[jQuery] problems with each() and JSON

[jQuery] problems with each() and JSON

Hi Folks,
i have a big roblem with a little getJSON request. At first..this is my code:
=== HTML ===
<button>dicken ajax-request ausführen!</button>
    <ul id="myList">
    </ul>
</body>
=== JavaScript ==
$(function(){
    $("button").click(function(){
        $.getJSON("myJson.js", myCallback);
            function myCallback (jsonObject){
                $(jsonObject.aString).each(function(){                   
                    $("#myList").append("<li>" + this + "</li>");
                });
            }
        });
});
=== The JSON document ===
{
    "anInt": 5555,
    "aFloat": 55.055,
    "aString": "testing",
    "aBoolean": true,
    "anArray": [
        1,
        "2",
        3.34,
        "dog"
    ],
    "anObject": {
        "prop1": "a value",
        "prop2": "another value",
        "prop3": -9999
    },
    "aNull": null
}
you can also see this online at <a href="http://pattentrick.de/my_jquery_json/index.html">http://pattentrick.de/my_jquery_json/index.html</a>
So here is finally my problem. I can just get numbers or bools of this JSON document. When i am trying to get a string e.g. nothing happens. No fanncy things, and no errors in my firebug console. I think its a problem with the each() function. I tried everything i could imagine till now. But nothing seems to work. Is there somone in this mailinglist who could help me...please?
Kind Regards,
The Pattentrick