TKAL AXlB, H 



force Hence the locus of 



.- determined by equations (5) 



100. It appears from the last ' at there in only 



one position of the resultant force in which it i* 



to the plane of the resultant c<>u]l<-. If we wish to transfer 

 tit.- force to any other point, we can do . 



Mg two forces, R and 7f. at that j^int ; 

 with the original force R will f..rm a couple; and i: 



be compounded v. original couple we hare 



. the moment of which is <J(K* + Ifjf) % v 

 notes the original moment and the distance to v 

 Jt has been moved. This moment is greater than K\ and 

 hence the stm in which A' acts when perpendicular tn 



the plane of the resultant couple is the oru of looM principal 

 therefore the central 



I. V. 7 - r - ' 



A is shewn in Art 98 to be - - n 



The principal moment will be the tame for every 

 point of the central axis, since when we have reduc* 

 forces to a single force and a couple in a plane perpend i 

 force, the force may be supposed to act at any 

 line of application, and the plane of the couple may be 

 I parallel to itself into any new position. See also Art 95. 

 > if we draw any plane perpendicular to the central axis, 

 i escribe a plane with radius p, and having its 



of the central axis, then, by the 

 last Article, tli.- principal moment for any point in : 



f A"//), and the angle at which the din 

 is IB inclined to the direction of R is given by the 



'. \Vhen a system ofjbroa acting on a rigid body u 

 reduced to two forces, and the* art represented by two strvigkt 



lines which do not meet and art not parallel, tke volume of 0+ 

 tetrahedron of which the two stray hi |MS art oppomtt tJy* 



oonstant 



