deletions | additions       diff --git a/Theory.tex b/Theory.tex  index 7ebf26b..ee15e7d 100644  --- a/Theory.tex  +++ b/Theory.tex 
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\section{theory} \section{Theory}  The study of whistler waves in ducting will still be determined by the dispersion relation given by the approximation of Appleton's Equation  \begin{tiny}{\[\eta^2=1-\frac{\omega_{pe}^2}{\omega^2\left((1+\frac{i\nu}{\omega})-\frac{\omega_{ce}^2\sin^2\theta}{2\omega^2\left(1-\frac{\omega_{pe}^2}{\omega^2}\right)}\pm\sqrt{\frac{(\omega_{ce}^2\sin^2\theta)^2}{4(1-\frac{\omega_{pe}^2}{\omega^2})}+\frac{\omega_{ce}^2cos^2\theta}{\omega^2}}\right)}\]}  \end{tiny}