8Ti. I .si 1 . 



/>" represent tin- nati: 'ii <>f the string; AB 



stretched length. I, 

 Snppns.- A'P' stretched into AP, and P'Q' into 



/'</. > = &r. Let .r/r = a, 



10 = the weight of the string, and W be tin- 

 attached weight. 



Let T be the tension at /', and T+&T the 



;it $. Tlu-n tin- rirmeiit i on 



by the forces T and T+&T at its ends, and by 



:ht; its weight is the KL that 



of P'Q, that is -^rw\ 



fore 



a 



or !//- /=: "? ultimately (1) ; 



fore T = 4- constant. 



a 



The value of the constant must be found by o' that 



when x' = a, T= IT; therefore 



W w -f constant ; 



therefore r=Tf+ 



o the element PQ may be considered ultimately uniform 

 and stretched by a tension T\ hence, by the ezpexim 

 law, 



(3); 



7 m 



therefore 1 + - , 



cut \ 



x x 



jratc ; thus 



.-*(>+!&- 



No constant is required because x = when x = 0. 



