How to specify table's height such that a vertical scroll bar appears?

Try using the overflow CSS property. There are also separate properties to define the behaviour of just horizontal overflow (overflow-x) and vertical overflow (overflow-y).

Since you only want the vertical scroll, try this:

table {
  height: 500px;
  overflow-y: scroll;
}

---

EDIT:

Apparently <table> elements don't respect the overflow property. This appears to be because <table> elements are not rendered as display: block by default (they actually have their own display type). You can force the overflow property to work by setting the <table> element to be a block type:

table {
  display: block;
  height: 500px;
  overflow-y: scroll;
}

Note that this will cause the element to have 100% width, so if you don't want it to take up the entire horizontal width of the page, you need to specify an explicit width for the element as well.

You need to wrap the table inside another element and set the height of that element. Example with inline css:

<div style="height: 500px; overflow: auto;">
 <table>
 </table>
</div>