DIY History | Transcribe | Scholarship at Iowa | Eccentricity of the Sextant by Frederic Furbish, 1893 | Eccentricity of the Sextant by Frederic Furbish, 1893, Page 120

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Eccentricity of the Sextant by Frederic Furbish, 1893

Eccentricity of the Sextant by Frederic Furbish, 1893, Page 120

[page][113?][/page]

The next step consists in the formation and reduction of the elimination equations. These are three in number and have the form.

(1) x + (([ab or nb?])/(aa))y + ((ac)/(aa))z + ((an)/(aa)) = 0.

(2) y + ((bc * 1)/(bb * 1))z + ((bn * 1)/(bb * 1)) = 0.

(3) z + ((cn * 2)/(cc * 2)) = 0.

From the preceding work we have log ((cn * 2)/(cc * 2)) = 7.595166(n) therefore ((cn * 2)/(cc * 2)) = -0.00393
Substituting in equation (3) and transposing we find z' = + 0.00393.

     In (2) substitute the value of ((bc * 1)/(bb * 1)) (the logarithm is given in the above work), the value of z' and the value of ((bn * 1)/(bb * 1)) ( the logs. of both bn * 1 and bb * 1 are given above). Forming the products, transposing and reducing we get y' = -0.00287. Similarly x' = -0.00216

     Returning to the original conditions upon which this series of equations was formed we find that x = 0.726900 + x' ,

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[page][113?][/page] The next step consists in the formation and reduction of the elimination equations. These are three in number and have the form. (1) x + (([ab or nb?])/(aa))y + ((ac)/(aa))z + ((an)/(aa)) = 0. (2) y + ((bc * 1)/(bb * 1))z + ((bn * 1)/(bb * 1)) = 0. (3) z + ((cn * 2)/(cc * 2)) = 0. From the preceding work we have log ((cn * 2)/(cc * 2)) = 7.595166(n) therefore ((cn * 2)/(cc * 2)) = -0.00393 Substituting in equation (3) and transposing we find z' = + 0.00393. In (2) substitute the value of ((bc * 1)/(bb * 1)) (the logarithm is given in the above work), the value of z' and the value of ((bn * 1)/(bb * 1)) ( the logs. of both bn * 1 and bb * 1 are given above). Forming the products, transposing and reducing we get y' = -0.00287. Similarly x' = -0.00216 Returning to the original conditions upon which this series of equations was formed we find that x = 0.726900 + x' ,