1888.] in a Liquid when the impulse reduces to a couple. 273 
that direction about which a right-handed wrench would turn OL 
towards OM. The twist-velocity is oF 
Rotation E 
Axis of screw 
Translation 
In the figure the plane through the axis of rotation OJ, and 
the direction of translation OM is the plane of the paper, the 
outer ellipse is the trace on this plane of the rotational ellipsoid, 
the inner ellipse is that of the translational ellipsoid, the dotted 
line drawn through A parallel to OJ is the axis of the instan- 
} sanyo ail 
taneous screw, and the distance OA is OFF OM: 
5. We shall now take a, y, z for the coordinates of J referred 
to the principal axes of the rotational ellipsoid, and /,, m,, n, for 
the direction-cosines of OJ, also the direction-cosines of the 
normal at J will be denoted by X, uw, v. The direction (A, p, v) is 
fixed in space. 
With this notation, we have 
=lp R= Tie ; Gap Piet tek (4), 
aot , —VonsIialor © Dineen sph: (5), 
whence 1,=cdA*/ap, m,=edB*/ap,  n,=edC*/ap...... (6), 
