[ IS? ] 
V. A Supplement to a Paper entitled iC Remarks on the Theory of the Dispersion of 
Light , as connected with Polarization .” % the Rev. Baden Powell, M.A. 
F.R.S. F.G.S. F.R.Ast.S., Savilian Professor of Geometry in the University of 
Oxford. 
Received February 6, — Read March 5, 1840. 
In a paper inserted in the Philosophical Transactions* I endeavoured to elucidate 
what appeared to me an important point in the wave-theory, viz. the connexion (first 
pointed out by Mr. Tovey) between certain conditions with respect to the arrange- 
ment of the setherial molecules, and the rectilinear or elliptic form of the vibrations ; 
thus affording a criterion of their nature, in the respective cases, by the evanescence, 
or finite value, of certain terms in the equations. 
Since the publication of that paper I have been led to review the subject in con- 
nexion with the valuable illustrations given by Mr. Lubbock of the views of Fresnel'|~, 
according to which it appears that the criterion just mentioned requires a material 
modification. I think it necessary therefore to submit to the Royal Society this short 
Supplement, in order to point out in what way the conclusions in my paper will be 
affected by these considerations. 
In the investigation last referred to it is established, 
1. That every system of molecules, constituted as here supposed, has at every point 
three axes of elasticity, at right angles to each other. 
2. That if these axes be taken as the axes of coordinates, then, in the fundamental 
equations of motion, deduced as in my paper, we shall have 
2 {\£ r Ay A 2 } A 7j = 0, (1.) 
and all terms of the same form in like manner = 0 ; so that the equations (13.) of 
my paper are reduced to 
jp = 2 {(<p r + ^ r A x 2 ) A §} 
^ = 2{(?r+4rA/)A))} > 
= 2 { (p r + ^ r A z 2 ) A 
( 2 .) 
* 1838, Part II. 
t London and Edinburgh Journal of Science, November, 1839. 
