340 RADIUS OF CURVATURE. 



for shortness the " centre of curvature." Also the radius of 

 the circle of curvature is called the " radius of curvature." 



If a straight line be drawn from any point of a curve in any 

 direction the portion of this straight line which is intercepted 

 by the circle of curvature at the assumed point is called the 

 chord of curvature at the assumed point in the assumed 

 direction. By the nature of a circle the length of the chord 

 of curvature will be obtained by multiplying the diameter of 

 the circle of curvature by the cosine of the angle between the 

 chord of curvature and the common normal to the curve and 

 the circle at the assumed point. 



321. If p be the perpendicular from the origin on the 

 tangent at the point (x, y] of a curve, we have 



du 



~ 



\dxj f 



^ ^ a .%. 



. dp "" dx* | A ^ \dx) f c?a? cZx' 2 I'*' dx 



therefore -/-= . ^ 



flte (* dy 



f te 



5cC/ C?C* 



Also, if r * = 



dr dy 



~- ~- 



~j- ~r- 



dx y dx 



sfn //* 



From these values of -~ and -7-, and the value of p given 

 in Art. 320, we see that, 



dp I dr 



_-C = _ rf _ 



dx p dx' 



and p = r - r . 



dp 



