deletions | additions       diff --git a/subsection_Varying_the_Polarization_Time__.tex b/subsection_Varying_the_Polarization_Time__.tex  index ac1ee5c..1763aae 100644  --- a/subsection_Varying_the_Polarization_Time__.tex  +++ b/subsection_Varying_the_Polarization_Time__.tex 
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\label{eq:mu}  \mu=\gamma\hbar\sqrt{I(I+1)}  \end{equation}  where \gamma is the known gyromagnetic constant for protons  and calculating I is the nuclear spin quantum number. We could calculate  $N$ for 125 mL of water, the volume that was used in this experiment. \subsection{Studying Larmor Precession}  We examined the relationship between precession frequency and magnetic field as discussed in the Methods section. we can see by Eq.~\ref{eq:precession} that precession frequency should vary linearly with magnetic field, which is what we see in Fig.~\ref{fig:precession}. The slope of the line is the gyromagnetic constant, and the intercept represents the frequency without any extra applied field.