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Recall that n was found in correction $c_4$ as $n=1.2385$ and with some algebra it is found that $P=2-n^2=0.466$.  \Subsection{Error in n and P}  Error in n is found by the equation   \[dn= \sqrt{\frac{\rho_s}{\rho}}\sqrt{\frac{1}{c_4}^2 dc_1^2 + \frac{-c_1}{c_4^2}^2} \frac{-c_1}{c_4^2}^2  dc_4^2}\]