of Edinburgh, Session 1882-83. 
161 
If CM represents the projection of o- on a plane perpendicular to 
^ (and we assume ^ to be perpendicular to the paper and the posi- 
tive’part of ^ above it), then CMi perpendicular to CM, Mj being 
n 
on the circumference of the circle of radius CM, and to the left of 
CM, will represent V. tfr. Taking MlC?^l ~u, being on the cir- 
cumference, we get 
C??! =^Y.^o- . 
This gives the direction of do-. We then draw the chord MM' 
parallel to and CN perpendicular to the chord, so that the 
angles 
MCN = MiC7^i = w, 
and therefore the length M.N = Cn^ x sin u. Hence we have 
do==2MN = WW. 
This construction is more laborious than the one which represents 
do when expressed by 
(32) rf<r=(p=-l)V(Vf<r.O, 
where V(V^o-. 1) represents CM, the projection of o on the plane 
perpendicular to and where y/V. (Vfcr. 0 represents CM', namely, 
the result of the rotation of CM to the amount of twice the angle of 
p round the axis 
The two components of dp produce, as it is now seen, a dis- 
placement which would take place if the system was invariably 
connected with a screw which, in moving in its nut, displaces itseK 
along the axis of the screw to a distance while the screw turns 
