JavaScript Menu Issue

Hello,
I have a very simple question that after looking through the API of jQuery and through this forum, I"m a bit stuck on…

I’m trying to target the second element of a ul based menu.

I have code that works for the first. This basically opens a sub ul menu on page load. I want the second to load on another page.

HTML Example:

noaccordion : no accordion functionality
collapsible : menu works like an accordion but can be fully collapsed
expandfirst : first menu item expanded at page load

<ul id=“menu1” class=“menu [optional class] [optional class]”>
<li><a href=“#”>Sub menu heading</a>
<ul>
<li><a href=“http://site.com/”>Link</a></li>
<li><a href=“http://site.com/”>Link</a></li>
<li><a href=“http://site.com/”>Link</a></li>


</ul>
<li><a href=“#”>Sub menu heading</a>
<ul>
<li><a href=“http://site.com/”>Link</a></li>
<li><a href=“http://site.com/”>Link</a></li>
<li><a href=“http://site.com/”>Link</a></li>


</ul>


</ul>

JS

function initMenus() {
$(‘ul.menu ul’).hide();

$.each($('ul.menu'), function(){
	$('#' + this.id + '.expandfirst ul:first').show();
});

$('ul.menu li a').click(
	function() {
		var checkElement = $(this).next();
		var parent = this.parentNode.parentNode;
		
		if($(parent).hasClass('noaccordion')) {
			$(this).next().slideToggle('normal');
			return false;
		}

		if((checkElement.is('ul')) && ($(this).hasClass("activeLink"))) {
		    if($(parent).hasClass('collapsible')) {
			$("ul:visible", parent).slideUp('normal');

		    }
		    $(this).removeClass("activeLink");
		    return false;
		}

		if((checkElement.is('ul')) && (!$(this).hasClass("activeLink"))) {
		    $("ul:visible", parent).slideUp('normal');
		    checkElement.slideDown('normal');
		    $("a.activeLink", parent).removeClass("activeLink");
		    $(this).addClass("activeLink");
		    return false;
		}
		
		if(!(checkElement.is('ul'))) {
			check2 = $("a.activeLink", parent).next();
		    if (check2.is('ul')) {
		    	check2.slideUp('normal');
		    }
		    $("ul:visible", parent).slideUp('normal');
		    $("a.activeLink").removeClass("activeLink");
		    $(this).addClass("activeLink");
		}
	}
);

}
$(document).ready(function() {initMenus();});

Thank you so much for your time in advance, its much appreciated.