258 GEM:I:U. rOBMI 



fore m 



st equation of equilibrium of Art. 187 

 written 



"Uji4-o; 



X 

 and the other two equations may 1 M similarly. 



Equation (2) of Art. 188, or equation (4) of Art. 196 becomes 



. 



provided T?I' be constant; that is, provided the string in its 

 unstretched state be uniform. 



/ 2V /ds\* 

 Since (! + ;:;) = (JT?) > tne l ast equation may 1>< 



connect 8 and ', and thus find the extension of the string. 



202. A\V may apply the preceding Article to the case in 

 -which tin; weiirht ;rinp; is the only force acting on it, 



the string bein_, r supposed originally uniform, and fixed at 

 points. 



i his case X= 0, Y= - fj, Z= 0, as in Art. 190 ; therefore 



- ..... 



From (1) T -j- = a constant = meg suppose ; 



tore T=m'cffBcc^jr ........................ (3), 



win-re ^ is the angle which the tangent to the curve at the 

 point (x t y) makc.-s with the axis of x. 



