Co, Montana. This was the steamship landing for the

Carroll Trail which terminated in Helena; via Roy, Hilger, Lewistown, Judith Jap, Martinsdale, White Sulphur Springs and Fort Logan.

Most of the settlement was washed away by high water in 1876, and the trail unused because for the next several years there was plenty

of water for the steamships to get to Fort Benton.

 

Carroll is indicated on Plate 70 of this 1894 Missouri River Commission map of the points that were set in 1885.

 

http://aa179.cr.usgs.gov/1894maps/P70.html

 

NONPID MRC BM 59-1 is there, but now only 500 feet from the river (1500 FT in the 1885 calls). NONPID BM 59-2 was not found on Friday.

Its adjusted L/L puts it right at the Fort Peck Reservoir full pool wave action beach. MRC CARROLL SR1191 is also unfound. I believe that

it's triangle is indicated on Plate 70 about 3/4 in northwest along the road that is truncated near the Telegraph Line label.

 

Note that this location does not match the calls in the DS.

 

SR1191

 

WILDER/CMR 220 RD COMING IN FROM THE WEST, GPS TRACK EAST TO WEST ALONG THE EDGE OF THE RIVER FLOOD PLAIN AND UP A FINGER RIDGE

 

Points along the line from the SW: BM 59-1, current edge of river right and left, 1885 call.

 

That's the background. My main reason for braving forty miles of bad road was to try to find and photograph traces of wagon tracks (found a few maybe's)

along the current Wilder/CMR 220 Rd; and to go to the 13 Jul 1875 L/L (47 34 48 108 24 00) for Carroll that was established by surveyors

attached to Capt William Ludlow on his mad dash reconnaissance from Carroll, Montana to Yellowstone National Park and back.

 

His 1876 Report: http://quod.lib.umich.edu/cgi/t/text/pagev...40&size=100

 

Star shots start on P 38, table of all points on P 52.

 

The location of the L/L is not logical - over a mile west of the accepted location of the landing, about 100 vertical up a steep slope to a small

bench on a finger ridge. Much easier to access knobs are close to Carrol. However, the published elevation is +/- 10 feet of the valley floor.

 

Would they have been working in some other datum such as was mentioned here a few months ago, or maybe just a bad clock?

 

Thanks for any input, kayakbird

Edited September 27, 2010 by kayakbird

[holograph]

Longitude was uncertain at that time. First, all the longitudes were astronomical longitudes, and were referenced indirectly to the Airy meridian at Greenwich, which is west of what is now accepted to be the zero longitude.

 

The report you found shows that Wood didn't have access to telegraphic longitude, and needed to rely on a chronometer instead. Chronometers were very hard to keep accurate when transported over land, so I'm not surprised that his determination might be off by a mile.

 

In general, most of the West was referenced directly or indirectly to the Salt Lake Pier longitude established by George Dean of the Coast Survey in 1869. In 1873, Lt. Wheeler established an astronomical station at Bozeman, MT, connected by telegraph to Ogden, Utah, and determined Bozeman's longitude to be W 111° 02' 36.64". On page 36 of the Ludlow report you linked to, you find a recommendation to establish "an Observatory on Mount Washburne, with a wire to Bozeman," meaning that a tie into the growing telegraphic longitude network could provide an accurate basis for mapping.

 

It is likely that Wood's datum was Wheeler's, and Wheeler had Salt Lake at 111° 53' 42.9", which is about a quarter-mile west of the modern location.

 

edit: Using Wheeler's published coordinates for the Bozeman station (111° 02' 36.64") and his description of the station location (about 100 feet northeast of the grave of Bozeman, which is in Sunset Hills Cemetery), it looks like Wheeler's Bozeman coordinates are about 0.9 mile west of the NAD83 coordinates. Assuming that Wood's longitude was based from Bozeman, that explains most of the 1 mile discrepancy you found.

Edited September 27, 2010 by holograph

[Bill93]

To get from astronomic position to geodetic position you use the deflection of the vertical, which is caused by irregularities in the earth's density distribution that make gravity point differently than the ellipsoid model would have it, the same thing that causes for the undulating geoid affecting elevations.

 

You get the values from the NGS Toolkit DEFLEC09 program. I'll leave it to you to figure out the signs from the DEFLEC documentation. I think the interpretation is:

USER LOCATION 47 33 36.05371 108 21 22.12415

Adjustments in arc seconds

Xi=4.56 latitude adjustment

Eta=2.27 longitude adjustment

Laplace=-2.49 azimuth adjustment

 

So it turns out for this location the adjustments are minor compared to the error due to time.

Edited September 27, 2010 by Bill93

[holograph]

To get from astronomic position to geodetic position you use the deflection of the vertical, which is caused by irregularities in the earth's density distribution that make gravity point differently than the ellipsoid model would have it, the same thing that causes for the undulating geoid affecting elevations.

 

You get the values from the NGS Toolkit DEFLEC09 program. I'll leave it to you to figure out the signs from the DEFLEC documentation. I think the interpretation is:

USER LOCATION 47 33 36.05371 108 21 22.12415

Adjustments in arc seconds

Xi=4.56 latitude adjustment

Eta=2.27 longitude adjustment

Laplace=-2.49 azimuth adjustment

 

So it turns out for this location the adjustments are minor compared to the error due to time.

 

Astronomic Lat = Geodetic Lat + Xi.

West Astronomic Lon = West Geodetic Lon - Eta / cos(Lat).

 

To account for the Airy meridian, subtract another 5.64 seconds. So the correction would be 9 seconds, making the astronomical coordinates N 47 33 40.61, W 108 21 13.12 relative to Airy. That actually increases the discrepancy by about 0.1 mile.

[holograph]

I re-read the Ludlow report, and it is clear from the report, and also from the time differences, that the chronometric time referenced St. Paul, Minn, which was also the point of embarkation for the expedition.

 

However, I couldn't find any mention in Ludlow's report of the exact location in St. Paul that was the basis of the calculations. So it is next to impossible to re-crunch the numbers.

 

Perhaps there was an assumed location in St. Paul. In the Lake Survey report of 1872, the astronomical station in St. Paul was located 451.3 feet east and 48.4 feet south of the southeast corner of "the new custom-house on Wabashaw street". The position of the southeast corner of the custom-house was used in several subsequent publications by the Army. The position was determined to be 40m 10.15s of time west of the Lake Survey observatory in Detroit, or 1h 4m 10.14s of time west of Washington, D.C.

 

As of 1873, the Army used a value of 5h 8m 12.12s for the longitude of Washington, D.C., so the longitude of the southeast corner of the custom-house in St. Paul would have been 6h 12m 22.26s, or 93° 05' 33.9". That is also the value quoted in several other Army publications.

 

There is a non-published PID PP2512 with the name ST PAUL CUSTOMHOUSE at N 44° 56' 44.8", W 93° 05' 41.1" NAD83.

 

Unfortunately, if you correct Wood's coordinates based on the St. Paul custom-house coordinates, it pushes Wood's station even further west of the crossing.

 

Most of the Ludlow report's longitudes are either 00 seconds or 30 seconds, so it looks like Wood may have computed most longitudes to the nearest half-minute or sometimes quarter-minute of arc. If that is the case, the published longitudes have a wide error.

[kayakbird]

Thanks to everyone for spending the time to feed me all the information. If birding is slow this winter maybe I'll get me a book.

 

It looks like all the positions except Fort Ellis (just east of Bozeman ) trend west. I'll be taking a look at the Judith River campsite tomorrow. I think that the person that got me to doing this research will be quite happy to accept 'chronometer' errors.

 

I just happen to be camped in the Missouri Breaks at the top of the road to Woodhawk Bottoms. Today, while drifting down the river from a successful hike to MORC SNAKE POINT SR1203, I read the note in the BLM River Guide for River Mile 130.8 R which indicates a L/L discrepancy for the Lewis campsite of 30 July 1806 - maybe a similar chronometer error, but the latitude would have to off also.

 

Thanks again, kayakbird

Edited September 29, 2010 by kayakbird

[+jwahl]

I haven't taken the time it deserves to examine your documents, but I notice that many of the observations were with a sextant. While they seem to be reported with a relatively high degree of precision, I am not sure if that is warranted. Perhpas there is more info in the documentation to explain this.

 

The other big thing that I notice (and others have mentioned) is what is the time reference? I do see observations for time which would mean astronomic time based on local solar noon meridian perhaps? Observations for many state boundary surveys in that era do have to be related to whereever they got the time. That involves transfer of the chronometer over distance and time with some drift. Then it might have been set by telegraphic time based on what.

 

One only has to look at other boundaries established with such means up until the 1910 era to realize there is considerable error there.

 

Now latitude should be darn close to true astronomic latitude, so that can be converted to a more modern geodetic value if you really know what ellipsoid was in use. I would expect latitude to be obtainable within a few seconds, however the sextant is of some concern.

 

- jlw

[kayakbird]

Pinpoint locations for the 1875 campsites is not required for my research of George Bird Grinnell's trip along the Carroll Trail. I went to several more locations during the last week and the latitude fit, but the longitudes were generally about a mile too far west. Their reports of fossil finds were pretty general and close is good enough.

 

Did find one location where I figured I was +/- 10 ft.

 

 

SR0858

 

Link to Ludlow Report P 56 is in GEO Log. kayakbird

Edited October 2, 2010 by kayakbird