Having Trouble Implementing A External DTD

I am having trouble implementing a DTD. I keep getting an error in my DTD saying:

"A well-formed document requires a root element."

In my XML document I get the error:

"The markup declarations contained or pointed to by the document type declaration must be well-formed."

DTD

<?xml version="1.0" encoding="UTF-8"?>
<!-- New document created with EditiX at Sun Jul 06 07:25:48 AST 2014 -->

<!DOCTYPE periodic
[
<!ELEMENT periodic-elements (periodic-element*)>
<!ELEMENT periodic-element (symbol, name, atomic-number, atomic_weight)>
<!ELEMENT symbol (#PCDATA)>
<!ELEMENT name (#PCDATA)>
<!ELEMENT atomic_number (#PCDATA)>
<!ELEMENT atomic_weight (#PCDATA)>]>

XML

<?xml version="1.0" encoding="UTF-8"?>
<!-- New document created with EditiX at Sun Jul 06 07:25:48 AST 2014 -->

<!DOCTYPE elements SYSTEM "C:\Users\Randy\Desktop\CMIS 170\Week 3\Homework 3\Homework3DTD.txt">
<periodic>
<element>  
  <symbol>FE</symbol> 
  <name>Iron</name> 
  <atomic_number>26</atomic_number>
  <atomic_weight>55.845</atomic_weight> 
</element>

<element>
  <symbol>Ir</symbol> 
  <name>Iridium</name> 
  <atomic_number>77</atomic_number>
  <atomic_weight>192.217</atomic_weight> 
</element>

<element>  
  <symbol>P</symbol> 
  <name>Phosphorus</name> 
  <atomic_number>15</atomic_number>
  <atomic_weight>30.973762</atomic_weight> 
</element>

<element>  
  <symbol>Uut</symbol> 
  <name>Ununtrium</name> 
  <atomic_number>113</atomic_number>
  <atomic_weight>284</atomic_weight> 
</element>

<element>  
  <symbol>Po</symbol> 
  <name>Polonium</name> 
  <atomic_number>84</atomic_number>
  <atomic_weight>209</atomic_weight> 
</element>
</periodic>

Any help would be appreciated.