1889-90.] Sir William Thomson on Constitution of Ether. 131 
XOX' being placed as follows, and the others correspondingly. Of 
the four rings mounted on XX', two are to be placed in the plane of 
YY', XX', the other two in the plane of ZZ', XX'. The circuital 
fluid motions are to he in opposite directions in each pair. 
8. The gyrostatic principle stated in § 5 of Art. C. of Yol. III. of 
my Papers, applied to our G frame, with the twelve liquid gyrostats 
thus mounted on it, shows that if, from the position in which it 
was given with all the rings at rest, it be turned through an 
infinitesimal angle i round any axis, it requires, in order to hold it 
at rest in this altered position, a couple in simple proportion to i; 
and that this couple remains sensibly constant, as long as the planes 
of all the gyrostats have only changed by very small angles from 
parallelism to their original directions. Hence, with this limitation 
as to time, our primary homogeneous assemblage of points, controlled 
by the gyrostatically dominated frame, G, G', &c., fulfils exactly the 
condition stated for the ideal ether of § 14 of Art. XCIX. of Yol. 
III. of my Papers, which is as follows : — It has no intrinsic rigidity, 
that is to say, no elastic resistance to change of shape ; but it has a 
i^a^'-rigidity, depending on an inherent quasi-elastic resistance to 
absolute rotation. It is absolutely non-resistant against change of 
volume and against any irrotational change of shape. Or it is 
absolutely incompressible. The model may be made so by intro- 
ducing struts between the points P of the primary assemblage and 
their nearest neighbours 0, O', &c., of the G frames according to § 70 
of “Molecular Constitution of Matter” (Proc. Roy. Soc. Edin ., July 
1889). 
9. If the velocity of the motion of the liquid in each gyro- 
stat be infinitely great, each G frame exerts infinite resistance 
against rotation round any axis; and if the bars and tubes con- 
stituting the edges of the tetrahedron, and the bars of the G frames 
were all perfectly rigid, the primary assemblage is incapable of rota- 
tion or of rotational deformation; but if there is some degree of 
elastic flexural yielding in the edges of the tetrahedron, or in the 
bars of the G frame, or in all of them, the primary assemblage ful- 
fils the definition of § 9, without any limit as to time, that is to say, 
with perfect durability of its quasi-elastic rigidity. 
10. A homogeneous assemblage of points with gyrostatic quasi- 
rigidity conferred upon it in the manner described in §§ 2-8 would, 
