$(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");
    
    });