74 STATICS. [126. 



which gives by integration y+C= V^-K 2 , the minus sign being 

 rejected since y increases with s. 



The constant C can be made to disappear by taking the origin 

 O r on the vertical through O at the distance O'O=c below the 

 lowest point O. We have, therefore, 



By means of this relation, s can be eliminated from the original 

 differential equation, and the result, 



can be integrated : 



c log + Vj^ 2 ) =*+ C. 

 = c when x=o, we find C=c\ogc\ hence 



Taking reciprocals and rationalising the denominator, we find 



hence, adding and subtracting, 



c * * c 



-(*< + * ) *=- 



126. The first equations of Art. 125, Tcosa=ff=ivc, Tsina 

 = ws y give for the total tension T at any point P 



Thus, while the horizontal component is constant, the vertical 

 component at any point P is equal to the weight of the portion of 

 the cord from the lowest point O to the point P, and the total ten- 

 sion is equal to the weight of a portion of the cord equal to the 

 ordinate of the point P. 



