JQuery finding the wrong elements in Chrome

Question

I use jQuery to iterate over an HTML table and dynamically populate the line numbers of each line (by filling in the line number in the text box):

function updateRowNums() {
  $('#myTable').find('tr').each(function(index) {
    $(this).find('input[id$="_rowOrder"]').val(index);   
  });
}

This function is called under:

$(document).ready(function() {
  // .. code truncated ... //
  updateRowNums();
});

This works great in Firefox. However, in Chrome (tried both 5.x and 9.x (beta)), and sometimes Safari, this populates a bunch of other fields that don't even match:

'input[id$="_rowOrder"]'

with line numbers. So basically it scatters the numbers around in other unrelated text fields ...

I am sure this is some kind of Chrome or jQuery bug, but I am just checking as this seems like pretty simple functionality. By the way, if I enter a warning in the code, then it works fine in Chrome, so this may have something to do with the load time of the document in Chrome:

function updateRowNums() {
  $('#myTable').find('tr').each(function(index) {
    alert("XXXXXXXXXXXXXXXXXXX");
    $(this).find('input[id$="_rowOrder"]').val(index);   
  });
}

, :

http://jsfiddle.net/eGutT/6/

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: http://jsfiddle.net/petersendidit/eGutT/14/

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