The Analyst Volume 7-8

The Analyst Volume 7-8

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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. 1880 edition. Excerpt: ...that the mean of the:1: -errors will be t--!--k units and the mean of the y-errors v--: --k units. The units of measure dz and Ay can be taken as small as we please, and the exponents in the polynomial will be regarded as whole numbers. In k observations, the most probable total effect, in the ac and ydirections, of the elementary error 211:2: and 3Ay for example, will be M2. 8(2A$)2 I5/l2.3(3Ay)1 and so on for other errors. The most probable algebraic sums of the:1: and y errors then will be---m/l_,, ml, " mA_,, '""'"'(m'i'mfi, l' '"-'/(__...1;.i.";i'"'-/i';i7--') 3) so that these are approximately the exponents of E and 17 in that term in the expansion of (2) whose coeflicient is a maximum. Hence the most probable error in the mean of the k observations, in the as and y directions respectively, is found by dividing the expressions (3) by k. It will be seen that the quotients thus obtained are the statical moments of the coeiiicients 1 about the axes of Yand X, these coefiicients being regarded as masses in a system of material points. The same quotients also represent the lever arms of the system about those axes, since the sum of all the masses /1 is unity. From the principle established in my article of March '80, p. 46, it follows that the lever arms of the system of coefficients in the expansion of ( 2) to' the in power, about the axes of X and Y respectively, are k times what they are in the_first power. According to (3) therefore, the maximum coefiicient in the expansion will coincide approximately with the centre of forces, or cen m, --an tre of gravity, of the whole expanded series of coefiicients, whether I: be finite or infinite. We shall hereafter get more

Product details

  • Paperback | 102 pages
  • 189 x 246 x 5mm | 195g
  • United States
  • English
  • black & white illustrations
  • 1236956842
  • 9781236956842