simplexml - get correct nodes - PHP

My xml file looks like this:

Code:

<data>
  <time-layout time-coordinate="local" summarization="12hourly">
    <start-valid-time period-name="Tonight">data</start-valid-time>
    <start-valid-time period-name="Thursday">data</start-valid-time>
    <start-valid-time period-name="Thursday Night">data</start-valid-time>
    <start-valid-time period-name="Friday">data</start-valid-time>
    <start-valid-time period-name="Friday Night">data</start-valid-time>
    <start-valid-time period-name="Saturday">data</start-valid-time>
    <start-valid-time period-name="Saturday Night">data</start-valid-time>
    <start-valid-time period-name="Sunday">data</start-valid-time>
    <start-valid-time period-name="Sunday Night">data</start-valid-time>
    <start-valid-time period-name="Monday">data</start-valid-time>
    <start-valid-time period-name="Monday Night">data</start-valid-time>
    <start-valid-time period-name="Tuesday">data</start-valid-time>
    <start-valid-time period-name="Tuesday Night">data</start-valid-time>
    <start-valid-time period-name="Wednesday">data</start-valid-time>
  </time-layout>
  <time-layout time-coordinate="local" summarization="12hourly">
    <start-valid-time period-name="Tonight">some data</start-valid-time>
    <start-valid-time period-name="Thursday Night">data</start-valid-time>
    <start-valid-time period-name="Friday Night">data</start-valid-time>
    <start-valid-time period-name="Saturday Night">data</start-valid-time>
    <start-valid-time period-name="Sunday Night">data</start-valid-time>
    <start-valid-time period-name="Monday Night">data</start-valid-time>
    <start-valid-time period-name="Tuesday Night">data</start-valid-time>
  </time-layout>
  <time-layout time-coordinate="local" summarization="12hourly">
    <start-valid-time period-name="Thursday">data</start-valid-time>
    <start-valid-time period-name="Friday">data</start-valid-time>
    <start-valid-time period-name="Saturday">data</start-valid-time>
    <start-valid-time period-name="Sunday">data</start-valid-time>
    <start-valid-time period-name="Monday">data</start-valid-time>
    <start-valid-time period-name="Tuesday">data</start-valid-time>
    <start-valid-time period-name="Wednesday">data</start-valid-time>
  </time-layout>
</data>

I need to access the "period-name" attribute of the "start-valid-time" nodes of the 2nd and 3rd "time-layout" nodes. I know to use xpath because the node names have hyphens, but I do not understand how to get the correct attributes from the correct nodes. Here is what I started with:

Code:

$xml = simplexml_load_file($xmlFile) or die ("Unable to load XML file!");
$simplexml= new SimpleXMLElement($xml);
$timeLayout =  $simplexml->xpath('/dwml/data/time-layout');
$timeLayout71 = $timeLayout[1];
$timeLayout72 = $timeLayout[2];
// from here down I start having problems
$startValidTime = $timeLayout71->start-valid-time; // can't do this b/c of 
// hyphens - how else can I do this??
echo $startValidTime[0]['period-name'];

Can someone help me figure out how to access the correct nodes?

Thanks for your help!