I had a little down time in the rain this morning so I revisited the Page Base.
I kinda sketched out the base to give myself an idea of the reductions taking place.
Then I set up a chart of the USC&G given data (green) from the base measure and the reduction. USC&G used a simple reduction to sea level(section length*[mean height of section/6,370,000]).
I also prorated the geoid separation per section and mean latitude per section along the 40degree azimuth (azimuth from south or north makes little difference) in order to compute a radius of curvature for each of the 8 sections.
Then I computed the GRS80 ellipsoid length for each section based on its average elevation, prorated ellipsoid ht and radius of curvature at it's mean latitude.
I still have 6.5mm "floating around" somewhere, between the NAD83 3D inverse and my comps, but I'm thinking it's in the "stepped" profile of the Base versus the 3D direct inverse.
P.S. I did this in the truck on a 10 year old toughbook while taking screenshots with my phone, so pardon the appearance.
Previous [msg=318897]thread[/msg]
I've cogitated a bit over this example, but haven't gone through the detail of your recent post yet.
I doubt the C&GS took any additional data on this line when they readjusted to get NAD83. Thus, attempts to match NAD83(xx) positions to the original distance measurements is really the question of how did they massage the original data to get numbers to put into that adjustment.
They probably didn't just use the old NAD27 distance on the Clarke ellipsoid directly when changing ellipsoids. They must have had a translation technique to convert the distance. Did they just convert the line's total NAD27 distance, or did they re-work the height factors for the segments? Since the ellipsoids are not a constant distance apart, there would be a slightly different conversion at each end of the line.
We didn't have NAVD88 yet, of course, so I guess they only had the computed difference between ellipsoid heights to work with and had to use the old leveling data or its NGVD29 expression.
I'm a lot deeper into the details than I understand, here.
One clarification to my above post; the 6.5mm difference I still have floating about is between my 8 section computed GRS80 ellipsoid distance the NGS software NAD83 ellipsoid difference.
Reading further in the 1901 report, the USC&G speaks about the aims, field procedures, and adjustment techniques used.
In the triangulation appendix 6 they discuss the base probable error, as well as, the triangulation errors and the errors when tying between the bases.
Have you come across anything that gives a distance of the base without taking into consideration the actual ground measurement? They would have had a computed distance solely by triangulation from the other nearby points. It would be interesting to know how close the computations were to that point by triangulation only had they not had a measured base there.
http://docs.lib.noaa.gov/rescue/cgs/003_pdf/CSC-0105.PDF
See pages 371-373 and 385-387.
http://docs.lib.noaa.gov/rescue/cgs/004_pdf/CSC-0111.PDF
Also see 1911 Appendix 4 page 237.
Shelton base to Page base 1 in 270,000 or about 3 cm.
Page base to Brown Valley base 1 in 67,000 or about 12 cm.
From 1911 App 4;
Here's a link to an article in a XLVIII No. 10 issue of Engineering News that gives a bit of insight into the process. Also some pictures.
See page 162 for the article.
Don't miss the review on pages 168-169 (PDF page 165-6), which gives a perspective on the techniques versus prior work.
