Latitude and Longitude in Practice
Place a theodolite (such as the Wild T4) next to the water tank near the airport at Hilo, Hawaii to measure the tank's latitude and longitude by the stars. National Geodetic Survey (NGS) predicts it will turn out to be 19.7323 deg North, 155.0412 deg West.
On the west side of the island is Keahole Point lighthouse; NGS data predicts the lighthouse's latitude and longitude by the stars will be 19.7244 N 156.0787 W. Based on those lat-lons, the distance from the Hilo water tank to the Keahole Point lighthouse computes to be 108.8 km — but the actual distance turns out to be 105.5 km.
Hawaii is an extreme case of a problem that exists everywhere. Ideally the T4's axis would point to the center of the Earth, but in practice it must be oriented by gravity — which is much affected by the 4000-meter mountain 50 km away. Each theodolite's axis was pointed at a different point in the earth, producing the 3-km error in distance.
So a different definition of latitude and longitude was needed. Around 1930 a marker "Oahu West Base" 21 deg 18 min 13.889 sec North, 157 deg 50 min 55.796 sec West was set as the origin of Hawaii's system, and the latitude-longitude of all other points was defined by distance and direction from that marker. The NGS now says in 1993 that point was 21-18-02.54891 N 157-50-45.90280 W using the present NAD83 system; was the old position off by 300+ meters? Well, yes, it was, but the errors between island points were much smaller than that. C&GS triangulated from island to island, calculating each point's latitude-longitude by its distance and direction from the previous points in the chain. Eventually they deemed the Hilo water tank to be at 19-43-54.526 N 155-03-26.463 W, which would make it 339191.7 meters from Oahu West Base on the Clarke 1866 spheroid. The NGS now figures those two points are 339192.8 meters apart.
Similarly in North America and everywhere else. The lat-lons that the NGS gave for the Empire State Building and a certain water tank in Anchorage in the NAD27 system would be different from the current ones, but the calculated distance between them was only 8.2 meters different from the current estimate.
Read more about this topic: Geographic Coordinate System
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