how to judge if there is scroll bar in UI

this is a really hard issue for me, which trun out  tormenting me a few days!!!

 

at the beginning, i used document.body.onscroll event,

 

document.body.onscroll=setBackToTop;
    function setBackToTop()
    { 
        var theTop=0;
        var isIE=document.all? true:false;
        if(isIE)
        {
            if   (document.documentElement   &&   document.documentElement.scrollTop)  
                theTop   =   document.documentElement.scrollTop;  
            else    
                theTop   =   document.body.scrollTop;            
            if(theTop>0)
                 document.getElementById("backtotop").style.display="inline";          
            else          
                document.getElementById("backtotop").style.display="none";      
        }
        else
        {
            if(window.scrollbars.visible)           
                document.getElementById("backtotop").style.display="inline";
            else
                document.getElementById("backtotop").style.display="none";   
        }               
    }

 

 

it works perfect in IE, how ever,ineffective in the FireFox

 

then I doubt every line of my code except "document.body.onscroll"

 

at last , some say:

window.onscroll is supported by IE5+, Firefox, Mozilla 1+, Opera 7+, Netscape 7+.
document.body.onscroll is supported by IE6+, Opera 7+.

 

God! then , I make "window.onscroll" take place of  "document.body.onscroll" , then my control "back to up " would like to display as my wishes.