Grid System for Progressive Maps in the United States Special Publication No. 59

The interesting question is what horizontal datum was behind those grid coordinates. My first thought is that it's the North American Datum of 1913. You see various statements about whether the New England Datum (of 1879/1880), the United States Standard Datum (of 1901), and NAD of 1913 were simply name changes as the network got extended or were actual readjustments. I think NAD 1913 was a name change, without readjustment, as Canada and Mexico were added onto the USSD network (later, NAD 27 *was* a readjustment). So when we see superseded USSD latitude and longitude on NGS data sheets for certain old horizontal controls, I think the NAD 13 values would be identical.

Do you know which USC&GS / NGS horizontal control stations were tied by Powell? Do any of Powell's records give his X and Y coordinates for those stations??ÿIf those stations are still in the NGS database, and their data sheets show USSD values, I suspect that running those USSD latitudes and longitudes through the methods of Special Publication No. 59 and would yield values that match Powell's X and Y.

NGS's NCAT online tool does offer transformations to and from USSD, and thus also to and from NAD 1913, if my above claim is correct.

I just noticed that the coordinates appear to be in varas. In Texas 1 vara = 33-1/3 inches.

@andy-nold I had noticed that the reference objects' distances were given in varas. I suspected that the grid coordinates would be in whatever unit is used in Special Publication No. 59, guessing that it would be US survey feet. But taking another look now, I see that No. 59's tables are in yards. The publication also discusses converting to meters. Yards and meters make sense, given that No. 59's motivation was artillery maps.

I am curious if any of Powell's records give both latitude / longitude and grid coordinates for any points. It would be interesting to see if Powell computed the grid coordinates in yards, meters, or varas!

@bill-c In my area, Diablo, Diablo Cairn and Eagle are mentioned. As are several railroad stations and water tanks that no longer exist. I looked at NGS's NCAT, but I was unable to make a conversion.

That's a really neat project. Those old coordinate systems were sometimes very good and sometimes not so good. This one is a polyconic projection designed to be moved westward, its origin that is, in order to cover areas west of the Atlantic coast while maintaining accuracy. It's based on the Clarke 1866 ellipsoid. The polyconic projection is similar to a Lambert Conformal projection, but its meridians are slightly curved whereas the Lambert meridians are straight lines.

Special Publication 59 includes a table of coordinates at 5-degree intervals. It should be possible to use those to develop a conversion into something more modern. The publication in pdf format is here: https://library.noaa.gov/Collections/Digital-Collections/USCGS-Special-Pubs

Page 151 has coordinates for the origin(s). Latitude 40 degrees 30 minutes north and longitude 105 degrees west is the origin for the survey and has coordinates 2,000,000 N, 1,000,000 E. Entering the table with geographic coordinates closer to the survey area should provide a decent connection to the coordinates in the survey and insight into how they might be converted into lat/lon or more modern rectangular coordinates.

It might also be possible to develop a Lambert LDP that comes close to duplicating the plane coordinates. The polyconic is tangent at 40-30N, 105W, so a tangent Lambert at the same place with the same grid coordinates at the origin might come close. The yards/varas problem will still be there, though.

I hope it's less costly than this one was: https://www.xyht.com/professional-surveyor-archives/where-theory-meets-practice-united-states-standard-datum/

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Well that's a great article. I was wondering what to call it and NAD makes sense with the updates being NAD27 and NAD83.

I need to recheck my distances. I assumed Powell was using varas but he may very well have been using yards.

Thanks for sharing.

You probably have some software that can use .prj files to convert or map. Here's one that I cobbled together that seems to get within a yard or two of the coordinates published in Special Publication 59.

PROJCS["Progressive Map Clarke 1866",
GEOGCS["GCS_North_American_1927",
DATUM["D_unknown",
SPHEROID["clrke_1866",6378206.4,294.9786982139]],
PRIMEM["Greenwich",0.0],
UNIT["Degree",0.0174532925199433]],
PROJECTION["Polyconic"],
PARAMETER["False_Easting",1000000.0],
PARAMETER["False_Northing",2000000.0],
PARAMETER["Central_Meridian",-105.0],
PARAMETER["Latitude_Of_Origin",40.500],
UNIT["Yard",0.9144018288]]

I tested a few points in DNR GPS and here's how they look:

Note that the last two are the inverse conversion of the coordinates on your sheets.

The inverse coordinates will be on the Clarke ellipsoid. You should be able to enter those lat/lon coordinates in NCAT and get NAD83 or whatever else would be useful.

By the way, the fit with a Lambert tangent at the same origin is terrible.

Keep us updated; there's a lot to be learned here.

Well, that's pretty dumb. I reversed the order of the xy plane coordinates for points 122 and 121. Here's the corrected output from DNR GPS:

This should be closer to where 122 was found.

From the OP - "when the angle of terrain exceeded my ambition.". LOVE IT! I am going to adopt it ...

@jamesf1 Glad you will get some utility out of it. We are headed back up the trail in the morning with a bigger cup of ambition and some fresh brewed coordinates that I hope will get us within a few feet of the rock mound. I understand that it is too tall to set up over (I may have read 6 feet tall somewhere). But, there is purportedly a traverse hub 3.1 feet away.

(Ignore the section lines in the topo. They are figments of GIS.)

I will try to get a picture of myself with the mound if I make it 2/3 to the top.

So the coordinates for 121 and 122 are in varas. That makes a big difference.

Yes, the coordinates published on the datasheets are in varas. We succesfully located 2 rock mounds and a 4"x4" cedar hub (disturbed).

The hub is lying between the two mounds.

In my opinion, the sharper mound on the left of the picture is the called for rock mound. Not sure who built the other apparent mound or why. There was also an old lathe in the vicinity. The NAD83 coords are N 31.089414?ø W 104.908895?ø

Shout out to Zach and Robert for making the climb. I was driving back from tying in K118 when they were headed back down the hill.

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Well, you've already found it,but I'll share this .prj anyway. It's the Progressive Map Polyconic projection on the Clarke 1866 ellipsoid with varas as units.

PROJCS["Progressive Map Clarke 1866 Varas",
GEOGCS["GCS_North_American_1927",
DATUM["D_unknown",
SPHEROID["clrke_1866",6378206.4,294.9786982139]],
PRIMEM["Greenwich",0.0],
UNIT["Degree",0.0174532925199433]],
PROJECTION["Polyconic"],
PARAMETER["False_Easting",1080000.0],
PARAMETER["False_Northing",2160000.0],
PARAMETER["Central_Meridian",-105.0],
PARAMETER["Latitude_Of_Origin",40.500],
UNIT["Vara",0.84666836]]

In DNR GPS, it produces these coordinates from the plane coordinates:

Amazingly close to the NAD 83 coordinates.

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+/-163 feet N70?øW by my calcs. Considering it all, amazingly close. In the heart of Apacheria. A few miles south of Victorio's last battle in Texas and a few more miles south of the last anglo-native american skirmish in Texas a year later.

Yes, and that's comparing a NAD 27 position directly to a NAD 83 position; different ellipsoids and other differences. If we use NCAT to convert the DNR GPS coordinates to NAD 83 (2011) we get 31.089417, -104.908892. That's an ellipsoidal distance of 0.4388 meters or about 17 inches.

Different tools, different eras, but the math is the same. The old computations were excellent and the modern software is, too. So one can be used to "duplicate" the other.

What a wonderful world!