ram 



id have ' 

 i"ii as bcfor 



respectively, the : <ul<l ha\ 



: and BO 0H \\"e may th<- 

 :' the inclination of the resultant to 

 each component : .nchan-v 



resultant will also remain unchanLred. 



consi rce x as >rces x and x", of 



i x is in the direction of .:, and ./-" is at ri^lit 



:-;i. Then l.y tin- prineii.lr- just ; have 



XX , X If 



- = - , and = - ; 



X Z X Z 



so that *' = ^, and*" ='7- 



Similarly y may be resolved into along the direction of z 



- at right angles to that direction. Thus the i 



./ and ij are equivalent to four forces, two in the dip 

 ;ind the other two at riirht angles to that direction ; 

 two are equal in magnitude and opposite in direction, so that 



h other: hence the resultant of the former 

 two must be equal to z. Thus 



H -- = z ; therefore z* = x* 4- y'. 

 z z 



.11 now give some simple ptopoaitiona whl(;li will 

 :iplify and illustrate the principles of the p: 



I. MlQ is a triangle; 

 middle points 

 ie sides BC, CA, AB 

 respectively: shew that 1 



sented by iL r ht 



AD, 1;. .ill be in 



equilibrium* 



