GENERAL EQUATIONS OF KQUlLIUIUi _'J7 



the | ;/, *), and then m will bo the mast of such tup- 



element o* of ' ;, the equilibrium of v. 



msidcrcd, becomes more nearly a particle the 

 we diminifth f* ; i in ice it is .- to consider the three 



equations of i stead of the six equations of Art 73. 



The three equations which we have found are theoretically 

 sufli /' tj y, andrn 



when we 



iluca of y and in terms of or, we know the equations 

 to the curve which the string forms. 



188. The equations for the equilibrium of a flexible string 

 may be written thus ; 



. 



1 ,/ 





Multiply these equations by T- , ^, and -^ respectively and 

 add ; then, since 



dxd*x 



aml 



wehave + m j + y + Z-0 ....... (2); 



therefore T-f jw(-V ^+ F ^ + Z fy ** -constant... (3). 



15 * 



