script src="http://ajax.googleapis.com/ajax/libs/jquery/1.8.2/jquery.min.js" type="text/javascript">

 Then it will not work in Google Chrome.  The library will not be included, because it is not encrypted.  It does not have a https prefix.   
One solution is to download all the query and jqueryui libraries, and put them on my server.  But I'm curious - if I don't do that,  would I be able to use an https prefix on these external libraries?   One problem is that some people may not want to use the https prefix on my site, so changing the library prefixes to https would make the site fail for them.