At the ceremonies for the Initial Point of the Minnesota and Dakota land surveys, there was some discussion of how accurately Capt. Lee had placed his post to mark astronomical latitude N43 30' which was to be the Iowa-Minnesota boundary.
The post has NGS data sheet AB9853 Its latitude is NAD 83(2007)- 43 30 02.85064(N)
The Laplace correction to astronomical azimuth here is -7.15 seconds, indicating a large deflection of the vertical that could have quite a bit of effect on astronomic in latitudes. So I ran DEFLEC09 and got Xi = 1.57 Eta = 7.54 showing most of the deflection is east-west.
The North American tectonic plate has been moving for 161 years since the astronomic observations were made. HTDP predicts 0.023 meter northward in the last 100 years or extrapolating 0.037 m in 161 years (It won't accept dates that early). That is on the order of 0.0012 seconds of latitude and within the precision of DEFLEC.
Then I would compute
43 30 02.85064 NAD83 latitude
0 0 1.57 Xi subtracted
--------------
43 30 01.28 Astronomic latitude
If this is right, he was off 130 feet, which is within his confidence range as quoted at the event.
Questions:
1. Am I basically doing this right? What did I leave out?
2. The readme for DEFLEC says "In order to have the deflections refer to the surface of the Earth (and not to sea level), a correction for the curvature of the plumbline was included." I think that would be about 0.03" change (if I used the right formula). But it didn't ask me for elevation. How does it know what correction to use?
Where Are His Calculations?
Without knowing which celestial objects he observed, what instruments he used, what predicted celestial positions he used and what corrections he made it is hard to discern if 130' is close or not.
I say it was close enough.
Paul in PA
Where Are His Calculations?
I don't have his calculations. I was not questioning whether he was "close enough", but rather "how close" and how to determine the difference. As I said,
>is within his confidence range as quoted at the event.
How Close He Was?
Is totally dependant on what he had to start with.
For instance did he have an astronomical instrument or a surveying instrument to observe with?
How well does it compare with the other points he might have set? Did he set the 43° for the North Dakota/Nebraska line?
Paul in PA
Captain Lee's Monument
Not sure what equipment Capt. Lee used. Talcott's crew used a 42-inch equal altitude and zenith telescope for their position surveys on the control stations along the border survey. Also, had a 30-inch portable transit and two chronometers.
They also stated during the presentation that Lee took his observations on the East side of the river and then transfered the position West across the river to set the cast iron post in 1849.
Captain Lee's Monument
We should have asked why the observations were made on the east side. The terrain shouldn't have prevented star sights from somewhere on the west side if not that point. Maybe it was easier to obtain provisions on the east side, and maybe there were still some Sioux in the area to the west that he wanted to minimize contact with?
I found a tutorial on astronomic vs geodetic measurements.
It looks like I may have subtracted when I should have added? That would make him further off.
The wording in the DEFLEC readme is not immune from misinterpretation:
A positive meridian component of deflection of the vertical (Xi)
indicates that the astronomic latitude will fall to the north of
the corresponding geodetic latitude of the point.
Does that mean the same numerical latitude is being held and the points fall thusly, or that the astronomic latitude will be a more northerly value at the same physical point?
But things I read say some books used the opposite sign convention. I'm not 100% sure his example is real world, because his point is 0.6 mile from JV4169 BOUNDARY MON 65. Could he be applying Xi backward from reference to a textbook?
Can someone straighten me out?
> I found a tutorial on astronomic vs geodetic measurements.
>
> It looks like I may have subtracted when I should have added? That would make him further off.
>
> The wording in the DEFLEC readme is not immune from misinterpretation:
> A positive meridian component of deflection of the vertical (Xi)
> indicates that the astronomic latitude will fall to the north of
> the corresponding geodetic latitude of the point.
>
> Does that mean the same numerical latitude is being held and the points fall thusly, or that the astronomic latitude will be a more northerly value at the same physical point?
>
> But things I read say some books used the opposite sign convention. I'm not 100% sure his example is real world, because his point is 0.6 mile from JV4169 BOUNDARY MON 65. Could he be applying Xi backward from reference to a textbook?
>
> Can someone straighten me out?
Bill - the deflection of the vertical in the meridian (Xi) is equal to the astronomical latitude minus the geodetic latitude. The deflection components are positive when the downward vertical is deviated to the south (or west) of the inward normal. This is equivalent to positive when the geoid is rising to the south (or west) relative to the ellipsoid. So yes,if Xi is positive, the astronomic latitude will have higher northerly value at the same physical point than the geodetic latitude.
Thanks for the help. I have gone through comparing geoid heights and come to the same conclusion.
That means Lee was at (today's) astronomic latitude N43 30' 4.42" and off by 447.5 ft unless there are other factors to consider.
Its still unclear to me if the Xi value is negative or positive in this instance. If using an astronomical latitude of 43d30m00s, then Xi would be negative, giving less error in this instance (about 130' as you stated). The ellipsoid isn't a physical reality, the geoid is, even accounting for the tectonic drift - the size of the deviation of the vertical is more a function of the chosen ellipsoidal reference system. That said, you would really need an accurate astronomical latitude determined before you can really say what the deflection of the vertical is or isn't.