Multiple Instance Install of WP

Hello,
I am installing multiple instances of WP (2 total) one on my domain:
http://destroyerofdarkness.info which has been successful and on my subdomain: http://trippingthelightfantastic.destroyerofdarkness.info. When I try to install this second instance (on the subdomain) it calls up the login page for the first instance (on the domain.)

Now, I know it is possible to do what I am doing, without creating a secondary mysql database, as I have done it before (a second database would cost me extra money) but I am unsure how to go about doing it.

Any help would be greately appreciated, THANKS in advance!

Regards,
Joseph