# The Theory of Measurements

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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. 1912 edition. Excerpt: ...of xi and x2: For the purpose of illustration, we will compute the probable errors of the values of xi and x2 obtained in the numerical problem worked out in article fifty-one. Referring to the numerical tables in that article, we find aa = 5; ah = 20; 66 = 90; n = 5; it = 9.60 X 10-4. Hence, by equations (100), By equations (vi), article fifty-one, the length L0 of the bar at 0C., and the coefficient of linear expansion a are given by the relations 1,0 = 1000 +; - = Since L0 is equal to xi plus a constant, its probable error is equal to that of xi by the argument underlying equation (ii), article sixty. Hence EL, = Ei = 0.016. To find the probable error of a, we have by equations (81), article sixty, But, since L0 is very large in comparison with x2, the second term on the right-hand side is negligible in comparison with the first. Consequently, without affecting the second significant figure of the result, we may put = #2 X 10-4 = 0.038 X 10-5. Hence the final results of the computations in article fifty-one may be more comprehensively expressed in the form Lo = 1000.008 0.016 millimeters, a = (1.780 0.038) X lO," when we wish to indicate the precision of the observations on which they depend. 66. Application to Problems Involving Three Unknowns.--The normal equations, for the determination of three unknowns, take the form aa xt + ab x2 + ac x3 = as, abx1 + Wx9 +!bex, = lb8, ac xi + be xi + cc x3 = cs. Solving by the method of determinants and putting The determinant D can be eliminated from equations (x), if we can obtain an independent expression for any one of the w's. The solution of the normal equations by Gauss's Method in article fifty-four led to the result The auxiliary cc 2 is independent of the...show more

## Product details

• Paperback | 62 pages
• 189 x 246 x 3mm | 127g
• Miami Fl, United States
• English
• black & white illustrations
• 1236577108
• 9781236577108