PROPERTIES OF THK I'KI Nd I'AL MM: 



ia shews that if we resolve L' t M\ N' along a straight 

 arallel to the direction of //, ami add tin- ivsolv.-d 

 :ain the same result whatever origin be < Thus 



the resolved part of any principal moment /// tin <i!r,>-ti,>n of It 

 is constant. By the resolved part of the principal moment in 

 ion of R we mean that part of the moment which has 

 its axis in the direction of //. 



From conations (1) of Art. 93 it appears that L 1 ' = L, 

 W = M, and N*= N, provided 



x y 



that is, if the point (a:', y ', z) be on a straight lino tin 

 the orijin pantUel to the direction of J!. Since the nriirin is 

 arbitrary, we may therefore assert that the vrinei} "I moment 

 'us unchanged, when the point to which it relates moves 

 along any straight line parallel to the direction of //. 



96. The equation to the plane through the origin perpendi- 

 cular to the direction of R is 



If we combine this equation with equations (5) of Ai 

 we obtain the co-ordinates of the point of intersection of this 

 plane with the central axis. 



AYe thus find for these co-ordinates 

 L2Z-N2X 



tf ' jft* ' It* 



which we will denote by A, &, I respectively. 

 If x', y, z 1 satisfy (1), then N'Z Y- MZ 

 or (N- x'2 l r + y'S-X) 2 y- (Jf- z'ZX + x'ZZ) 

 = ^"2 F- J/2Z- x'tf = tf(h-x). 

 arly Z'2Z- N'2X=R* (k-y 1 ), 



