how to add new <li> to <ul> onclick with javascript

How do I add a list element to an existing ul using a function from an onclick? I need it to add to this type of list ...

<ul id="list">
<li id="element1">One</li>
<li id="element2">Two</li>
<li id="element3">Three</li>
</ul> 

... another list item with the id "element4" and text "Four" under that. I tried this function but it doesn't work...

function function1() {
  var ul = document.getElementById("list");
  var li = document.createElement("li");
  li.appendChild(document.createTextNode("Element 4"));
}

I don't know JQuery so Javascript only please. Thank you!!