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The Theory of Errors and Method of Least Squares

The Theory of Errors and Method of Least Squares


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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1900 Excerpt: ...error of a single measurement, and the final determination of the angle. i-35: n643'49.64 o.28. 8. In example 7, taking the means of the six groups of four observations each, determine the probable error of the first of these means: i, considered as a measurement of four times the weight of those in example 7; 2, directly as one of six observations of equal weight; 3, as a determination from its four constituents. i, o.67; 2, o.'j2; 30, i.oo. 9. An interval of 600 units as determined by a micrometer was forty times measured to determine the error in the pitch of the screw, with the following results: 600.0 604.8 600.7 601.4 602.0 602.6 600.0 602.4 599.7 606.1 602.4 603.4 602.7 602.7 600.7 602.4 599.5 604.7 601.6 603.1 603.7 600.9 601.4 602.1 604.6 602.1 601.7 601.8 602.1 601.4 602.9 603.6 603.9 602.2 601.4 600.6 602.3 600.8 602.9 603.6 Find the probable value of the interval and its probable error. 602.22 0.157. VI. The Facility Of Error In A Function Of One Or More Observed Quantities. The Linear Function of a Single Observed Quantity. 84. If the value of an observed quantity X be subject to an error x, the value of a given function of X, say Z--f (X), will be subject to a corresponding error z. Assuming x to follow the usual law of facility, h being the measure of precision and r the probable error, we have now to determine the law of facility of z, for any form of the function f. Let us first consider the linear function Z=zmX] b, where m and b are constants. The case is obviously the same as that of the simple multiple mX, the relation between the corresponding errors being z = mx. The probability that the error z falls between z and z + dz is the same as the probability that x falls between x and x + dx...


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Product Details
  • ISBN-13: 9781153178778
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 36
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 115317877X
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 82 gr

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