If this is not a typo, you are missing $ or jQuery at the beginning:
$("#first_link").click(function() { adjust_menu(); });
Or a little shorter and maintaining context:
$("#first_link").click(adjust_menu);
In any case, you should see an error on your console (if you execute it when #first_link present (for example, `document.ready)), always check the console to see what happens.
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