Transactions . 1814 776679 70 Ml10913749107125126 ABSORPTION OF CARBON BY STEEL. 473 Iii order to correlate the value of the various elements in theircarburizing effect a mathematical investigation was each steel an equation can be formed connecting the increasedweight with the percentage of the various elements present. Thiswill give us as many equations as we have steels, and the problemthen resolves itse
Transactions . 1814 776679 70 Ml10913749107125126 ABSORPTION OF CARBON BY STEEL. 473 Iii order to correlate the value of the various elements in theircarburizing effect a mathematical investigation was each steel an equation can be formed connecting the increasedweight with the percentage of the various elements present. Thiswill give us as many equations as we have steels, and the problemthen resolves itself into an equalization of the errors of observation,analysis and weight entering into each equation by a consideration ofthe remaining ones. This can be done by the method of least the elements were first considered, and much time was spent insolving this problem. This proved a mathematical success, but a flatfailure from a practical standpoint. ^ B2- -A 9 1 ! II . i i ii ! L JL -1 1 1 11 11J U u U. Fig. 1.—Carburizing Box. By the method of least squares a problem containing more equationsthan unknowns is solved by reducing the excess equations to a number-equal to the unknown quantities. These final equations are knownas normal equations; they are solved by the ordinary processes ofalgebra. In this case they were solved by the method of are many difficulties in the way of the solution of such a prob-lem, some of which are as follows: (a) The correct formation of the original equations. (b) The presence of elements occurring in nearly constant amounts. (c) The presence of elements having little or no influence on the-rmal result, 474 ABSORPTION OF CARBON BY STEEL. The formation of the original equation is the most importantsource of error. For example, the amount of carbon absorbed maynot be a straight-line function of the percentage of some one relationship may be expressed by a curve or a broken line or acombination of the two.
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Keywords: ., bo, bookcentury1800, bookdecade1870, booksubjectmineralindustries
