\end{equation}
where $k_B$ is Boltzmann's constant, $T$ is the absolute temperature,
and $\avg{x^2}$ denotes the expectation value of $x^2$ as measured
-over a very long interval $t_T$,
+over a very long interval $t_T$. Solving the equipartition theorem
+for $\kappa$ yields
+\begin{equation}
+ \kappa = \frac{k_BT}{\avg{x^2}} \;, \label{eq:equipart_k}
+\end{equation}
+so we need to measure (or estimate) the temperature $T$ and variance
+of the cantilever position $\avg{x^2}$ in order to estimate $\kappa$.
+
\nomenclature{$k_B$}{Boltzmann's constant,
$k_B = 1.380 65\E{-23}\U{J/K}$\cite{codata-boltzmann}}
\nomenclature{$T$}{Absolute temperature (Kelvin)}
\begin{equation}
\avg{A} \equiv \iLimT{A} \;.
\end{equation}}
-Solving the equipartition theorem for $\kappa$ yields
-\begin{equation}
- \kappa = \frac{k_BT}{\avg{x^2}} \;, \label{eq:equipart_k}
-\end{equation}
-so we need to measure (or estimate) the temperature $T$ and variance
-of the cantilever position $\avg{x^2}$ in order to estimate $\kappa$.
To find $\avg{x^2}$, the raw photodiode voltages $V_p(t)$ are
converted to distances $x(t)$ using the photodiode sensitivity