Elements Inside An Element

I'm using the $ function to get an element using ID:

function $(e){return document.getElementById(e)}
I'm trying to extend this function to use it like this:
$("myID").s("div");
In order to get all the elements that are DIV inside element ID "myID". So I wrote this:
$.s=function(es) {return document.getElementsByTagName(es);}

But that's not working.
What did I do wrong?

Also, Is it possible to to somehow extend it to use with endless number of inside tag/id? like: $("a").$("b").s("div").$("c") ?