66 STATICS. [115. 



Thus, the analytical conditions of equilibrium can be written in 

 the form 



Graphically, to the former corresponds the closing of the force- 

 polygon, to the latter the closing of the funicular polygon. 



115. Weight ; Centre of Gravity. The most important special 

 case of parallel forces is that of the force of gravity which acts 

 at any given place near the earth's surface in approximately 

 parallel lines on every particle of matter. 



If g be the acceleration of gravity, the force of gravity on a 

 particle of mass m is 



w=mg, 



and is called the weight of the particle or of the mass m. 

 For a system of particles of masses m v m 2 , ... m n we have 



The resultant W of these parallel forces, 



where Mis the mass of the system, is called the weight of the 

 system. 



The centre of the parallel forces of gravity of a system of 

 particles has, by Art. no, the co-ordinates 



2<mg 

 or since the constant g cancels, 



This point is called the centre of gravity of the system, and is 

 evidently identical with the centre of mass, or centroid (see 

 Art. 13). 



