270 Mr A, E. H. Love, On the Motion of a Solid [Oct. 29, 
The following communications were made to the Society : 
(1) The Motion of a Solid in a Liquid when the impulse 
reduces to a couple. By A. E. H. Love, B.A., St John’s College. 
1. Amone the possible modes of steady motion of a solid 
in a liquid, two are of special interest. It has been shown by 
Kirchhoff that any solid is capable of a steady motion of trans- 
lation parallel to either of three mutually perpendicular directions, 
and we owe to Lamb the discovery that when the force-resultant 
of the impulse vanishes there are three possible steady motions, 
in which the solid moves on one or other of three screws fixed 
in it. These screws are at right angles to each other and do not 
in general intersect, but lie along three alternate edges of a 
rectangular parallelepiped. Lamb also pointed out that, in case 
the impulse reduces to a couple, the. motion whether steady or 
not is given by equations which are completely integrable, and 
described a geometrical representation of it. The object of this 
paper is to express the motion and position of the solid in this 
case explicitly in terms of the time. It seems well in the first 
place briefly to recapitulate Lamb’s theory. 
2. Let us suppose then that the axes of reference fixed in 
the solid are parallel to the three directions of steady translation. 
The kinetic energy in the general case being 7’, where 
2 
OP = (6.15 Cosy Cann Cage Cigs Cogn Crgre Cassin LARUE NORTD 
the choice of axes reduces the part 
(Cy Coo. C555 Cog, C54) CHU, v; w)” 
to a sum of squares, and the three axes of steady translation are 
parallel to those of the quadric 
GOR GOW OE ZS Le 
Supposing these axes to be the axes of reference, ¢,,, c,,, and ¢,, 
vanish, and the three conditions expressing that the impulse 
reduces to a couple give 
CS ae (C,4P sed] a C.e)s 
and two similar equations, and the kinetic energy is thus reduced 
to a quadratic function 7” of p, g, 7, viz. — 
2 2 2 
CROC c 
7 py? 14 24 34 
Pui == 79 (e.- St = Pai aa a) ., 
11 22 33 
GisCl. ode 
ue 2qr (c Os 16 Be 25 Coq cutee si 
7 C1 C, C55 
