246 
Proceedings of the Royal Society of Edinburgh. [Sess. 
the well-known equivalent of Euler’s three equations. Stability or 
instability will be determined by the usual considerations. 
Again, if the momentum >^( = ^cr) remains constant in amount but 
changes direction with uniform angular speed, we may write 
But 
Hence 
= rj = 'Y(x)YJ — Y WfJi(T . 
/3 = Y oo/xcr — fxY WO" -e fxa by ( 1 ) . 
(T = V 0)0" , 
and the body will describe a circular path with uniform speed. 
The radial component of force is 
— S\Jpf3 = — SUpco/xo- 
= + Sp-o-VwUp 
Bor/Jicr 2Tj 
Tp r 
where r is the tensor of p, and T.^ the kinetic energy of translation, the 
same relation as in ordinary dynamics. 
The tangential component of the force is 
- S \J<rj3 = - SUo-Va./to- = , 
vanishing when a is parallel to a principal axis of pt. 
If vibrations are set up about a position of stable equilibrium, any 
damping action will bring the body to move so that the axis of greatest 
mass will lie along the tangent to the path, and the motion will be 
sustained as in ordinary dynamics. 
{Issued separately July 6, 1922.) 
