1888-89.] Sir W. Thomson on Constitution of Matter. 723 
§ 67. To aid conception, make a tetrahedronal model of six equal 
straight rods, jointed at the angular points in which three meet, 
each having longitudinal elasticity with perfect anti-flexural rigidity. 
These constitute merely an ideal materialisation of the connection 
assumed in the Boscovich attractions and repulsions. A very telling 
realisation of the system thus imagined is made by taking six equal 
and similar bent bows and jointing their ends together by threes. 
The jointing might be done accurately by a hall and double socket 
mechanism of an obvious kind, hut it would not he worth the 
doing. A rough arrangement of six hows of bent steel wire, merely 
linked together by hooking an end of one into rings on the ends of 
two others, may he made in a few minutes ; and even its defects 
are not unhelpful towards a vivid understanding of our subject. 
We have now an element of elastic solid which clearly has an 
essentially definite ratio of compressibility to reciprocal of either of 
the rigidities (§ 27 above), each being inversely proportional to the 
stiffness of the hows. Now we can obviously make this solid incom- 
pressible if we take a boss jointed to four equal tie-struts, and joint 
their free ends to the four corners of the tetrahedron ; and we do 
not alter either of the rigidities if the length of each tie-strut is equal 
to distance from centre to corners of the unstressed tetrahedron. If 
the tie-struts are shorter than this, their effect is clearly to augment 
the rigidities; if longer, to diminish the rigidities. The mathe- 
matical investigation proves that it diminishes the greater of the 
rigidities more than it diminishes the less, and that before it annuls 
the less it equalises the greater to it. 
§ 68. If for the present we confine our attention to the case of the 
tie-struts longer than the un-strained distance from centre to corners, 
simple struts will serve ; springs, such as bent hows, capable of 
giving thrust as well as pull along the sides of the tetrahedron, are 
not needed ; mere india-rubber elastic filaments will serve instead, 
or ordinary spiral springs, and all the end-jointings become much 
simplified. A realised model accompanies this communication. 
§ 69. The model being completed, we have two simple homo- 
geneous Bravais assemblages of points ; reds and blues, as we shall 
call them for brevity ; so placed that each blue is in the centre of a 
tetrahedron of reds, and each red in the centre of a tetrahedron 
of blues. The other tetrahedronal groupings (Molecular Tactics, 
