•204 REV*. RI. O’BRIEN ON SYMBOLIC FORMS DERIVED FROM THE CONCEPTION 
and yX|3'=sinw 
D/3'.y=c4' cos 
Wherefore the annual precession of the pole is 
f -- - COS zs sm 7i7 Jc 
ct indicating that its direction is perpendicular to the solstitial colure, and retro- 
grade as regards the sun’s motion. 
I have gone through this example because in every step it shows the use of the 
symbolic forms. 
VI. Application of the Symbolic Forms to Physical Optics. 
(108.) The use of the symbolic forms u.v and uXv in Physical Optics is very 
remarkable; but as this paper is already so long, I can only just allude to the 
subject. 
In the Transactions of the Cambridge Philosophical Society I have shown (in a 
paper read March 17, 1847), that if v denote the displacement at the point {u) of an 
uncrystallized medium, where 
u=X(x,-\-y^-\-%y 
and if A and B be two constants (namely, the coeflScients of direct and transverse 
elasticity) ; then 
And this result I obtained by merely considering the disa^rrangement of the medium 
about the point u, without any assumption respecting the constitution of the medium, 
except that it possessed direct and transverse elasticity. 
Now if we employ the letter Cl to denote the operation 
the above equation, by the aid of the symbolic forms, immediately assumes the simple 
form 
d’^v 
-^=-KCl{Clxv) — '&{'DCl .y-v ( 1 .) 
The symbol Cl has a very important signification when written before any quan- 
tity, U, which is a function oi x,y and x: for the direction of the line OU is that 
direction perpendicidar to which there is no variation of while the magnitude of 
IIU is the rate of variation of U in that direction, i. e. as we pass from point to point 
of the medium in the direction of OU. 
Again, QxiJ denotes the rarefaction of (he medium, at the point (w), resulting from 
