( 658 ) 



In a time dt the element ds of the wire describes a surface 



dio 

 C S — dsdt. 

 ds 



If the wire at the ends is \ertical tlie whole wire will therefore 



describe an area 



"ƒ' 



1 dia 



dt I C S — ds — nCSdt. 

 ds 



Now if the velocity of the wire is v, and the distance between 

 the vertical ends d^, the same area will be vd^ so that we have 



. = ^-. (///) 



or if the angle between the ends is 2«, and P the weight at each end, 



. = 1^^ i'li.) 



flj sin a 

 We shall next consider the form taken by the wire if it descends 

 as a whole with uniform velocity. It is determined by the condition 



dio dx 



C S r= V— , 



ds ds 



or 



du> 71 dx 



{is dj ds 

 As Q do>=:ds, Q being the radius of curvature, this equation becomes 



d'y 



dx^ n 



-dj 



Taking the axis of x horizontal at the highest point of the line, 

 the axis of y vertical downwards we have for x = 0, 



dx 

 therefore 



dy TV 



-^ z=tg — X , 

 dx fZj 



-:ry 

 cos — X := e 

 d. 



The normal pressure at the highest point is 



On — 



d. 



