diff --git a/report.tex b/report.tex
index 4ef13f4..ff294bf 100644
--- a/report.tex
+++ b/report.tex
@@ -745,7 +745,28 @@ $}
   \right] + \shift{^i} \Partial{_i} \Theta,\\
   \pt \lapse ={}& - \mu_L \lapse^2 \hat{K} + \shift{^i} \Partial{_i} \lapse,\\
   \pt \shift{^i} ={}& \mu_S \lapse^2 \Gam*{^i} - \eta \shift{^i} +
-  \shift{^j} \Partial{_j} \shift{^i},
+  \shift{^j} \Partial{_j} \shift{^i},\\
+  \pt \dlapse{_i} ={} & - \pdv{\mu_L}{\lapse} \lapse^2 \hat{K} \dlapse{_i} - 2 \mu_L
+  \lapse \hat{K} \dlapse{_i} - \mu_L \lapse^2 \Partial{_i} \hat{K} +
+  \dshift{^j_i} \dlapse{_j} + \shift{^j} \Partial{_j} \dlapse{_i},\\
+  \pt \dshift{^i_j} ={} & \pdv{\mu_S}{\lapse} \lapse^2 \Gam*{^i} \dlapse{_j} + 2 \mu_S
+  \lapse \Gam*{^i} \dlapse{_j} + \mu_S \lapse^2 \Partial{_j}
+  \Gam*{^i} - \pdv{\eta}{\lapse} \dlapse{_j} \shift{^i} - \eta
+  \dshift{^i_j} + \dshift{^k_j} \dshift{^i_k} + \shift{^k}
+  \Partial{_k} \dshift{^i_j},\\
+  \pt \dchi*{_i} ={} & \frac{2}{3} \left[ \dlapse{_i} \left( \hat{K} + 2\Theta \right)
+    + \lapse \Partial{_i} \left( \hat{K} + 2\Theta \right) -
+    \Partial{_i} \dshift{^j_j} - \frac{1}{2} \shift{^k}
+    \dsmetric*{_k_l_j} \Partial{_i} \smetric*{^l^j} - \frac{1}{2}
+    \smetric*{^l^j} \shift{^k} \Partial{_i} \dsmetric*{_k_l_j} - \left(
+    \Gam*{^j_j_k} - \frac{3}{2} \dchi*{_k} \right) \dshift{^k_i}
+  \right] + \shift{^k} \Partial{_k} \dchi*{_i},\\
+  \pt \dsmetric*{_{ijk}} ={} & -2 \dlapse{_i} \Ktf*{_j_k} -2 \lapse \Partial{_i} \Ktf*{_j_k} +
+  \dshift{^l_i} \dsmetric*{_l_j_k} + \shift{^l} \Partial{_l}
+  \smetric*{_i_j_k} + 2 \dsmetric*{_{il(j}} \dshift{^l_{k)}} + 2
+  \smetric*{_{l(j}} \Partial{_{|i|}} \dshift{^l_{k)}} - \frac{2}{3}
+  \dsmetric*{_i_j_k} \dshift{^l_l} - \frac{2}{3} \smetric*{_j_k}
+  \Partial{_i} \dshift{^l_l},
     \end{aligned}
     $}
     \]