of Edinburgh, Session 1881 - 82 . 
531 
This origin, which is analogous to the centre of a system of 
parallel forces, has been called by Minding the central point of a 
system of non-parallel forces. 
We have now, owing to (6) , 
(7) p = (<£' + u)h ' . 
We also designate by rj the vector moment of the forces in respect 
to the origin now chosen, so that 
(8) 7) = %Ya/3 ; 
and the condition (3) will be 
(9) Sflfy = 0. 
Owing to the definitions (5) and (8) we have now generally for 
any vector w , 
( 10 ) (<h — — 
Hence for co = h , by (6) » 
In virtue of (9) this becomes simply , 
(11) <//&'= &y 
From this, and from (6), we deduce 
Srjfiti = 0 , and — 0 . 
These relations show that the direction of h' , rj , are trirect- 
angular, and that 
( 12 ) = Trj . 
Let i ' , f , be two unit-vectors forming a trirectangular system 
with h ' , and let i ! ^ , f Q be their initial directions, so that 
i' =pi' 0 9 , f =Pfo9. 
From 
P= -i'Bi'p-j'Sfp-V&Vp 
we deduce, owing to (6) , 
h>p = — <f>i'Sip — <j>m/p , 
where the results c pi' , <f>f are constants for the same reason as </>//. 
VOL. xi. 3 x 
