[jQuery] Adding class to a parent element- traversion help?

[Vinoj]

I've got the following as my jquery code:
<script type="text/javascript">
        $(document).ready(function() {
        $(".bc-wrapper:empty").(this).parent().addClass("none");
        });

</script>

And the html is:

<div class="bottom-content">
   <div class="bc-wrapper">

     </div>
</div>

The css is as follows:
.bottom-content {
        display: block;
        width: 215px;
        border: 1px solid #ccc;
        float: left;
        margin-right: 20px;
        }
.bc-wrapper {
        padding: 5px;
        }
.none {
        visibility: hidden;
        border: none;
        }

----------------------------------
Basically in this example, I'd like the bottom-content class to be
hidden if the bc-wrapper class has no content. Unfortunately, I
believe I've written my code wrong (in all the different variations
I've tried) for jQuery because nothing is happening. Even when I check
with Firebug, there's no class attached anywhere.

Any thoughts?