6s 
Mr. Robertson on the Precession 
In GB take GV equal to RN ; and in GC take GW equal to 
Rr, and VW being drawn it will be parallel to the axis TS. 
For as NR is perpendicular to AB, and Rr or NM to DC, by 
article 4, the angle RNM, or (34. I.) its equal RrM, is equal 
to the angle VGW. Also, on account of the equals, VG : GW 
: : Mr : rR, and therefore (6. VI. ) the angles rRM, GWV are 
equal. Let TS meet HK in O, and LQ in I ; and let DC meet 
HK in X. Then as the angle OIR is equal to the angle OXG, 
each being a right one, and as the angles IOR, XOG are 
equal, the angle IRO, or MRr is equal to the angle OGX. 
Consequently the alternate angles XGO, GWV are equal, 
and therefore TS, VW are parallel. Hence it is evident that 
if the axes AB, DC, and also GV, GW the angular velocities 
round them be given, the axis TS is easily found, being pa- 
rallel to VW. It is proper to observe that GV, GW are to 
be set off on that side of TS towards which the body is moving, 
in consequence of the revolutions round DC, AB. 
7. From the last article it is evident that VW is equal to 
RM, and consequently equal to the angular velocity, with 
which the body revolves about the axis TS. If therefore CGB 
be aright angle, then the angular velocity V W = s/' VG*-|- G W\ 
In other cases the value of VW may be easily calculated by 
plane Trigonometry. 
8. It is to be remarked, for the sake of precision, that the 
linear velocity, of any point, is as the angular velocity multi- 
plied into the radius of the circle in whose circumference it 
revolves. Thus the linear velocity Ps (Fig. 5.) of the point 
P in the circumference FPE, is as its angular velocity in the 
same, multiplied into the radius of the circle FPE, as is evi- 
