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On the Algebraical and Numerical Theory of Errors of Observations and the Combination of Observations

On the Algebraical and Numerical Theory of Errors of Observations and the Combination of Observations


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About the Book

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. 1875 edition. Excerpt: ...is the smallest possible. This is all that we can do. We cannot assert that our result shall be correct; or that, in the case before us, its actual error shall be small, or smaller than might be given by many other combinations; but we can assert that it is probable that its actual error will be the smallest, and that it is certain that, by adopting this rule in a very great number of instances, we shall on the whole obtain results which are liable to smaller errors than can be obtained in any other way. 65. Now if we know the probable errors, or the proportion of probable errors, of the individual observations, (an indispensable condition, ) we can put known symbols for them, and we can put undetermined symbols for the combination-weights; and, by the precepts of Part II, we can form the symbolical expression for the probable error of the result. This probable error is to be made minimum, the undetermined quantities being the combinationweights. Thus we fall upon the theory of complex maxima and minima. Its application is in every case very easy, because the quantities required enter only to the second order. Instances will be found in Articles 68 to 72. 66. It sometimes happens that, even in the measures of an invariable quantity, combinations of a complicated character occur. Different complex measures are sometimes formed, leading to the same result; in which some of the observations are different in each measure, but other observations are used in all or in several of the measures; and thus the measures are not strictly inde pendent. We shall call these "entangled measures." The only caution to be impressed on the reader is, to be very careful, in forming the separate results, to delay the exhibition of their probable errors...


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Product Details
  • ISBN-13: 9781152449244
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 26
  • Spine Width: 1 mm
  • Width: 189 mm
  • ISBN-10: 1152449249
  • Publisher Date: 01 Apr 2013
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 68 gr


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