An elementary course of infinitesimal calculus . 160, that the tangents fco the given curve are normalsto the locus of Q, so that this locus fulfils the above defini-tion of an involute. And, by varying the constant, weobtain a series of involutes of the same curve. As a concrete example we may imagine a string to be woundon a material arc of the given shape, being attached to a fixedpoint on it. The curve traced out by any point on the freeportion of the string will be an involute. This is in fact theorigin of the term. Ex. 1. The tractrix is an involute of the catenary; see Art.134. Ex. 2. I

An elementary course of infinitesimal calculus . 160, that the tangents fco the given curve are normalsto the locus of Q, so that this locus fulfils the above defini-tion of an involute. And, by varying the constant, weobtain a series of involutes of the same curve. As a concrete example we may imagine a string to be woundon a material arc of the given shape, being attached to a fixedpoint on it. The curve traced out by any point on the freeportion of the string will be an involute. This is in fact theorigin of the term. Ex. 1. The tractrix is an involute of the catenary; see Art.134. Ex. 2. I

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An elementary course of infinitesimal calculus . 160, that the tangents fco the given curve are normalsto the locus of Q, so that this locus fulfils the above defini-tion of an involute. And, by varying the constant, weobtain a series of involutes of the same curve. As a concrete example we may imagine a string to be woundon a material arc of the given shape, being attached to a fixedpoint on it. The curve traced out by any point on the freeportion of the string will be an involute. This is in fact theorigin of the term. Ex. 1. The tractrix is an involute of the catenary; see Art.134. Ex. 2. In an involute of a circle of radius a we have,evidently, # = P = ^ (2), if the origin of f be properly chosen. Hence, integrating, s = W (3), no additive constant being required, if s be measured from thecusp (j/ = 0). 428 INFINITESIMAL CALCULUS. [CH. X In this particular case (of the circle) it is evident that all theinvolutes are identically equaL It is therefore customary tospeak of the involute of a circle. The curve is shewn in Fig. 127.. Pig. 127. If a constant length be measured along the normal to agiven curve, from the curve, the locus of the point thus(letermined is called a parallel to the given curve. If GP, CP be two consecutive normals to the given