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. 1858 Excerpt: ...one which is most probable or requires the least total amount of alteration of the observations, having respect to the different weights or probable errors of each mean bearing. Now in order that may be a minimum, we must have du =, or o = w xl-dxl + w2x, -dx2 + + to, xm dx-(a) but by differentiating the equations ( 1 ...
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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. 1858 Excerpt: ...one which is most probable or requires the least total amount of alteration of the observations, having respect to the different weights or probable errors of each mean bearing. Now in order that may be a minimum, we must have du =, or o = w xl-dxl + w2x, -dx2 + + to, xm dx-(a) but by differentiating the equations ( 1 ) we have the following: --which establish n relations between the m differentials; we may therefore determine n of them, in terms of the remaining m--n, and thus the number of differentials in (2) is reduced by substitution from m to m--n, which are perfectly arbitrary; and therefore making their coefficients respectively equal to zero, there will result m--n equations between the quantities x, which, together with the n equations of condition, will suffice to determine these corrections. But the method practically adopted is that of independent multipliers, which is as follows: --Multiply the equations (3) by indeterminate quantities, .... ., and adding their sum to the equation (2) multiplied by--1, we have the following system of equations: -- = (--, + A, a, +, b, + x3c, +... q, ) dxl + (--wjct + A, a, + jb2 + 3, +... Xnq, ) dx, + (-tom + A.a, + jm + A3cm +... Kqm) dxm, Now as there are n arbitrary quantities A, we may assume n of these coefficients of the differentials equal to zero; the quantities A being thus determined, and then substituted in the remaining coefficients, the expression will take the form = + Qdx, +... containing m--n differentials; and these being independent, it follows that P = o, Q = o, &c.... which amounts to putting at once each of the coefficients of the m differentials in (4) separately equal to zero; therefore we have...
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Add this copy of Account Of The Observations And Calculations, Of The to cart. $15.42, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
Add this copy of Account Of The Observations And Calculations, Of The to cart. $26.58, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2022 by Legare Street Press.
