--- manual/s_examples/baroclinic_gyre/fourlayer.tex	2001/10/24 15:21:27	1.3
+++ manual/s_examples/baroclinic_gyre/fourlayer.tex	2001/10/24 19:43:07	1.4
@@ -1,4 +1,4 @@
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/baroclinic_gyre/fourlayer.tex,v 1.3 2001/10/24 15:21:27 cnh Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_examples/baroclinic_gyre/fourlayer.tex,v 1.4 2001/10/24 19:43:07 cnh Exp $
 % $Name:  $
 
 \section{Example: Four layer Baroclinic Ocean Gyre In Spherical Coordinates}
@@ -133,13 +133,13 @@
 \begin{eqnarray}
 \label{EQ:model_equations}
 \frac{Du}{Dt} - fv + 
-  \frac{1}{\rho}\frac{\partial p^{'}}{\partial \lambda} - 
+  \frac{1}{\rho}\frac{\partial p^{\prime}}{\partial \lambda} - 
   A_{h}\nabla_{h}^2u - A_{z}\frac{\partial^{2}u}{\partial z^{2}} 
 & = &
 \cal{F}
 \\
 \frac{Dv}{Dt} + fu + 
-  \frac{1}{\rho}\frac{\partial p^{'}}{\partial \varphi} - 
+  \frac{1}{\rho}\frac{\partial p^{\prime}}{\partial \varphi} - 
   A_{h}\nabla_{h}^2v - A_{z}\frac{\partial^{2}v}{\partial z^{2}} 
 & = &
 0
@@ -154,10 +154,10 @@
 & = &
 0
 \\
-p^{'} & = &
-g\rho_{0} \eta + \int^{0}_{-z}\rho^{'} dz
+p^{\prime} & = &
+g\rho_{0} \eta + \int^{0}_{-z}\rho^{\prime} dz
 \\
-\rho^{'} & = &- \alpha_{\theta}\rho_{0}\theta^{'}
+\rho^{\prime} & = &- \alpha_{\theta}\rho_{0}\theta^{\prime}
 \\
 {\cal F} |_{s} & = & \frac{\tau_{x}}{\rho_{0}\Delta z_{s}}
 \\
@@ -166,11 +166,14 @@
 
 \noindent where $u$ and $v$ are the components of the horizontal
 flow vector $\vec{u}$ on the sphere ($u=\dot{\lambda},v=\dot{\varphi}$).
+The terms $H\hat{u}$ and $H\hat{v}$ are the components of the term
+integrated in eqaution \ref{eq:free-surface}, as descirbed in section
+
 The suffices ${s},{i}$ indicate surface and interior of the domain.
 The forcing $\cal F$ is only applied at the surface.
-The pressure field $p^{'}$ is separated into a barotropic part
+The pressure field, $p^{\prime}$, is separated into a barotropic part
 due to variations in sea-surface height, $\eta$, and a hydrostatic
-part due to variations in density, $\rho^{'}$, over the water column.
+part due to variations in density, $\rho^{\prime}$, over the water column.
 
 \subsection{Discrete Numerical Configuration}
 
@@ -179,7 +182,7 @@
  $\Delta \lambda=\Delta \varphi=1^{\circ}$, so 
 that there are sixty grid cells in the zonal and meridional directions. 
 Vertically the 
-model is configured with a four layers with constant depth, 
+model is configured with four layers with constant depth, 
 $\Delta z$, of $500$~m. The internal, locally orthogonal, model coordinate 
 variables $x$ and $y$ are initialised from the values of
 $\lambda$, $\varphi$, $\Delta \lambda$ and $\Delta \varphi$ in