diff --git a/antoine.py b/antoine.py
index 68068c4..e2dd90b 100644
--- a/antoine.py
+++ b/antoine.py
@@ -1,3 +1,6 @@
+import numpy as np
+# change number 1
+
 def antoine( a, T):
     # Ps = antoine( a, T)
     #
@@ -22,5 +25,9 @@ def antoine( a, T):
     # Modified by: Tyler R. Josephson
     # Changed comment
     
+    a=np.asarray(a,dtype=int)
+    T=np.asarray(T, dtype=int)
+    # change number 2, making a and T into arrays
+    
     Ps = 10.0**( a[:,0] - a[:,1] / ( a[:,2] + T ) )
     return Ps
diff --git a/raoult_law_kvalue.py b/raoult_law_kvalue.py
index 4bff56e..cbea295 100644
--- a/raoult_law_kvalue.py
+++ b/raoult_law_kvalue.py
@@ -1,7 +1,7 @@
 from antoine import antoine
 import numpy as np
 
-def raoult_law_kvalue( T, P, a, *gamma):
+def raoult_law_kvalue( T, P, a, * gamma):
     # Calculates the equilibrium coefficient from Raoult's law
     # INPUTS:
     #
@@ -31,7 +31,7 @@ def raoult_law_kvalue( T, P, a, *gamma):
     
     ns,nc = a.shape
     # makes np array of zeros
-    K = np.zeros(ns) 
+    K = np.zeros(ns) # This line initializes K values
     Ps = antoine(a, T)  
     K = Ps/P
     if gamma: