CHAPTER VII. 



! OREMS 09 A SYVrEX OP FORCE* 



..' it ia proved that the force* acting on ft 



body may be reduced to a force R and ft couple 0, and 



< /' - U ', when Y arc the moments of 



rces roii - rectangular axes arbitrarily cliofttn, 



us that neither L t J/, nor .V can be greater than O; 



henoe, for ft given origin, ffo raMiftaif moMiif (7 i* mater 



than the moment of the fonxt about any other axil. For thia 



reason O is called the principal mom*** of the force*. 



From the equations in Art. 7-.. which determine the direc- 



tion of the axis of </, it follows that O cos ia the mo meat 



of the forces about an axis which passes through the given 



-i, and makes an angle <f> with the axis of principal 



The value of R in Art. 72 is independent of the 



io origin of co-ordinates; R is in far- 

 hiiltunt .:' :: given forces, supposing each of them moved 

 parallel to it*- It' until they are all brought to act at the same 

 . The value of 0, however, depends on the origin we 

 ftssume. If we take a point whose co-ordinates are x', ; 



lenote by L\ Jf, A" the moments of the forces round 

 straight lines through this point parallel to the co-ordinate 

 axes, and by ff the principal moment of the forces with respect 

 we have, by Art 81, 



I. 



-L- 

 ir-jfWJ 



2V - A" 



