• George Biddel Airy, Esq., A.M, F.R.S., Astronomer Royal
  • Originally Published 1830
  • Encyclopædia Metropolitana, Volume V, Article: Figure of the Earth
    • Pages 185-260
    • Specific numbers on Page 240
  • a = 20,923,700 feet = 6,377,543.76 meters
  • b = 20,853,810 feet = 6,356,241.288 meters
  • Direct PDF Download
• Alexander Ross Clarke
  • Published 1833
  • Account of the Observations and Calculations, of the Principal Triangulation; and of the Figure, Dimensions and Mean Specific Gravity of the Earth as Derived Therefrom
  • Survey of Great Britain
  • a = 20,927,005 feet = 6,378,551.12 meters
  • c = 280.4 feet = 85.47 meters
  • https://books.google.com/books?id=DKELAQAAIAAJ
  • Direct PDF Download
• Friedrich Wilhelm Bessel
  • Published 1841
  • Astronomische Nachrichten 333 and 438
  • a = 3,272,077.14 toises = 20,922,829.22 feet = 6,377,278.35 meters
  • b = 3,261,139.33 toises = 20,852,888.96 feet = 6,355,960.55 meters
  • Astronomische Nachrichten 333:
    • https://books.google.com/books?id=44VCAQAAMAAJ&pg=PA333&lpg=PA333
    • Direct PDF Download
  • Astronomische Nachrichten 438
    • https://books.google.com/books?id=3tLAyPYQlyEC&pg=PA55&lpg=PA55
    • Direct PDF Download
• Sir George Everest
  •  Published 1847
  • Account of the Measurement of Two Sections of the Meridional Arc of India between the Parallels of 18° 3′ and 29° 30′
  • a = 20,920,902 feet = 6,376,690.93 meters
  • b = 20,853,642 feet = 6,356,190.08 meters
  • https://books.google.com/books/about/An_Account_of_the_Measurement_of_Two_Sec.html?id=ne82AQAAMAAJ
  • Direct PDF Download
• “Transcontinental Triangulation and the American Arc of the Parallel”
  • Published 1900
  • Ocean to ocean survey. Shows triangulation with spherical excess.
  • Page 221 for Spherical Excess
  • From page 901 of the PDF, number 3 in the list is the primary result of this survey.
  • a = 6,377,912 meters
  • b = 6,356,309 meters
  • https://geodesy.noaa.gov/library/pdfs/Special_Publication_No_4.pdf
  • Direct PDF Download: Transcontinental Triangulation and the American Arc of the Parallel
• “The Figure of the Earth and Isostasy from Measurements in the United States”
  • Published 1909
  • Used the results from several surveys to determine the equatorial and polar radius of the earth.
  • Page 174 has the conclusions of the computations.
  • a = 6,378,283±34 meters
  • b = 6,356,868 meters
  • https://hdl.handle.net/2027/hvd.hnwwbh
  • Direct PDF Download

Spherical Excess

For a triangle on a plane, the sum of the interior angels is 180°.  For a triangle on a sphere, the sum of the interior angles must be more than 180°.  The amount over 180° is called “spherical excess”.

• “The California Washington Arc of Primary Triangulation 1913”

  

  

  

  

  
  

  

  

  

  

  
  

  

  

  
  
  • See pages 22-31 of the PDF for examples of spherical excess.
  • Direct PDF Download: The California Washington Arc of Primary Triangulation 1913
• “Geodesy primary triangulation on the 104th meridian and on the 39th parallel in Colorado Utah and Nevada”
  • See page 62 for Spherical excess example.
  • Direct PDF download: Primary Triangulation on the 104th Meridian and on the 39th Parallel in Colorado Utah and Nevada 1914

Overview of several different measurements circa 1906:

History of the Determination of the Figure of the Earth from Arc Measurements