JQuery :: Pass Dynamically Assigned Variables As Objects

function get_states(country_element,state_element){
countryElementIDHash = "#" + country_element;
stateElementIDHash = "#" + state_element;
$(stateElementIDHash).empty();
var geonameId = $(countryElementIDHash).val();
$.getJSON("[URL]",
{ 'geonameId': geonameId },
function(data) {
if (data.geonames == null) alert('No regions');
$.each(data.geonames, function(i,item){
$(stateElementIDHash).append($('<option>' + item.name + '</option>'));
});
});
}

I'm writing a function to populate a SELECT based on the select value of another SELECT. I can't figure out why this isn't working. It has something to do with not having "'s in my $(). for example: If this function wasn't dynamic.

The code:
$(countryElementIDHash).val(); could simply be
$("#country option:selected").val();
How can I pass dynamically assigned names into a $() ?