

CATKXARY. 



But * = y* + 2yc by equation (2) of Art. 184, i 



This shews that the tension at any jmmt is the weight >f 

 a portion of string whose length is the ordi: 

 tin oi-ijin U-ing at a distance c below the lowest point. 



Hence, if a uniform string hang freely over any two points, 

 the extn-mitii-rj <>t' tin- string will lie, in the same horizontal 

 lin. when the string is in equilibrium. 



186. To determine the constant c, the points of suspension 

 and the length of the string being given. 



Let A and B be the fixed 

 omities, Cthe lowest point 

 of the curve. 



OC =c, OM=a, 



j, c^=r. * 



Also let a + a = A ] 



-^*j a); 



r-fr-vl 



then //, /.% X are known quantities, since the length of tho striiiLT 

 and the positions of its ends are given. From Art. 184 



Equations (1) and (2) are theoretically sufficient to enable 

 us to eliminate a, a , b, b', /, and I' and to determine c. \\V 

 may deduce from them 



c "-e" fl -e" c ); 



