OK, so you have one blog that is in a database and -
supposedly - is using the default wp_ prefix.
This blog, let's say, lives at
As I stated above: If, and only if you are going to install the second blog in the same database (for example, when the host gives you only 1 database), then before installing the second you will have to put your info into the config file of the second blog, so you'll be using something like wp1_
and this blog will live at
I repeat, if you have lots of mysql databases in your hosting package, forget this whole stuff, put them in different databases.
Even if you have the two blogs that HAVE to have the files installed in different directories, the login or admin won';t be as you wrote, but like this:
And a final note: if you have 2 blogs that means 2 times all the files uploaded to your server, including the wp-config.php file. If you have 10 blogs = ten wp-config files, one in every directory.