228 LI Mi:r 



If the forces are such that m(Xdx+ V 



ntial of some function of x, y, z, as/(;r, y, z), 

 ' 



T+f(x,y,z)=conat&nt. 



If the forces are such that their resultant at every point 

 of tli is perpendicular to the tangent at tliat point, 



we have 



therefore, by (3), T is constant. 



In the equations (1) transpose the terms 

 the right-hand side, then square and add ; thus 



Hence if p be the radius of absolute curvature of the curve 

 formed by the string, and FmBs the resultant external force 

 en the element &, so that F* = A M + 1 M + Z\ 



-"- .................... 



< 



If T be constant -=- = : hence in this case wi-F varies as - . 



08 p 



Fn>m the equations of equilibrium in Art. 187, we dcdutc l.y 

 oration, 



Square and add ; then 



(5) 



constants that enter when we integrate the different i;il 

 equations of equilibrium must be determined from the special 



