Find element via parameterized css selector

Question

This works:

<html>
<head>
<title>JQuery Show/Hide w/ Animate</title>
<script src="js/jquery-1.8.2.js"></script>
<script src="js/jquery-ui.js"></script>
<script>
    function show(button) {
        var idx = button.attr("id").substring(1);
        $("div#menu" + idx).show();
        $("div#menu" + idx).animate({ height: '300px' }, 300);
    }
    function hide(button) {
        var idx = button.attr("id").substring(1);
        $("div#menu" + idx).animate({ height: '20px' }, 300, "swing", function() { $("div#menu" + idx).hide(); });
    }
    $(document).ready(function() {
        $("div#menu1").hide();
        $("div#menu2").hide();
        $("#s1").click(function() { show($(this)); });
        $("#s2").click(function() { show($(this)); });
        $("#h1").click(function() { hide($(this)); });
        $("#h2").click(function() { hide($(this)); });
    });
</script>
</head>
<body>
<div id="menu1" style="font-size: xx-large;">Menu 1</div>
<div id="menu2" style="font-size: xx-large;">Menu 2</div>
<div><button id="s1">Show 1</button><button id="s2">Show 2</button>
     <button id="h1">Hide 1</button><button id="h2">Hide 2</button></div>
</body>
</html>