1889-90.] Sir William Thomson on Constitution of Ether. 129 
one of the points P, P', P", P'", or all of them, he moved in any 
manner. The position of the frame G is always fully determinate. 
This is illustrated by a model accompanying the present communica- 
tion, showing a single tetrahedron of the primary assemblage and a 
single G frame. The edges of the tetrahedron are of copper wire slid- 
ing into glass tubes. The wires and tubes are provided with an eye 
or staple respectively, through which a ring passes to hold three ends 
together at the corners. Two of the rings have two glass tubes and 
one copper wire linked on each, while the other two rings have each 
two copper wires and one glass tube. 
4. Eeturning now to our multitudinous assemblage, let it be dis- 
placed by stretchings of all edges parallel to PP', with no rotation of 
PP', or P"P'". This constitutes a homogeneous irrotational deforma- 
tion of the primary assemblage. The frames G, G', &c., experience 
merely translatory motions without any rotation, as we see readily 
by confining our attention to G and the tetrahedron PP'P"P'". 
Consider similarly five other displacements by stretchings parallel 
to the five other edges of the tetrahedron. Any infinitely small 
homogeneous deformation of the primary assemblage (§ 1 above) 
may be determinately resolved into six such simple stretch- 
ings, and any infinitely small rotational deformations may be pro- 
duced by the superposition of a rotation without deformation, upon 
the irrotational deformation. Hence an infinitely small homogeneous 
deformation of the primary assemblage without rotation produces 
only translatory motion, no rotation, of the G frames ; and any in- 
finitely small homogeneous displacement whatever of the primary 
assemblage, produces a rotation of each frame equal to, and round 
the same axis as, the rotational component. 
5. It now only remains to give irrotational stability to the G 
frames. This may be done by mounting gyrostats properly upon 
them according to the principle stated in §§ 3-5 of Article C. of Yol. 
III. of my Papers, and in my Address to the Institute of Electrical 
Engineers, 10th January 1889. Three gyrostats would suffice, but 
twelve may be taken for symmetry, and for avoidance of any 
resultant moment of momentum of all the rotators of one frame. 
Instead of ordinary gyrostats with rigid fly-wheels, we may take 
liquid gyrostats as described below § 6, and so make one very small 
step towards abolishing the crude mechanism of fly-wheels and 
VOL. xvn. 26/5/90 i 
