206 
REV. M. O’BRIEN ON SYMBOLIC FORMS. 
The conception of distortion alluded to in Sect. V. applies to (3.) in a very remark- 
able manner ; for if we put 
then n' is H distorted by the line Aia-f-Aa/S-f-Agy ; and v’ is v distorted by the line 
B,a-l-B 2 | 8 -}-B 3 y. In using the expression “ distorted by,” I anticipate a signification 
which I hope to explain in a future paper; but the fact is, CL' is a distributive function 
of CL and Ajce+Aa/S+Agy (see art. 105), and therefore, symbolically, CL' is C. multi- 
plied by Aia-t-Aa/S+Agy. 
Now the equation (3.) becomes 
d'^v 
^=n'(a.t;)-(Dn.)V, 
or, for transverse vibrations, simply 
g=-(Dn.)V. 
But I must reserve the consideration of this remarkable equation, merely remark- 
ing here that it shows very clearly how the force brought into play by the disarrange- 
ment of a medium resulting from transverse vibrations is altered by the crystalliza- 
tion. In the uncrystallized medium the force is, by ( 1 .), 
-(Dn.)X5l«-fB;?f3+B(y), 
and in the crystallized medium it is 
-(Dn.)^(B,|«+B2;?^-fB3^y). 
In one case it is found by performing the operation — (DH.)^ on v, in the other bv 
performing the same operation on v distorted as by the threefold expansion of the 
medium, consisting of a drawing out in the direction a in the proportion of Bi to B, 
in the direction j3, of Bj to B, and in the direction y, of Bg to B. 
Upper Norwood, SutTey, 
April 19, 1852. 
