382 LOGARITHMIC CURVE. 



In tliis case the curve begins at the pole and makes 



an infinite number of revolutions round it ; r can never be- 

 come so great as a, to which value however it continually 

 approaches. Hence r = a is the equation to an asymptotic 

 circle, to which the curve continually approaches as 6 in- 

 creases without limit. 



If we give to negative values, we have a branch similar 

 to that obtained from positive values of 6. It is represented 

 in the figure by the dotted portion. 



352. We shall now give the equations and the figures of 

 a few curves which frequently occur in problems. 



The Logarithmic Curve. 

 The equation to this curve is 



X 



or, which is an equivalent form, 



The curve extends to infinity 

 both in the positive and negative 

 directions of the axis of x. As x 



