multiple sites not finding default themes etc

I have a complicated problem concerning multiple sites using a single drupal installation.

Drupal is installed at www.mydomain.com.

.htaccess is set up with

RewriteRule ^(.*)$ /index.php?q=$1 [L,QSA]

(the rewrite base is commented out).

The default site works fine.
I want the second site to be located at www.mydomain.com/directory/

I located a settings file at sites/www.mydomain.com.directory/settings.php and I set the base_url to be http://www.mydomain.com/directory.

When I point my browser to http://www.mydomain.com/directory/ I get the rough frame work of my site, but it is not themed. Drupal does not seem to be resolving the urls properly for www.mydomain.com/directory/themes etc.

Or is this a complicated .htaccess problem?

All help appreciated,
Simon