72 COXMTKiNS OF EQni.IUKIl M. 



7.v [tripe tli.- in-'iM'-nf of the l- bout 



: we resolve I\ into tin- force leltoth 



Of .: anl (J liculai to tin- UUI of .:. when 



itself the resultant of X, and )',. The moment of ',', w > tn 

 repect to the axi- <-!'.: is equal to the algebraical sum of the 

 moments of its com JIM uu] ) ; that is, t< )"..'-,- 



6 X in Art. TL' denotes tin- niff| o/" ^e // 

 forces round the axis of 2, and similar meanings ari-r i.r L 

 and M. 



II . the forces acting on a ri^M body will b- in 

 briuin it' t/ir sinus of the resold ''< / tn 



three straight lines at r /'//< f ,,<//<* to each other vanish 

 the sums of the moments of the forces with respect (<> tlusc 

 atntujht lines also rnniah. 



Conversely, if the forces are in equilibrium, the sum of 

 the resolved parts of the forces in any direction will vanish, 

 and als > the sum of the moments of the forces with resp 

 any straight line. 



7'-. In order to interpret the meaning of (1 we r.b 

 that if we keep to the same ri/m. the moment of this e'.uj.le 



the direction of j independent of the 



directions of the co-ordinate axes. For /?, being the resultant 

 of all the given forces, supposing them applied at a point . 

 course independent of the directions of the axes. It bv a new 



< of axes we obtain 16 resultant nniple. then // 



and G must be equivalent to R and G\ and the. 

 7?, G, 7?, G' must form a system in equilibrium* 

 this is impossible unless G = G' and the axes of G and G' are 

 coincident or parallel. 



f-e the direction of the co-ordinate axes is arbitrary, sup- 

 pose the axis of a; to coincide with the axis of U ; then 14 n ? 

 N= 0, and L and G are identical. 



Hence G is equal to the sum of the moments of / 

 forces with respect to the str'u'yht lin< /r///V// is the axis <>/ 



77. Mippose a force Parting at the point (x, y, z], and let 



A'. ) . '/. be its components parallel to the uce. Then, by 



:_'. /' at the point (x, y, z) is equivalent to P at the 



origin, together with the couples Zy - / )'/ - Ay 



