how do I make content scroll dynamically in a DIV on Iphone's safari or android's webkit?

Question

my code:

for(var myLine = 0; myLine < 100; myLine++)
      document.getElementById("myDiv").innerHTML += "line " + myLine + "<br>";


...............

<div style="position:...etc; overflow:auto;" id="myDiv"></div>

this works without a glitch in every browser on all non mobile platforms. However... when this is implemented on iPhone (Safari) or Android (webkit) the div gets filled up with the text but no scrollbar is generated when the text runs past the height of the div and the user can't "push" the content down either. So effectively overflow is always "hidden" no matter what.

I'm curious if there's some alternative approach that I'm overlooking or if this is just a bug I have no way to get around at the moment.