Node.js Express won't serve absolute URL .js files

I have two files in /public/widget, help.html and help.js

http://localhost:8084/widget/help.html

in the address bar works fine

but

http://localhost:8084/widget/help.js

is not served ('Cannot GET'), even though my express use config:

app.use(express.static(path.join(application_root, 'public')));

Any js inside an html file with relative path is served fine. (ie, if I use

  <script src="/widget/help.js"></script>

life is good; but

  <Script src="http://localhost:8084/widget/help.js"></script>

is not served. (I need the absolute url for referencing the .js in remote pages)

Here is my full Express config:

// parse application/x-www-form-urlencoded
app.use(bodyParser.urlencoded({ extended: false }));
app.use(bodyParser.json());
app.use(cookieParser());
app.use(morgan('dev')); // log every request to the console
//checks request.body for HTTP method overrides
app.use(methodOverride('X-HTTP-Method-Override'))    //checks request.body for HTTP method overrides
//Where to serve static content
app.use(express.static(path.join(application_root, 'public')));

I must be doing something dumb! Any ideas?