diff --git a/hw4.Rmd b/hw4.Rmd
index 02596c7..d9cae30 100644
--- a/hw4.Rmd
+++ b/hw4.Rmd
@@ -98,6 +98,27 @@ If $t \geq 86 400$, subtract $86 400$. If $t < 0$, add $86 400$.
 6. Compute the amplitude of ionospheric delay
 $$ A_I = \sum_{n=0}^{3} \alpha_n(\phi_m/\pi)^n $$
 If $A_I < 0$, then $A_I =0$.
+
+7. Compute the period of ionospheric delay
+$$ P_I = \sum_{n=0}^{3} \beta_n(\phi_m/\pi)^n $$
+If $P_I < 72 000$ then $P_I = 72000$.
+
+8. Compute the phase of ionospheric delay
+$$ X_I = \frac{2\pi ( t-50400)}{P_I}$$
+
+9. Compute the slant factor (ionospheric mapping function)
+$$ F=\left[1 - (\frac{R_E}{R_E + h} \cos E)^2\right]^{-1/2} $$
+10. Compute the ionospheric time delay
+$$
+I_1 = \begin{cases}
+  [5 \cdot 10^{-9} + A_I \cos X_I] \times F, & \quad |X_I| < \pi/2 \\
+  5 \cdot 10^{-9} \times F, & \quad |X_I| \geq \pi/2
+\end{cases}
+$$
+The delay I1 is given in seconds and is referred to the GPS L1 or
+Beidou B1 frequencies.
+
+
 ```{r simulate}
 # input constants
 lat = 45.33709 # phi