Textarea overflow problem

Question

I have this textarea inside a jQuery UI dialog:

<div style="width:350px;height:100px;overflow:scroll;">
<textarea cols="50" rows="1000" id="txtarr"  wrap="off"></textarea>
</div

I want to add scroll bar - to see 50 of the rows,to see the others - the user must scroll. But it doesn't work.

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Like I have text ,that overflows 100px and I add vertical scroll with overflow:scroll; , but with the textarea it doesn't work.