. Journal. ). Y Let us suppose now (Fig. 2) that the curve VVrepresents the desired Qi-isopoeic. What we |seek is the point on this curve for which thevalue of P is as small as possible, where P=ax-f-by-(-cz. j Now for varying values of the parameter P ithis equation represents a family of parallel straight lines. Since x+y+z = 100, we can write ;the equation in the form (a—c)x+(b—c)y= jP—100 c, the co-ordinates x and y being measured ,in the usual way along the axes ZX, ZY respec-tively (Z being the origin). To fix our ideas,suppose that a>b>c, , Z the cheapest, X theclearest raw ma
. Journal. ). Y Let us suppose now (Fig. 2) that the curve VVrepresents the desired Qi-isopoeic. What we |seek is the point on this curve for which thevalue of P is as small as possible, where P=ax-f-by-(-cz. j Now for varying values of the parameter P ithis equation represents a family of parallel straight lines. Since x+y+z = 100, we can write ;the equation in the form (a—c)x+(b—c)y= jP—100 c, the co-ordinates x and y being measured ,in the usual way along the axes ZX, ZY respec-tively (Z being the origin). To fix our ideas,suppose that a>b>c, , Z the cheapest, X theclearest raw material. If y and x denote the ]intercepts on the axes ZY, ZX respectively at anyone of the family of parallel straight lines, then clearly ~=y-—. Measure off ZL proportional to a—c, ZM proportional to b—c. Then linesparallel to LM constitute the family of parallelstraight lines in question. Draw a tangent to ;VV parallel to LM, touching VV at T. Thecomposition corresponding to the point T is the. X FIG. 3. Then T is the point on the given isopoeic forwhich P possesses either a minimum or maxivmmvalue. In the former case the composition corres-ponding to T is the desu-ed solution. In the latterease the optimum mixture is evidently a mixtureof two constituents.* 1^ This is also the case should the curve \ \ inot admit of a tangent from R. In both cas^-sno problem requiring geometrical solution arises,for it will be immediately obvious that the cheapest •Unless the isopoeic is a closed cune contained inside tlietriangle and admitting of two tangents. DONNAX—THE GRAPHICS OF BLENDING IN CHEMICAL INDDSTRIES. [J«n. mixture giving a product of the desired qualitycan be manufactured fix>m two constituents orvler that the \ilts obtained by this •hould possess teohnical vahie, it is necessaryto pay attention to the prices, a, b, c. These pricesmust include any miditional cost required forivfining, should tliis i-eliuing be carried out in
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectchemist, bookyear1882
