JSON.stringify returns empty

I'm doing some work with WebSQL: creating an object to send via ajax to a server-side script to do some more complex work. I've read a couple dozen tutorials on similar tasks, but for whatever reason, my code returns an empty object as a result of JSON.stringify():

function submit_entries(){
    url = "http://myurl.com/process.cfm"
    send_data = new Object();
    db.transaction(function(tx){
        tx.executeSql('SELECT * FROM mytable', [], function(tx, results){
            var len = results.rows.length, i;
            for(var i = 0; i <len; i++){
                send_data["person"+i] = {};
                send_data["person"+i].fname = results.rows.item(i).fname;
            }
        });//end tx.executeSql
    });//end db.transaction
    send_ajax(send_data);
}

function send_ajax(send_data){
    console.log(send_data);  // log 1
    var send_str = JSON.stringify(send_data);
    console.log(send_str); //log 2
    console.log($.parseJSON(send_str)); //log 3
    /*$.ajax({
        url: url,
        data: send_str,
        type: "post",
        contentType: "application/json",
        dataType: 'json',
        success: function(){
            console.log('yay it might have worked.')
        }
    })*/
}

The first log will output an object. The second an empty set of braces "{}" and the third will output an empty object. I've tried this without the nested "person"+i objects and get the same results.