CATENARY. LOGARITHMIC SPIRAL. 



382; 



is increased numerically in -the negative direction, y tends 

 to the limit zero, so that the axis of x is an asymptote. 



353. The Catenary. 



The equation to this curve is 



- f -^ 



%/ ^ 



It is the curve in which a flexible string 

 would hang if suspended from two points, 

 as is shewn in works on Statics. 



354. The Logarithmic Spiral. 



The equation to this curve is 





 r = be e , 



or r = ba 6 . 



Taking the first form we have 



d& 



tan 9 = r -j- c. 



Since <j> is thus constant the curve is also called the 

 equiangular spiral. 



The dotted part arises from negative values of d. 



