Adding multiple e-mail alias addresses to an account

Are you trying to add a second email account to Mail, or just add a second "(apparently) from" address to an existing account?

If the former, we need to know some more detail, like:
(1) who is the existing account, .mac or bellsouth?
(2) Which are you trying to add, .mac or bellsouth?
(3) I assume your ISP is Bell South?
(4) What are the names of the smtp servers and what are their respective smtp server port numbers?
(5) Are either of them using SSL on the smtp server?
(6) I don't remember whether Tiger Mail has it or not, but in Leopard Mail, on the menu bar under "Window" there is a selection "Connection Doctor." If applicable to Tiger Mail, what does it say about your connections?
(7) Which account can you send mail through and which one can't you send mail through?
(8) Are your receiving mail okay through either or both accounts? Which one(s)?

Now if you are trying to add a second "(apparently) from" address to an existing account, in Mail Prefs > Accounts > mail account > Email Address, just add a second email address separated by a comma like so:
user@mac.com, user@bellsouth.net
You could have an issue with bellsouth or .mac requiring the domain name in the apparently from email address to match the domain name of the smtp mail server.

OK, so you are trying to make two addresses for the same email account, earthsista@bellsouth.net, first.last@bellsouth.net, and these are not separate unique accounts, right? (My ISP allows multiple email addresses to be associated with an ISP account but they are in fact distinct accounts with separate username and separate passwords as separate accounts, so I could have an account and my spouse could have an account -- but I would have to login to the user config website and create that second account).

Have you talked to tech support at BellSouth to see whether you can do this? They may be enforcing some kind of requirement that the "from" address username@bellsouth.net has to match the login username when sending mail.

When receiving mail at that address, unless you have made some provision for BellSouth's POP or IMAP server to associate first.last to earthsista, I can't see how they would recognize it as a valid account on their POP or IMAP server. Mail addressed to first.last would appear to be an invalid user. Have you made that provision with the ISP? That's not something that you can just do with Preferences in Mail and have the POP/IMAPserver somehow pick up on that.