Ah good old Google - I found a code example without having to code one myself
Right first thing you will need to do is to ensure your div has a height (which it already does in your code) and you also need to set it's overflow property to "scroll":
Code:
<style>
.scrollbar{
width: 300px;
height: 200px;
border: 1px solid black;
overflow: scroll;
}
</style>
Now have a look here:
http://developer.mozilla.org/en/docs/DOM:element
You'll notice that an element (such as a div) has a series of "offset" & "scroll" width, heights etc. I believe these are what you want to use. Click on OffsetHeight or ScrollHeight and look at the examples they give you (the pictures). This will help you understand exactly what they measure.
Then there's this code example:
http://radio.javaranch.com/pascarell...837038219.html
As you can see from the example, it automatically moves to the bottom or the DIV.
That should get you started - I'll have a tinker with it myself later and see what I come up with.