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Chris Spencer edited data analysis rhosrho.tex
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\subsection{$\large{\frac{\rho_s}{\rho}}$ and Temperature}
The temperature dependence of the value $\frac{\rho_s}{\rho}$ and finding how it changes,not just at the values of $c_1$ and $c_4$ for the lowest temperatures, but all values of $c_1$ and $c_4$ for all measured temperatures. $\frac{\rho_s}{\rho}$ can be found by the equation \[ \frac{\rho_s}{\rho}=\left(\frac{n c_4}{c_1}\right)^2\]
figure 9 shows the plot of $\frac{\rho_s}{\rho}$ vs Temperature and it can be seen that $\frac{\rho_s}{\rho}$ begins to approach zero at $T_{\lambda}$ as predicted by the two fluid model.
\subsection{Error in $\frac{\rho_s}{\rho}$ calculation}
Error can be found by \[ d\left(\frac{\rho_s}{\rho}\right)=\sqrt{\left(\frac{1}{c_1}\right)^2 dc_4^2+\left(\frac{-c_4}{c_1^2}\right)^2 dc_1^2 } \]