

STIII NO 8TRETCI1ED BT A V 



< stretched length of the 'lien j.u:- 



l x 1 - a', we have 



- the tame as would be produced if an 

 ngth a', the weight of which might be neg- 

 1, were stretched by a wei. hi II ' + JIT at its ci 



200. In the soluti preceding problem we m 



have arrived at equation (2) bv observing t 



equal to the weight of the string below 



t together with II'; but the method we adopted is 



ul as a guide to the solution of similar problems. 



superfluous to notice an error int.* which 



i its often fall; since the element &c is acted on 



tension T at one end, and T+ BT or ultimately T at "the 



P is considered the stretching force, and instead 



i- n !. 'I'iii-i \s..-:!i ! of :. > OOOMgMDM it" 



:->r it would illy nnvnmt to using JX instead of X in 



(3) ; but mfo**kfr arise from not adhering to one system or 



It should be observed that if a string without 



it be acted on by a force T at each end, it i* in the same 



of tension as if it were fastened at i and acted on 



by a force Tat the ot 



201. The equations of Art 187, and *. may be aj>- 



to an eloMtic string in equilibrium. Tlu-y may also be 

 modified as follows, if we wish to introduce the unstretched 

 length of the string instead of the stretched length. 



Let ' and oV represent the natural lengths which become 

 . and fit by stretching ; let m'&V be the mass of an element 

 before stretching, and mo the mass of the same element after 

 stretching; then 



Mfc-ttW, 



T. S. 17 



