. Spons' dictionary of engineering, civil, mechanical, military, and naval; with technical terms in French, German, Italian, and Spanish . 1590 FRICTION. This curve, termed the anti-friction curve by Christian Schiele, is known to mathematicians asthe tractrix; it has been erroneously identified with the catenary. This curve was invented byChristian Huygens and received its name from a supposition that it is the curve which would bedescribed by a weight drawn on a plane by a string of a given length, the extremity of which iscarried along the directrix A B, Fig. 3082. Euler has shown that this
. Spons' dictionary of engineering, civil, mechanical, military, and naval; with technical terms in French, German, Italian, and Spanish . 1590 FRICTION. This curve, termed the anti-friction curve by Christian Schiele, is known to mathematicians asthe tractrix; it has been erroneously identified with the catenary. This curve was invented byChristian Huygens and received its name from a supposition that it is the curve which would bedescribed by a weight drawn on a plane by a string of a given length, the extremity of which iscarried along the directrix A B, Fig. 3082. Euler has shown that this conclusion is wrong, unless. the momentum of the weight which is generated by its motion be every instant destroyed. SeeEuler, Nova. Cômm. Petrop. 1784. However, to Schiele is due the credit of applying this curveto effect an important mechanical requirement. The characteristic property of the anti-friction curve, or tractrix, is that the locus of a point T,on the tangent P T, at a given distance from the point of contact, is a straight line A X, which iscalled the directrix of the curve. To find the equation to the Anti-friction Curve.—Let the intercept (P T) of the tangent betweenthe directrix A X and point of contact P be put = a. Then by the general formula for the sub-tangent -^ = (a^ — ir\^ : dy From integrating [1] we obtain («2 - y^f [1] = «J,( y / [2] In general terms J,, (jj) is put to represent the dual logarithm of y to the base B = 1 • 00000001 ; but 108 corresponds with the hyperbolic log. of y to eight places of decimals. \, (jj) lO to any of the dual bases B„ or 6„, is termed the loga
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