[jQuery] Can't use selectors in reference to a named object?

[Pete]

The following doesn't work as expected and I don't understand why--can
someone explain, please?

$('form').each( function() {
        var thisForm = $(this);
        alert(thisForm.attr('id') + ' [' + $('thisForm
> :input.required').length + '/' + $('thisForm > *').length + ']');
)};

That I'm expecting the above to do is alert whenever a form is found
in the page, stating that form's ID value and how many of it's total
inputs are classed as 'required'.  But all I get is e.g. "login [0/0]"
and I don't understand why.

Can jQuery not use my thisForm object in this way?  If not, how can I
store a reference and then call selections based on that object?

Thanks in advance.  I've been using jQuery for a little while now and
find it hugely useful, but stuff like this still utterly confuses me.