‘ 498 PROF. THOMSON’S ELEMENTS OF A MATHEMATICAL THEORY OF ELASTICITY. 
plagiedral faces, discovered by Sir John Herschel to indicate the optical character, 
whether right-handed or left-handed, in different specimens of quartz crystal, or cor- 
responding to the distinguishing charaeteristics of the crystals of the right-handed 
and left-handed tartaric acids, obtained by M. Pasteur from racemic acid, or corre- 
sponding to the dipolar characteristics of form said to have been discovered in elee- 
tric crystals. 
Article XVL — Application of Conclusions to Natural Crystals. 
In a paper on the Thermo-elastic Properties of Matter, which I hope to be able 
before long to lay before the Royal Society of Edinburgh, I intend to demonstrate 
that a body, homogeneous when regarded on a large scale, may be constructed to 
have twenty-one arbitrarily prescribed values for the coefficients in the expression for 
its potential energy in terms of any prescribed system of strain coordinates. This 
proposition was first enunciated in the paper on the Thermo-elastie Properties of 
Solids, published last April in the Quarterly Mathematical Journal alluded to above. 
We may infer the following. 
Prop. A solid may be constructed to have arbitrarily prescribed values for its six 
Principal Elasticities and an arbitrary orthogonal system of six strains, specified by 
fifteen elements, for its principal strain-types; having, for instance, five arbitrarily 
chosen systems of three rectangular axes, for the normal axes of five of the principal 
strains, and those of the sixth consequently in general distinct from all the others. 
Cor. There is no reason for believing that natural crystals do not exist for which 
there are six unequal Principal Elasticities, and six distinct strain-types for which 
the three normal axes constitute six distinct sets of three principal rectangular axes 
of elasticity. 
It would be easy to add arbitrary illustrative examples regarding Principal Elasti- 
cities, and to investigate the principal strain- types and the equations of elastic force 
referred to them or to other natural types, for a body possessing the kind of symmetry 
as to elastic forces that is possessed by a crystal of Iceland spar or by a crystal of 
the cubical class (which may be included with the former in an investigation on a 
very obvious plan). 
