GENERAL EQUATIONS OP BQ11I -'.:' 



instance* of each particular problem. Thus the co- 



i the ends of the - 



are attached may be given, nn-1 tin- l.-njtSi of the string. 



H the forces represented bj mA'&j, mYlt, and mZt* 



; on each elemct .oea /', a .iy act at 



the extremities ot : ; in this case if T t and f t denote 



- of T at the two 10 string, we must 



have T t equal in magnitude to /', and opposite to it in 



. and similarl 



/ / 

 189. From equations (1) of Art IBS, eliminate r and ^ ; 



then we have 



/<P* dx d*x <fr 



this shews that the resultant external force which acts on an 

 ut of of the string lies in the osculating plane at the 

 point (x t y, ). 



190. The general equations of equilibrium become, when 

 all the forces are in one plane, namely, that of (x, y), 



ose A'-O, so that the external force is parallel to the 

 i\v ; the n'ret equation gives 



- a constant, C say, 



Q 



Tm "3x *) 



Z 



Hence the second equation becomes 





