THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
745 
The Structural Rotational, or Helical, Quality of Certain Substances. 
36. The quality of rotatory polarization, exliibited by quartz and turpentine, depends 
on the structure of the optical medium, and therefore must be expressed by a term 
in the potential-energy W. When symbols of difterentiation are imagined for the 
moment as separable from their operands, this term must be of the third degree in 
{djdx, cljdy, cl/dz); and it must be quadratic in {i, y, Q. It can thei'efore only involve 
the rotation (f g, h) and its curl, each of them linearly f therefore, being a scalar, 
the only form it can have is that of their scalar product; thus the term we are in 
quest of must be 
or what is the same 
- 0 [fV^^ + gVf + kv%]. 
This is in fact the term invented ly MacCullagii for the purjoose of explaining the 
rotational phenomena of liquids, and of quartz in the direction of its optic axis, and 
shown by him and subsequent investigators to account for the facts. In the case of a 
crystalline medium, we might have for this term the general function of {f g, h) and 
its curl, that is linear in both ; but probably in all uniaxial crystals, certainly in quartz, 
the principal axes of this term are the same as the principal axes of optical elasticity of 
the medium. 
On the Elasticity of the Primordial Medium. 
37. The objection raised by Sir G. G. SxoKEst in 1862 against the possibility of a 
medium of the kind contemplated by MacCullagu’s energy-function, and since that 
time generally admitted, is that an element of volume of such a medium when strained 
could not be in equilibrium under the elastic tractions on its boundaries, but would 
require the application of an extraneous couple of amount proportional to its surface, 
and therefore very great in proportion to its mass, in order to keej^ it balanced. Such 
a state of matters is of course in flagrant contradiction to the character of the elasticity 
of solid bodies, and can only occur if there is some concealed rotational phenomenon 
going on in the element, the kinetic reaction of which can give rise to the requisite 
* [(Added June 14.) The rotatory term in the energy function cannot involve differential coefficients 
with respect to the time; for to obtain the structural type of rotation these would have to appear in the 
second degree, which would make the term, as. it involves only (/, cj, h), of the fourth order in dift’e- 
reiitial operators; cf. ‘ Brit. Assoc. Report,’ 1893, “ Magnetic Action on Light,” § 3. Thus MacCullagh’s 
term involves on the present theory only the one hypothesis that the medium is self-contained, and not 
effectively under the influence of anothei’ intei’penetrating medium.] 
t Sir Geokge Stokes corroborates my impression that his criticism is expressly limited to media the 
elements of which are at rest and self-contained, and that it is not to be regarded as effective against a 
medium of gyrostatic quality or of the gMasi-magnetic quality described below. 
MDCCCXCIV.—A. 5 C 
