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A Text-Book on the Method of Least Squares

A Text-Book on the Method of Least Squares


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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1884 edition. Excerpt: ...weight. From remote antiquity the arithmetical mean of the measurements has always been regarded as the best or most probable value of the quantity sought; and, as shown in Art. 44, this is confirmed by the fundamental principle of the Method of Least Squares. Let z be the most probable value of the measured quantity, n the number of observations, and M any observation. Let r be the probable error of a single observation, and ra the probable error of the adjusted value z. Let also v be any residual obtained by subtracting M from z. The most probable value of the quantity is the arithmetical mean, expressed, as in Art. 44, by formula (8), z =. The probable error of a single observation, as shown in Art. 65, is, by formula (20), Lastly, as shown in Art. 64, the probable error of the mean is, by (19). r n Formula (8) indicates the method of adjustment, while (20) and (19) determine the precision of observation and of the mean. After finding z, each observation is subtracted from it, giving n values of v. The squares of these are taken, and their sum is Sz2; then r is computed, and lastly, r0. If desired, r0 can be also found directly from formula (21), which is the same as (19). 81. As an example, consider the following twenty-four measurements of an angle of the primary triangulation of the United-States Coast-Survey, made at the station Pocasset in Massachusetts, and recorded in the Report for 1854: --The most probable value of the angle is found by adding the observations, and dividing the sum by twenty-four. This is 116 43'49."64. Subtracting from this the first reading gives 5.19 for the first residual, which is placed in the column headed v. The square of this is 26.94, which is placed in the column headed v2. The sum of all these...


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Product Details
  • ISBN-13: 9781152051720
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 38
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1152051725
  • Publisher Date: 01 Apr 2013
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 86 gr


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