$(function() {   
                
                        var theWindow        = $(window),
                            $bg              = $("#bg"),
                            aspectRatio      = $bg.width() / $bg.height();
                                                                
                        function resizeBg() {
                                
                                if ( (theWindow.width() / theWindow.height()) < aspectRatio ) {
                                    $bg
                                        .removeClass()
                                        .addClass('bgheight');
                                } else {
                                    $bg
                                        .removeClass()
                                        .addClass('bgwidth');
                                }
                                                        
                        }
                                                                
                        theWindow.resize(function() {
                                resizeBg();
                        }).trigger("resize");
                
                });