272 Mr A. E. H. Love, On the Motion of a Solid [Oct. 29, 
3. Now it will be most convenient to take as axes of reference 
three axes fixed in the solid parallel to those of the steady motions 
when there is no force-resultant of the impulse. We shall call 
these for shortness the three principal rotational axes of the solid, 
and the ellipsoid 7” (2, y, z)=constant when referred to these, 
its principal axes, we shall call the rotational ellipsoid. The ellip- 
soid @(a, y, z)=constant when referred to the same axes will 
be called the translational ellipsoid, since the former serves to 
give the motion of rotation of the solid, and the latter that of 
translation. The principal axes of the translational ellipsoid do 
not in general coincide with those of the rotational ellipsoid, so 
that we must take for the equation of the former 
(@, 0 og, LOx, 4.2) —— 0... (1). 
and for that of the latter 
a at: y" ate a = 2 
A? B C2 =e SAO ADO OR AOCOOM OOO Da OS ( ). 
Let G be the constant impulsive couple, and }# the constant 
energy of the motion. The ellipsoid (2) is to be made to roll on a 
plane, which is normal to the axis of the impulsive couple G; 
the distance of the centre of the ellipsoid from the plane is to 
be ow se and the angular velocity about the radius vector 
OT to the point of contact J is vl - p, where p is the length of OJ. 
It is to be noted that 
B=p/A’?+q¢/B + Bee 
G = p’/A* + q?/B* + 7°/C* 
The quadric (1) is cut by OJ in the point P and OM is the 
perpendicular on the tangent plane at P; calling OP and OM, 
p' and a, the velocity to be impressed on the system of ellipsoid 
and plane is u/, Zt aD in the opposite direction to OM. This 
po” 
is Lamb’s construction. 
4. The solid is twisting on an instantaneous screw whose 
axis is parallel to OJ, and whose pitch is 2g The axis of the 
screw cuts a line through O perpendicnlar to the plane MOP at 
ae” 
a distance from O equal to S.v/e ae , the line is to be drawn in 
@D. 
